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PROCESSES IN BIOLOGICAL VISION: including, ELECTROCHEMISTRY OF THE NEURON This material is excerpted from the full β-version of the text. The final printed version will be more concise due to further editing and economical constraints. A Table of Contents and an index are located at the end of this paper. James T. Fulton Vision Concepts [email protected] April 30, 2017 Copyright 2004 James T. Fulton

Transcript of ELECTROCHEMISTRY OF THE NEURON

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P R O C E S S E S I NBIOLOGICAL VISION:including, ELECTROCHEMISTRYOF THE NEURONThis material is excerpted from the full β-version of the text. The finalprinted version will be more concise due to further editing andeconomical constraints. A Table of Contents and an index are locatedat the end of this paper.

James T. FultonVision Concepts

[email protected]

April 30, 2017 Copyright 2004 James T. Fulton

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1Released: April 30, 20172Salmon, T. (2012) Vision Science IIIb: Binocular Vision http://arapaho.nsuok.edu/~salmonto/vs3.html 3Blomhoff, R. ed. (1994) Vitamin A in Health and Disease. NY: Marcel Dekker

7 Dynamics of Vision 1

The dynamics of the visual process have not been assembled and presented in a cogent manner within the academicvision literature. On the other hand, several authors have presented cogent descriptions applicable to the clinical level.The material assembled by Salmon at Northeastern State University2 in Oklahoma is exemplary (but superficial for thepurpose at hand). The dynamics associated with the mechanism of interpreting symbols and character groups, calledreading, has not been presented at all. Only the major eye movements related to reading have been studied in significantdetail. Even the adaptation characteristic of vision as a function of illumination level has not been presented from atheoretical perspective, and the empirical data has not been analyzed in sufficient detail to provide a coherentunderstanding of the process. When assembled as a group, the mechanisms and processes associated with forming thechromophores of vision provide a new, interesting and unique perspective on the formation of those chromophores. ThisChapter will assemble the pertinent data with respect to a variety of processes where their dynamic aspects are crucialto the visual function.

7.1 Characteristics & Dynamics of Retinoids in the body

The following material is based on extensive empirical investigations that were largely lacking with regard to anycontiguous theory of what the goals of the mechanisms involved were from the perspective of the visual modality. Theinterpretations provided here take advantage of the hypothesis of this work; that the family of retinines, known as theRhodonines() are the fundamental chromophores of animal vision. As noted in Section 3.6, these chromophores do notrequire chemical combination with an opsin to form the operational receptor of light. No opsin is found associated withthe chromophores of Insecta or Mollusca. Opsin is a structural substrate in Chordata supporting the physical orientationof the chromophore coating the individual opsin discs.

7.1.1 Introduction

This section will develop the dynamics of the retinoids from the perspective of transport through the blood stream andoperation within the retina. Sections 4.6.2 & 4.6.3 developed the schematic aspects of the transport mechanisms relatedto both the transport and operation of the retinoids. A later chapter will develop the temporal characteristics associatedwith these processes as they relate to perception in vision. The complete absorption, transport and metabolism of theretinoids in the body are well beyond the scope of this work. However, a brief, first level, scenario is required to avoidthe “floating model” trap and to interpret the known data concerning the retinoids in vision properly. The goal of thischapter is to present one such overall model and scenario.

7.1.1.1 Overall Baseline

Vitamin A plays a major role in the animal body. The term retinol (the alcohol) and vitamin A are frequently consideredsynonymous in the clinical and biological literature. However, at a more detailed level, the term Vitamin A shouldprobably be considered a synonym for retinoid that may be present in the alcohol, aldehyde or acid form. Thismodification allows these three forms to target different elements within the body and/or provides greater selectivityamong the elements of the body for acquiring the desired chemical form.

In 1994, Blomhoff edited an important volume on Vitamin A in Health & Disease3. On page 2 of this very importantwork, he cited the 1982 IUPAC–IUB Joint Commission on Biochemical Nomenclature, “Vitamin A is a generic termreserved to designate any compound possessing the biological activity of retinol, whereas the term retinoids includesboth naturally occurring forms of vitamin A and the many synthetic analogs of retinol, with or without biological activity.” In this work, the term retinoids will be subdivided into two pertinent groups, the retinenes (non-resonant retinoids)and the retinines (resonant retinoids consisting of two oxygen atoms terminating a conjugated carbon chain). Theretinines exhibit a spectral absorption that is non-isotropic and maximum along the axis connecting the two oxygenatoms. This resonant absorption is at a wavelength different from the isotropic absorption of the non resonant retinoids.

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4http://en.wikipedia.org/wiki/Resonance_%28chemistry%29

The retinoids are normally transported from the liver to the target location by what are called retinoid binding proteins(RBP). These may be present in a variety of forms, both in the blood stream or individual cell types. The followingdiscussions will only address the RBP’s related to the visual modality. These retinoids are absorbed from the intestine,aided by a series of enzymes that play a crucial role in preparing them for transport to the liver. The Blomhoff text isthe most definitive work on this subject known at this time. Figure 1 of that text shows the stick versions of themolecules of interest here in their most recently agreed forms with the two methyl groups sharing a carbon of the β-ionone ring shown pointing upward. In actual fact, the retinoids are not planar molecules and cannot be adequatelyrepresented in a 2-dimensional configuration (Section 5.5.8). This configuration is used in the “2nd Order calculations(Section 5.5.8.3.1) of the an-isotropic spectral absorption of light by the retinine, Rhodonine(5) in this work. Thisabsorption occurs at 610 nm under the endothermic conditions associated with most mammals. The numeric, 5, definesthe location of the carbon bonding with the oxygen atom of the β-ionone ring in the L–channel chromophore of vision.

7.1.1.1.1 Scenario requirements

Any realistic scenario must be anchored by the following factors:

+ The organism ingests either carotenes or Vitamin A as a source (the fundamental chromogens) of the chromophoresof vision.

+ The blood stream of the animal is antagonistic to the delicate retinoids. The retinoids are particularly subject tooxidation.

+ Up to four separate types of Rhodonine (the actual chromophores) are deposited in liquid crystalline form on individualsubstrates of protein material in the Outer Segments of a mosaic of photoreceptor cells in each eye of the animal.

The challenge is to determine at least one scenario in which the retinoids can traverse the available pathways betweenthe small intestine and the retina without being exposed to destructive chemistry.

7.1.1.1.2 Reinterpretation of Data Base

Until now, the mechanisms of the binding proteins related to vision have always been discussed on the assumption thatthey bound only the retinenes. The situation is more complex. The same generic complex, a retinol binding proteinpresent in the serum (SRBP), and a molecule named transthyretin (TTR) may absorb/adsorb a retinol molecule andtransport it to other locations unmodified, for a variety of purposes. It may also modify the retinol as part of the transportand/or delivery step. In the case of vision, there are clear indications that the delivered material is not a retinene but aretinine (with two i’s), a diol version of a retinene. The retinines may have been encountered in the biochemicallaboratories studying SRBP and the CRBP/CRABP’s where they have been described as non-canonical forms ofretinol.

A definition of non-canonical form may be difficult to find. For the purpose of this discussion, “the basic concept behindthe canonical structure is whether two consecutive bonds are appearing in equilibrium or not; C if the bonds appear to be in equilibrium the situation will be called canonical,C if not, the situation will be non-canonical and the process can be well understood by resonance.”

Resonance is distinguished from isomerism. An isomer is a molecule with the same chemical formula but withdifferent arrangements of atoms in space. Resonance contributors of a molecule, on the contrary, can only differby the arrangements of electrons. Therefore the resonance hybrid cannot be represented by a combination ofisomers4.

Upon recognizing that both the retinenes and the retinines are processed by these binding proteins, readdressing the database in the literature is necessary. This is necessary to discover how the additional process flexibility introduced by thissituation is used and where the resultant processes take place.

Much of the information associated with the SRBP + TTR complex has been gather in the context of its use in nutrition.However, the complex is used in many other contexts, including vision but also in transporting material to the testes inmale animals as an example.

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5Luo, Y–R. (2003) Handbook of bond dissociation energies in organic compounds Boca Raton, FL: CRC Press

Furthermore, the literature is generally unclear whether the particular author is speaking about the holo- or apo- formof the protein. Making this distinction is absolutely necessary if the dynamics of the transport mechanism is to beunderstood. In the visual case, the post transport apo- protein may not be identical to the pre transport apo- form (seeSection 7.1.1.2.3).

Most of the stoichiometry of the SRBP + TTR complex has focused in the fact that a complex of two molecules of SRBPand one molecule of TTR has been found easiest to crystallize for purposes of X-ray analysis in order to gain maximumknowledge of the conformation of these materials in complex. However, this is not the criteria for asserting this ratiois involved in the physical transport of retinol. Goodman has provided a cartoon illustrating his view of the options forloading the complex in 1984, Figure 7.1.1-1, published originally in 1979 by Smith & Goodman in an obscure press.Goodman’s caption notes the RBP and T4 combine with TTR at different and largely independent sites, whereas thecombining of RBP and TTR designed to upload (and protect) retinol involves a more stabilized situation.

It is also useful to collect and reinterpret the data in theliterature with respect to the stereochemistry of theretinenes, and presumably the retinines, at differentlocations in the body and the eye.

Although the retinenes are the chromogens, and not thechromophores of vision, some of their characteristicsprovide an invaluable foundation for the study of theretinines (specifically the Rhodonine family). Theretinenes are also critical to the formation of the specificRhodonines and their method of transport to the RPE.

7.1.1.1.3 The BIG QUESTION–What is theshape of retinol in various environments

Advances in the art of crystallography have brought newattention to the question of what is the precise structuralshape of retinol/retinal. More specifically, what are thespecific distances between the two oxygen atoms in theindividual resonant conjugated retinine, Rhodonines()?

The typical text book stick version of these moleculesgave way to the ball and stick version during the thirdquarter of the 20th Century that relied upon poorly knownbond lengths of chemistry. That era was followed by thecomputer generated ball and stick version of the last quarter of the 20th Century, that continued to rely upon poorly, butbetter known chemical bond lengths for more complex well documented molecules. Just prior to the start of the 21st

Century, the era of computer reconstituted geometry of molecules based on their x-ray diffraction patterns provided muchmore definitive dimensions of the centroids of individual atoms in a 3D environment for any molecule that could becrystallized. The early computerized data, typified by the Jmol and Jsmol databases of the Royal Society of Chemistry(RSC) continues into 2016 to suggest Retinol_393012 is a planar molecule. Recent data from the crystallographycommunity confirms that it is not, at least when in the liquid crystalline configuration of biology.

Upon close examination of the Jmol files of the Royal Society of Chemistry (acting as a storagefacility and not performing curation on the Jmol data sets), most of their files only present 2Drepresentations of a given molecule and the visualizer used attempts to recreate a 3Drepresentation based on plausible (to the computer) constraints. As a result, this section canonly present plausible representations of the chemicals found to be important in olfaction.

The RSC indicated to this investigator that if undefined stereo-centers are indicated on theirmain page for a chemical, their 2D & 3D representation of the molecule are at bestapproximations. They also indicated that various visualizers will prepare a reasonablerepresentation of the molecule using stored bond lengths (of uncertified or identifiedprecision). Luo has presented a full handbook5 of bond dissociation energies BDE), (a quantityusually believed to correlate with bond lengths) for individual bonds between two atoms as

Figure 7.1.1-1 Goodman’s cartoon model of alternateloadings of the SRBP-TTR complex. (S)RBP will be usedhere to describe the protien when in the bloodstream. Notethe uploading of thyroxine, T4, is distinctly different fromthat of retinol. See text. From Goodman, 1984.

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6http://wiki.jmol.org/index.php/File_formats/Formats/XYZ 7Rhodes, G. (2006) Crystallography made Crystal Clear, 3rd Ed. NY: Elsevier

found in large numbers of molecules. Just the BDE’s for the C-H bond of the saturatedhydrocarbons covers four pages of significantly different molecules with a range from 95 to105 kcal/mole.

Relying upon any visualizer to estimate the distance between two orbitals in a molecule istotally unacceptable within the research community!!!

The Jmol program will have long term positive impact on organic and biological chemistry.However, at this time, it lacks significant curation and fact checking by the RSC. The staff listed onthe RSC website in 2015 was surprisingly limited in its chemistry credentials. As a result, virtuallyanyone is allowed to submit a molecular description to the Jmol library. Not even the sources nameis required to be included in the record submitted. There appears to be no peer-review of thesubmissions.

News flash: The Jmol files are no longer available in 3D based on the cancellation of theirinternet security certification based on the “Cessation of Activity” as of 15 October 2015. Itappears these files are being supplanted by the JSmol files curated by the same RSC. However, the JSmoldatabase was taken off the internet for an unspecified period as of 19 Nov 2015 (as was the ability to contact thecurator via the website). While the JSmol files examined frequently have more header information than the Jmolfiles, the information is frequently disguised with a dummy author’s name (Marvin) appearing on large numbersof JSmol files. No citation has been provided to date regarding the bond lengths used in the Jmol and JSmol filesthe RSC has provided.

The XYZ file format most frequently used with Jmol files is designed to accommodate a number of variants as definedby the Jmol.org6. A major problem arises when incomplete data sets from undefined sources are incorporated into thedatabase without significant curation.

See Sections8.4.1.2.3 & 8.6.1.6.3 (interim xxx) of “The Neuron and Neural System” for a broader discussion of thisproblem.

- - - -

The recent crystallographic data for retinol shows retinol to be three dimensional with a significant dihedral angle of –58degrees (Table III in Cowan, 1990) between the (nominally planar) β-ionone ring and the (nominally planar) aliphaticconjugated side-chain. Cowan specifically defines the dihedral angle as the angle between the C5-C6 bond and the C7-C8 bond.

In the case of the holo-SRBP molecule incorporating a retinol molecule, the group attached to C5 is not in the plane ofthe aliphatic side chain and it is not located along the top of the β-ionone ring as typically drawn in ball and stick formon paper. These differences can have a major impact on the resonant properties of the retinines as developed by Plattin the source book of 1964, “Systematics of Electronic Spectra of Conjugated Molecules.” See Section 5.5.7 for detaileddiscussions of this early work. Fortunately, Platt’s early work predicted spectra for the retinines that could be and wereconfirmed in both the laboratory and in commercial products of the photographic film industry. However, there remainedconsiderable argument in the psychophysical community concerning the long wavelength peak associated withRhodonine(5), the long wavelength photoreceptor of biological vision as discussed in Section 5.5.10.3.

The question remains, what is the precise structural configuration of each of the Rhodonines when in a liquid crystallinearray deposited on a protein substrate (opsin in the vision of Chordata) or directly on the lemma (microvilli in the visionof Insecta and Mollusca) of a sensory neuron. It has been shown that crystallography can determine the parameters ofa molecule when it is in the liquid crystalline form (as of 2016). The technique itself is still in a period of refinementto eliminate certain estimating errors in the mathematical transforms involved. See Section 7.1.2.1 where the papers ofCowan (1990), Monaco (2009) and others are discussed. Currently crystallography involves a considerable dangerrelated to the “Bayesian Trap.” See Rhodes7 (3rd ed., 2006).

7.1.1.2 Terminology

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8White, A. Handler, P. & Smith, E. (1973) Principles of Biochemistry, 5th ed. NY: McGraw-Hill pg. 209, 401,403, 6619Sporn, M. Roberts, A. & Goodman, DeW. (1984) The Retinoids, vol. II, NY: Academic Press pp 42-8510Saari, J. (1994) Retinoids in Photosensitive Systems, Chap. 9 of Sporn, M. Roberts, A. & Goodman, D. TheRetinoids: Biology, Chemistry, and Medicine, 2nd Edition NY: Raven Press11Ong, D. (1985) Vitamin A-Binding Proteins. Nutrition Reviews, vol. 43, no. 8, pp. 225-23212Ganguly, J. (1989) Biochemistry of Vitamin A. Boca Raton, FL: CRC Press 13Chen, C. & Heller, J. (1977) Uptake of retinol and retinoic acid from serum retinol-binding protein by retinalpigment epithelial cells. J. Biol. Chem. vol 252, no 15, pp 5216-522114White, A. Handler, P. & Smith, E. (1973) Op. Cit. pg. 23615White, A. Handler, P. & Smith, E. (1973) Op. Cit. pg. 403

In discussing the dynamics of the retinoids in the body, using the terminologies found in pharmacology, nutrition andcomplex proteins is common. Typically the materials involved are known by their functional characteristics and not theirdetailed formulas. This is primarily due to the extremely high complexity of many of these molecules. This complexityis apparent in their molecular weight and in their detailed geometry. There are several important sources of backgroundmaterial8,9,10,11,12. However, no source in the literature recognizes the resonant forms of the retinoids proposed here. Theydo describe, in various levels of detail, the multiple stages in the transport of the retinoids of vision from ingestion bythe species to their occurrence in the retina. Chen & Heller13 also identify a “retinoid-like material.” They stress itcannot be a retinoid on grounds that are not supported here, but are compatible with the conventional wisdom of theliterature. This work offers an alternate reason they cannot be simple retinoids.

The above sources do not address the actual retinoids used as the chromophores of vision. They routinely make theassumption that it is always Retinol in a molecular combination with a putative protein, Opsin--frequently involving aspecific stereo-chemical configuration. The result is that their introductory remarks and overall description of thetransport of the relevant retinoids of vision must be discounted.

After recognizing the putative Rhodonines in liquid crystalline form as the chromophores of vision, the data baseprovided by the above authors can be reinterpreted. With this reinterpretation, new information and fewer dichotomiesappear concerning the vision process.

One of the dichotomies that will be explained later is between the work of Bridges and Ganguly. Bridges shows IRBPworking in conjunction with 11-cis-retinol, 11-cis-retinal and rhodopsin. Alternately, Ganguly holds that IRBP onlybinds to the all-trans- form of the retinoids. Ganguly does not recognize the possibility that there are multiple forms ofhis retinoids. More recent work in crystallography of retinol also supports its utilization in the all-trans-retinol form.

Focusing on the transport proteins associated with vision has been traditional in the above sources. However, taking abroader view may be advisable. Proteins are usually described in terms of three major classes; transport proteins,enzymatic proteins and structural proteins. This is an inadequate classification for the materials found between theingesting of Vitamin A and the deposition of the liquid crystalline forms of Rhodonine on the structural proteins, Opsin.Considering a broader range of processes and clarifying definitions is necessary.

7.1.1.2.1 Enzymatic activity

In discussing the enzymatic chemistry of vision, it is important to differentiate between enzymes, substrates and surfaces.It is also necessary to differentiate between accelerants and transporters. Much of the reaction chemistry of vision ofinterest here appears to involve reactions at, on, or in passing through a surface. Besides the reaction chemistry, thereappears to be important transport activity. This activity may place additional requirements on the enzymes used. Inaddition, many reactions involve materials that accept or give up functional groups. If these materials are present alongwith an enzyme, their definition becomes awkward. They are labeled either a coenzyme or a co-substrate. Bothdehydrogenation and demethylization are important processes in the formation of the chromophores of vision.

Overall, enzymes are large protein molecules and the material they catalyze are much smaller molecules14. Modernworks frequently define ribosomes as particulate bodies within cells that act as (or are) enzymes15. In most of thefollowing discussion, a retinoid of molecular weight less than 300 will be considered the substrate. Most of the transportproteins will be considered enzymes. They are not consumed in the transportation process. However, the transportprotein associated with moving the retinoid from the liver to the RPE is apparently changed in the process and is

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16Chen, C. & Heller, J. (1977) Uptake of retinol and retinoic acid from serum retinol-binding protein by retinalpigment epithelial cells. J. Biol. Chem. vol 252, no. 15, pp-5216-5221

discarded following this function. It is more appropriately considered a co-substrate.

7.1.1.2.2 Naming enzymatic Proteins

An enzyme is a protein performing as an organic catalyst. There are many overlapping classes of enzymes and thenaming conventions used have changed over the years. In early works, the enzyme is named by using the root of thesubstrate name and adding the suffix -ase. In more recent work the name has brought together the name of the initialsubstrate, the name of the final reaction material, and the process involved followed by the suffix -ase. Two importantexamples are retinol-rhodonine-dehydrogenase and retinol-rhodonine-demethylase. Even these labels are inadequatefor two separate reasons. First, they do not show that oxygen was added to the substrate at the point of dehydrogenationor demethylization. Second, each of them occurs in two distinct reactions. The solution is to add a parenthetic label tothe Rhodonine describing the carbon atom where the oxygen atom was added to the molecule. An alternate and moresuitable naming convention would be retinol-rhodonine( )-monooxygenase. This leaves the question of whether ahydrogen or a methyl was removed implicit in the parenthetic term. It also indicates that the oxygen was not obtainedfrom a free oxygen molecule, O2. For Rhodonine(5) or (9), a demethylization would be involved. For Rhodonine(7)or (11), a dehydrogenation would be involved.

7.1.1.2.3 Transport Proteins

A protein associated with the movement of a material, at the molecular level, within the organism is called a transportprotein. The movement may be intra-cellular, extra-cellular or across the cell wall boundary. Traditionally, visionresearch has assumed that a transport protein has not been chemically changed while carrying out its transport function.However, this is no longer true.

Transport proteins are usually named by preceding the hyphenated expression “-binding protein” by the name of thematerial being transported. Thus, RBP is the traditional abbreviation for a Retinoid-Binding Protein. In this work, amore precise description is needed. Many more specific expressions have been developed to describe binding proteinsrelated to the retinoids. These expressions also require more careful definition.

Although it has not become common in the literature, it is also important to recognize where the binding protein underdiscussion resides. The literature has defined a set of RBP’s that are found within various cells. These have been labeledwith a C for a prefix, i.e., CRBP. Other RBP’s found extra-cellularly in the bloodstream should also be labeled. It issuggested that these be labeled with an S (for serum) as a prefix. Other authors have use P (for plasma) to describe thetransport proteins in the blood stream16. For reasons to be developed below, distinguishing certain RBP’s that may existextra-cellularly in the region of the small intestine and the liver is also useful. These will be described by the prefix L.The L identifies the Lacteal channels of the intestine and liver. However, the L could be considered as indicating alymphatic channel or mere presence in the liver.

When defining a transport protein, two significant situations occur: when the binding protein is attached to the targetmaterial, the holo- situation, and when the binding protein is not attached to the target material, the apo- situation. Whenspeaking of a binding protein, authors generally assume the holo- situation. This is unfortunate. Important changes canoccur at the beginning or end of the transport process.

Until now, all of the binding proteins of vision were assumed to be binding to either retinol or retinal. In this work, athird condition must be addressed. The resonant nature of the Rhodonines shows that these materials can exhibit thechemical characteristics of an alcohol or an aldehyde of retinene, depending on the environment. Therefore, it is verydifficult to specify whether the given binding protein is specific to either Retinol or Retinal, or the resonant form--Rhodonine. No current literature demonstrates that any of the binding proteins of vision are specific to either Retinolor Retinal and simultaneously discriminatory with respect to Rhodonine. Because of this fact, the R in the name of abinding protein must be interpreted as standing for a retinoid. As a minimum, the retinoid may be either a retinine (aRhodonine) or a Retinene.

Assigning a name to a putative enzyme is common in biochemistry. It can aid in discussion. However, such names havetended to proliferate in the literature, with or without adequate demonstration of the existence of such an actualsubstance. Correlating the various names used by different authors can be difficult. The following list defines the namesused in this work. Following the list is a table showing some aliases found in the older literature. The list of aliases is

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incomplete.

RBP--1. As used here, a generic descriptor for a Retinoid Binding Protein. 2. Traditionally, a descriptor limited to a Retinol Binding Protein. This brief descriptor is usually expanded toprovide more detailed information concerning a specific situation.

CRBP-- 1. As used here, Cellular Retinoid-Binding Protein, an enzyme. Usually, the substrate found inter-cellularlyis the resonant form of the retinoid, i. e., Rhodonine. For the cellular case, it is more appropriate for the R to stand forRhodonine. This material is putatively associated with the transfer of the Rhodonines from the RPE cell wall to thestorage locations within the RPE cells. 2. traditionally cellular retinoid-binding protein.

CRABP-- Traditionally, an intercellular enzyme associated with retinoic acid as a substrate. It is not normally used inthe formation of the chromophores of vision. Found in the inner segments of the photoreceptor cells where it is used forgrowth and metabolism.

CRABPII-- An intercellular enzyme associated with retinoic acid as a substrate. Generally found associated with theskin. It is not normally used in the formation of the chromophores of vision.

CRALBP--1. As used here, cellular Retinoid-(aldehyde) binding protein. This enzyme is not modified during itsfunction. In general, the substrate found inter-cellularly contains the resonant form of the retinoid, i. e.,Rhodonine. For the cellular case, it is more appropriate for the R to stand for Rhodonine. This material isputatively associated with the enzymatic transfer of the Rhodonines from the storage locations, and thepinocytosis region, within the RPE cells to the RPE cell wall facing the IPM.

2. Traditionally the less specific cellular retinaldehyde-binding protein.

IRBP– 1. As used here, a Rhodonine-binding protein found in the Interphotoreceptor matrix (IPM) of the retina of theeyes of several species of animals. It is probably able to transport all four forms of Rhodonine enzymatically. IRBP onlybinds to the all-trans- form of the retinoids. (Ganguly, pg. 155.) 2. Traditionally Interstitial Retinol Binding Protein.

LRBP– Lacteal retinoid binding protein. The protein material encapsulating the retinoid(s) absorbed through theintestinal wall for transport to the liver. The implication is that this material is transported via the lymphatic system.

PRBP– See SRBP

SRBP–A retinoid-binding protein resident in the serum of the blood stream. SRBP appears in three forms; a pre-holoSRBP, a holo-SRBP and a post-holo-SRBP. Both the pre-holo-SRBP and the post-holo-SRBP have been labeled apo-SRBP in some literature.

pre-holo SRBP is able to complex with many retinoids, but preferentially with all-trans-retinaldehydeholo-SRBP incorporates a retinoid and appears to be a co-substrate along with an associated protein, TTR. holo-SRBP + TTR is the tranport entity for the retinoids via the bloodstream.post-holo-SRBP is the residue when holo-SRBP is functionally destroyed after delivering its retinoid to theRPE.

TTR–The plasma protein transthyretin. Formerly known as prealbumin. The protein also binds to one molecule ofthyroxine.

Some characteristics of the above binding proteins involved in vision have been tabulated. An important scenario beginsto appear.

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17Ong, D. (1994) Cellular Transport and Metabolism of Vitamin A: Roles of the Cellular Retinoid-BindingProteins Nutrition Rev vol 52(2), pp S24-S31

TABLE 7.1.1.2-1PROTEINS THAT BIND RETINOIDS

SPECIFIC PROTEIN ALIAS FUNCTIONS WITH DISTRIBUTION DISTRIBUTION SIZEIN BODY IN EYE

LactealsLRBP CRBP(II) Retinol in digestion In intestine Not reported

BloodstreamSRBP CRBP(?) Wide distribution 12kDa

pre-holo-SRBP apo-CRBP Retinol to form In circulatory system Not reportedRhodonine

holo-SRBP holo-CRBP Rhodonine & TTR In circulation & cells Not reported post-holo-SRBP apo-CRBP Nothing, a residue In circulatory system Not reported

TTR In circulatory system Not reported 55kDaNon-retinal areas

CRABP retinoic acid (all-trans-) Wide distribution Not reported 15.4kDa CRABPII retinoic acid (all-trans-) Skin Not reported ~16kDa

RetinaCRBP alcohol only Wide distribution 16.6kDaCRALBP aldehyde only Only in eye Only in RPE 33; 36

IRBP Only in eye Only in IPM 140kDa

Values from many sources. Sizes mainly from Berman, 1991, pgs 320 & 377, Marmor & Wolfensberger pg 137 andGamble & Blaner, 2000.

The enzyme LRBP transports simple retinoids, generally the retinenes, extracelluarly from the point of ingestion to theliver for storage. The co-substrate SRBP, in conjunction with TTR withdraws retinol from the liver, converts it to oneof the four Rhodonines and transports the new material extracelluarly to the RPE interface with the blood stream. Theenzyme CRBP accepts the Rhodonines at the RPE cell wall and delivers it to a storage area (pigment globule or granule).When needed, the enzyme CRALBP transports the Rhodonine to the RPE interface with the IPM. At that interface, theenzyme IRBP receives and transports the Rhodonine extracelluarly to its point of deposition on the disks.

Ong has provided a more expansive table. However, he includes some “baggage” that may not be appropriate to visionwithin the current context. He has defined a specific RBP found only in the intestine and labeled CRBP(II). It ispossible that this protein is pre-holo-SRBP in the more recent vernacular presented above since it is described as extra-cellular and found in the intestine. It is also possible that this protein is more appropriately labeled an LRBP.

Goodman has studied the mechanism employed to transport Retinol between the liver and the target location via thebloodstream. This mechanism involves an RBP that he described as the plasma RBP or PRBP. When dealing only withthe circulatory system, many authors have used the root RBP to describe the material they are discussing. The targetmay be unrelated to vision. Some authors have chosen to use the expression serum RBP or SRBP for a material morespecifically defined with respect to vision than that of Goodman. The term SRBP will be used here to describe theparticular co-substrate (since the material is modified) that transports the retinoids to the RPE cells.

Ong provides some very useful caricatures of the overall metabolic situation from the medical ornutritional perspective. However, they are highly conceptual. They are not supported by detaileddiscussion or equations. As an example, it is implied that CRBP(II) aids in the transport of Retinolfrom the intestine to the liver by way of the bloodstream. However, CRBP(II) is not shown in thebloodstream. The only Retinol in the bloodstream is shown enclosed in the “RBP/TTR bottle” (Seebelow). Note the large question mark in the middle of the “target cell.” In his Figure 3, he impliesthere is no 1:1 relationship between photoreceptor cells and RPE cells. Ong updated his 1985 paperin 199417. The large question mark remains in his caricature.

In his discussion, he at times drops the suffix associated with retinol or retinal in favor of the moregeneral retinoid. He may have found this necessary since some binding proteins were less specific

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18Ganguly, J. (1989) Biochemistry of Vitamin A. Boca Raton, FL: CRC Press pg 6619Livrea, M. & Packer, L. (1993) Retinoids. NY: Marcel Dekker, inc. pp 92-100 & Chap. 1220Johnson, A. Merlini, G. Sheldon, J. & Ichihara, K. (2007) Clinical indications for plasma protein assays:transthyretin (prealbumin) in inflammation and malnutrition Clin Chem Lab Med vol 45(3), pp 419–42621Sporn, M. Roberts, A. & Goodman, D. (1994) The retinoids, 2nd ed. NY: Raven Press pg. 363

than desired in the conventional literature (of retinoid movement in metabolism). He does include acaveat that the retina and the testis are special cases. Note also his intimation that the Muller cells ofthe retina are positioned quite similarly to the retinochrome cells of the arthropod eye.

Ganguly has summarized many measured parameters relating to the serum RBP’s18. Livrea & Packer have also providedinformation on the RBP’s and more data on TTR19.

7.1.1.2.4 Specifics related to TTR and its relationship to RBP

Johnson et al. have also provided valuable data related to TTR20, “TTR is a globular, non-glycosylated protein with amolecular mass of 54.98 kDa. With one complexed molecule of retinol-binding protein (RBP; 21 kDa), the total massis approximately 76 kDa, which is still small enough to diffuse out of the vascular space as readily as albumin (66.3 kDa)or transferrin (79.6 kDa); slightly less than 50% of each of these proteins is normally intravascular as a result.” They citethree very old references.

Johnson et al. describe the function of TTR in detail, “The protein migrating anodal to albumin on non-sieving, routineserum electrophoresis at pH ~8.6 was initially noted to bind thyroxin (T4) and was thus given the name thyroxin-bindingprealbumin, or TBPA. However, it was subsequently shown to bind triiodothyronine (T3) and holo-retinol-bindingprotein (RBP with retinol, or vitamin A) as well, and the name was changed to transthy(roxin) retin(ol) to denote its dualtransport function. TTR is a tetramer of four identical subunits. Although each of the four monomers has a binding sitefor RBP, the tetramer binds only one molecule of RBP with high affinity and possibly a second with lower affinity. Thebinding affinity for apo-RBP (RBP without retinol) is very low, and the loss of retinol (e.g., uptake by tissues) resultsin the separation and renal excretion of free apo-RBP, accounting for the very short biological half-life of RBP of ~ 3.5hours. Each TTR monomer also has two binding sites for thyroid hormones, but binding of one molecule of T3 or T4significantly reduces the affinity of the second site. Binding affinity for T3 is lower than that for T4. The TTR-RBPcomplex normally transports approximately 20% of circulating thyroid hormones (70% is transported by thyroxin-binding globulin or TBG, the rest by albumin) and 90%–95% of retinol/vitamin A. The complex is more important forretinol transport than for thyroid hormones.” Emphasis added.

When discussing the synthesis of TTR, Johnson et al. note, “Essentially all plasma TTR is synthesized by the hepaticparenchymal cells. . . .” With regard to catabolism, “TTR is catabolized primarily by the liver and by excretory loss viathe kidneys and gastrointestinal tract. Its biological half-life is approximately 2.5 days and is not altered by stress oracute inflammation.”

Johnson et al. have also noted, “Serum concentrations of TTR are very low in the fetus and neonate, rise slowly to reacha maximum in the fifth decade of life, and then decline slowly.” A table of values is provided. The changes with ageare indeed slow. Genetically, “The gene coding for TTR is located on chromosome 18q (26). There are over 100 knowngenetic variants, including a few with increased or decreased binding affinities for thyroid hormones but clinicaleuthyroidism. Many of the genetic variants are associated with deposition of amyloid in tissues, resulting in a group ofautosomal dominant hereditary amyloidoses. Plasma concentrations of TTR are essentially normal in these disordersand are not helpful in diagnosis; however, some variants do show altered electrophoretic mobility.” Understanding thesemultiple gene codes could be an important factor in understanding the onset of AMD within families.

Johnson et al. did not discuss the question of local clearance of TTR or SRBP from the vascularization of the eye as itmight relate to AMD.

7.1.1.2.5 The CRBP’s of vision

Most descriptions of cellular retinoid binding protein (CRBP) do not differentiate between the holo- and apo- form.Some form of CRBP is reported to exist in nearly every cell in the body.

Saari, writing in Sporn21 has defined LRAT--An enzyme based on lecithin as esterfying all-trans-retinol to all-trans-

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22Wolken, J. (1975)Photoprocesses, photoreceptors and evolution. NY: Academic Press pp. 34-3923Wolken, J. (1966) Vision, Biophysics & Biochemistry of the retinal photoreceptors. Springfield, Il: CharlesC. Thomas, pg. 30

retinyl palmitate (along with some oleate and stearate) within the RPE. This description is considered archaic in thiswork. The enzyme CRBP (as defined above) performs the same function in this work but the substrate has already beenconverted to Rhodonine. The Rhodonines are always found in the all-trans- configuration. It is likely, the variouslycolored globule (or granules) stored in the RPE are made up of these palmitates, oleates and/or stearates.

7.1.1.2.6 Structural Proteins

The only structural protein of concern in this work is Opsin, the substrate produced by the IS of the photoreceptor celland used as a substrate for the chromophores of vision, the Rhodonines.

7.1.1.3 Properties of the fundamental chromogens

Animals are generally able to ingest and use both carotene from plant sources and Vitamin A from animal sources. Thephylogenic and environmental history of the animal determines whether the animal can use a specific form of thecarotene and/or vitamin A. Carotene exists in at least four forms22. α−carotene when cleaved at its center in the presenceof oxygen leads to one molecule of Vitamin A1 and one molecule of Vitamin A2. β-carotene on the other hand leads totwo molecules of Vitamin A1 when similarly cleaved. Vitamin A1 (also known as Retinol1) is used by animals ofmarine origin. This category includes the mammals living in the sea and on land. Vitamin A2 (also known as Retinol2)is used by freshwater-based animals ( primarily freshwater fish). The vision literature has focused more on β-carotenethan on α-carotene because of its higher utility for man. The literature also claims a wider occurrence of β-carotene innature. Although a family similar to the carotenes, the xanthophylls contain additional oxygen in their ring structure.It is not clear whether they are used by animals to create the chromophores of vision. A xanthophyll with an oxygenreplacing the methyl group at position 5 (using Karrer’s notation) would form Rhodonine(5) upon cleavage as above.However, all available data suggest that the chromophores are created in the RPE from retinol feedstock.

Recently, a third form of Vitamin A has been recognized. Vitamin A3 (also known as Retinol3) has been identifiedamong the flies (Diptera of Odonta) of Insecta. See Section 1.2.1.1. The material appears to arise from decaying plantmaterial.

The scenario discussed below will not be detailed to the point of differentiating between Vitamin A1 and A2.

Vitamin A1 is readily available commercially in pure, all-trans- form. It is provided as a white crystalline materialresembling table salt to the naked eye. The crystals are of the rhombic form. Under the microscope, the individualcrystal appears yellowish with tinges of blue due to scattering. More details of the specific crystalline structure areavailable in Section 5.5.4.1. The individual molecules of Vitamin A can be enclosed by a cylinder approximately 5Angstrom in diameter and 15 Angstrom long23. When discussing vision, the three-dimensional molecule is most easilyrepresented in two dimensions by placing all of the ligands containing single methyl groups, C18, C19 & C20, on the sameside of the molecule. This accentuates the structural similarity of the chromophores of vision.

Recently, x-ray crystallography has identified the precise 3D arrangement of Vitamin A. The molecule involvesa significant dihedral angle between the β-ionone ring and the aliphatic carbon chain (Section 7.1.2.1). Themolecule is not planar. Crystallography is destined to play a major role in understanding the transduction processin the vision, gustation and olfaction modalities.

Recognizing that Vitamin A plays more than one role in the animal body is important. It has a critical role to play inthe growth and nutrition of virtually every cell in the body. Simultaneously, it plays an extremely important role invision. Differentiating the pathways and mechanisms used to distribute Vitamin A in these different roles is important.

7.1.1.4 State of the ART in crystallography versus molecular modeling

Crystallography plays a critical role in determining the precise nature of the chromophores of biological vision, just asit did in its earliest days in the field of receptors for photographic film. In photographic film, the molecules of interestwere generally simple organics and did not involve proteins. In biological vision, the same is true of the actualchromophores. However, their transport and manipulation by various proteins results in much more complex moieties.

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24http://www.rcsb.org/pdb/static.do?p=general_information/about_pdb/nature_of_3d_structural_data.html 25Glusker, J. Lewis, M. & Rossi, M. (1984) Crystal Structure Analysis for Chemists & Biologists. NY: Wiley-VCH

To understand the precise structure of these moieties, very sophisticated crystallographic techniques at the highestavailable resolution and precision are required.

The Protein Data Bank (PDB) of the Royal Society of Chemistry has provided a rational overview of the field of x-rayand solution NMR crystallography as applicable to the current subject matter24. It develops several key points on firstreading:C 80% of the data in the PDB originated from x-ray analysis, 16% from NMR and 2% from theoretical modeling.C protein crystals as used for diffraction studies are highly hydrated ("wet and gelatinous") so structures determined fromcrystals are not much different from the structures of soluble proteins in aqueous solution. Some molecules have beenstudied both by crystallography and by solution NMR, and in these cases the agreement has been excellent.

This statement is encouraging that the crystallographic results will closely relate to the liquid crystalline state inwhich most chromophores are actually found.

C X-ray crystal diffraction usually cannot resolve the positions of hydrogen atoms or reliably distinguish nitrogen fromoxygen from carbon. This means that the chemical identity of the terminal side-chain atoms is uncertain for Asp, Glnand Thr and is usually inferred from the protein environment of the side chain (i.e. the side chain orientation which formsthe most hydrogen bonds or makes the best electrostatic interactions is selected and built by the crystallographer as themost plausible choice). Sometimes there is also uncertainty about whether an atom that is not part of the protein is abound water oxygen or a metal ion.

These situations are unfortunate for the subject of this Section. The role of oxygen is critical to understandingthe transport and manipulation of the retinenes/retinines of this section.

C NMR determines structures of proteins in solution, but is limited to molecules not much greater than 30 kD. NMR isthe method of choice for small proteins which are not readily crystallized, and yields the positions of some hydrogenatoms. The results of NMR analysis are an ensemble of alternative models, in contrast to the unique model obtained bycrystallography.

The PDB overview provides an excellent discussion of the requirements and shortcomings of the x-ray crystallographymethod. They quote Rhodes in “Crystallography Made Crystal Clear.” On page 183, Rhodes offers this caveat:

"All crystallographic models are not equal. ... The brightly colored stereo views of a protein model, which are in factmore akin to cartoons than to molecules, endow the model with a concreteness that exceeds the intentions of thethoughtful crystallographer. It is impossible for the crystallographer, with vivid recall of the massive labor that producedthe model, to forget its shortcomings. It is all too easy for users of the model to be unaware of them. It is also all tooeasy for the user to be unaware that, through temperature factors, occupancies, undetected parts of the protein, andunexplained density, crystallography reveals more than a single molecular model shows."

Solution NMR does not appear appropriate for the delineation of the “complexed” molecules described below.

7.1.1.4.1 Critical role of disorder and delocalization in chromophore transport ADD

The results obtained using crystallographic techniques are greatly impacted by the degree of disorder within theasymmetrical unit examined by x-ray irradiation. Similarly, interpreting the results obtained through crystallographictechniques is greatly impacted by the state of delocalization of the electrons of the groups within the asymmetrical unit.Glusker, Lewis & Rossi define these terms25;

Disorder– 1. A disturbance to the regular organization of an entity (here a crystal).2. Lack of regularity. In crystal structures, it implies that there is not exact register of the contents ofone unit cell with those from all others. The atoms or molecules in the crystal structure pack randomly(non-periodically) in alternative ways in different unit cells.

Delocalization of electrons– The π bonding in a conjugated system is not consider to consist of localized bonding, butto have the electrons delocalized over the entire system of double bonds.

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Disorder is inherent in the intrinsically liquid crystalline materials of the biological system. It is due to the presence offree water molecules within the cavities of a given protein or more complex structures that are the target of investigation.They lead to a loss in resolution in the electron density maps relied upon to ascertain the molecular structure of anorganic molecule.

Delocalization of electrons is also inherent among the chromophores of vision (unless the chromophores are separatedby differential crystallization or similar techniques) due to their variable length of conjugated chains in a specificcrystalline sample. Such delocalization leads to a loss in resolution of both the electron density maps and the differenceelectron density maps forming the foundation of further analyses to identify the specific molecules and /or chemicalgroups (including peptides) within a macro-molecule.

7.1.1.4.2 Lack of chromophore planarity plays a critical role in crystallographyADD

The use of molecular overlays, based on simple structural models using only 2D ball and stick models, as an aid tointerpreting electron maps in crystallography is limited if the molecule is not planar and the bond lengths are not shownin proportion to their actual length. The “gold standard” of molecular overlays uses a projection from a 3D ball and stickmodel that matches the projection of the electron density map being reviewed. Otherwise, subtle relationships may beoverlooked in the investigators evaluation of his representations.

7.1.1.4.3 Application of molecular modeling and visualization versus crystallography

Currently, the art of modeling molecules and visualization of those models in 3D space is moving forward rapidly.However, the majority of this modeling is being performed ab initio based on the best available set of bond lengths,angles, etc available to the modeler. An unfortunate result of the establishment of multiple databases to hold the resultsof these activities has been the lack of adequate curation of these databases. The more opportunistic databases havebegun to fall by the wayside. One of the databases of wide scope is that of the Royal Society of Chemistry (RSC).However, this database remains uncurated and unsupervised as of 2015. The result is a large number of Jmol and JSmolfiles in that database that are missing (ostensibly required) header information and lack of any discussion of thesophistication of the rules used in the modeling by a given submitter. See Section 7.1.1.1.3.

For the novice, PDB-101 provides an overview of the capabilities provided by the PDB consortium;http://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/introduction . Another online introduction is calledBioinformatics for the terrified; http://www.ebi.ac.uk/training/online/course/bioinformatics-terrified

See also Section 7.1.2.4 for a broader discussion of this problem as it relates to the vision modality.

As noted above, a technique advancing at a similar rate is that of x-ray crystallography. While a complex, computerintensive technique, it does appear to converge on the actual conformation of any size molecule to a precision higherthan that of molecular modeling.

7.1.1.4.4 Unique 3rd order protein structures described via crystallography

Crystallography has begun to explain the structure of various proteins at a level not generally defined in molecularmodeling. These structural features involve unusual hydrogen bonds and disulfide bonds.

Glusker et al. have illustrated the presence of hydrogen bonds in the helical structures within proteins (page 486). Theynote quite succinctly, “The α helix is the most common conformational component of proteins, and a single helix maycontain up to 40 amino acids. The polypeptide chain is wrapped in a right-handed spiral manner, held together by intra-chain hydrogen bonds, Figure 7.1.1-2. “This helix has 3.6 residues per turn and a translation per residue of 1.5Angstrom (3.6 x 1.5 = 5.41 Angstrom for one complete turn, cf., the 5.1 Angstrom α repeat). Pauling predicted that thishelical structure would be stable as a result of favorable hydrogen bonding patterns.” The interior diameter of thesehelices is quite small, typically about 5 Angstrom. No other molecular structure can occupy this space.

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26Bernstein, P. Law, W. & Rando, R. (1987) Isomerisation of all-trans -retinoids to 11-cis retinoids in vivo ProcNat Acad Sci USA vol 84, pp 1849-185327Newcomer, M. Jamison, R. & Ong, D. (1998) Structure and Function of Retinoid-Binding Proteins inJamison, R & Ong, D. eds. Fat Soluble Vitamins, Vol 30 of the series, Subcellular Biochemistry, Quinn, P. &Kagan, V. eds. Chapter 3

The disulfide bond is important in forming sheets ofpeptides within a protein. Wikipedia notes, “A disulfidebond, also called an S-S bond, or disulfide bridge, is acovalent bond derived from two thiol groups. Inbiochemistry, it is considered a functional group. Theterminology R-S-S-R connectivity is commonly used todescribe the overall linkages. The most common way ofcreating this bond is by the oxidation of sulfhydrylgroups. . . . Cystine is composed of two cysteines linkedby a disulfide bond. Disulfide bonds in proteins areformed between the thiol groups of cysteine residues bythe process of oxidative folding. The othersulfur-containing amino acid, methionine, cannot formdisulfide bonds.

The disulfide bond is about 2.05 Å in length, about 0.5 Ålonger than a C–C bond. The disulfide bonds are strong,with a typical bond dissociation energy of 60 kcal/mol(251 kJ mol-1). However, they are about 40% weakerthan C–C and C–H bonds,

7.1.2 Transport Scenario for the retinoids

Beginning during the 1970's, the biochemists recognizedthat the chromophores of vision were not formed withinthe photoreceptor cells of vision. Clearly, thesechromophores were found within the RPE (Section4.6.2.2.3). They were either created within the RPE orduring the transport of retinenes from the liver. Bernstein, Law & Rando summarized this situation in198726. A series of retinoid binding proteins (RBP) areinvolved in the formation and transport of both thechromogens and chromophores of vision. In thisparadigm shift, the biochemists have not encountered orexplored the technique by which the chromophores aretransported from within the RPE cells across the IPM andthrough the outer membrane of the photoreceptor cells.They have made the assumption that the disks were located externally to the photoreceptor cell.

Beginning in the 1990's, the nutrition community came to recognize that all retinoids were not processed the same,whether ingested orally or by injection. In 1998, Newcomer, Jamison & Ong even noted that the family of chemicalslabeled Vitamin A in the nutrition literature were processed and participated differently with respect to vision and otherlargely hormonal activities27.

“In addition, the eye has RBP’s which are distinct for that organ: a cellular retinal/RBP (CRalBP) and aninterstitial/interphotoreceptor retinoid-binding protein (I–RBP).”

Note the distinction between retinal used specifically in the first clause and the term retinoid used in the second clause.This distinction is critical, as developed in this work. It is proposed here that the retinoids of the IRBP take on fourresonant forms, the Rhodonines() in the latter reference, related to the spectral absorption of the retina. In the case of

Figure 7.1.1-2 View of an α helix. The segment shown isfrom the protein crambin. From Glusker et al., 1984.

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28Niles, R. (1998) Control of retinoid nuclear receptor function and expression in

the CRBP’s within the RPE cells specifically, there may be several different RBP’s involved (Sections 4.2.6, 18.8.3.6.2& later sections of 7.1.2). Volume 30 of the series, “Sub-cellular Biochemistry was dedicated to the latest papers in fatsoluble vitamins.

The Newcomer et al. paper provides detailed information concerning the various retinoid binding proteins, includingthe specific structure and conformation of most of those relevant to vision. It defines three functional classes for whichthe structural motif characteristics are available, extracellular, intracellular binding proteins and the nuclear receptors.It is explicit as to why retinoic acid is processed differently than the retinoids utilized in vision. It provides less detailedinformation as to the changes in the RBP’s of vision since it relies upon the chemical theory of the neuron and vision.It does provide useful information concerning the unique character of the extracellular IRBP’s found within the IPM ofthe retina. These characteristics are associated with the electrolytic theory of the neuron and the resonant properties ofthe retinines. It does not enumerate or discuss the other extracellular RBP’s, the serum RBP’s or SRBP’s.

A new field of research has arisen since 1990 concerning potential processes related to the retinoids that is within thenucleus of a cell, and not just within the soma. Newcomer et al. describe the nuclear receptors proteins as controllinggene transcription within the nucleus of cell. It does address the RAR ( retinoic acid receptor and isoforms α, β & γ)and RXR (retinoid X receptor and isoforms α, β & γ). Here again they differentiate between the retinoic acid receptorsand the less defined retinoid X receptors. They indicate the former are related to morphogenesis, spermatogenesis andthe maintenance of epithelial tissue, and the latter to vision. Niles has provided additional specific concerning thesenuclear receptor functions related to the retinoids28. His Introduction is quite conceptual and based on the conventionalwisdom of the time, i.e., he defines retinol alone as vitamin A whereas the medical literature defines vitamin A asincluding the esters of the retinoids. His text is devoted to the specifics of the RAR and RXR family, but the materialrelated to the RXR family is brief and requires additional research as to the specific retinoids targeted. Niles suggeststhe RXR family may also target retinoic acid. Niles discusses the locations of the genes involved on specificchromosomes within the cell nucleus.

The precise role of each of the RBP’s varies between investigators in the current literature. Figure 7.1.2-1 attempts tosummarize the RBP’s as currently identified and delineated. The first group are RBP’s found within various cells. Thesecond group are concerned with the initial transport of the retinoids from the intestine to the liver (for storage or furtherprocessing). The lower group cnsist of RBP’s specifically designed to transport the retinenes from the liver and deliverthem in modified form (the retinines) to the RPE cells, in conjunction with the cellular RBP’s found within the RPE cells.

The LRBP are particularly effective in protecting the retinyl esters from oxidative destruction by elements within thevascular system. The SRBP’s are particularly designed to protect the retinoids during vascular transport in conjunctionwith a second RBP previously named transthyretin, TTR. Iindividual mpolecules of SRBP and TTR form a “bottle andstopper” that is particularly effective in delivering a retinene molecule to the RPE cell interface with the vascular system(Section 7.1.2.2.1). During its delivery, the retinene is converted to one of four resonant retinoids known as retinines,Rhodonine(). Within the RPE cell, the retinines are manipulated to their storage areas by one of the CRBP’s variouslylabeled, CRBP, CrolBP or CRalBP (I) by various investigators during different time periods. The Newcomer et al. paperprovides details of the structures of some of these cellular RBP’s.

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29Schreiber, R. Taschler, U. Preiss-Landl, K. Wongsiriroj, N. Zimmermann, R. & Lass, A. (2012) Retinyl esterhydrolases and their roles in vitamin A homeostasis A review: Biochimica et Biophysica Acta vol 1821(1), pp113–123

Schreiber et al. have provided a recent large scale review of vitamin A homeostasis29. Nearly every major sectionconcludes with a statement that more research is needed in the area, and Figure 1 includes a question mark in each ofthe seven major areas depicted–and many conceptually defined esterase’s. Still, it is a very significant source. The focusis on a wide variety of enzymes, retinyl ester hydrolases, REH, that have been documented relative to the various roles

Figure 7.1.2-1 The currently identified retinoid binding proteins, RBP’s ADD. A; RBP’s found within various typesof cells. B; RBP receptors within the nucleus of selected cells. C; RBP’s associated with various terminal cells ormatrices. D; RBP’s used in the transport of the previously identified species on the left. See text.

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30Rigtrup, K. Kakkad, B. & Ong, D. (1994) Purification and Partial Characterization of a Retinyl EsterHydrolase from the Brush Border of Rat Small Intestine Mucosa: Probable Identity with Brush BorderPhospholipase B Biochem vol 33, pp 2661-2666

of the vitamin A1 derivatives. Schreiber et al. continue the differentiation between the retinoic acid BP’s and the retinoidBP’s introduced above.

Summarizing the reviews by Newcomer et al. & Schreiber et al., there are several forms of vitamin A1 of interest inhuman physiology plus the proto-vitamin, beta carotene. These forms appear to be processed differently within theintestine and possibly within and during transport to the liver.

beta-carotenes a proto-vitamin that is cleaved into two retinoids during absorption aty the intestinal wall.retinol the most commonly defined form of the alcohol of the retinene (non resonant) form of retinoidretinal the most commonly defined form of the aldehyde of the retinene (non resonant) form of retinoidretinoic acid the non-resonant form of retinene most commonly associated with non-visual uses of retinene

Rhodonine() the resonant (retinine) form of the retinoids found within the IRBP and probably stored withinthe RPE as esters.

Beta carotene is ingested from plant-based foods. It follows a different absorption path and is reported to be lessefficiently absorbed than the retinenes. The esters of retinol and retinal are ingested from animal-based foods. Retinoicacid appears to be ingested and transported across the intestinal wall in its native acid form. The differences betweenthe absorption of these species appears to be important in the treatment of night vision and macular dystrophy (Section18.8.3.6.2 & Sections 18.8.9.3 through 18.8.9.5).

A very superficial survey at the local pharmacy indicated that most of the vitamin A supplements describe theirsource as fish liver oil (no indication of whether it is from fresh water fish, vitamin A2, or marine fish, vitaminA1. One offering indicated 30% of the vitamin A content was β–carotene. A product from Nature Madeindicated it contained retinol palmitate (a retinyl ester). Cod fish (Gadidae) are one marine source of vitamin A1.See Section 1.2.1.1.

Rigtrup et al. have provided considerable detail relevant to the absorption of vitamin A and its precursors30. TheirAbstract notes,

“Retinol esterified with long-chain fatty acids is a common dietary source of vitamin A, that is hydrolyzed priorto absorption. An intrinsic brush border membrane retinyl ester hydrolase activity had previously beendemonstrated for rat small intestine [Rigtrup, K. M., & Ong, D. E. (1992) Biochemistry 31,2920-29261. Thisactivity has now been purified to apparent homogeneity by a three-column procedure to obtain a protein ofapparent molecular weight of 130 000. The purified protein retained the pattern of bile salt stimulation, specificityfor the acyl moiety of the retinyl ester, and the K, values previously observed for the activity present in theisolated brush border membrane. This protein also had a potent phospholipase activity, while having littlemeasurable ability to hydrolyze triacylglyceride and cholesteryl ester substrates. The retinyl ester hydrolaseenzyme was localized to the distal two-thirds of the small intestine.” Italics added for emphasis.

They go on in their main text,

“We discovered two distinguishable activities. One is of pancreatic origin (possibly cholesterol ester hydrolase)and primarily hydrolyzed esters with fatty acyl chains of less than 10 carbons in length. The other is intrinsic tothe brush border membrane and constituted the majority of brush border activity toward long-chain retinylesters that are typical of those that would be found in the diet.”

“The retinyl ester hydrolase activity was stimulated more strongly by unconjugated bile salts, while thephospholipase activity was stimulated more strongly by their taurine-conjugated analogs.”

“The enzyme is not simply a nonspecific lipase. For example, pancreatic cholesterol ester hydrolase is alsoknown as carboxyl ester hydrolase (or lipase) because it has a broad specificity, capable of significant hydrolysisof long and short-chain triacylglycerols, phosphatidylcholines, retinyl esters, and nonphysiological esters such

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31Sikkens, E. Cahen, D. Koch, A. et al. (2013) The prevalence of fat-soluble vitamin deficiencies and adecreased bone mass in patients with chronic pancreatitis Pancreatology vol 13, pp 238–24232Dutta, S. Bustin, M. Russell, R. et al. (1982) Deficiency of fat-soluble vitamins in treated patients withpancreatic insufficiency Ann Inter Med vol 97(4), pp 549–55233Chader, G. (1984) Vitamin A. In Handbook of Experimental Pharmacology, NY: Springer-Verlag, vol. 69,pp. 367-384

as p-nitrophenyl acetate, as well as cholesterol esters.”

“Hydrolysis in the proximal third of the small intestine, where the intrinsic enzyme is absent, is most likelycarried out by the trihydroxy bile salt-requiring activity of pancreatic origin (Rigtrup & Ong, 1992).”

They conclude by suggesting an alternate name for the enzyme they studied most completely.

Sikkens et al. have reported on pancreatitis and related diseases leading to fat-soluble vitamin absorption problems in201331. They identified a specific cohort of 40 patients. “Very few studies have addressed the subject of fat-solublevitamin deficiencies and low bone density in this patient group.” Their study only isolated a very few vitamin Adeficient subjects and they referred to the study by Dutta et al. of 1982.

Dutta et al. provided a large clinical study of pancreatic insufficiency leading to deficiencies in the fat-soluble vitamins32.The study showed the serum vitamin A levels and the degree of night vision sensitivity loss among primarily chronicalcohol pancreatitis sufferers.

The following sub-sections strongly support the hypothesis of this work that there are four distinct chromophores ofanimal vision, the Rhodonines, that they are each a diol and thereby members of the retinine family rather than thesimpler retinenes that include retinol. The retinines are delivered to the RPE cells of the retina in complete diol form,and that groups of each specific Rhodonine type are stored in separate globules within the RPE prior to their dispersalto the outer segments of the photoreceptors after exudation into the IPM of the retina. These globules have frequentlybeen described as granules, inplying a granular nature. An alternate description has been as micelles, implying a liquidcrystalline spherical state with the hydrophilic portion of each molecule facing outward, and the hydrophobic portionfacing inward.

Section 7.1.2.5 will review the literature of retinoid transport for non-visual purposes within the body.

7.1.2.1 Transport of the visual modality retinoids within the body

The goal of this subsection is to understand both the delivery of the Rhodonines to the RPE cells and the IPM of theretina, and the removal from the retina of the unloaded SRBP-TTR complex and the disposal or reuse of its components.The delivery begins with the acquisition and protective storage of one molecule of retinol within a SRBP-TTR complex.The protective aspect is necessary because of the increased delicacy of the retinene as it is converted to a retinine (a diol,Section 5.5.8) during its transport.

There are a variety of caricatures in the literature describing the flow of the retinoids through the system. Most of thesecaricatures illustrate different concepts in individual areas. Chader presents a particularly artistic caricature from apharmacological perspective33. However, it may not treat the blood/RPE interface adequately from a chromophorechemistry perspective. Because of this complication, no overall flow diagram will be presented at this time. See Section7.1.1.4.3.

7.1.2.1.1 Summary premises of retinoid transport within the vascular system

The following premises outline the discussion appearing in the following sections and place it in context with the largertheory;

1. The visual capability of all animals, including humans, employs a fundamentally tetrachromatic retina consisting ofchromophores sensitive in the ultraviolet (UV-), short wavelength (S-), medium wavelength (M -) and long wavelength(L-) spectral regions.2. The chromophores of all animal vision consist of a group of resonance conjugate retinoids, described as members ofthe retinine family to distinguish them from the retinene family.3. These chromophores do not incorporate any protein material such as opsin. The opsin of Chordate vision is asubstrate upon which the retinines are arranged as contiguous single layer liquid crystals. Opsin is not used, and has not

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been identified in the retinas of Insecta or Mollusca.4. The individual ligand of retinol identified within the opsin molecule of Chordata is present to facilitate the creationof opsin prior to its secretion by the inner segment of the sensory neurons of the retina. This ligand is not employed inthe transduction of light within the visual modality. Its absorption cross section relative to the cross section of theindividual molecule of opsin is minuscule and is not adequate to support a high sensitivity (quantum counting) retina.5. For each of the four spectral types of sensory neuron receptors found in the retina of vision of most species, theappropriate chromophore is present as a single layer liquid crystal wherein all of the excited electrons generated in thatliquid crystal are shared in a single excited state that delivers energy to the villi or microtubules of the sensory neuron.6. The energy is received and transduced directly into an electrical signal by an active semiconductor device, similar toa man-made transistor, and defined as an Activa.7.The discs of opsin secreted by the individual inner segments of a sensory neuron are in direct contact with the inter-photoreceptor matrix (IPM).8. The secreted discs of opsin are coated with a liquid crystalline chromophore stored by and released into the IPM fromthe retina photoreceptor epithelium (RPE).9. The coated discs and chromophores have a life expectancy of approximately one week in the human species. Thesediscs are continually destroyed and the chromophoric material recovered upon their arrival at the RPE in order to makeroom for the newly secreted discs at the inner segment interface. This process avoids a problem with cosmic ray damageto the eye.10 The recovered chromophore material is stored as separate granules within the RPE cells until the requiredchromophore material is secreted back into he IPM where it proceeds to coat newly formed opsin substrates. Thesegranules are documented in the literature.11. Some chromophoric material is lost in the recovery and re-secretion process. Thus there is a need to replenish thereservoir of chromophores within the RPE cells.

12. Retinol, and retinal, are very low electrical band gap molecules that are not compatible with the chemicalenvironment of the vascular system.13. Retinol (al) are transported from the stomach to the liver protected from the vascular environment.14. Similarly, retinol (al) is prepared for transport to the RPE cells within the liver by complexing with an apo-retinoid-binding protein (RBP). The apo-RBP will be identified as a pre-holo-RBP in this description.15. The holo-RBP complex involves a single ester now formed by chemical reaction between the pre-holo-RBP and aretinene structure. The new retinoid structure is now resonant due to its conjugated structure extending between its twooxygen atoms. This structure is a pro-retinine (with a second i) rather than a retinene (with a single i) The oxygen atomof the ester was provided by the RBP.16. To complete the protection of the now even more sensitive retinine, a TTR is employed to physically isolate the onlyexternal atoms of the retinine component of the complex. The TTR stopper remains capping the bottle formed by theRBP while the “overall complex” moves via the vascular system to the vascular surface of the RPE cells (adjacent toBruch’s membrane.17. Upon arrival at the RPE interface, the TTR cap is discarded back into the blood stream and the pocket of the holo-RBP is interfaced with a similar pocket on a cellular retinine-binding protein (CRBP).18. The retinine is released from the holo-RBP complex with the oxygen atom previously forming an ester with the RBPnow an integral part of the resonant conjugate retinine. 19. The retinine is drawn into the protected environment of the RPE cell by the CRBP and stored as part of achromophoric granule (see premise 10).20. The post-holo-RBP has now lost at least one oxygen atom from its pre-holo-RBP configuration and possibly becomestructurally unstable due to the large void in its interior. In either case, the post-holo-RBP is no longer viable as a RBP.21. The post-holo-RBP is released back into the vascular system with the intent it be moved to the kidney and clearedfrom the body of the animal.22. Failure of the vascular system to remove the post-holo-RBP and the TTR molecule from the immediate region ofBruch’s membrane can result in the buildup of drusen (and not fuscin) within the choroidal vascularization of the eyenear Bruch’s membrane. This can result in the earliest stage(s) of the medically recognized condition known as maculardegeneration.

7.1.2.1.2 Ingestion or manufacture of Vitamin A

Wikipedia (ca. 2017) declares, “All-trans-retinol is by definition vitamin A.” This naive declaration appears to be untruefor a variety of reasons.1. The entire nutrition community considers β-carotene a protovitamin A and discusses it as a legitimate source ofvitamin A. It is easily hydrolyzed into all-trans-retinol in the proximal intestine.2. InterPro notes, “Vitamin A has three active forms (retinal, retinol and retinoic acid) and a storage form (retinyl ester).”This latter description is more appropriate when concerned with vision.

To make real progress in understanding the role of vitamin A in homeostasis, and certain diseases associated with vision,

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34Reboul, E. (2013) Absorption of Vitamin A and Carotenoids by the Enterocyte: Focus on Transport ProteinsNutrients vol 5, pp 3563-358135Rémond, D. Shahar, D. Gille, D. (2015) Understanding the gastrointestinal tract of the elderly to develop dietary solutions that prevent malnutrition Oncotarget vol 6(16), pp 13858-13898

β-carotene, retinol, retinal, retinoic acid and the retinyl esters must be considered. In a review, Reboul has provided aremarkably clear interpretation of the situation of these molecules in the context of enterocyte absorption in the intestinaltract34. From his position as a nutritionist, his Abstract is remarkably comprehensive.

“Abstract: Vitamin A deficiency is a public health problem in most developing countries, especially in childrenand pregnant women. It is thus a priority in health policy to improve preformed vitamin A and/or provitamin Acarotenoid status in these individuals. A more accurate understanding of the molecular mechanisms of intestinalvitamin A absorption is a key step in this direction. It was long thought that ß-carotene (the main provitamin Acarotenoid in human diet), and thus all carotenoids, were absorbed by a passive diffusion process, and thatpreformed vitamin A (retinol) absorption occurred via an unidentified energy-dependent transporter. Thediscovery of proteins able to facilitate carotenoid uptake and secretion by the enterocyte during the past decadehas challenged established assumptions, and the elucidation of the mechanisms of retinol intestinal absorptionis in progress. After an overview of vitamin A and carotenoid fate during gastro-duodenal digestion, our focuswill be directed to the putative or identified proteins participating in the intestinal membrane and cellular transportof vitamin A and carotenoids across the enterocyte (i.e., Scavenger Receptors or Cellular Retinol BindingProteins, among others). Further progress in the identification of the proteins involved in intestinal transport ofvitamin A and carotenoids across the enterocyte is of major importance for optimizing their bioavailability.”

The opening and closing sentences are particularly important in the context of Public Health in the developing and thirdWorlds. The primary sources of Vitamin A in these areas are usually described as green vegetables. Most of theVitamin A is derived from the organic chemical and protovitamin carotene. Carotene gives the fruit of green vegetablestheir orange color. In the more developed world, the primary source are the preformed sources of retinol, primarily theretinyl esters (with retinol palmitate the most important). Since Vitamin A is stored in the liver of Chordata, the liverof prey is a valuable and concentrated source of Vitamin A for carnivores. Whereas most preformed Vitamin A can beabsorbed through intestinal wall, carotene apparently cannot. The protovitamin β-carotene is believed to be attackedin a dioxygenase cleavage in the intestine that creates two molecules of Vitamin A. All of the forms of vitamin Aabsorbed through the intestinal wall are sensitive to destruction by oxygen and are generally protected by transfer to theliver for storage via the lymph system.

Following storage in the liver, the vitamin is transported throughout the body via the blood system. The portionsupporting vision is apparently transported as an alcohol, retinol, in complex with a variety of retinol-binding proteins,RBP’s. These are described in greater detail below.

Reboul notes that for the last forty years, absorption through the intestinal wall has been largely conceptual. Beginningwith the turn of the Century, new studies have shed more light on the actual mechanisms involved. He notes a criticallyimportant aspect, “Although passive diffusion may occur at pharmacological concentrations of these compounds, aprotein-mediated transport is clearly involved at dietary doses.” Reboul then presents an Overview of the conventionalwisdom from the perspective of the nutritionist in his Section 2. He notes the measured mean absorption efficiency ofβ-carotene is relatively low, even though its range is wide, from 3% to 90%. The mean absorption efficiency of theretinyl esters appears to be higher with a range of 75% to 90%. He asserts, “the data obtained in healthy subjects haveshown that gastric lipase does not significantly hydrolyze retinyl palmitate. The hydrolysis of esters of vitamin A thusoccurs essentially in the duodenum” where other enzymes are available. The pancreatic juice contains two main enzymesthat could perform this hydrolysis: cholesterol ester hydrolase (CEH) and pancreatic lipase (LP). The results of in-vivoexperiments in mice suggest the in-vivo hydrolysis of retinyl esters is achieved by the LP, together with the pancreaticlipase-related protein 2 (with citation). “It is conceivable that some esters are taken up intact by the intestinal cell andhydrolyzed intracellularly.”

He presents a figure 1 in his section 3 that is highly conceptual and will not be pursued here. See instead, the figuresin Section 18.8.3.6.2 of this work. Section 3 also includes current research material that has not yet become settledunderstanding. Part of it involves potentially additional mechanisms involving absorption and/or transport enhancerslabeled more briefly as “transporters.” Section 4 suggests that genetic differences may be related to the relatively broaddifferences in absorption efficiency among individuals.

Some 56 subsequent papers have cited Reboul as of 2017. Remond et al. have provided an in-depth discussion (15 pagesof citations) of digestion in the elderly35. A paper by McClements et al. has attempted to define a classification system

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36McClements, D. Li, F. & Xiao, H. (2015) The Nutraceutical Bioavailability Classification Scheme:Classifying Nutraceuticals According to Factors Limiting their Oral Bioavailability Ann Rev Food Sci Tech vol6, pp 299-32737 Bonrath, W. Bruins, M. Mair, P. et al. (2015) Vitamin A in Kirk-Othmer Encycl Chem Tech NY: John Wiley38Saeeda, A. Hoekstraa, M. Hoekea, O. et al. (2017) The interrelationship between bile acid and vitamin Ahomeostasis Biochim Biophysica Acta - Mol Cell Biol Lipids vol 1862(5), pp 496–51239https://www.drugs.com/pro/pancrelipase.html

for the bioavailability of various ingested pharmaceuticals that may be of interest moving forward36. The articlehighlights potential strategies for increasing the oral bioavailability of nutraceuticals based on their nutraceuticalbioavailability classification scheme ,NuBACS, where the designation, B*A*T*. The symbols are described asbioaccessibility (B*), absorption (A*), and transformation (T*) within the gastrointestinal tract (GIT). Bonrath, et al.have prepared an Encyclopedia entry on the history and industrial preparation of Vitamin A37. Saeed et al. have alsoattempted to define several aspects of Vitamin A absorption in liver disease38. These papers do not always recognizethe variety of molecules found under the generic label, Vitamin A.

The following citation provides substantial data on the action of pancreatic lipase on fatty acids, triglycerides.Pancreatic lipase ppt - SlideSharehttps://www.slideshare.net/fathima1995/biochemistry-pancreatic-lipase-pptNov 27, 2013 - PANCREATIC LIPASE DONE BY: BARAKATHU PEER FATHIMA INDIA Pancreatic Lipase

Slide 10, from Figure 22.3 of the 2012, 7th Edition of “Biochemistry” shows how this lipase breaks down a triglycerideto a monoglyceride, Figure 7.1.2-2. In the case of retinol palmitate, it may go farther and free the retinol from thepalmitate, shown here as R2, along with the remaining acetate group.

Drugs.com notes the ability of a commercial pharmaceutical to take this last step,

“The pancreatic enzymes in “Pancrelipase” catalyze the hydrolysis of fats to monoglycerides, glycerol and fattyacids, protein into peptides and amino acids, and starch into dextrins and short chain sugars in the duodenum andproximal small intestine, thereby acting like digestive enzymes physiologically secreted by the pancreas39.”

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Figure 7.1.2-2 Breakdown of triglycerides by pancreatic lipase. It is suggested that this same enzyme might free apalmitate at R2 and the acetate group from the retinol group thereby supporting absorption of the retinol molecule throughthe wall of the small intestine. See text. From Fathima, 2012.

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40Dowling, J. & Wald, G. (1960) in Vitamins and Hormones, vol 18, pg 537

Figure 7.1.2-3 The general metabolism of Vitamin A. When removed from storage, Vitamin A travels different pathsfor vision and for growth and maintenance. That used in vision is transported within the SRBP/TTR complex. Thematerial labeled “rhodopsin” in this figure is best described as an aggregate and not a chemical. Light electronicallyexcites the chromophores but does not isomerize them. Modified from Dowling & Wald, 1960.

Figure 7.1.2-3 presents a simple schematic of the general metabolism of Vitamin A in vision. This figure can becompared with the earlier version of Dowling and Wald40. It provides more detail concerning the transport of VitaminA and a more detailed description of the use of Vitamin A in vision. While being transported to the RPE cell interface,the material contains one ligand that can be described as an aldehyde. However, this ligand is not exposed to attack.It is contained within the transport complex. In passing through the RPE cell wall, it is converted into a Rhodoninewhere it is stored. During transport from the color granules of the RPE, it is again complexed with a transport proteinbefore deposition onto the Opsin substrate. After deposition, the resulting coated substrate is conceptually describedas rhodopsin. However, this is not a compound, only a conglomerate from a physical perspective. Upon excitation bylight the Rhodonine chromophore of the conglomerate is excited. Excitation is terminated by the creation of a freeelectron in the dendrite associated with the disk stack and the chromophore is immediately ready for re-excitation. Norequirement exists for the chromophore to be transported back to the RPE for purposes of stereochemicalreconfiguration.

Figure 7.1.2-4 illustrates how the retinoids progress through the animal body in order to support the visual function.

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Figure 7.1.2-4 The general flow of Retinoids within the animal body and various steps used to recover thechromophores. Top, the interconversion of the chromogens of vision. Middle, the conversion of Vitamin A into thechromophores of vision. Bottom, the alternative approaches to the extraction of the chromophores of vision from retinalextracts. Aggressive extraction causes the chromophores to be destroyed, resulting in residues frequently identified asretinol or retinal using simple chemical tests. Low energy extraction and recrystallization allows the separation of thetrue chromophores. See text.

The figure also shows how they may be recovered for scientific evaluation. Vitamin A plays many roles in the growthand operation of the animal body. Its importance in vision has been recognized (indirectly) for thousands of years. Itwas recognized that lack of certain foods in the diet led to night blindness--a lack of photoreceptor sensitivity (Section4.6.3.3). In more recent times, a lack of vitamin A in the diet has been shown to result in poorly formed outer segmentsassociated with the photoreceptor cells of the retina. The upper portion of the figure illustrates the many forms of theretinoids used in the initial ingestion, storage, and transport of the material. These materials can all be consideredchromogens. Only the material shown being transported down to the RPE cells will ultimately become chromophores.The proto chromophores are first transported to the liver by LRBP. They are withdrawn from the liver by the holo-SRBP+TTR complex. After delivery to the RPE cells, the material is transported by the CRBP’s within the RPE. The material

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41Chen, C. & Heller, J. (1977) Uptake of retinol and retinoic acid from serum retinol-binding protein by retinalpigment epithelial cells. J. Biol. Chem.. vol. 252, no. 15, pp. 5216-522142DeLuca, L. (1977) the direct involvement of vitamin A in glycosly transfer reactions of mammalianmembranes. Vitamins & Hormones. vol. 35, NY: Academic Press. pp. 1-5743Chader, G. (1984) Vitamin A. Hdbk. Exp. Pharma. Vol. 69 pp. 367-38444Nickerson, J. Borst, D. Redmond, T. Si, J-S. toffenetti, J. & Chader, G. (1991) The molecular biology ofIRBP: application to problems of uneitis, protein chemistry, and evolution. In Molecular Biology of the Retina:basic and clinically relevant studies. NY: Wiley-Liss, Inc. pp. 139-161

appears to be converted from a chromogen to a chromophore as part of the transfer process between the holo-SRBP +TTR complex and the CRBP’s within the RPE cell receptor locations.

There appears to be a difference in how the retinoids are transported within the blood stream. For those destined to beused in the formation of the chromophores of vision, they appear to be transported by a specific group of retinol-bindingproteins. These retinol-binding proteins appear capable of interacting with unique binding sites found on the surfaceof RPE cells. The nature of this interaction is critical to the formation of the resonant retinoids, the Rhodonines.Heller41 has studied the transport of the retinoids in considerable detail. In the above paper with Chen, he has shownthat there are no receptor sites on the photoreceptor cells for the type of retinol-binding protein used to transport theretinoids to the RPE. His conclusion is that the retinoids used to form the chromophores can only enter the IPM via theRPE cells. The retinoids required for growth and normal metabolism must enter the photoreceptor cells by a differentmechanism, probably via a complex with serum albumin. He also found that retinoic acid cannot participate in theinteraction with the RPE receptors. This is probably due to two aspects of the molecular structure of retinoic acid. First,the carboxyl group is probably too stable to give up one of its oxygen atoms in the interaction. Second, the presence oftwo oxygen atoms in the terminal ligand of the acid prevents it taking up another oxygen at one of the critical locationsalong the polyene chain of the retinoid required to form a Rhodonine.

Heller, working in vision, and both DeLuca42 and Chader43 working in pharmacology, have found an unidentified groupof “retinol-like” materials in their studies. Chen & Heller stressed the fact that the material found in the RPE cells andin the IPM is retinol-like but not retinol. An exception occurs in the 2nd paragraph of the abstract to the paper wherean editor has reduced “retinol-like” to “retinol.” It is proposed that their retinol-like material of page 5220 is Rhodonine.Here again, this work does not support Heller’s rationale (for the material not being retinol) but it does support hisconclusion.

Once the material has been transformed into the resonant form of the retinoids in the above interaction, the chromophoresbecome attached to a second group of retinol-binding proteins. More specifically Rhodonine-binding proteins supporttheir transport through the RPE cells and onto their final destination in the disks of the Outer Segments. This subjectwill be discussed in detail in the next Section. Whereas the Rhodonines are transported by diffusion through the IPMto reach the formative region of the disks, this is not the case for their return. The Rhodonines are transported back tothe RPE by the physical motion of the disks as they are replaced, on a regular basis, through growth. This presents adifferent mechanism than generally assumed in the literature and restated by Nickerson, et. al44. It eliminates the needto return the stereo-isomer of the chromophore to the RPE for regeneration as a functional chromophore after eachexposure to light.

The lower section of the figure attempts to illustrate the various avenues to the recovery of the chromophores of vision.The right-hand path is meant to describe the conventional techniques using sodium salts and other chemically aggressivemedia that normally reduce the Rhodonines back to their chromogens. Alternately, the recovered material is only testedfor the presence of a retinoid in aqueous solution. In either case, the experiment fails to isolate the individualchromophores of vision. The left-hand path in the figure is meant to describe an alternate path using less aggressivemedia. It also recognizes the importance of the liquid crystalline state in the isolation of the individual chromophores.The suggested path is through multiple recrystallizations of the material recovered from the Outer Segments.

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A major question arises as to the routing of the artery supplying blood to the oculars relative to the blood-brain-barrier(BBB). The BBB is generally associated with the walls of the vascular conduits entering (or leaving) the brain. Thegoal of the BBB is to isolate the CNS from dangerous chemicals that might exist within the general circulation.

The SRBP-TTR-Rhodonine loop has two potential points of origin; the choroid plexus located within the BBB of theCNS or the liver. The liver has traditionally been considered the major source of the SRBP-TTR-Retinol complex thateventually delivers Rhodonine() in one of its four forms to the RPE cells and/or the IPM of the retina.

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45Dowling, J. & Wald, G. (1960) Vitamins & Hormones. Vol. 18 pg. 53746Goodman, DeWitt. Op. Cit. pg. 42-8247Gamble, M. & Blaner, W. (2000) Factors affecting blood levels of Vitamin A In Livrea, M. ed. Viatmin Aand Retinoids: An Update. Berlin: Birkhauser Verlag pg 1-1648Vahlquist, A. Peterson, P. & Wibell, L. (1973) Metabolism of the Vitamin A-transporting protein complexEur J Clin Invest vol. 3, pp 352-36249Soprano, D. & Blaner, W. (1994) Plasma retinol-binding protein In Sporn, M. Roberts, A. & Goodman, D.eds. The Retinoids. NY: Raven Press pp 257-282

The simplest routing of the retinal artery would be to avoid the BBB completely.

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Comments appear occasionally in the literature suggesting that Arthropoda and Mollusca do not use Vitamin A. Thismay be correct regarding growth and general stasis. However, the measured spectral performance of their visual systemssuggests that their chromophores exhibit the same resonant conjugated structure as for Chordata. Although this structurecould be obtained through other processes, Vitamin A appears to be the most efficient source for such chromophores.As noted in Section 1.2.1.1, there are multiple forms of Vitamin A

7.1.2.1.3 Visual retinoid transport within the vascular system EDIT

[xxx combine with next section or move into 7.1.2.2 ]Although many older vision-related documents say that Vitamin A (now Retinol) is transported through the bloodstreamas a free alcohol45, this is not supported in more recent documents focusing specifically on the retinoids. Many morerecent articles in the literature suggest that the retinoids of vision are so sensitive to oxidation that they cannot existwithin the circulating bloodstream, and quite probably, within many body cells. Protection of the retinoid is an importantresponsibility of the RBP’s. It also accounts for the presence of RBP’s peculiar to the Lacteal region, the bloodstreamand within the cells of the RPE.

Goodman46 described the actual situation in detail, prior to the putative existence of the resonant retinoids that canemulate the retinenes. He said that Retinol was stored in the liver. When needed by the organism, Retinol is combinedwith an RBP for protection and then released into the bloodstream. However, the transport of Retinol through the animalbloodstream involves another complication. Although a single binding protein can aid the transport of a single delicateretinoid, it cannot fully protect it from attack. To achieve both transport and protection in a hostile medium, the retinoidrequires a more complex transport mechanism. The binding protein involved, which will be labeled SRBP accordingto the above nomenclature, apparently encloses most of the retinoid but requires another protein, plasma transthyretin(TTR) to protect the retinoid fully. The analogy has been made to a cork and a bottle. The SRBP is the bottle containingthe retinoid and TTR is the cork. He noted the fact that a different species of SRBP has been isolated from fish. He didnot specify, but it can be assumed, he is speaking of fresh water fish where the retinoids present are related to VitaminA2. It has also been noted that the holo-SRBP complex is released from the Liver. After the retinoid is delivered to itstarget location, the apo-SRBP is filtered out of the bloodstream and destroyed. It does not re-circulate. This lack ofconservation of a valuable binding protein suggests another option. It is possible that the SRBP released by the liverin holo- form is not identical to the apo-SRBP leaving the target site. This would imply that the retinoid absorbed bythe target site may differ from the retinoid released by the liver. As a working hypothesis, it can be assumed that theretinol released by the liver is transformed into Rhodonine within the bottle. This would occur through a change in theactual chemical structure of the “SRBP.” The implication being that the protein found in apo-SRBP within the liver andthat found in the bloodstream are different. In this scenario, the apo-form found in the bloodstream could not be reusedin a re-circulating mode.

Without being more specific, Gamble & Blaner47 have given the half-life of “RBP-bound retinol” as 12 hours based onValquist, Peterson & Wibell48. In a well-nourished Western population, the concentration of the combination is givenas 2-3μmol/liter based on Soprano & Blaner49. Gamble & Blaner also provide additional information on the molecularweights of the SRBP and TTR and their gross interrelationships with retinol. They also address the human geneproducing SRBP.

If Retinol requires the protection of an SRBP plus plasma transthyretin to move from the liver to the target location,another question must be addressed. How does retinol get from the small intestine to the liver where it is combined with

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50Stacy, R. & Santolucito, J. (1966) Modern College Physiology. St. Louis: C. V. Mosby pp. 318-32051Ong, D. op. cit. pp. 225-232

the SRBP? Although not widely discussed, Stacy & Santolucito50 present caricatures and say: “There are two routes ofabsorption in the intestine: (1) absorption directly into the bloodstream, and (2) absorption into the lacteals, which arethe lymphatic vessels of the intestinal mucosa.” Thus, two options are presented. After absorption, retinol could moveto the liver through the lacteals, thereby avoiding the bloodstream. Alternately, retinol could combine with another RBPwhile passing through the intestinal wall. Both approaches could logically employ an LRBP (CRBP(II)) such as thatdiscussed by Ong51.

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Monaco (2000) provides good information on how the SRBP + TTR may load the retinol molecule prior to transport.

As asserted by Monaco (2000), “The ligand transported by the complex is exclusively all-trans retinol though the affinityof RBP for other retinoids, most notably retinoic acid is quite similar [32].” As developed below, and in Section 7.1.4.1[xxx confirm ], this statement may be too strong and only apply to the uptake of all-trans retinol and not apply strictlyto the form of the retinol during transport following the uptake.

The details of how retinol is transported within the SRBP + TTR complex may still be controversial. However, thegeneral pattern can be described based on the literature. Figure 7.1.2-5 is in color to support the following discussion.There is a black & white version in Monaco (2000) that shows the structure but not the inter-relationships between themoieties. Both figures show the tunnel through the TTR where thyroxine would be found if the complex weretransporting thyroxine. In this figure, the total complex is carrying two retinol molecules, one in each SRBP connectedby a hydrogen (London) bond associated with the alcohol group at the end of the conjugated aliphatic chain. Thishydrogen bond joins the TTR molecule at a glycine peptide in position 83. In the human variant of this complex,Monaco (2009) indicates the retinol is joined to the SRBP by an ester-bond nominally at carbon position 5 of the β-ionone ring of retinol as shown in the left frame of [Figure 7.1.2-4 ]. Monaco did not discuss this statement further anddid not indicate why the ester could not occur at other locations along the retinol backbone. As propose here, anddeveloped in Sections 5.5 and specifically 5.5.10.1.2 to explain the spectral performance of the four uniquechromophores of the Rhodonine family, the ester can be formed at carbon 7, 9 or 11 of the retinol. This alternative esterlocation may result in a different peptide of the SRBP being involved in the ester.

[XXX coordinate with figure xxx ]

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52Potterton, E. McNicholas, S. Krissinel, E. Cowtan, K. & Noble, M. (2002) The CCP4 molecular-graphicsproject. Acta Crystal D Biol Crystal vol 58, pp 1955–1957.

Monaco (2009) provided a clearer model of just the single holo-RBP (RBP4) as prepared by Potterton et al52. and shownhere as Figure 7.1.2-6. The figure does not appear in the cited reference; that paper describes a new open sourcemolecular-graphics program in development. The monomer corresponds to the right monomer of the above figure wherethe hydroxyl group of the retinol is protected from the solvent by the adjacent TTR. No details are shown concerningthe potential existence of the retinoid combined with the RBP to form an ester.

Monaco describes this protein as follows, the figure “is a ribbon representation of the molecule showing the bound retinolas a space-filling model. The secondary structure assignments for human RBP4 are for the beta strands the following:strand A, residues 22–30; B, residues 39–47; C, residues 53–62; D, residues 68–78; E, residues 85–92; F, residues100–109; G, residues 114–123; and H residues 129–138. The alpha helix spans residues 146–158. The open end of thebarrel is delimited by four loops joining strands A–B (residues 31–38), C–D (residues 63–67), E–F (residues 93–99),and G–H (residues 124–128). The first three are close to the retinol molecule and amino acids present in them participatein the contacts with TTR, the fourth is far from the ligand and is not involved in contacts with TTR in the complex. Theloop connecting strands C and D has been found to be disordered in several X-ray structures which indicates a certaindegree of flexibility which might be related to retinol release.

Figure 7.1.2-5 Model of the structure of the hexameric complex (RBP)2-TTR containing retinol as determined by x-rayanalysis of the orthorhombic crystals. The RBP molecules are shown in red, one of the TTR dimers is in green andyellow, and the other is in blue and turquoise. The retinol molecules are represented as space-filling models with greycarbon atoms and a red oxygen. See text. From Monaco, 2009.

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53Peterson, P. & Berggård, I. (1971) Isolation and Properties of a Human Retinal-transporting Protein J BiolChem vol 246(1), pp 25-33

The old papers of Peterson & Berggard and of Peterson appear important to this work. Peterson & Berggard diddemonstrate the ready availability of many oxygen atoms in both aspartic acid and glutamic acid peptides in humanRBP53. These oxygen bearing peptides are relatively rare in other proteins; remarkably, they are the dominant fractionsin Table IV. “The results of the present study are in agreement with the observations that the retinol-transporting proteinis acidic, and has a molecular weight of 21,000 and a sedimentation constant of 2.3 S. In contrast to Kanai et al., who

Figure 7.1.2-6 Ribbon representation of the plasma holo-RBP (RBP4) molecule. The bound retinol is represented asa CPK model wih its OH exposed to the solvent on the surface of the protein. Note the oxygen of the hydroxyl groupshown at the left extreme of the CPK model. The figure was prepared with the program CCP4 mg. See text. FromPotterton et al., 2002.

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54Peterson, P. (1971) Characteristics of a Vitamin A-transporting Protein Complex Occurring in Human SerumJ Biol Chem vol 246(1), pp 34-4355Newcomer, M. Jones, T. . . .Rask, L. & Peterson, P. (1984) The three-dimensional structure of retinol-bindingprotein EMBO J vol 3(7), pp 1451-145456Hase, J. Kobashi, K. Nakai, N. & Onosaka, S. (1976) Binding of Retinol-binding Protein Obtained fromHuman Urine with Vitamin A Derivatives and Terpenoids J Biochem vol 79(2), pp 361-371 J Biochem (1976) 79 (2): 373-380

isolated two forms of the protein, with and without retinol, we have isolated four molecular forms of urinary RBP.”Kanai did record the very high percentages of aspartic acid (15.8%) and glutamic acid (10.7%) in RBP. Thesepercentages varied somewhat in their processing. Kanai also noted regarding the effectiveness of th protection providedby RBP, “The magnitude of the protective effect is indicated by the fact that retinol (bound to RBP) remains intact inwhole plasma kept for several weeks at 4VC, whereas retinol itself is highly unstable and decomposes rapidly in solutionin organic solvents when exposed to traces of oxygen or to light.” Peterson & Berggard also observed, “One possiblemode of action might be a dissociation of RBP from prealbumin, whereafter vitamin A is emitted from RBP anddeposited in a target cell. The free RBP could then be excreted into the urine. This view is supported by the observationsthat small amounts of RBP occur in free form in serum and that free urinary RBP seems to have a lower binding affinityto prealbumin than RBP which is prepared from the RBP-prealbumin complex.” It may be that the free urinary RBP haslost one or more oxygen atoms and is the residue, apo-RBP, after delivering a retinine to the RPE cells. In a subsequentpaper, Peterson noted, “Experiments on serum indicated that the characteristics of serum RBP1 were different from thoseof urinary RBP.” On page 38, Peterson54 noted, “The result of the chromatography is shown in Fig. 6. Theprealbumin-RBP material had apparently dissociated and emerged as two components. Immunological analyses by thesingle radial immunodiffusion technique showed that only the protein fraction eluted last consisted of RBP.” In figure8, Peterson showed a distinct separation between the serum RBP-TTR complex (presumably containing retinol), purifiedserum RBP and urinary RBP using an immunodiffusion analysis. A key assertion on page 42 was, “ The plasma RBPand urinary RBP were identical except for a higher content of aspartic acid in the plasma preparation (see Peterson &Berggard, 1971).” The loss of an oxygen atom from an aspartic acid peptide at one or more location along the RBPmolecule is exactly what would be expected according to the theory of this work! Table III indicates the surprisinglyhigh number of aspartic acid and glutamic acid residues in both TTR and RBP. After a brief discussion, Petersonsurmised, “A mechanism dissociated RBP from prealbumin close to or in connection with the target cells would thusbe required.” This appears to refer to the delivery of the retinol to the RPE cells. His closing discussion appears tosupport this work. “There were clear differences in the content of aspartic acid between the serum and the urinary RBP.”

The 1984 paper by Newcomer et al. provides more information on the electrical charge of the holo- SRBP55. C “Human RBP has been sequenced and is composed of 182 amino acid residues (Rask et al., 1979).” C “The complex containing all trans-retinol has recently been crystallized by Newcomer et al. (1984b) and we are nowable to describe its tertiary structure.” C “Figure 1 shows that RBP from three species (Sundelin et al., 1984) displays a mutation-free area involving theN-terminal residues, the C-terminal base of the ca-helix and the loop region around residue 80. This region is rich incharged residues, e.g., 10 out of the first 20 residues in the sequence are charged, which may explain why RBP andprealbumin dissociate at low ionic strength.” They also note, “It is not known how the transfer of retinol from itshydrophobic environment in RBP to the receptor is accomplished, but after the delivery RBP has virtually lost its affinityfor prealbumin (Peterson, 1971). Such apo-RBP, isolated from urine (Peterson, 1971), does not crystallize under thesame conditions as the holo-protein.” They also note, “ These data taken together suggest that RBP has differentconformations depending on the binding of its ligand. Indeed, removal of the retinol from our model leaves a large,empty volume in the hydrophobic interior of the molecule. This would be most unusual and we must assume that thesheets collapse, probably triggering other conformational changes.” They also note, “The β-ionone ring of the retinollies deepest in the pocket, with the isoprene tail stretching out almost to the surface of the protein. The molecule is totallyburied within the protein (Figure 4), with the area accessible to a water molecule essentially zero. Only the very tip ofthe retinol is non-zero with the value of 1 Angstrom2 and this could be due to errors in the coordinates. The hydrophobicnature of the retinol binding site is consistent with the observations that RBP may interact with many different retinylderivatives provided they contain the β-ionone ring and the conjugated double bond system of the isoprene side chain(Hase et al., 1976).” The retinines, a.k.a. Rhodonines(), of this hypothesis are clearly retinyl derivatives. Hase et al56.found “The apo- and holo-forms of RBP were separated by DEAE-Sephadex column chromatography andelectrophoresis, and the presence of two types of both forms, that is, two apo-RBP's (Apo I and Apo II) (2) and twoholo-RBP's (Holo I and Holo II) (6) was demonstrated.” After some calculations, “Based on this calculation, thepreparation contained 86% apo- and 14% holo-forms of total RBP. The ratio of Apo I to Apo II was roughly calculatedto be 3 : 4 and that of Holo I to Holo II was 4 : 3.” Their goal was specific, “In the present study, we purified RBP fromurine freshly collected from patients with "Itai-Itai" disease, and found that the apoforms were more abundant than theholoforms. We then investigated the binding of apo-RBP with vitamin A derivatives and some related terpenoids, in

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57Sivaprasadarao, A. & Findlay, J. (1994) The retinol–binding protein superfamily in Blomhoff, R. ed. VitaminA in Health and Disease. NY: Marcel Dekker Chapter 4

order to seek a correlation between the binding affinity and the chemical structure of terpenoids.” During their studies,Hase et al. noted the high relative affinity of β-ionone (the stand-alone molecule) and β-ionylideneacetic acid. Theyexceeded the affinity of retinol to RBP. The state-of-the-art in the time of Hase et al. was not as advanced as now. Asa result, the interpretations of those investigators must be re-examined carefully. However, their factual data issupportive of the hypothesis of this work.

Figure 7.1.2-7 reproduces an alternate view of holo-RBP with the ribbons labeled57. The accompanying text providesmany more explicit facts about the configuration of the RBP. Page 92 describes the location of various residues mostlikely to interact with the retinoid.

Figure 7.1.2-7 Ribbon representation of 3D holo-RBP in Blomhoff. Retinol is shown in the binding pocket. The twoloop surrounding the tip of the retinol molecule facing the viewer, appear to interact with the receptor as well astransthyretin. From Sivaprasadarao & Findlay, 1994.

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58Rask, L. & Peterson, P. (1976) In Vitro Uptake of Vitamin A from the Retinol-binding Plasma Protein toMucosal Epithelial Cells from the Monkey’s Small Intestine J Biol Chem vol 251(20), pp 6360-636659Rask, L. Anundi, H. & Peterson, P. (1979) The Primary Structure of the Human Retinol-binding ProteinFEBS Letters vol 104(1), pp 55-59

The early work of Rask & Peterson also appears important to the hypothesis of this work even though the target wasintestinal cells58. There conclusion was, “It is therefore suggested that there is a receptor for vitamin A on the cell surfacewhich recognizes the protein part of the protein. ligand complex.” They note, “The fate of the newly absorbed retinolin the cells has been studied and will be reported elsewhere. The fate within intestinal cells may differ from that in RPEcells. Rask et al. have reported the complete sequence of human RBP59 as shown in Figure 7.1.2-8. The presence ofso many peptides of aspartic acid and glutamic acid should be noted. Each of these peptides contains a carboxyl groupunrelated to the atoms involved in chaining the peptides. These sources of oxygen atoms available to participate in ahydrogen bond with the aliphatic portion of retinol insures the possibility of forming an ester at multiple carbon locationsof the retinol. Upon expulsion of the retinine from the RBP pocket, the apo-RBP will be different from the holo-RBP.

Figure 7.1.2-9, also from Rask et al. (1979) shows the preponderance of carboxylic groups within their RBP. Resolvingwhich of the carboxylic groups are most amenable to esterification with retinol is a remaining challenge. Monaco (2009)has provided additional detail with regard to the monomer.

“The secondary structure assignments for human RBP4 are for the beta strands the following: strand A, residues22–30; B, residues 39–47; C, residues 53–62; D, residues 68–78; E, residues 85–92; F, residues 100–109; G,residues 114–123; and H residues 129–138. The alpha helix spans residues 146–158. The open end of the barrelis delimited by four loops joining strands A–B (residues 31–38), C–D (residues 63–67), E–F (residues 93–99),and G–H (residues 124–128). The first three are close to the retinol molecule and amino acids present in themparticipate in the contacts with TTR, the fourth is far from the ligand and is not involved in contacts with TTRin the complex. The loop connecting strands C and D has been found to be disordered in several X-ray structureswhich indicates a certain degree of flexibility which might be related to retinol release.”

Figure 7.1.2-8 Peptide sequence of human RBP from Rask. See text. From Rask et al., 1979.

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60Zanotti, G. Marcello, M. Malpeli, G. et al. (1994) Crystallographic Studies on Complexes between Retinoidsand Plasma Retinol-binding Protein J Biol Chem vol 26(47), pp 29613-2962061Malpeli, G. Folli, C. & Bemi, R. (1996) Retinoid binding to retinol-binding protein and the interference withthe interaction with transthyretin Biochim Biophys Acta vol 1294, pp 48-5462Monaco, H. Mancia, F. Rizzi, M. & Coda, A. (1994) Crystallization of the macromolecular complextransthyretin-retinol-binding protein J Mol Biol vol 244, pp 110-11363Bellovino, D. Morimoto, T. Tosetti, F. & Gaetani, S. (1996) Retinol Binding Protein and Transthyretin AreSecreted as a Complex Formed in the Endoplasmic Reticulum in HepG2 Human Hepatocarcinoma Cells ExperCell Res vol 222, pp 77–83

Zanotti et al. have provided details on the various angles and planes associated with retinol with sufficient precision toallow detailed discussion of how the retinol might be joined to the apo- RBP in order to support the conversion of theretinene to one of the retinines60. They also examined the conformation of the RBP and TTR most supportive of theirforming an RBP + TTR complex. Malpeli et al. have studied the RBP interface with TTR in bird species in order to ginfurther knowledge of the mechanisms involved61. They data may be helpful but is not critical to the discussions in thissection.

Monaco (1995) has indicated that a maximum of two RBP molecules per TTR tetramer are required to support retinoltransport. Monaco et al. provide detailed data supporting this maximum value62. They provided more specificity, “Thecomplex circulating in blood is thought to be formed by one tetramer of TTR plus one monomer of RBP (the RBPconcentration in normal human plasma is about 2mM and that of TTR about 4.5 mM) but it has also been shown thatin vitro it is possible to form the complex with the stoichiometry of two RBPs per TTR tetramer.” Subsequently,Bellovino et al63. have stated explicitly in their abstract, “Retinol binding protein (RBP), the retinol-specific carrier,circulates in blood as a 1:1 complex with the homotetrameric protein transthyretin (TTR). Both RBP and TTR aresynthesized and secreted by the hepatocyte. In this work, we have demonstrated, using HepG2 cells as a model system,that the association between the two proteins occurs inside the cell before secretion.” They further note, the secretionis from the endoplasmic reticulum. They also assert the RBP is only secreted in holo-RBP form in the presence ofretinol. Bellovino et al. also introduced the concept of a chaperone supporting the formation and secretion of the holo-RBP + TTR complex. When the retinene/retinine is delivered to the RPE cells of the retina, this work proposes that the oxygen of the esterremains with the retinene to form a resonant conjugate retinine when the hydrogen bond at the TTR is also severed. Thisconversion may occur in conjunction with the binding proteins within the target RPE cell. If this release of an oxygenatom from the holo-SRBP occurs, the apo-SBRP is now a different molecule (still of great complexity but possibly

Figure 7.1.2-9 Schematic outline of the various fragments and peptides used to establish the amino acid sequence ofRBP. See text. From Rask et al., 1979.

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64Cowan, S. Newcomer, M. & Jones, T. (1990) Crystallographic refinement of human serum retinol bindingprotein at 2 Angstrom resolution Protein Struct Funct Bioinform vol 8, pp 44-61

folded differently and recognizable by the organism as a different molecule). As discussed on conjunction with thedrusen of macular degeneration (Section 7.1.4), this now foreign molecule must be removed from the choroidalvascularization of the retina to prevent the accumulation of material within the finer arteriole between the RPE and thechoroid. Monaco (2000, pg 67) has addressed these changes by asserting, “The most important is a conformationalchange on the loop extending from amino acids 34 to 37, in particular, Leu 35 and Phe 36. The space left empty by theremoval of the vitamin is filled in both cases by the aromatic ring of Phe 36 and solvent molecules and the movementof the Phe side chain drags the nearby amino acids into positions which are different from those adopted in the holo-protein.” More analysis is needed here since Leu does not contain an oxygen readily available for forming an ester (orhydrogen bond), with retinol. It is possible a nearby peptide provides the required oxygen atom. It is possible that theesterification of the retinol to a retinine occurs in conjunction with the transfer of the retinol to the RPE cell.

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[xxx edit into previous material ]The sensitivity of the retinoids to oxidation also provides a clear understanding of the reasons for the two barriersassociated with the Inter Photoreceptor Matrix (IPM.) The IPM must be isolated from oxidizing agents to avoiddestruction of some of its constituents. The Outer Limiting Membrane (OLM) and Bruch’s Membrane (and/or the “tightjunction” shown in Ong) between the cells of the Retinal Pigment Epithelium (RPE) provide an isolated cavity. Thesebarriers around the IPM serve to isolate the delicate retinoids within this space from oxidation by the plasma perfusingthe remainder of the retina.

When the Vitamin reaches a location where it is needed, it passes through the cell wall by a chemical exchange in whichthe transport protein releases the vitamin and the vitamin is transformed into a different compound. In homeostasis,Vitamin A is transformed into Vitamin A Acid as it passes through the cell wall and it is then used in the growth and/ormaintenance of a specific cell. In chromogenesis, the retinoid is converted to a resonant form of the retinoid, Rhodonine,in passing through the wall of the RPE cell.

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Cowan et al. provided a valuable paper in 199064 including new and very detailed material concerning retinoid transportby retinoid-binding proteins (RBP) resulting from x-ray crystallography. They also include valuable data on the cellularretinoid-binding proteins, such as CRBP, CRBPII and CRABP discussed in Section 7.1. They noted, “These proteinsare highly homologous to each other but are specific for their ligands. They are members of another super-family ofproteins that includes fatty acid binding proteins.”

Some assertions related to the spectrum of retinol cite very old references that did not anticipate the retinines as the actualchromophores of vision. The use of the label isoprene tail is slightly misleading when recognizing the actualchromophores of vision. The β-ionone ring of retinol is generally associated with the original isoprene structure. Theschematic figures of Cowen et al. showing 2nd and 3rd order structures are not as clearly labeled as in Newcomer et al.of 1984 although the diagram of figure 6 and Table II contain the same information for the human species. They did notcomment on the very high proportion of aspartic and glutamic acid residues in the schematic of the amino acid sequenceof human RBP.

Cowen et al. note the ability of the RBP to bind both retinol and retinal. This is important because when in the resonantconjugate form, the distinction between these two labels is actually lost. They note citations in the literature related toRBP binding to various cis- isomers of all trans-retinol and all trans-retinal. However, they note, “Although we havemodeled these compound in RBP, we consider the models to be speculative (and of no biological relevance).”

Figure 13 of the Cowan et al. paper may show correct distances. However, the reader is cautioned that the representationof retinol in a 2D ball and stick form is very misleading. There is actually a very large dihedral angle between C5-C6and C7-C8 as shown in Figure 1 of Cowen and more fully documented in Calderone (2003) as discussed below. In 1990,Cowan et al. give this angle as 62 degrees. Either of these large dihedral angles place the oxygen at C5 in rhodonine(5)at a significantly different distance from the oxygen at C15 than previously used in this work to calculate the longwavelength absorption spectrum of the L–channel chromphores of vision (Section 5.5.8.2). This large dihedral anglefrom crystallography is not incorporated into the Jmol file of the Royal Society of Chemistry database and displayedby ChemSpider as of April 2017.

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65Zanottia, G. & Berni, R. (2002) Retinoids in Mammals: A Crystallographic Perspective Croatica ChemicaActa vol 75(3), pp 835-84566Calderone, V. Berni, R. & Zanotti, G. (2003) High-resolution Structures of Retinol-binding Protein inComplex with Retinol: pH-induced Protein Structural Changes in the Crystal State J Mol Biol vol 329, pp841–850

Cowen et al. discuss the potential for a recognizable family of proteins based on x-ray crystallography whose functionis to solubilize small lipid molecules. They explore a variety of molecules that might belong to such a class but do notappear to include the cellular RBPs of the RPE. They do cite Jones et al. (1988) as providing a comparison of RBP andCRBP families. They note a variety of errors in the reported alignments of many of their candidates drawn from theliterature. The closing paragraph of Cowen et al. suggesting that the post holo-RBP may no longer be viable is worthyof careful consideration.

Section 5.5.8.3.1 discusses the 2nd order spectral peak of the L-channel chromophore based on x-ray crystallographicmeasurements.

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Zanotti & Berni provided a useful review in 200265. Figure 3 shows the relative size of the SRBP and TTR proteinsrelative to each other and to retinol. They noted, “The molecular mechanism of ligand binding and release for plasmaRBP remains to be clarified.” The remainder of the paragraph following this assertion is useful but largely speculative.They do note the position of the retinene within SRBP leaves the hydroxyl group largely exposed to solvents in theabsence of TTR. This group is readily replaced by an aldehyde or an acid group without decreasing this exposure oraffecting the binding to the SRBP. Much of the paper is dedicated to cellular retinol binding proteins (CRBP’s). Theuse cartoons to demonstrate the close familial relationship between all of these retinol binding proteins. The extracellularportion of this family are generally classified as extracellular lipid-binding proteins (eLBPs or lipocalins).

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Calderone et al. have presented very high resolution data relating to holo-RBP66. The material is quite detailed andappears relevant to this discussion. As they noted in 2003, “the mechanism of retinol binding and release remains to beclarified.” They also noted, “It has been proposed that the release of retinol might require a reversible transition of theprotein to a poorly structured state, perhaps a molten globule state, under the influence of mild denaturing conditions,such as a relatively low pH.7–9. The retinol–RBP complex might be subjected to mild denaturing conditions, possiblyfacilitating the delivery of the ligand from its carrier protein, on or near the plasma membrane of target cells.” Theconversion of the retinene, retinol, to one of the Rhodonines could involve such “mild” denaturing. However, theliterature suggests the apo-RBP is not viable or reusable and is disposed of by the kidneys. Calderone et al. describeRBP as consisting of 183 amino acid residues. Calderone et al. note the earlier work of Cowan et al. and assert withregard to the retinol, C “The C15–OH bond is nearly perpendicular to the plane of the polyene chain (Figure 1(b)), such that the O atom canparticipate in two H-bond interactions: one with the amide N atom of Q98 (OH–N, 2.85 D) and the other with watermolecule 295 (OH–WAT295, 2.72 D). In turn, the latter solvent molecule is H-bonded to the amide carbonyl O atomof F96 (WAT295–O, 2.71 D) and is kept in place in a tetrahedral arrangement by H-bond interactions with two additionalwater molecules (WAT381, 2.84 D, and WAT425, 2.61 D) (Figure 1(b)).”Their comments related to the β-ionone ring portion of the retinol are considerably more complex. C “The C5–C6–C7–C8 dihedral angle, defining the orientation of the β-ionone ring with respect to the polyene chainplane, is 54 degrees, a value that compares quite well with those for retinol bound to the other RBPs whose structure isknown, as well as for some retinoid compounds in the solid state (see Cowan et al. (1990) for a discussion of torsionangle values). Instead, negative values for the same angle characterize retinol bound to rat CRBP I and II and tozebrafish CRBP (–84 degrees). The C5–C6–C7–C8 dihedral angles for RBP and CRBP-bound retinol molecules aresuch that the orientation of the β-ionone ring with respect to the plane of the polyene chain is opposite in holo-RBPscompared to holo-CRBPs. Therefore, retinol undergoes a significant conformational change when it is delivered byholo-RBP to plasma membranes and is subsequently bound by CRBPs within the cytoplasm of target cells. This changecan be assumed to be induced by the quite different and strong interactions established between the vitamin and residueslining the binding cavities of the two types of carrier proteins.” This work indicates that, in the process of generatingthe long wavelength chromophore, rhodonine(5), C5 becomes esterified with one of the nearby aspartic acid or glutamicacid residues during the formation of holo-RBP and that the oxygen atom at the root of this ester remains with theretinine when it is released at the RPE lemma. As a result, the molecule delivered to the CRBP is not retinol (a retinene)but a rhodonine (a retinine). Calderone et al. continue, “Therefore, retinol undergoes a significant conformational changewhen it is delivered by holo-RBP to plasma membranes and is subsequently bound by CRBPs within the cytoplasm oftarget cells. This change can be assumed to be induced by the quite different and strong interactions established between

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the vitamin and residues lining the binding cavities of the two types of carrier proteins.” It is proposed that this lastquotation can by interpreted to mean; the retinol is no longer a retinene but is transformed to a resonant conjugate retininewhen it is released at the RPE lemma. Calderone et al. note the presence of several water molecules within the cavitycontaining the β−ionone ring of the retinene. One of these could be the result of a condensation reaction forming theproposed ester between the retinol and the RBP. Calderone et al. describe the positions of these water molecules in somedetail (page 844). They go on to discuss potential RBP/retinol interactions in the vicinity of the β-ionone ring.“Residues R60, R62, D39 and D68 are involved in a network of interactions occurring at the protein surface, in a regionthat is possibly critical for retinol binding/release (Figure 2). In fact, as mentioned above, the loop 62–67 has been foundto be relatively disordered in the RBP structures. The network of salt bridges/H-bonds they form is quite well preservedat the various pHs, except for pH 2, at which pH value the R62–D68 and D68–R60 interactions become looser.”

The conclusions of Calderone et al. appear significant to this discussion. They note their work with the crystalline formof the molecules may record results that differ from those that would be obtained in solution.C “In the crystal structures of holo-RBP that we have determined, the ligand is bound nearly unaltered and the overallstructure appears to be preserved at pH as low as 2. In contrast, holo-RBP in solution undergoes denaturation andconcomitantly releases retinol at pH below 4–4.5. The latter processes are impeded until the crystal state is preservedby crystal packing forces, and the pH-induced modifications that we observe in the crystal state can be considered to berepresentative of changes occurring at the initial stages of the acidic denaturation of RBP.”C “The flexible state of RBP that we observe in the crystal state at low pH is likely to represent a key intermediate in theprocesses of protein denaturation and retinol release.”

Calderone et al. note, “Coordinates have been deposited at the Protein Data Bank as 1KT6 (holo-RBP at pH 9),1KT7 (holo-RBP at pH 7), 1KT5 (holo-RBP at pH 4), 1KT4 (holo-RBP at pH 3) and 1KT3 (holo-RBP at pH 2)for immediate release.”

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67Monaco, H. (2009) The Transthyretin–Retinol-Binding Protein Complex In Richardson, S. Cody, V. ed.Recent advances in TTR Evolution, Structure & Functions. NY: Springer available online Chapter 8

Monaco has presented a summary of the knowledge across many fields related to the holo- RBP + TTR complex in200967. His figure 8.5, compares the RBP and the TTR sequences of six different species and that of the human usingthe sequence alignment program CLUSTAL W. In 1984, Monaco indicated the RBP had a molecular weight of 20,600and consisted of 182 amino acids; this figure from 2009 shows 183 amino acid residues. A black dot identifies in eachcase a residue involved in the contacts between the RBP and the TTR in the complex. It is reproduce here withadditional notation as Figure 7.1.2-10. The results are very interesting for the aspartic acid (D) and glutamic acid (E)residues, those capable of providing oxygen to form an ester between the RBP and the retinol. The numbers below thematrix indicate the number, but not the position of aspartic or glutamic acid residues nearly fully conserved between thespecies shown. Such a high concentration of these residues (25 out of 180+) within the RBP’s suggests they have a roleto play that has not been recognized in the literature.

It is proposed here that the high number of oxygen orbitals provided by the many aspartic and glutamic acid moleculespresent in the RBP’s found in the liver can support the transition of the retinenes to retinines at various locations alongtheir conjugated carbon chain (thereby forming each of the desired rhodonines(). Alternately, it is possible that amolecule of retinol is required to be present in the liver in order to seed the creation of an RBP with an oxygen orbitalshared between these two moieties at one of the preferred locations. With the association of a TTR cap, the resultingcomplex containing a retinine can be transported to the RPE and delivered as a specific rhodonine, leaving the post holo-RBP residue non-viable for future retinene acquisition and transport.

7.1.2.2 Transport of the retinoids within the retina

[xxx combine with section 7.1.2.1.2 under a new name and edit ]See Section 4.6 for more of the detailed material on this subject

Figure 7.1.2-10 Primary structure sequence alignment of the RBPs of six vertebrate species. The numbers below thematrix indicates a column containing either aspartic or glutamic acid that is nearly 100% conserved. However, thelocation labeled 10,24 & 25 are less than 100% conserved due to changes in the chicken. See text. Modified fromMonaco, 2009.

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68Crouch, R. & Ma, X-J. (2000) The role of Vitamin A in visual transduction In Livrea, M. ed. Vitamin A andRetinoids: An Update. . . Berlin: Birkhauser Verlag pp 59-72

In the case of vision, it appears Vitamin A passes from its protective capsule in the blood stream through the cell wallinto the RPE. In the process is converted into a “double ended” molecule exhibiting two separate functional groupscontaining a polar atom, oxygen. It appears that this double ended characteristic makes it very easy to transport themolecule through a series of environments within the RPE. This is advantageous on the way to its target location as aliquid crystalline coating on a target substrate, opsin, in the disks of the Outer Segment, OS. The double ended structureof the chromophores is actually a resonant structure. This structure can be described as having an oxygen atom doublebonded to one end of the molecule and a hydroxyl group singly bonded to the other end. Alternately, it can be describedas having one oxygen atom attached to each end of the conjugated carbon chain by 1.5 bonds. In the first case, if a moreaggressive molecule attempts to attach itself to the doubly bonded oxygen atom, the oxygen atom will drop one of itsbonds to the retinoid. This will cause the oxygen atom on the other end to release the hydrogen atom in the hydroxylgroup and to establish a second bond with the retinoid. If a more aggressive molecule attempts to attach itself to oneof the oxygen atoms by a single bond, the situation is different. The other oxygen bond will now exhibit a double bondwith the conjugated carbon chain in order to maintain correct electrical balance. In this case, there is no need to considerin detail whether a hydrogen atom was captured or released by the Rhodonine molecule. However, the concept of a polaratom connecting to a conjugated backbone by 1.5 bonds implies that hydrogen or other simple molecules are availableto share a single charge with the Rhodonine molecule at any time via a hydrogen bond.

The general flow of the retinoids from the bloodstream to a coating on the disks of the outer segment is illustrated inFigure 7.1.2-11. This figure is heavily modified from, but uses the style of, a recent figure by Crouch & Ma68. Theretinol is shown being locked into the SRBP-TTR bottle during transport through the bloodstream by an esterificationwith the SRBP. Upon transfer through the cell membrane of the RPE, the material is converted into a retinine as theoxygen of the ester remains with the retinoid. The oxygen is shown associated with C5 in the figure as an example. Thisis the configuration of the L–channel chromophore of vision. It could be shown alternately at the C7, C9 or C11 positionand represent the other chromophores (see Section 5.5.8).

The material is transported and/or stored within the RPE through a second esterification assumed to be related to C15in the figure (as assumed by Crouch & Ma). This is a logical assumption if only one type of cellular retinoid bindingprotein is present within the RPE. On the other hand, there may be a variety of such proteins within the RPE. Thiswould suggest that these CRBP’s might be selective for the individual chromophores of Rhodonine. In that case, it ismore likely the temporary esterification may occur at the oxygen associated with C5, C7, C9 or C11 on a selective basis.This appears to be the case in practice. If so, it accounts for the variety of CRBP’s found in the RPE. This option isshown below the “OR” line in the figure.

The chromophores of vision pass through the RPE cell membrane into the IPM following a similar procedure as whentransferring from the bloodstream to the RPE. Here, the chromophore appears to be esterfied with a single IPM retinoidbinding protein (IRBP). This leaves the steric specific portion of each chromophore free to associate with its like kindin a liquid crystal on the surface of the disks. When released by the IRBP, the chromophore becomes part of the liquidcrystalline structure that is optimally sensitive to light of a particular visual wavelength. This material can be excitedby a photon as shown at the lower right. This excited material can be de-excited by the transfer of energy to the neuralsystem. Following de-excitation, the material is again sensitive to light. This process does not involve any steric change(isomerism) or require the transport of any retinoid back to the RPE through the IPM. The excitation and de-excitationevents are instantaneous for all practical purposes.

Eventually (typically seven days in humans), the chromophores on the surface layer of the disks are recovered byphagocytosis by the RPE. The chromophores are then returned to an esterfied state in preparation for storage, or transferto the IRBP of the IPM for reuse.

This sequence can be compared with a similar but more conventional conceptual sequence proposed by Crouch & Ma.Their sequence is not completely conventional since it suggests the chromophores of vision reach the photoreceptorspace via the RPE. They present a floating model. It does not address the question of whether their putativechromophore is embedded within a rhodopsin molecule or if it passes through the mitochondria of the photoreceptor cell.

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69Noy, N. Slosberg, E. & Scarlata, S. (1992) Interactions of retinol with binding proteins: studies with retinolbinding protein and with transthyretin Biochemistry vol 31, pp 11118–2470Fex, G. Larsson, K. & Nilsson-Ehle, I. (1996) Serum concentrations of all-trans and 13-cis retinoic acid andretinol are closely correlated J Nutritional Biochem vol 7(3), pp 162-16571Monaco, H. (2000) The transthyretin-retinol-binding protein complex. Biochim Biophys Acta vol 1482, pp65–72

Figure 7.1.2-11 Proposed flow of chromogens (-phores) between the bloodstream and the disks. Box on the leftrepresents the capsule formed by SRBP & TTR to transport retinol via the bloodstream. R represents a RBP ligandwithin the RPE. R’ represents the RBP ligand within the IPM. Zigzag lines represent membrane walls. Dashed lineon right represents the nominal (non-membrane) edge of the outer segment within the IPM. Barred molecule at lowerright indicates the molecule is in a quantum-mechanically excited state. Modeled after a competitive figure in Crouch& Ma, 2000.

7.1.2.2.1 Transfer of the retinines from the SRBP + TTR to the RPE cells

[xxx condense this material. ]It is important to describe the status of research related to the SRBP-TTR-retinene in nutrition prior to discussing thedetails of SRBP-TTR-Rhodonine transport within the vision modality. At least three investigative teams have madesimilar comments within their published reports.

C As Noy et al69. noted in 1992, “. . .the exact function that may be served by binding of RBP to specific receptors inthe plasma membranes of target cells is unclear.”C As noted by Fex et al70. in 1996, “The origin and role of all-trans and 13-cis retinoic acid in serum is unknown.”CA As noted by Monaco in 200071, “Though the exact mechanism of vitamin delivery is still a matter of debate, evidencefor the presence of cell surface receptors has been presented. The kinetics of the process leading to the transfer ofretinol to the target cells has shown that the vitamin is transferred from the complex so that there is not a previousdissociation step of the two proteins which instead separate from one another after the loss of the vitamin.” Thisquotation may not be sufficiently granular, separation may occur in conjunction with retinine transfer.

As shown by their titles, these papers were not concerned with the use of retinol in the visual modality, and theirobservations do not apply to the purpose of supporting vision. However, they contain a great deal of detailed informationconcerning the SRBP-TTR-retinoid complex. The numbers shown in brackets lead to specific citations in each papersupporting the above quotation. Where appropriate, these citations will be addressed below.

The nutrition literature focused on SRBP-TTR-retinene transport is quite extensive, the operational aspects of thisliterature are not relevant to the transport of SRBP-TTR-Rhodonine(). However, much technical information in thisliterature elucidates the detailed mechanisms involved in SRBP-TTR-Rhodonine transport.

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72Naylor, H. & Newcomer, M. (1999) The Structure of Human Retinol-Binding Protein (RBP) with Its CarrierProtein Transthyretin Reveals an Interaction with the Carboxy Terminus of RBP Biochem vol 38, pp 2647-265373Sivaprasadarao, A. & Findley, J. (1988) The interaction of retinol-binding protein with its plasma-membranereceptor

Describing SRBP-TTR-Rhodonine transport is complicated because most of the literature relates to the role of thesimpler SRBP-TTR-thyroxine loop or the SRBP-TTR-retinene loop and their role in nutrition. The SRBP-TTR-retinolloop was originally investigated as the SRBP-TTR-thyroxine loop. In many of these cases, the use of the term loop maynot be justified; the transport phenomenon may not involve returning to the starting point, or reuse of some of thetransport materials.

This section and its subsections will provide a logical progression from these positions to a much better understandingof the role of the SRBP-TTR complex within the vision modality. The method of transporting what is initially a retinene,but that is converted into a retinine (a diol) before, or in connection with, the transfer of the Rhodonines (specificretinines) to the plasma membrane of the target RPE cells will be developed.

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[xxx ]Monaco (2000) indicated that when at the RPE lemma, the TTR moiety was removed exposing the hydroxyl group atposition 15 of the retinol while the rest of the molecule remained enclosed within the SRBP moiety.

Naylor & Newcomer have provided very detailed data at the peptide level regarding the SRBP/TTR interface. They alsonote, “The retinol is encapsulated by the β-barrel in the binding cavity in a hand-in-glove-like fit with the ring end ofthe retinol innermost. Only the hydroxyl of the retinol is solvent accessible72.

7.1.2.2.2 Clearance of the residues of SRBP & TTR from the RPE cell area

This work is more interested in the clearance of any residues of the holo-SRBP + TTR complex after delivery of theretinine to the RPE cells because of the potential buildup of such residues in the form of drusen within the immediatearea of the RPE-choroid space and causing macular degeneration (Section 7.1.2.3, the next section).

Sivaprasadarao & Findley73 addressed the transport potential of SRBP and CRBP in detail but not in the vocabulary ofthis work and not with respect to the visual modality (in 1988). “As the interface between plasma and the cytoplasm,plasma membranes are a critical part of the transport system for retinol, but the mechanism(s) in vivo by which thevitamin is transferred from extracellular RBP to the intracellular binding proteins has not yet been rigorouslyestablished.” They did note the apparent difference between their holo-SRBP and the post-holo-SRBP forms, “Theresults therefore suggest the presence of at least two forms of RBP, with distinct receptor-binding kinetics, theslow-dissociating component corresponding to high-affinity binding.” In their discussion, they further note, “However,these observations provide experimental support for the proposition (Rask & Peterson, 1976) that RBP undergoes amarked loss in affinity for the receptor upon delivery of its bound retinol to the target cell.”

7.1.2.3 Potential buildup of drusen resulting in macular degeneration

[xxx see Dave Goggin email of 6 May 2016. Send draft with cover letter to Dr Duncan ]This sub-section is in direct support of Section 18.8.9.3.1 discussing the medical state-of-the-art with regard to maculardegeneration.

The movement of retinene between the blood stream and the RPE in the space between Bruche’s membrane and the RPEinvolves very low energy chemical reactions. If these reactions are interfered with, it is possible to generate extraneousmaterial, generally described as drusen that cannot be removed by the bodies normal processes. Drusen (singular,"druse") are tiny yellow or white accumulations of extracellular material that build up between Bruch's membrane andthe retinal pigment epithelium of the eye. Drusen are made up of lipids, a fatty protein (this description from theAmerican Academy of Ophthalmology appears to lack precision). Clinically, drusen is observable by theophthalmologist, frequently consisting of particles larger than 25 microns in diameter.

There is a large literature on drusen examined from the immunological perspective.

Crabb et al have provided a report on their investigations into drusen based on a presumed protein base for these

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74Crabb, J. Miyagi, M. Gu, X. et al. (2002) Drusen proteome analysis: An approach to the etiology ofage-related macular degeneration PNAS vol 99(23), pp 14682-14687 doi/10.1073/pnas.22255189975Umeda, S. Suzuki,, M. Okamoto, H. et al. (2005) Molecular composition of drusen and possible involvementof anti-retinal autoimmunity in two different forms of macular degeneration in cynomolgus monkey (Macacafascicularis) FASEB J. express article 10.1096/fj.04-3525fje

materials74. Their discussion offers two important statements. “Drusen are a hallmark risk factor for developing age-related macular degeneration (AMD), yet little is known about their molecular composition or mechanism offormation. The progression of AMD might be slowed or halted if the formation of drusen could be modulated.” “Wasteproducts from the RPE and blood components from the choriocapillaris provide a ready source of extracellular materialfor oxidative modification and drusen formation. Over time, oxidative modifications and subsequent immune-mediatedevents could cause the expansion of drusen on Bruch’s membrane. Accordingly, we hypothesize that oxidative proteinmodifications are causally involved in drusen formation.” Oxidative transformation as outlined int the previous and nextsubsection of this work are at the very foundation of the chemical reactions at sites on the RPE lemma facing Bruch’smembrane. It is difficult to relate the various proteins identified by abstract labels in Crabb et al. with the morefunctional labeling used in this work and the work of other investigators.

A paper by Umeda et al. provides more recent data on drusen and presents a figure 2, reproduce in an expanded formas Figure 7.1.2-13, more compatible with the operations described earlier in this section75. They noted as of 2005, “Atpresent there is no fundamental cure for AMD, although some success in attenuating choroidal neovascularization hasbeen obtained with surgical excision or photodynamic therapy.” “Although the most prominent lesion of AMDinvolves the RPE and Bruch’s membrane, it is degeneration, dysfunction, and death of photoreceptors and itsconsequences that account for the vision loss. Very little is known about the pathophysiology of this disease process.”“Drusen in both late and early onset monkeys showed immunoreactivities for apolipoprotein E, amyloid P component,complement component C5, the terminal C5b-9 complement complex, vitronectin, and membrane cofactor protein.LC-MS/MS analyses identified 60 proteins as constituents of drusen, including a number of common components indrusen of human age-related macular degeneration (AMD), such as annexins, crystallins, immunoglobulins, andcomplement components.”

There are two separate papers on the Internet by these authors with the same title and credentials. However, thefigures are different. The paper incorporating this figure 2 is http://www.fasebj.org/content/19/12/1683.full.pdfThe other paper is http://www.fasebj.org/content/early/2005/09/30/fj.04-3525fje.full.pdf . It contains other usefulfigures.

There is little text accompanying this figure. “A possible pathological pathway whereby autoimmunity against annexinII could contribute to drusen formation is:1) anti-annexin II immunoglobulins bind to the basal plasma membrane of the RPE;2) the inactive C1 serum protein interacts with the Fc portion of the immunoglobulin;3) this leads to formation of the C5b9 membrane attack complex;4) causing damage to the RPE cells followed by shedding of the cell membranes in the sub-RPE space. Immune complexformation might continue in the resultant drusen cores leading to further development of drusen.”

The original figure also lacks definition so important in discussing failure modes of a complex physiological structure,such as the relationship between Bruch’s membrane and the lemma of the RPE cells. The location and role of verhoeff’smembrane in protecting the inter-photoreceptor matrix (IPM) from infiltration by chemically active substances is notrecognized or discussed.

The normal condition in this figure shows two ellipses (on the right) at the vascular/RPE interface representing anunknown process under way. The ellipses are shown in each frame of the figure. This process was not discussed in thetext. It is proposed here that this process involves the delivery of retinenes/retinines to the RPE interface by theSRBP/TTR “bottles” described above. Subsequently the bottle components are released and returned to the kidneysand/or liver for recycling and the capture of additional retinene stored in the liver.

“Furthermore, the codistribution of IgG and terminal complement complexes in drusen suggests an immuneresponse directed against retinal antigens and immune complex formation. This hypothesis is supported by the presenceof putative anti-retinalautoantibodies in the sera of patients with AMD. Anti-retinalautoantibodies have previously beenreported in a number of retinal diseases, including retinitis pigmentosa, paraneoplastic retinopathies, and retinalvasculitis.”

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This work suggests an alternate source of macular degeneration, based on the first figure developed in Section 4.5. Priorto proceeding, the reader is asked to review the terminology of Section 7.1.1.2.3.

The items of primary interest are labeled SRBP (a retinoid-binding protein resident in the serum of the blood stream)and TTR (The plasma protein transthyretin previously known as prealbumin). As discussed above, SRBP is believedto form a “bottle” capable of holding one molecule of a retinene. TTR is believed to associate with the SRBP to forma “cork” for the bottle. When loaded, the bottle is used to transport a single molecule of a retinene from the liver to theRPE of the retina. The retinene-SRBP complex is labeled holo-SRBP in this work. Following arrival and deposition

Figure 7.1.2-13 Conceptual schematic of potential disease conditions (drusin buildup) associated with the vascular/RPEinterface forming the Rhodonines. Left column; Routine operation of the vascular/RPE interface leading to potentialaccumulation of debris. Right two columns; autoimmune activity at the vascular/RPE interface proposed by Umeda etal. The failure of the routine operation of the vascular/RPE interface may lead to the accumulation of debris betweenthe RPE cells and Bruch’s membrane. See text. Expanded from Umeda et al., 2005.

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76Schlett, J. (2016) OCT Angiography: Open Eyes BioPhotonics July/Aug pp 21-2577Nita, M. Strzalka-Mrozik, B. Grzybowski, A. Mazurek, U. & Romaiuk, W. (2014) Age-related maculardegeneration and changes in the extracellular matrix Med Sci Monit vol 20, pp 1003-1016 DOI: 10.12659/MSM.889887

at the RPE, it is believed the two proteins constitute “debris” that must be returned via the bloodstream to either thekidneys or liver. The post-holo-SRBP is no longer biologically viable. The failure of complete debris removal afterrelease of the protein “bottle” parts following delivery of the retinenes to the RPE cells may mediate maculardegeneration.

Frame A of the left column of the figure shows a single RPE cell with its phagocytosis mechanism shown along the topedge that is used to digest old outer discs from the outer segment of the animal photoreceptor neurons. Newchromophores are exuded into the IPM from this same surface. The reclaimed and new proto-photoreceptor material(chromophore pigment) is stored within the RPE as individual granules, labeled here U, S, M & L. This depiction isdifferent from that of Umeda et al. where the solid discs are described as the nucleus of individual RPE cells. Note themultiple ellipses along the lower edge of the frame differs from the normal condition, not specifically described, ofUmeda et al. There may be separate stenolytic sites along the lemma of the RPE for each chromophore type or only one.

Frame B shows the SRBP + TTR & Retinal complex arriving at the RPE cell via the bloodstream from the liver. Whencomplexed, SRBP and a retinene are frequently described as holo-SRBP. As discussed above, there may be four distinctforms of this complex if the retinal is converted to one of the Rhodonines during transport. Alternately, there may beonly one form and the retinal is converted to a distinct form of the Rhodonines as part of the transfer from the complexto the RPE at one of four lemma locations.

Frame C shows the fragments of the complex as they are released from the reaction sites on the RPE lemma. Absentthe retinene, the SRBP is frequently described as apo-SRBP. In this work, the term post-holo-SRBP is used. Thesefragments must be removed promptly in order to allow additional complexed material to react at the RPE lemma. Aconstriction or blockage of the vascularization can prevent removal.

Frame D shows the result of failure to remove the debris over an extended period. The debris may accumulate on eitherside of Bruch’s membrane. With time (aging), the debris can proceed to block the arteriole and/or force the RPE cellsaway from their location relative to Bruch’s membrane. On a large scale, the forcing of the RPE away from Bruch’smembrane result in a displacement of the outer segments of the photoreceptors away from the focal plane of the stage1 optical system. This action can cause both perceived optical distortion and defocusing of the image within the foveola.If the debris blocks the arteriole, it can cause necrosis of the RPE cells in a surrounding area. This debris buildup isusually associated with the “dry” type of macular degeneration. Death of the RPE cells can cause additional disruptionof the normal RPE/IPM/Photoreceptor operating cycle (Section 4.5) and ultimately destruction of the photoreceptors.

Once overwhelmed, the disruption of the RPE allows the arteriole blood to encroach on the space between Bruch’smembrane and the RPE, penetrate Verhoeff’s membrane (Section 18.8.3.6.2) and eventually enter the inter-photoreceptormatrix (IPM) space (Section 4.5). A more detailed figure supporting this discussion also appears as Figure 18.3.6-19in Section 18.8.3.6.2 This is described as the “wet” type of AMD. The oxygen of the intruding blood is highlydetrimental to the operation of the rhodopsin chromophores coating the outer disks. The resulting failure of the outerdisc stack leads to the necrosis of the sensory receptor neurons and associated elements.

Most visual micrographs acquired by ophthalmologists show isolated, typically yellowish, “spots.” The locations ofthese spots are becoming better understood through the latest optical coherence (sometimes computer-aided) tomography(OCT). See Section 18.8.3.5. A key point is the micrographs show isolated spots, yet the AMD causes total loss ofvision over areas larger than that of individual spots, suggesting occlusion of the blood flow. Recent Fourier type OCTis able to identify locations of blood flow interruption (pers. comm. Dr. C. Eifrig MD FACS). A popular trade magazinehas provided a very good overview of the rapid introduction of OCT angiography equipment that does not requireintroduction of dyes into the bloodstream76.

It is quite plausible that an immune response is elicited to aid in the removal of the debris blocking the arteriole andmaintain normal vision until the system is overwhelmed and the RPE cells are disrupted. (initially resulting in the dryform of age-related macular degeneration, AMD).

Nita et al. have recently presented a lengthy review paper with finding that are highly correlated with the aboveanalyses77. However, the terminology is totally different except for the importance of Bruch’s membrane (BrM) and theflow of material into and out of the arteriole channels adjacent to the membrane.

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They do succinctly note, “Age-related macular degeneration (AMD) is the leading cause of permanent,irreversible, central blindness (scotoma in the central visual field that makes reading and writing impossible,stereoscopic vision, recognition of colors and details) in patients over the age of 50 years in European and NorthAmerica countries, and an important role is attributed to disorders in the regulation of the extracellular matrix(ECM).”

The difference between that work and this is their focus. The Nita et al. paper deals with the detailed analyses of a widevariety of structural materials found associated with the extracellular matrix ((ECM, (Bruch’s membrane and thechoriocapillaris). However, it does not explore the transport oriented materials and the operational aspects of the RPEand Bruch’s membrane relative to the visual modality. They note, C “The 2–4 :m-thick BrM . . .is composed of 2 basement membranes – 1 for the RPE cells and 1 for the endotheliumof the choriocapillaris.” C “Between the basement membranes are 2 layers (inner and outer) of structural collagen, composed of collagen typeI and type III (fibrillar). Both of the collagen layers embrace the middle layer of the BrM, like a sandwich built mainlyof elastin.”

Nita et al. also note, “RPE cells control the synthesis of all the structural elements of the BrM, mainly the most abundantproteins – collagen type I, collagen type IV, and laminin (which is not a collagen) – as well as the metalloproteinasesand their tissue inhibitors.” However, this is not the principle role of RPE cells and may in fact be highly speculative.

It is not clear if the TTR (transthyretin) is among the molecules described in the Nita et al. paper. The paper is focusedon structural materials rather than operational materials involved in the visual modality. They do note, “Deposition ofthese new structures increases the thickness of basal laminar deposits to a high degree and simultaneously worsens thenutrient and oxygen supply of the RPE/photoreceptors, which in turn maintains neovascularization. The basal deposits,with diameters of over 25–30 :m, turn into clinically visible soft drusen, which are conducive to serous [sic] separationof the RPE from the ECM.”

Nita et al. also note, C “MMP-1 degrades collagen I, II, III and the decrease in its activity favors the development of soft drusen.”C “RPE cells, when exposed to blue light (relative AMD risk factor), diminish TIMP-3 production, which consequentlycauses an increase in the amounts of various collagens and in the development of early dry AMD;C “on the other hand, TIMP-3 demonstrates a protective influence, since it inhibits the development ofneovascularization.”

These statements are supportive of the operational role, and potential failure mode of the ECM leading to AMD asdescribed in this work. Their figure 2 is highly complex and probably primarily speculative. However the discussionunder the heading, “Histological and Clinical Aspects of Changes in the ECM and Other Mechanisms” appear highlycompatible with the analyses of this work. Their figure 3 discusses the disintegration, and presumed removal, of avariety of molecules from the ECM. It is worth noting that the turnover of the transport proteins, SRBP & TTR are atleast an order of magnitude more frequent than the replacement of any structural protein explored by Nita et al.

The Umeda et al. and Nita et al. papers are inconsistent as to the degree and specific location ofneovascularization related to AMD. In this work, as indicated in the figure above, the situation may involveinfiltration of blood plasma into the IPM region via penetration of Verhoeff’s disrupted membrane, with orwithout growth of vascular tissue.

The potential infiltration of blood plasma into the IPM establishes a functional as well as clinical link between a retinaltear and AMD. In both cases aggressive chemicals from either the vitreous humor of the ocular or the vascular matrixadjacent to the choroid can contaminate the IPM and damage the outer segments of the sensory neurons.

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78Starzak, M. (1984) The Physical Chemistry of Membranes. NY: Academic Press Fig. 2.7, Pg. 4279Crouch, R. Chader, G. Wiggert, B. & Pepperberg, D. (1996) Retinoids and the visual process. Photochem.& Photobiol. vol. 64(4) pp. 613-621

Figure 7.1.2-14 Proposed transport of the retinoids withinthe RPE. (a) The four Rhodonines showing their pairs ofbinding sites when in the aqueous state. (b) A cartoonshowing the various configurations of Rhodonine(5) andother moeities in the course of transferring rhodonine fromone location to another in the RPE.

7.1.2.4 Transport of Rhodonine within the RPE/IPM space of the retina

A similar process has been described in a cartoon byStarzack78 where two different cations compete for twoidentical binding sites. Figure 7.1.2-14 illustrates thesituation for retinol after it has arrived at the RPE andbeen converted into a resonant retinoid. It can beconverted into any one of four retinoids of theRhodonine family (a). Each of these forms can thenparticipate in the transport process as shown in (b).Referring to (a), Rhodonine (5) is shown with its twopolar groups in solid black. [When displayed in twodimensions, the retinoid molecules in this work areshown with the $-ionone ring rotated to place the #5carbon at the top of the ring. This orientation places the#5 carbon in line with the conjugated chain to stress thefamilial similarity of the Rhodonines. Each of thesegroups shares 1.5 bonds with the backbone of themolecule because of its resonant character. ForRhodonine(5), the leftmost polar group is located at thetop of the $-ionone ring, at the location of carbon #5,and the rightmost polar group is associated with carbon#15. Similarly, Rhodonine(7) has its leftmost polargroup attached at carbon #7, Rhodonine(9) at carbon #9and Rhodonine(11) at carbon #11. Each of thesemolecules exhibits a different physical length betweenits two polar groups. These different physical lengthsand the slow wave nature of the resonant structureaccount for the spectral absorption characteristic of eachof these molecules. (b) illustrates how one of theRhodonines, here Rhodonine(5), can be transportedwithin the retinal structure. Assume it is normally storedin one of the color centers of the RPE in its neutral butresonant form (caricature 1). A transport protein such asCRAIBP binds to the polar atom associated with the #5carbon (caricature 2)and moves the combined structureby diffusion through the RPE to the RPE/IPM interface.At that interface, a second transport protein, such asIRBP, located in the IPM binds to the polar atomassociated with carbon #15 (caricature 3). The firstbinding protein, which is still in the RPE, releases fromthe Rhodonine molecule. The result is caricature 4. Thecombined molecule now moves by diffusion to an endpoint such as a disk of an outer segment. At that point,the second transport protein releases the Rhodoninemolecule and the neutral molecule is now free. It is alsoin the proper position to assume its place in the liquidcrystal on the surface of the protein substrate, stipulated to be opsin.

Crouch has presented a flow diagram, using two-dimensional stick models of rhodopsin, as part of a recent reviewarticle79. The article assumes the chemical theory of the neural system to describe the movement of the retinoids fromthe blood serum, through the RPE and on into the IPM (and apparently their return to the RPE at a later time. Althoughit loosely follows the flow suggested by this work, it does not appear to represent the most recent literature on retinoidtransport. This is particularly true with respect to the transport of the chromogens of vision in the bloodstream. Nor doesit explain how the putative rhodopsin is transferred from the disks to the RPE, regenerated in the RPE, and transferred

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80Rask, L. Anundi, H. & Peterson, P. (1979) The primary structure of the human retinol-binding protein. FEBSLetters, vol 104, no. 1, pp 55-5881Gamble, M. & Blaner, W. (2000) Factors affecting blood levels of vitamin A In Livrea, M. ed. Vitamin A andretinoids: an update. . . . Basel Switzerland: Birkhauser Verlag pp 1-16

back to the disks in a timely manner. Figure 7.1.2-15 presents a simpler diagram based on the more recent literatureand this work for comparison. It is based on the discussion of Section 7.1.1.4.3 concerning three conditions. (1) is theinability of the retinoids employed in the formation of chromophores to travel to the RPE unprotected in the bloodstream.(2) involves the concept of the chromophores as resonant forms of a retinoid. (3) involves the electronic excitation ofthe chromophores leading to electronic de-excitation (as opposed to de-excitation via conversion to a stereoisomer). Theconclusion is drawn that the retinoids destined to become chromophores are converted to a Rhodonine as part of thetransport process through the bloodstream.

In this figure, free retinol is stored in the liver before distribution through the vascular system (a). While retinol maybe transported through the bloodstream in its native form for some purposes, the material destined for use in thechromophores of vision requires special handling. To pass through the bloodstream and then pass through the cell wallof the RPE cells and eventually reach the disks of the Outer Segment. It is uniquely packaged. This figure shows aputative scheme for accomplishing the steps necessary to transform the retinol into chromophores during this transit.Alternate schemes can be suggested. However, this one provides a method for the chromophores (while complexed andin dilute form) to be selectively deposited on the appropriate spectrally selective disks within the retina. It suggests thatretinoid transport and conversion occur simultaneously in a well-orchestrated sequence.

Frame (b) shows retinol in its native form, and packaged within four transport “bottles.” For continuity, it also showsan open empty bottle known to depart the area of the RPE and to travel the bloodstream until it reaches the kidneyswhere it is disposed of. This scheme suggests there are four distinct retinoid binding sites within the SRBP of the blood.These could result from four different specific variants of SRBP that each contained one site or a single SRBP thatcontained multiple binding sites. Rask, et. al. have sequenced the entire SRBP molecule using a fractionationtechnique80. Their results speak of three carboxyl groups occurring in human SRBP. They also speak of four methionylresidues (these do not contain carboxyl groups). However, their data shows a plethora of glutamic acid and aspartic acidsites that each contain a complete carboxyl group. This situation suggests that SRBP could make available carboxylgroups at a variety of locations depending on the stereochemistry of the molecule. These locations could support theformation of all four Rhodonines. See Section 4.6.3. Only the determination of the stereographic structure of SRBPcan support the determination of the exact mechanism of retinol to Rhodonine conversion in the SRBP bottle.

It is proposed that the location of the reactant carboxyl group of the SRBP (shown by the rectangular nib along the innertop edge of the bottle) varies in a yet to be determined way. It is this site that complexes with retinol. Following thiscomplexing, the content of the bottle is protected by the “stopper” of TTR and can travel the bloodstream free fromchemical attack.

Upon reaching the RPE cells of the retina, each bottle becomes attached to an individual cell wall where it can insert theretinoid into the cell. In doing this, the SRBP forfeits the oxygen atom. The SRBP residue is then transported to thekidney for elimination.

Gamble & Blaner have recently noted the fact the stopper TTR has a total weight of 55 kDa and contains four identicalsubunits81. The presence of four subunits suggests a role for TTR similar to that described above for the subunits ofSRBP. In this case, the SRBP acts as a more passive carrier and the stereo-connection between retinal and TTRdetermines the ultimate form of the rhodonine precursor delivered to the RPE cells. They suggest the larger TTRprevents the SRBP-retinal complex from renal filtration. In this case, the residue of SRBP and a remnant of TTR wouldbe unsuitable for reuse and would be cleared from the system by the kidneys. Gamble & Blaner noted that, “Deletionof the gene for TTR is not lethal, and in fact, TTR deficient mice are phenotypically normal despite circulating RBP-ROH levels which are only approximately 5% of normal.” They did not discuss the potential for impaired vision inthese mice.

Frame (c) suggests that the retinoids, which now contain two oxygen ligands per molecule are transported within the RPEby a second family of RBP’s. The research in this area has not yet coalesced. There are suggestions that there are twodistinct families of CRABPs. One would be used to transport the retinoids to spectrally specific storage locations withinthe RPE cells. The second would be used to transport the retinoids from storage to the cell interface with the IPM.These options are discussed in TABLE 7.1.1.2-1 above. At the RPE/IPM interface, the retinoids are transferred to asubsequent RBP designated IRBP because of its location within the IPM. By attaching to the retinoids as suggested byframe (d), the unique spectrum determining feature of each type of retinoid is exposed. This allows these retinoids to

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Figure 7.1.2-15 Overall scheme for retinoid transformation for both chromophore formation and operation. All of themolecules shown contain a conjugated carbon chain. Molecules with two black ligands (oxygens) also contain aconjugated carbon chain between the two oxygens, have an unpaired electron and are resonant. Molecules with onlyone black ligand are not resonant. Each of the chromophores in (e) are easily raised to an excited state by photons sharingtheir individual resonant wavelength. See text.

be transported to and be assimilated into a spectrally specific liquid crystalline coating being formed on the opsinsubstrate of each disk.

Frame (e) illustrates the chemistry of the individual fully formed chromophores as they are stored in the RPE and asfound on the disks of the Outer Segment.

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82Farber, D. & Chader, G. (1988) The molecular biology of the retina. Progress in Clinical and BiologicalResearch, vol. 362, NY: Wiley-Liss83— (1990) Methods of Enzymology. Vol. 189 pg. 32584Cunningham, L. Yang, L. & Gonzalez-Fernandez, F. (1999) Interphotoreceptor retinoid-binding protein(IRBP) is rapidly cleared from the Xenopus interphotoreceptor matrix Exper Eye Res vol 68, pp 399-41085Loew, A. & Gonzalez-Fernandez, F. (2002) Crystal structure of the functional unit of interphotoreceptorretinoid binding protein Structure vol 10, pp 43-4986Pfeffer, B. Wiggert, B. Lee, L. Zonnenberg, B. Newsome, D. & Chader, G. (1983) The presence of a solubleinterphotoreceptor retinol-binding protein (IRBP) in the retinal interphotoreceptor space. J. Cell Physiol., vol.117, pp. 333-341

Chen & Heller have noted that their retinol-like material is found in two forms within the RPE. It is found complexedwith one of the above rhodonine-binding proteins (mol. wt. >1.5 x 106) and it is also found in a free form of lowmolecular weight (<1000) material. The four Rhodonines have a molecular weight of either 285 & 299 (two of each). They went to analyze the cytosol of the RPE using radioactive labeled retinoids. They found that about one third of thetotal material was in the form of a complex with an RBP. The rest was free “retinol-like” material. The free materialwas found in a spot corresponding to retinol using thin layer chromatography. Because of the slight difference inmolecular weight between the chromogens (retinol, mol. wt. 286.4 ) and the chromophores, this would be expected. Thequestion becomes how accurately was the location of the “spot” measured and did the spot show an unusual broadeningor even a dual peak in density? Their processing would need to be reconsidered to determine whether it may havedegraded the material with a weight less than 1000 from the palmitate to a “free retinoid.” As palmitates, the molecularweight of the retinoids would have been 444 and 448.

Farber & Chader have edited a review focused on IRBP82. Liou, Geng & Baehr, writing in the that review, develop thefact that IRBP also exhibits a fourfold feature in its genetic structure and that it is apparently not related to the otherRBP’s. They claim it is secreted from the photoreceptor cells based on Hollyfield, et. al. It may originate in theneighboring glial cells. The fourfold gene feature may support the option found in this work that there are four separateIRBPs that preferentially transport the four chromophores of vision across the IPM to the photoreceptor extrusion cup.The molecular weight of IRBP is given as 134,200 in Methods of Enzymology (1990)83. The half-life of IRBP has beenmeasured at ~11 hours in Xenopus84. Loew & Gonzalez-Fernandez have recently characterized the IRBP molecule indetail85.

It is suggested that most of the non-protein material in the IPM consists of fuels to support the electrolytic processespowering the photoreceptor cells of the neural system.

7.1.2.4.1 Nature of the RBP’s in the RPE

Based on this work, there are several RBPs within the RPE that perform individual and specialized functions. Thesefunctions all relate to the transport of the chromogen or chromophore material between the interface with the bloodstream and the IPM and their temporary storage. This task also involves the recirculation of chromophoric materialrecovered by phagocytosis of the old disks of the disk stacks.

The precise terminology used for these RBPs has been improving in the literature with each decade. Therefore, weighingthe ideas presented in the earlier literature carefully is important. There appear to be two distinct RBPs in the RPE space.One of these, CRBP, is involved in the transfer of the chromophoric material to the pigment globules of the RPE forstorage. The other, CRALBP, is used to transfer the same material to the IPM for application. Because of their function,the names are derived from their Cellular Retinoid Binding Protein characteristics. Initially, it was assumed CRBPpreferentially bound the alcohol form of the retinoid. Therefore, the letters AL were added to the second protein isolated,based on its proclivity for binding to aldehydes in-vitro. Since these materials are generally involved in the transfer ofRhodonine and not retinol or retinaldehyde, these names are mostly of historical significance. Rhodonine has twoseparate ligands. One of them is an alcohol and the other an aldehyde.

Pfeffer, et. al.86 have provided molecular weights for these soluble glycoproteins. Their values are 15,000 Daltons forCRBP and 33,000 Daltons for CRALBP.

7.1.2.4.2 Criticality of IRBP based on genetic mutation testing

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87Ripps, H. et.al. (2000) The rhodopsin cycle is preserved in IRBP “knockout” mice despite abnormalities inretinal structure and function. Vis. Neurosci. vol. 17, pp. 97-10588Jones, G. Wiggert, B. Crouch, R. Cornwall, M. & Chader, G. (1989) Bovine IRBP and amphibianphotoreceptors: retinoid transfer and protection. Invest. Ophthal. Vis. Sci. Suppl. vol. 30, pg. 48889Okijama, T.-L. Wiggert, B. Chader, G. & Pepperberg, D. (1994) Retinoid porcessing in retinal pigmentepithelium of toad (Bufo marinus). J. Biological Chem. vol. 269, no. 35, pp 21983-21989, fig 790Inouye, L. Albini, A. Chader, G. Redmond, T. & Nickerson, J. (1989) Exp. Eye Res. vol. 49, pp. 171-18091Berman, E. (1991) Biochemistry of the Eye. NY: Plenum pp 375-380

Ripps, et. al87. have recently reported significant tests on the visual performance of mice genetically modified to interferewith IRBP utilization in the IPM. The exact expression of the mutation is not clear and several of the tests would notbe expected to be significant based on this work. In what they describe as "knock-out" (IRBP--/--) mice, significantchanges were recorded in the cross section of the retinas. The outer nuclear layer, containing the nuclei of thephotoreceptor cells, was attenuated to less than 50% of its normal thickness and the Outer Segments were shortened anddisorganized. Assume for the moment that the IRBP is secreted from the soma or inner segment of the photoreceptorsin the outer nuclear layer. Under this assumption, it is not clear whether the absence of IRBP in the IPM was due tofailure of the cells to produce the protein or whether it was due to the failure of the cells to secrete the protein into theIPM.

The Ripps, et. al. paper assumes that IRBP plays a role in moving 11-cis-retinol from the RPE to the Outer Segmentsof the photoreceptors and then plays a role in moving all-trans-retinol back to the RPE on a recurring basis. Jones, et.al.88 make an alternate statement that IRBP can transfer the aldehyde form of the retinoid to bleached rod cells restoringtheir sensitivity to light. However, his suggested kinetics differ from those of a simple transfer between membranes.Okajima, et. al89. have presented a caricature showing IRBP simultaneously moving 11-cis-retinal in both directions andal-trans-retinol in one direction within the IPM. This work does not support any of the above conflicting hypotheses atthe detail level. First, it assumes the material transported from the RPE is Rhodonine (which exhibits both alcohol andaldehyde ligands simultaneously). Second, it assumes the chromophoric material is only transported hydraulically fromthe RPE to the interior of the extrusion cup of the inner segment. Third, the theory does not require the chromophorematerial to be returned to the RPE for re-isomerization.

7.1.2.4.3 Nature of IRBP in the IPM

Based on this work, IRBP has only one function, to transport chromophores from the RPE interface to the formativelocation of the disk stack in the IPM. It is not involved in the transport of isomerized chromophore back to the RPE.

Pfeffer, et. al. have studied this material in detail and compared it with some other retinoid-binding-proteins.IRBP is a soluble retinoid-binding-protein of 146,000 Mr, (250,000 Daltons) that can also be described as a glyco-protein, found exclusively in the IPM space (Pfeffer, et. al. speak of this space as the extracellular matrix, ECM). Besidethe Outer Segments, the space is also known to contain glycoconjugates and collagens as well as other soluble materials.When using centrifugal techniques on whole retinas, it is found with other RBP’s predominantly, if not exclusively fromthe RPE. These RBPs include CRBP of 15,000 Daltons and CRALBP of 33,000 Daltons. They considered the fact thatCRBP and CRALBP were not found in their IPM wash one of their most significant findings. It strongly suggests thatIRBP is the only RBP in the IPM. Liou, et. al., writing in Farber & Chader noted no significant sequence similarity ofIRBP with other RBP’s except in two short segments.

IRBP is a large and elongated molecule. It has a nominal length of 240 Angstroms and consists of four replicated units,a tetramere (Loew & Gonzalez-Fernandez, 2002). It has an axial ratio of about 7:1. It is a very large molecule comparedto the retnoids with a length of 15 Angstrom and a diameter of 7 Angstrom. Each of the four 77 by 25 Angstrom sectionsof IRBP exhibit at least two pockets large enough to accomodate stereo-chemical combination with a Rhodoninemolecule. It is widely distributed in the IPMs of the vertebrates.90 Additional material concerning IRBP has beencollected in Berman91.

The recovered IRBP was found to bind to many materials such as cholesterol and tocopherol. However, these materialsare not normally found in the IPM space protected by Bruch’s membrane and the Outer Limiting Membrane. Nor arethey found in the closely packed RPE cells and the closely packed photoreceptor and glial cells of the retina. It has alsobeen found to bind to a variety of fatty acids. However, this binding may have been a consequence of the extractiontechnique.

There are several statements in the literature suggesting that IRBP is produced through the Golgi apparatus in the

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92Ripps, H. Peachey, N. XU, X. Nozell, S. Smith, S. & Liou, G. (2000) The rhodopsin cycle is preserved inIRBP :knockout: mice despite abnormalities in retinal structure and function. Visual Neurosci. vol. 17, pp. 97-10593Anderson, R. Benolken, R. Dudley, P. Landis, D. & Wheeler, T. (1974) Polyunsaturated fatty acids ofphotoreceptor membranes. Experimental Eye res. vol 18, pp. 205-21394Hollyfield, J. Fliesler, S. Bayvorn, M. Jong, S-L. Landeres, R. & Bridges, C. (1985) Synthesis and secretionof interstitial retinol-binding protein by the human retina. Invest. Ophthal. Vis. Sci. vol. 26, pp. 58-6795Hogan, M. Alvarado, J. & Weddell, J. (1971) Histology of the Human Eye Philadelphia, PA: W. B. Saunders pg 435

photoreceptor cells and excreted into the IPM. It is not clear whether the alternative possibility, of production in glialcells, was actively considered92.

Ripps, et. al. state in their summary, “the results of these studies indicate that the rhodopsin cycle can occur in theabsence of IRBP.” This is additional evidence that the actual photoexcitation/de-excitation cycle does not involve thetransport of chromophores to the RPE for regeneration.

In addition to the short term situation described in the previous paragraph, Ripps, et. al. make the additional statementmore applicable to the long term situation: “In the absence of IRBP, lipid depletion could lead ultimately to abnormalitiesin the turnover rate of disk membranes, biochemical changes in membrane composition, and a reduction in the receptor-mediated ERG.” The statement is attributed to Anderson, et. al93. This position appears compatible with a premise ofthis work that so-called cones are in fact immature or degenerate rods.

7.1.2.4.4 Proportion of IRBP in the IPM

Several authors have recently referenced a paper by Pfeffer, et. al. They stress the predominance of IRBP in the IPMspace. These include a paper by Nickerson, et. al. writing in Farber & Chader as well as the above paper by Ripps, et.al. Two statements are made;

+ “In the monkey, it accounts for about 70% of the protein in this space.”

+ “In this connection, it is important to recall that IRBP constitutes >70% of the soluble proteins of the IPM.”

Pfeffer actually said something slightly different. They were developing a very gentle technique of removing materialfrom the IPM without causing physical or chemical damage. In their discussion concerning IRBP, they noted that: “Aconsistent amount (about 30% of the total found in unwashed retina) of this protein does remain with the retina followingwashing using the methods described here.” Thus, they extracted 70% of the available IRBP and left 30% behind. Theysaid IRBP was the predominant soluble glycoprotein present but made no comment concerning the amount of IRBP asa percentage of the total IPM content or of the amount of total protein present. Their conclusion was that the IRBP waspresent in the original IPM as an extracellular soluble or loosely bound, peripheral glycoprotein, except for the 30% leftbehind on washing the IPM. This 30% was thought to be either more tightly bound to the other structures present ormerely not extracted by the technique employed. In this work, it is proposed that this material was essentially trappedin the space between the disks of the Outer Segment with some possibly temporarily bound to the liquid crystallinechromophore during the deposition process.

7.1.2.4.5 Sources of IRBP in the IPM

Hollyfield, et. al94. have provided the results of an autoradiographic study focused on IRBP production in the peripheralretina. Their work clearly shows that IRBP is formed in the retinal space occupied by the Inner Segments ofphotoreceptor cells and various glial cells. Hogan, et. al. have shown the morphology in the area of the inner segments,Mueller cells and the OLM at 24,000x95. Their imagery clearly shows the “fiber baskets” of the Mueller cells are locatedin the IPM. They could secrete IRBP into the IPM using materials absorbed from the INM without involving thephotoreceptor cells in this process.

Although less than conclusive in proving the glial cells were not involved, Hollyfield, et. al. represent that the nucleotide,3H-fucose, was incorporated into IRBP and the resulting material secreted into the IPM in time scales of less than 30minutes. They made the assumption that IRBP was formed within the photoreceptor cells. Based on that assumption,they found that after four hours of incubation, all cells in various retinal layers retained a uniform concentration of thenucleotide except the photoreceptor cells (and the ganglion cells). They say that 75% of the material present after 30

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96Johnson, A. Merlini, G. Sheldon, J. & Ichihara, K. (2007) Clinical indications for plasma protein assays:transthyretin (prealbumin) in inflammation and malnutrition Clin Chem Lab Med vol 45(3), pp 419–42697Goodman, D. Peters, T. Robbins, J. & Schwick, G. (1981) Prealbumin becomes transthyretin J Biol Chem vol256, pp 12–498Monaco, H. (2000) The transthyretin-retinol-binding protein complex. Biochim Biophys Acta vol 1482, pp65–7299Noy, N. Slosberg, E. & Scarlata, S. (1992) Interactions of retinol with binding proteins: studies with retinolbinding protein and with transthyretin Biochemistry vol 31, pp 11118–24100Kim, C-I. Leo, M. & Lieber, C. (1992) Retinol Forms Retinoic Acid via Retinal Arch Biochem Biophys vol 294(2), pp. 388-393101Bienvenu, J. Jeppsson, J. & Ingenbleek, Y. (1996). Transthyretin (prealbumin) and retinol binding protein.In xxx Serum proteins in clinical medicine, vol 1. Foundation for Blood Research pp 1-9 Very limitedcirculation in 1996.102Fex, G. Larsson, K. & Nilsson-Ehle, I. (1996). Serum concentrations of all-trans and 13-cis retinoic acid andretinol are closely correlated. J Nutritional Biochem vol 7(3), pp 162-165103Yves, I. & Jacques, B. (2008). Plasma transthyretin indicates the direction of both nitrogen balance andre t inoid s ta tus in hea l th and d isease . Open Cl in Chem J vol 1 , 1-12 .http://benthamopen.com/contents/pdf/TOCCHEMJ/TOCCHEMJ-1-1.pdf104Blomhoff, R. & Blomhoff, H. (2006) Overview of Retinoid Metabolism and Function J Neurobiol DOI10.1002/neu

minutes was lost from the inner segments of the fully mature photoreceptors (labeled rods in their work) at the end ofa four-hour period. The shorter photoreceptor cells (considered immature in this work and labeled cones in their work)only lost 11% from their inner segments in the similar time period. The cells in the inner nuclear layer (apparently nucleiof the photoreceptor cells as a group) actually lost 14%, which was more than the inner segments of the immature cellslost. Their figure 4 would suggest that their so-called cone inner segments were no more functional in the preparationof IRBP than the material of the inner plexiform layer (which does not contain any mitochondria or other manufacturingmedia). Their investigations continued. They showed that the nucleotide was recovered primarily from IRBP in the IPMwash. They also addressed the consumption of the nucleotide by the ganglion cells in the production of non-IRBPrelated material.

7.1.2.5 Background: SRBP +TTR complex in non-visual applications

Considerable data from several investigators related to the tetrameric SRBP’s has appeared. Johnson et al96. haveprovided useful background related to TTR and this work defining the Rhodonines and suggesting the precise operationof these tetrameres during transport from liver to the RPE cells may be described more fully. Both SRBP and TTR arerecognized to have an affinity for, at a minimum, the simple retinenes. These affinities might suggest they are capableof contributing an oxygen atom required to convert a retinene into a resonant conjugated molecule, a retinine (spelledwith two i’s). The question then becomes, whether this proclivity can place the donated oxygen atom at the appropriatelocation along the retinine molecules to create the four distinct Rhodonines?

Quoting Johnson et al. again in condensed form, transthyretin “was subsequently shown to bind holo-retinol-bindingprotein (RBP with retinol, or vitamin A) as well, and the name was changed to transthy(roxin) retin(ol) to denote its dualtransport function. TTR is a tetramer of four identical subunits. Although each of the four monomers has a binding sitefor RBP, the tetramer binds only one molecule of RBP with high affinity and possibly a second with lower affinity. Thebinding affinity for apo-RBP (RBP without retinol) is very low, and the loss of retinol (e.g., uptake by tissues) resultsin the separation and renal excretion of free apo-RBP, accounting for the very short biological half-life of RBP of ~ 3.5hours. The TTR-RBP complex normally transports approximately 90%–95% of retinol/vitamin A.” They cite Goodmanet al97., Monaco98 and also Noy et al99.

Additional investigations have been reported by Kim et al100., Bienvenu et al101, Fex et al102 Yves et al103 and summarizedin a review by Blomhoff & Blomhoff104.

The conceptual material related to vision (specifically rhodopsin and its formation) presented in Blomhoff & Blomhoff(2006) is conventional wisdom summarized from other sources and is not supported here. Many of the process stepsdescribed can be replicated in-vitro but they have little relevance to the in-vivo situation. As Fex et al. have noted,“Many tissues are known to be able to transform retinol to retinoic acid in-vitro. The origin and the role of 13-cis

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retinoic acid is obscure, as it does not bind to retinoic acid receptors (RAR:s).” The lack of continuity in the Blomhoff& Blomhoff presentation is indicated by their assertion, “It is clear, however, that an additional and yet unidentified11-cis retinol dehydrogenase is the major enzyme responsible for the oxidation of 11-cis retinol to 11-cis retinal in thevisual cycle.” These materials, identified conceptually in the 1940's, are not the actual photoreceptors used in vision.They offer no detailed schematics of how retinol is modified to generate a family of materials exhibiting the spectralresponse of the four signaling channels of the photoreceptors of vision, UV–, S–, M –, & L–.

The review by Yves et al. focused on nutrition is extremely important in the context of vision. The abstract notes, “Thelevel of TTR production by the liver also works as a limiting factor for the cellular bioavailability of retinol and retinoidderivatives which play major roles in the brain ageing process.” The paper provides very detailed information about theformation and utilization of TTR in the transport of “retinol.” They go on, “The choroid plexus is the sole site ofmammalian brain involved in TTR production. Its synthesis rate by the choroid epithelium is estimated 25 to100 times higher than that of the liver on a weight basis. As a result, TTR is a major component of CSF (CNS inthis work), constituting 10 to 25 % of total ventricular proteins conveying up to 80% of intrathecal thyroxine. TTRthus constitutes an hormonal carrier-protein fulfilling important ontogenic and functional properties in mammaliannervous structures, a concept further corroborated by the observation of its increased CSF concentration during theneonatal period. The data imply that choroidal TTR facilitates the uptake of thyroxine from the bloodstream, governingits transport and delivery to brain tissues following a kinetic model developed by Australian workers. In comparison,CSF contains 10 to 100 times lower RBP and retinol concentrations than plasma whilst retinyl esters from dietary originare virtually absent.” The choroid plexus is a network of blood vessels in each ventricle of the brain. The network isderived from the pia mater and produces the cerebrospinal fluid. It is also a component of the blood-brain-barrier.”These pronouncements add a different perspective related to the SRBP + TTR + retinene complex. They suggest theliver to retina pathway may pass via the blood-brain-barrier. They further note, “strongly suggesting that its retinolligand is released in free form and readily taken up by membrane or intracellular receptors of neural cells. The dual TTRproduction, plasma-derived and choroid-secreted, allows complementary stimulation of brain activities.” They go onto note a 1994 citation, “The prominent place occupied by TTR in defining distal retinoid bioavailability has been toolong unrecognized despite the warning expressing that ‘overlooking the crucial role of TTR in vitamin A-metabolismresults in unachieved or even misleading conclusions’.”

Following this assertion, the paper proceeds down a narrow path that does not recognize the crucial role of the retininesin the visual modality. It begins with, “Retinol is a precursor substrate that must undergo a two-step oxidation procedureto release firstly retinal and thereafter the two active all-trans- and 13-cis-retinoic acids (RAs).” that requiresreinterpretation in the context of vision. The transport mechanisms, including their two-step process to generate retinoicacid, presented by Kim et al. and their conclusions are irrelevant to vision, but the data may be quite useful.

The term “two-step” process has long been associated with the loading of the SRBP-TTR complex with a singlemolecule of retinol converted to a single molecule of retinal in step one, and the conversion of a single moleculeof retinal into a single molecule of retinoic acid in step two. This process may be critical to the nutritionalprocess; however, the defined two-step process employed in nutrition is not relevant to theSRBP-TTR-Rhodonine loop. The loading of the SRBP-TTR complex with either all-trans retinol or all-transretinal is irrelevant since, the objective is to convert either of these molecular forms into the resonant all transRhodonine() form through an additional stage of oxidation.

This work does not address any role for retinoic acid in any stereographic form. It does begin to involve other criticalretinol binding proteins (RBP), even though they may involve species that are actually retinol derivatives. “Theintracellular activities exerted by retinoid compounds are mediated by a large variety of specific receptors among whichare cellular-RBP (CRBP), cellular-RA-BP (CRABP), . .” These RBP’s are discussed in other subsection of this chapter.

Additional comment of Yves et al. appear relevant after reinterpretation, “Because protein malnutrition is a commonfinding in as much as 50 % of elderly AD and MID patients, many of them could well suffer permanent hyporetinolemiastill accelerating the declining concentration of retinoid molecules observed over the course of normal ageing.” Also,“In murine models, early depletion of retinoids causes deposition of amyloid β-peptides, initiating the formation ofAlzheimer plaques. In aged animals, cognitive and memory deficits are associated with down-regulation of theexpression of retinoid receptors which may recover their full activities under RA supplementation. Administration ofRA similarly restores expression of proteins involved in the control of amyloidogenic pathways. Along the samepreventive line is the demonstration that retinol disaggregates preformed amyloid β-fibrils, more effectively than doesRA.”

Yves et al. conclude in a related but distant perspective, “The last section devoted to brain maturation and functioningin elderly persons paves the way for new diagnostic and therapeutic approaches. The revival of older RCC studiesallows to throw deeper insight into more recent findings and to enlarge the scope of current research.”

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105Monaco, H. (2009) The Transthyretin–Retinol-Binding Protein Complex In Richardson, S. & Cody, V. eds.Recent Advances in Transthyretin Evolution, Structure & Biological Functions. Berlin: Springer-VerlagChapter 8106Crist, R. Vasileiou, C. Rabago-Smith, M. Geiger, J. & Borhan, B. (2006) Engineering a rhodopsin proteinmimic J Am Chem Soc vol 128, pp 4522-4523107Wang, L. & Li, Y. & Yan, H. (1997) Structure-function relationships of cellular retinoic acid-binding proteinsJ Biol Chem vol 272(3), pp 1541-1547

The Fex et al. (1996) paper provides considerable data concerning the concentrations of various retinenes at variouslocations within the animal physiology. But the dynamics focused on are those of converting retinol to retinal to retinoicacid. This pathway is important in nutrition and general health but not relevant to vision. They do note, “Retinol issecreted from the liveer in a 1:1 (mol:mol) complex with its carrier protein, the retinol-binding protein (RBP a lowmolecular weight protein that, in the blood is complexed (1:1) to another protein, transthyretin (TTR). One of the effectsof this complexation is to prevent the RBP:retinol complex from being lost in the urine.

Monaco (2000) is a remarkably concise paper exhibiting very few sentences that can be interpreted in multiple ways.The paper includes many SRBP-TTR complex parameters of importance with some information on how the retinoidsare complexed within this two element complex.

The paper contains many discussions relevant to nutrition and some relevant to vision. When referring to vision, it issuggested Monaco’s assertion, “The ligand transported by the complex is exclusively all-trans retinol though the affinityof RBP for other retinoids, most notably retinoic acid, is quite similar.” should be modified to assert, “The ligand initiallyloaded into the complex is exclusively all-trans retinol. . .” The result is more compatible with a potential discharge ofa different retinoid by the complex, and the potential change in the precise formula of the apo-SRBP and/or the apo-TTR.

In the nutritional context, Monaco also described the SRBP molecule as shaped like a calyx. and noted, “Into this calyx,the retinol molecule binds with the β-ionone ring buried deepest and with the alcohol moiety pointing to the outside onthe surface of the molecule. Recall that the presence of the vitamin bound to RBP is correlated to the formation of amore stable complex with TTR.” Monaco notes, “Though it was initially thought that removal of the retinol moleculefrom the calyx would result in major conformational changes, X-ray crystallographic studies of human and bovine RBPhave shown that the transition from holo- to apo-protein involves only very subtle modifications. The most importantis a conformational change on the loop extending from amino acids 34 to 37, in particular, Leu 35 and Phe 36. The spaceleft empty by the removal of the vitamin is filled in both cases by the aromatic ring of Phe 36 and solvent molecules andthe movement of the Phe side chain drags the nearby amino acids into positions which are different from those adoptedin the holoprotein.” This change may be all that is necessary for the apo-SRBP to be subject to attack and removal byimmunological elements of the body. Simultaneously, Monaco has discussed TTR and described, “The two dimers ofthe tetramer are separated by a channel and in contact through symmetry related loops. The channel, about 10 Angstromin diameter, has been shown to be the ligand-binding site.” There are two implications from these statements in thenutritional context; first, it is the TTR that is the “bottle” and the SRBP is the “cork.” Second, the apo-SRBP in itsmodified conformation is subject to attack.

Monaco provided a broader scope focused on the participation of SRBP + TTR in the visual modality in a review in2009105. That paper is addressed in Section 7.1.2.1.3.

7.1.2.6 Important extraneous material related to retinoic acid

Crist, et. al. have recently provided some useful data in spite of a concept of the photoreceptors not supported here106.They studied a material described as CRABPII (cellular retinoic acid binding protein II) but did not describe where itwas normally found in the body of the subject. One of their principle citations asserted this protein is only associatedwith the skin, and not even the lungs107. The retina was not mentioned. They also modified this material in a numberof ways to strengthen it ability to act as a host to retinoic acid.

While CRABPII may be useful as an experimental tool, it is not normally associated with either retinal or retinol anddoes not normally occur within the retina. It is not likely to qualify as a protein mimic of rhodopsin. Crist, et. al. notethe low affinity of all-trans-retinal and CRABPII. It appears their experiments would be more productive if theyemployed either CRBP or CRALBP (Section 7.1.1.2.3) in conjunction with retinol or retinal respectively, and tried toadd an additional oxygen to the retinylidene backbone. This would form one of the proposed rhodonine chromophoresof vision after release of the rhodonine from the cellular protein.

7.1.3 A precise redefinition of the aspects of the Visual Cycle involving retinoids GOOD/EDIT

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108Saari, J. (2000) Biochemistry of visual pigment regeneration Invest Ophthal Vis Sci vol 41(2), pp 337-348109Gonzalez-Fernandez, F. (2002) Evolution of the visual cycle: the role of retinoid-binding proteins J Endocrinvol 175, pp 75-88110Bok D. (1990) Processing and transport of retinoids by the retinal pigment epithelium.Eye. vol. 4 ( Pt 2), 326-32. Review.

The visual cycle has historically defined the putative circular movement of trans-retinal from within a molecule ofrhodopsin in an individual disk of the outer segments to the RPE for reconstitution as cis-retinal and its return to therhodopsin molecule described above within a cycle time commensurate with adequate availability of the resulting cis-rhodopsin for photon excitation. This concept is fatally flawed for at least three reasons. First, it does not recognize theprodigious quantities of retinal that would need to be moved to the RPE per second to support such a physical transportmechanism. Second, it does not recognize the presence of multiple, stereochemically distinct, chromophores within thephotoreceptors. Third, the suction-pipette experiments of Baylor et al. (Section 5.5.10) demonstrate the continued stableoperation of a photoreceptor in-vivo while isolated from the RPE. No exchange of retinal species between the RPE andthe photoreceptor cell was possible under these conditions.

Saari has noted the difficulty of the transport problem in his Friedenwald Lecture for 2000108. “The transcellularmigration of the retinoids during bleaching and regeneration is all the more remarkable, considering the anatomyof the journey. The relatively insoluble retinoid must leave the disc membranes, diffuse through a cystoliccompartment to reach the plasma membrane of the rod outer segment, traverse the plasma membrane, diffuseacross the subretinal space to reach the plasma membrane of the RPE cell, enter into the reactions of the visualcycle in this cell, and make the return journey!” Interestingly, he omits the additional problem of extracting theretinal moiety from within its surrounding opsin molecule and its reinsertion following the above trek.

Gonzalez-Fernandez describes the above trek in more detail109. “All-trans retinaldehyde released from vertebraterhodopsin is first reduced to all-trans retinol by an outer segment retinol dehydrogenase. The all-trans retinol thendoes a remarkable thing. It leave the outer segment, crossed the IPM and the traverses the apical RPE cellmembrane . . . .” [Underline added] He goes on to describe the reconstitution of the 11-cis-retinol prior to itsreverse travel back to becoming a ligand within a previously depleted rhodopsin molecule.

Both authors provide conceptual schematics of their concepts.

Third, the above visual cycle concepts do not recognize the routine replacement of the complete disks of the outersegments at a nominal rate of ten disks per day per outer segment (Section 4.5.1).

The electrolytic theory of vision described in this work eliminates the entire visual cycle as described above. In theelectrolytic theory, the visual cycle is subdivided into two components, the transduction-related visual cycle and thehomeostasis-related visual cycle.

In the transduction visual cycle, the excited electrons generated by photo-excitation within the liquid crystalline coatingof the individual disks of each outer segment only travel to the edge of the disk before being de-excited as part of thetransduction process (Section 5.xxx). The interval between the excitation of an electron within the excited state of theliquid crystalline coating and its de-excitation at the disk/neurite interface is measured in milliseconds or less. Thisrelatively short time constant is a parameter in the adaptation process (Section xxx). There is no requirement for thetransport of any chemical moiety over any distance or through any membranes as part of the transduction visual cycle.

The homeostasis visual cycle relates to the routine replacement of the chromophores of vision as part of the replacementof the disks in order to maintain functional viability of the outer segments.

7.1.3.1 Gross retinoid transport in vision

Figure 7.1.3-1 shows the flow of retinoids through the biological system in support of vision. The result is moreextensive than a similar figure by Chader.and more specific than a similar figure originated by Bok but publishedwidely110. The figure differentiates between the vascularization from the liver to the choroid artery and the venous flowaway from the retina to agree with earlier figures in this work.

As in Chader, the figure shows two possible methods of retinol transport from the intestine to the liver. The literatureis conflicting on whether Vitamin A is carried via the blood system or via the lymphatic system and whether it is carriedin association with chylomicra or a lymphatic retinoid-binding protein, LRBP. This work supports the lymphatic/LRBP

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111Berman, E. (1991) Biochemistry of the Eye. NY: Elsevier pp 49-53112Goodman, DeW. (1979) Vitamin A and retinoids: recent advances. Fed. Proc. vol. 38, pp 2501-2503113Sporn, M. Roberts, A. & Goodman, DeW. (1984) The Retinoids, vol 2 pp 42-85

transport path/mechanism. There is general agreement that the retinoids are stored as esters in the liver111. Chaderreferences Goodman (1979)112 who speaks of the retinoids being transported from the liver in the bloodstream via an RBPin conjunction with plasma albumin, PA. Later work, by the same author113, suggests a more complicated method forthe transport of the retinoids to be used in chromophore generation. This method involves transport of the retinoid ina “bottle” formed by a specific serum retinoid-binding protein, SRBP, and a stopper of plasma transthyretin, TTR. Thesedifferent studies had different purposes. It can be assumed that the transport of retinoids in the bloodstream has at leastthree end purposes, the growth of the organism, the reproduction of the organism, and provision of the chromophoresof vision. It is proposed here that each of these objectives may use a specific and different form of transport. Thediagram illustrates this by showing three branches to the arterial system. In this depiction, the ()RBP label is genericand applies to the three paths. The parentheses can be filled by specific labels for different types of RBP’s. The morespecific label of SRBP + A + TTR applies to the vision-related path. Both the growth and vision transport mechanismsserve the RPE cells via the choroid artery (probably using two different receptor areas on the surface of each cell).

By eliminating the reference to the cis- form of retinol and replacing the broken arrow notation by a double endedRhodonine symbol, the caricature by Bok is very similar to this figure. Whereas Bok does not discuss how the putativeretinol is converted back and forth from trans- to cis- within a timescale acceptable to the visual process (seconds orless), no such problem exists with Rhodonine.

[xxx edit below here while citing the earlier parts of chapter 7 as well. ]Section 4.6 discussed the options of how the retinoid (probably retinol) could be converted into one of the Rhodoninesas part of the transition between the blood stream and the location of the storage of the esters of Rhodonine. This pathmay or may not require the participation of the ribosome structures within the RPE cells. In either case, the Rhodoninesare stored in up to four different color globules within each RPE cell. It is most appropriate to consider these globulesas micelles because they do display the color associated with an individual Rhodonine in liquid crystalline form ratherthan the non-resonant color near 500 nm associated with the material in granular form. It appears they are transportedto the storage areas by CRBP and released through esterification. They are removed from storage and joined toCRAIBP through hydrolysis when required to support disk fabrication by the photoreceptor cells. CRAIBP transportsthe Rhodonine to the RPE cell wall facing the IPM where it is handed off to the IRBP for short-term storage within theIPM. The IRBP is responsible for delivering the Rhodonine to the new disks forming within the extrusion cup of thephotoreceptor cells. The Rhodonine is deposited onto the Opsin substrate of the disk as a liquid crystalline film. Thefilm completely surrounds the disk.

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Figure 7.1.3-1 Gross caricature of retinoid transport in vision. ER, endoplasmic reticulum. The choroid included hereis inside the blood-brain-barrier. The vascular path below the choroid path and that stressed here does not pass throughthe blood-brain-barrier. See text for discussion. Compare to Chader (1984)

The unique transport mechanism of SRBP + A + TTR suggests that the retinoid retinol may be converted into theRhodonine as part of its encapsulation in the bottle. The SRBP-TTR combination would be destroyed in this scenariowhen it releases the new Rhodonine at the RPE interface because it would have lost at least an oxygen atom to the newRhodonine. This would explain why the “apo-SRBP,” shown here as the post-holo-SRBP, is not reused after deliveryof the retinoid/Rhodonine, but is decomposed in the kidney. This apo-RBP would not be a viable form of the original

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Dynamics of Vision 7- 55apo-RBP (pre-holo-SRBP) formed in the liver. It may also explain why the retinoid retinoic acid is not employed in theformation of the chromophores. Retinoic acid contains a carboxyl group that already contains two oxygen atoms.Because of the additional stability of this structure compared with the alcohol or aldehyde, the molecule is not compatiblewith binding to SRBP. It is also not compatible with the addition of another oxygen to its structure at a location requiredfor vision.

The Rhodonine material, in the liquid crystalline film, is capable of repeated excitations by light and de-excitations bylocal quantum-mechanical means for an indefinite length of time. No requirement exists for the chromophoricmaterial to be transported back to the RPE for reactivation.

After a period of about 7-10 days in human, each disk has traveled from the extrusion area to the phagocytosis area ofthe RPE cells. The entire disk is reabsorbed by the RPE cells at this time and the materials are salvaged. Rhodoninethat is still viable is transported back to the storage areas within the RPE cells, probably by CRABP or CRALBP.Material degraded from viable Rhodonine, by any means, is treated as debris and returned, along with the Opsin residues,to the vascular system for disposal in the kidneys.

This group of mechanisms avoids many question marks in the Bok figure. It also eliminates the need to penetrate theputative Outer Segment membrane of that work.

7.1.3.2 The overall visual cycle related to homeostasis

With the demise of the previous visual cycle, the homeostasis visual cycle can now be redefined as follows. The visualcycle describes the physical renewal of the outer segments of the photoreceptors in order to maintain their functionalviability. The gross physical steps include generation of new opsin-based disks by extrusion at the inner segment/outersegment interface and the simultaneous phagocytosis of old disks as they arrive at the outer segment/RPE interface. Thegross chemical steps include the liquid crystalline coating of the new opsin-based disks with one of four appropriatechromophores (the resonant retinal derivatives known as the Rhodonines) with material primarily recovered from theon-going phagocytosis process. The four required chromophoric materials are stored as esters within the RPE cells indistinctly separate pigment granules (Section xxx).

The dynamics of the proposed visual cycle are described in expanded form in Figure 7.1.3-2 based on the staticconfiguration shown in Section 4.5.

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114Gamble, M. & Blaner, W. (2000) Factors affecting blood levels of vitamin A In Livrea, M. ed. Vitamin Aand retinoids: an update Basel: Birkhauser Verlag115Gonzalez-Fernandez, F. (2002) Op. Cit.116Chader, G. Pepperberg, D. et al. (1998) Retinoids and the retinal pigment epithelium In Marmor, M. &Wolfensberger, T. eds. The Retinal Pigment Epithelium. NY: Oxford Press pg 139

The virgin material retinal is brought to the RPE layer via the blood stream and processed into four unique chromophoreprecursors (retinyl esters) that are stored in the pigment granules before being transported to the newly formed disks ofeach spectrally specific outer segment. It also shows how the chromophores from the phagocyzed disks are recoveredand stored as retinyl-esters in the pigment granules. When needed, the chromophore precursors are converted into theprecise chemical form of the chromophores in the process of transporting them to the virgin disks.

The literature has specifically noted the retinoid binding proteins used to transport the retinoids, SRBP, TTR and IRBPare all tetramers114,115,116, a situation analogous to the tetrameres of Rhodonine. They contain four subunits of a structurethat can participate in a stereochemical reaction with the retinoid being transported. Johnson et al. (2007) noted thatthe subunits were only identical in the first order; the subunits exhibited different levels of participation in variouscomplexing activity.

The current challenge is to define precisely how these RBP’s support the required stereochemical transformations. Asnoted in Sections 4.5.2 and 7.1.2, the chromophore precursors exist in four separate non-resonant forms before reachingthe IRBP’s. Whether four distinct IRBP’s are needed to support the transport of the chromophores and their conversionto their resonant form within the IPM is open to further study. Note there is no role or need for an IRBP to transportchromophore related material from the disks of the OS through the IPM back to the RPE cells. This transport functionis provided by the normal disk movement and phagocytosis. Each RPE cell is in contact with 24-44 individualphotoreceptor cells and digests on the order of 2000-4000 disks each day! (Berman, pg 399).

While both the SRBP’s and the TTR are known to be tetrameres, it is not clear how each support the transport andconversion of retinal into the resonant Rhodonine-esters before, or on, being delivered to the pigment granules (Section

Figure 7.1.3-2 Details of the flow of retinoids supporting the outer segments via the RPE ADD in tetrachromats. TheUV channel in humans, and other large mammals, is of limited operational importance due to absorption of incident lightbelow 400 nm by the lens. The elements remain functional in all mammals, and totally operational in smaller mammals.

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117Berman, E.(1991) Biochemistry of the Eye. NY: Elsevier pg 390118Besch, D. Jagle, H. Scholl, H. et al. (2003) Inherited multifocal RPE-diseases: mechanisms for localdysfunction . . . Vision Res vol 43, pp 3095-3108119La Cour, M. & Tezel, T. (2006) The retinal pigment epithelium In Fishbarg, J. ed. The Biology of the Eye.NY: Elsevier pp 253-272120Bessant, D. Ali, R. & Bhattacharya, S. (2001) Molecular genetics and prospects for therapy of the inheritedretinal dystrophies Cur Opin Gen Devel vol 11, pp 307-316121Gonzalez-Fernandez, F. ((2002) Beyond carrier proteins J Endocrin vol 175, pp 75-88

7.1.2). Section 7.1.3.2.1 will develop the subject of transport through the blood stream using the SRBP + TTR “bottleand cork” at a more detailed level.

The literature discusses the presence of several largely conceptual RBP’s within the RPE cells, the CRBP’s and theCRALBP’s. While the terminology suggests CRBP combines with retinol and CRALBP combines with the aldehyde,retinal, this is not the case. Saari, 2000) discussed this fact in detail. “First, the protein (CRALBP) has a high-affinitybinding site for either 11-cis-retinal (Kd, 10 nM) or 11-cis-retinol (Kd, 60 nM).” They did not describe the ability of thismaterial to bind to a resonant form of these same materials, the Rhodonines. He notes its presence in both RPE andMueller cells of the retina.

CRBP and/or CRALBP probably play roles in interfacing with the external RBP’s at the membrane of the RPE cellsand moving the chromophore precursors to and from the pigment granules. However, the specific chromophoreprecursor processed by these RBP’s are probably not retinol and retinaldehyde as conventionally assumed. How theyinteract stereochemically with the chromophore precursors is currently unknown.

In the following discussion, a slightly different nomenclature will be used for the RBP’s. A single CRBP will besubscripted to detail its specific function.

Under the electrolytic theory of vision, the disks of the outer segments have been extruded by the inner segments andare external to the photoreceptor cell. Therefore, the chromophores and/or their precursors need to cross cell membranesonly at the RPE/bloodstream and the RPE/IPM interfaces. Figure 7.1.3-3 shows the simpler visual cycle under theelectrolytic theory compared to the previous theory as characterized in the “working model” by Saari (figure 4) andelaborated upon by Bok (figure 1-24 in Tso), by Bridges et al. (figure 2-2 in Tso), by Berman117 (figure 7.15), Besch etal118. and by La Cour & Tezel119. Bessant et al. give an alternate view of the retinal (Vitamin A) cycle that differs fromthese other investigators and uses different nomenclature120. Most of these figures are conceptual in character. Noneof these investigators address the stereochemical properties or the spectral differentiation of the chromophores processesin the visual cycle. None note the tetrameric character of the various RBP’s.

Two complete disks are shown along with one disk in the process of phagocytosis at the end of its nominal one weeklife in an outer segment of the human retina. As new disks are extruded, they are uniformly coated with one species ofthe liquid crystalline Rhodonines. This makes them photosensitive.

When a photon of light impinges on the liquid crystalline layer, an electron is raised from the ground energy band to theexcited energy band. This excited electron can travel to the location of one of the neurites connected to the adaptationamplifier Activa of the photoreceptor cell. At that location, the excited electron transfers its energy to the neurite,generates a free electron within the neurite, and returns to the ground state as shown. This completes the transduction-related visual cycle (with no transport of chemical materials).

Virgin disks are coated with Rhodonine delivered to the disks by the RBP known as IRBP based on its presence in theIPM. This spectrally specific Rhodonine is already in its resonant form and can join its spectral specific brethren bystereochemical association. The Rhodonine transported by the IRBP is obtained from CRBPX,2 by a handshakemechanism at the RPE/IPM interface. The CRBPX,2 in turn obtains its Rhodonine from a spectrally specific pigmentgranule where it is stored in ester form (as palmitates or stearates). The pigment granule obtains most of its store fromCRBPX,3. CRBPX,3 obtains its RhodonineX from the phagocytosis mechanism. Some RhodonineX obtained from thephagocytosis mechanism is unusable and is discarded via the bloodstream. This shortfall is compensated by acquisitionof new RhodonineX from the bloodstream by CRBPX,1 in a handshake with the RBP known as SRBP. It is not knownwhether SRBP exists in four distinct forms or not. However, it is clear the Rhodonines are in resonant ester form whendelivered to the pigment granules by CRBPX,1. Several investigators have suggested the enzyme LRAT (lecithin:retinolacyltransferase) is required to support the esterification of the retinoids at the pigment granules121.

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Figure 7.1.3-3 A schematic of the homeostatic and transduction visual cycles. The separate transduction-related visualcycle is shown within the dashed box. The weight of the arrows shows the volume of material carried within the maintransport loop relative to the limited amount of new material brought from the blood supply. See text.

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122Berman, E. (1991) Biochemistry of the Eye. NY: Elsevier pp 399-406

Note specifically that the IRBPX only transports chromophores in one direction, from the RPE to the virgin opsin-baseddisks. The return of the chromophores to the RPE is via the movement of the disks toward the RPE and their ultimatephagocytosis.

The overall movement of moieties within the homeostasis visual cycle is shown in a more concise block diagram inFigure 7.1.3-4. The proposed movements for each of the ultimate chromophores is much simpler, and more defined,than that described by Bridges et al. in Tso (figure 2-7). Note the transduction-related visual cycle is shown at the lowerright as a distinctly separate mechanism from the homeostasis-related visual cycle. The transduction-related visual cycledoes not involve any movement of moieties in the space defined in this figure. The free electron is transferred to theneural system.

In this figure, it is clear that a form ofretinol or retinal is stored in the liverand is distributed throughout the bodyby being encapsulated in a “bottle”consisting of the protein SRBP andTTR, transthyretin. At some pointduring the distribution, at the RPE cellplasma membrane or upon depositionin the pigment granule, the retinal isconverted to one of the four resonantforms of retinal, the Rhodonines.They are resonant in the sense thatthey consist of a conjugated carbonchain terminated by two oxygen ions.In this configuration, it is impossibleto delineate either an alcohol oraldehyde form explicitly. The fact thematerial is now in resonant form isobvious because the material stored inthe pigment granules is highly coloredwhereas retinol and retinal arecolorless. The Rhodonines are storedin the pigment granules as esters,which retain the resonant form of theRhodonine moiety.

The resonant material stored in thepigment granules exhibit spectralpeaks associated with the fourRhodonines (Section 5.5.9).However, the width of their absorptionspectra is believed to be narrowindicating they are not in the liquidcrystalline state.

Because the resonant form of the Rhodonines cannot be described as either alcohols or aldehydes, the designationshistorically used for the RBP’s present in the RPE cells, CRBP and CRALBP, are not useful. It is more useful todesignate the RBP’s by their function until a more precise method of naming is developed. Thus the CRBP’s aresubscripted first to indicate their association with a specific Rhodonine and second to indicate their role; 1 = movementto bulk storage, 2 = movement to the IPM interface, 3 = recovery during phagocytosis and return to bulk storage. Asshown at upper right, degraded Rhodonine may be transported to the bloodstream by another RBP of yet unspecifiedform. Berman has provided an in-depth discussion of the phagocytosis and remnant elimination process122.

The weight of the arrows is indicative of the volume of chromophoric material being transported. The system is a closedloop with minor input of new material to replace degraded material. A possible cause of the degradation is cosmic raydamage in long life animals. Such regeneration and disposal of damaged material is only known to occur in the eyes

Figure 7.1.3-4 Block diagram of proposed homeostasis visual cycle in thechordate eye. The transduction visual cycle is shown at lower right. Thesubscript X can represent the UV, S, M or L form of rhodonine or theassociated carrier. See text.

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Gonzalez-Renandez attempted to define the visual cycle to include the invertebrates in 2002. H he did not providesubstantive data supporting a visual cycle in these species. He did include an interesting observation. “To date, IRBPhas not been identified in any invertebrate retina. Furthermore, we have not been able to identify the IRBP gene in theDrosophila database which is now virtually complete.” The lack of any IRBP in the vertebrate retina appears to doomhis proposition.

As noted earlier, the IRBP’s are only used to transport Rhodonines to the disks of the outer segment. There is norequirement that the Rhodonines be returned to the RPE by chemical transport. Return transport is provided by themovement of the disks and their subsequent phagocytosis. It is not known whether separate IRBP’s are required for eachmember of the Rhodonine family or whether a single IRBP can transport all varieties of Rhodonine with their selectivedeposition, on spectrally specific disks, based on their own stereographic arrangement..

7.2 Dynamics of radiation-chemistry and the photoreceptor cell

To interpret the radiation-chemistry of vision correctly, understanding the operation of the photoreceptor cells of theretina in detail is necessary. The photochemical aspects of the Outer Segment of these cells have been discussed inChapter 5. The electrophysiology of these cells will be discussed in Section 10.8.7. The fundamental circuit diagramsof the photoreceptor cells developed in that section are reproduced here as Figure 7.2.1-1 for convenience. Frame Adescribes the morphology of each cell and emphasizes the extracellular nature of the disk stack of the Outer Segment.Only the dendritic structure of the photoreceptor cell extends into the region of the Outer Segment. The zigzag linesurrounding the cell in frame B and C represent the electrolytic environment surrounding the cell. Note this environmentis divided into two regions, the IPM and the INM. This physical and electrical division plays a significant role in theclinical evaluation of the retina. While frame B shows the electrical circuits of the photoreceptor cell in their correcttopology, these circuits are usually rearranged in electronics, as shown in frame C, to emphasis an important feature.The two Activas are arranged in a differential pair with a common emitter impedance (2). This circuit exhibits severalspecial properties discussed in Section 10.8.7. The leftmost Activa employs a unique structural arrangement thatintroduces a highly nonlinear output current as a function of the input excitation. This circuit is the adaptation amplifierof the visual process and is discussed in Section 12.5.3.

The detailed structure of the disk stack has been presented in Section 4.3.2 through 4.4.2.

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Figure 7.2.1-1 The morphology and electrophysiology of the photoreceptor cell from Section 10.8.5.3. See text fordetails.

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123Clark, D. Benichou, R. Meister, M. & Azeredo da Silveira, R. (2013) Dynamical Adaptation inPhotoreceptors PLOS: Comp Biol •DOI: 10.1371/journal.pcbi.1003289

Recently, Clark et al. provided a simple differential equation for the dynamic properties of the photoreceptors123.They described their approach, “We introduced a new phenomenological model that captures the response andadaptation properties of cone photoreceptors. The DA model is expressed as a first-order differential equationin time (Eq. (2)) and relies upon a single non-linearity.” Their Table 1 is a useful bibliography. Their modelresults in a response that is the difference between two exponentials. It can fit a wide variety of idealizedqualitative data. They describe their extensive “fitting” operations in the caption to Table 2. However, theirmodel does not incorporate any absolute delay term, any temperature term or the more general adaptationmechanism associated with the sensory neuron as opposed to the transduction mechanism alone (which theyattribute to the “photoreceptors” and this work attributes to the disk stack of the above figure alone). Their modeldoes not address the totally different dynamics of the long wavelength transduction mechanism. Their range ofadaptation does not approach the multiple orders of magnitude actually encountered in vision.

7.2.1 Radiation Chemistry

Photosensitive chemical compounds, upon radiation by photons of a few electron-volt energy, have many reactive andnon-reactive options. The initial process involves absorption of the energy and the transfer of the molecules of thematerial to an excited state. One of the following events must then occur:

1. The energy can be re-radiated within a very short time, 10-9 seconds, leaving the material unchanged. The resulting phenomenon is called fluorescence.2. The energy can be stored for an appreciable period of time, 10-5 seconds or longer (even minutes or hours),before re-radiating a photon of somewhat lower energy and again leaving the material unchanged. Theresulting phenomenon is called phosphorescence.3. The molecule can de-excite by “internal conversion.” The result is a thermal loss of energy4. The energy can be transferred to another structure thereby returning the original molecule to its ground state.5. The molecule can use the absorbed energy to rearrange itself. The process is known as isomerization.6. The molecule can dissociate into its component ligands or atoms.

The first four options are nondestructive and essentially conservative, although some energy may be lost thermally inthe process. The last two are destructive of the original molecular structure. Options 5 and 6 are the only processes thatactually use the energy absorbed from the photon to do work. They require additional energy to return the constituent(s)to their original configuration. Option 4 was little known during the early work in vision and it was not adequatelyconsidered. Option 4 is quite conservative in energy and requires no physical rearrangement of the material. It hasbecome a well-understood process in recent years and can be used in a continuous process without requiring anyadditional energy source. In fact, it is the mechanism used in nearly all gas and liquid lasers. It is also the primarymechanism that makes possible color photography based on the underlying silver halide process.

Lacking knowledge of option 4, option 5 was promoted by Hubbard, and subsequently Wald and others, as the mostlikely process used in vision. Validation of this isomerization hypothesis as a fundamental mechanism in vision isnotably lacking after 50 years. In vision research, option 5 has always been a stumbling block because of two questions.Where does the energy come from to restore the isomerized material to its original condition? The amount of energyrequired can be significant in the confined metabolic system of the eye. How is the rearrangement associated with option5 reversed in a timely manner?

The dynamics of option 2 and 3 are quite similar and both have relevance to the vision process. This will be seen as themodel develops. Option 6 will not be explored in this work. Clearly, the visual process does not consume a significantamount of chromophore material.

7.2.2 Excitation of a Liquid Crystal

The photon excitation of a liquid crystal has been discussed in Chapter 5. It is a complex process involving anisotropicabsorption in exchange for a greatly increased absorption cross section. The important point to note here is that the

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124Zollinger, H. (1991) Color chemistry. NY: VCH pg. 303125Wang, Q, Schoenlein RW, Peteanu LA, Mathies RA, Shank CV. (1994) Vibrationally coherentphotochemistry in the femtosecond primary event of vision. Science. vol. 266, pp. 422-424 126Degrip, W. (1999) In Rhodopsin and phototransduction. NY: John Wiley & Sons, pg. 104

process is quantum-mechanical in nature and can be described as photoelectric in character as opposed tophotoconductive or photothermal. As a result, the rules of quantum mechanics apply to this absorption as do the rulesof quantum mechanics.

7.2.3 De-excitation of a Liquid Crystal

As discussed briefly in Section 7.2.1, the relevant de-excitation process in vision involves the transfer of energy fromthe excited liquid crystalline chromophore to another material through a quantum mechanical process. This process iscompletely conservative with respect to the physical structure of the chromophores. As with excitation of thechromophore, this transfer is also quantum-mechanical in nature and subject to the statistics of quantum mechanics. Zollinger has addressed the transfer of energy from an excited dye to an oxidizing or reducing agent124. However, hedid not address the potential for transferring energy between two crystalline states. In vision, the hydronium liquidcrystal of the dendrites can receive energy from the chromophoric crystals.

7.2.4 Dynamics of excitation

The dynamics of creating an exciton within the energy bands of a liquid crystalline material upon the absorption of aphoton involves two separate mechanisms. The actual absorption of the photon results in a near instantaneous creationof an exciton. However, the probability of absorption depends on the availability of unexcited n-electrons. Whereasabsorption under “dark adapted conditions” can occur within a few hundred femto-seconds, the observation of the signalat the Activa within the inner segment occurs much later. The time of absorption followed by transport of the chargewithin the liquid crystal and de-excitation at the dendrite is on the order of 10's to 100's of microseconds.

7.2.4.1 The dynamics of photon absorption

Wang has employed differential bleaching to determine the excitation time of the visual photoreceptor material at 200femto-seconds when using 500 nm excitation light125. He used a variable wavelength probe to measure the change inthe absorption coefficient. His data shows nearly the same excitation time for all wavelengths of light from 570 to 630nm. There is some indication that the time for the 620 and 630 nm light may be completed in about 100 femto-seconds.Following this excitation, the absorption coefficient remains constant for more than three picoseconds. This data iscompatible with the excitation time expected. The open-ended value, “more than three picoseconds,” leaves the questionof de-excitation time undefined.

Although the above experiments did not quantify the absorption coefficient, De Grip, et. al. have given a value of 0.67for the quantum yield126. This value, although not defined in detail, is quite compatible with the value obtained bycalculation based on the signal-to-noise properties of light. See Chapter 17.

7.2.4.2 The dynamics of excitation/de-excitation (small signal case)

In most areas of Physical Chemistry, the description of the excitation process is very simple; there are only one or twonon-bonding electrons present and once they are excited by radiation of an appropriate wavelength, the molecule istransparent to additional radiation at that wavelength. The decay time of the excited electron(s) is easily observed. Thereis little interest in illustrating the process in any greater detail. In the case of chromophores in the liquid crystalline statehowever, the number of shared non-bonding or n-electrons can be quite large. In the region of 109 n-electrons can befound in the OS of a photoreceptor if they are all shared via the spaceframe created by the structural protein, Opsin.Further, the decay process can have different time constants depending on the de-excitation involved. In this situation,the dynamics of photoexcitation and de-excitation are not trivial. The process is probabilistic and will be labeled as“withdrawal with delayed replacement,” a variant of the extreme cases called “withdrawal with replacement” and‘withdrawal without replacement” generally described in Probability Theory. In this process, a time delay is encounteredbefore replacement. This time delay can be attributed to any of a number of causes. The principle cause is related tothe excited state the electrons go into. An additional factor is whether the de-excitation is controlled entirely by theinternal structure of the crystal or by an external process. If the electrons are excited into a singlet state, de-excitationis generally rapid and described as fluorescence. If they go into a triplet state, the natural process of de-excitation is

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127Lewis, A. & Perreault, G. (1982) Emission spectroscopy of rhodopsin and bacteriorhodopsin. In Methods inEnzymology, vol. 88, Biomembranes, part I 128Davson, H. (1962) The eye. New York: Academic Press, vol. 2, pg 450-454

usually one of phosphorescence. However, in some situations, the crystal may be in intimate contact with a substrateor other structure that can cause de-excitation before the normal phosphorescence.

In the case of chromophores having two identical (possibly similar) auxochromes symmetrically located at the extremesof a conjugated chain, phosphorescence requires a forbidden transition and it is not observed in these molecules. Thesemolecules may remain excited for an extended period until thermal or other external processes accomplish the de-excitation. This is the situation normally observed in vision research. 1.) Lewis & Perreault127 as late as 1982 indicatethe chromophores of vision do not exhibit significant fluorescence or phosphorescence and many investigators reportthe chromophores, once “bleached” remain excited for long periods. The periods are frequently described in terms ofhours. Most frequently, the preparations are left unattended in the laboratory overnight. 2.) If the above forbiddentransition, is only present when identical auxochromes are involved, this would be strong evidence for the symmetry ofthe visual chromophores. It would essentially eliminate the possibility that the chromophores of vision are describedin terms of the Amidic system, i. e. contain a nitrogen atom. This situation would in turn prevent the chromophores fromparticipating in a Schiff-base bond to the substrate as proposed by Collins & Morton in 1950. Morton & Pitt furtherrationalized the Schiff-base behavior proposed by Collins & Morton in 1955 using terms such as “a fortuitous artifact.”See Dartnall128 writing in Davson for a discussion of this area.

The energy band structure of a complex organic molecule such as the Rhodonines in the liquid crystal state is verycomplex. There are a large number of unpaired electrons subject to excitation, and an equal number of empty excitedstates. Following excitation, these electrons will remain in one of the excited state for a period of time until they areused in some additional process or they return to their original ground state. In either case, explaining the dynamics ofthe process using a first order differential equation with constant coefficients is possible.

Figure 7.2.4-1 shows the basic flow diagram, an appropriate electronic equivalent circuit and the basic equationsinvolved. The rate of generation of excited states is proportional to the input radiant flux times the absorption crosssection times the number of available electrons in the n-electron band of the energy band diagram. The rate of decayof electrons from the excited state is proportional to the number of excited electrons in the π* band. An auxiliaryequation is that the total number of excited and unexcited electrons is fixed and finite. This fact is emphasized in theequivalent circuit by showing a capacitor in the lead connected to ground--the excitation process cannot draw on aninfinite supply of electrons. This would only be the case if the circuit were connected directly to a ground.

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Figure 7.2.4-1 Basic flow diagram, equivalent electronic circuit and applicable equations.

If a complete solution to this problem is desired, another factor must be considered. It involves the transport of excitedelectrons from their excitation point to their de-excitation point on the π* surface of the liquid crystal forming the surfaceof the disk. The concept is simple, however, the mathematics involves Bessel Functions. When the first excited electronis created, it has very little tendency to move toward the edge of the crystal. Once two or more excited electrons areformed, they will repel each other and move to the periphery of the disk, where the dendritic structures are. As ever moreexcited electrons are formed, the fields generated will cause more rapid movement of the excited electrons to theperiphery. Thus the time to reach the edge is an inverse function of the field strength that is itself a function of theabsorbed flux rate. This problem is solved in transmission line theory. It represents a pure delay term in the overallsolution of the photoexcitation/de-excitation problem. Here the delay is inversely proportional to the absorbed flux asindicated in much of the test data (but not accounted for in the accompanying analyses). Appendix A addresses thedetails of this phenomenon. For the immediate purpose, defining a short term transit delay is adequate, Tt, that is afunction of the incident photon flux. This delay can be considered the quotient of the average distance traveled by theexcitons (between their point of creation and their point of disappearance) divided by the short term average transitvelocity of those excitons. However, it is also highly temperature dependent and its full expression must include atemperature term.

Many equivalent electrical circuits can be employed to model this process. They differ in what electrical term is relatedto what term in the original system. For instance, the radiance, F, is taken as the number of photons per unit area perunit time. When multiplied by the cross sectional area of an OS and a time interval, the resulting flux has units ofphotons. This quantity can be related to either a charge or a current in a circuit using a current generator. Alternately,it can be related to a voltage (or the derivative of voltage) in a circuit using a voltage generator. The form is optional.Here:

+ the total incident flux is in photons and can be equated to individual electrons, q, in the equivalent circuit.

+ F•σ is taken as a flux rate, photons per second, where s is the effective absorption cross section of the liquid crystalchromophore. The total flux rate due to absorption by a single Outer Segment can be related to the current, dq/dt in theequivalent circuit.

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Dynamics of Vision 7- 67+ Tt is the transit delay between the excitation of an exciton and its return to the ground state.

Based on the above conditions and definitions, the excitation problem can be put into the form of a standard differentialequation. The solution of this equation depends on the form of the forcing function, qf. Appendix A contains solutionsto this standard form for a variety of forcing functions. That of most interest here is for a forcing function defined asan impulse. This corresponds to the short flash of light generally used to measure the intrinsic response of photoreceptorcells in the laboratory. Flashes of 50 msec or less qualify as an impulse up through the photopic region of vision.

7.2.4.2.1 Excitation/de-excitation with transport delay, the P/D Equation

Introduction of transport delay complicates the form of the complete P/D Equation considerably. However, it doesdescribe the process of photoexcitation followed by de-excitation in detail. This is particularly true after the effect oftemperature is included. The complete derivation of the P/D Equation is provided in Appendix A. The P/D Equation,describing the current injected into the neural system by a single disk in response to an impulse stimulus, in final formis:

Eq. 7.2.4-1

under the condition that σ •F•τnot equal 1.00

Note carefully that the first exponential term contains the imaginary operator, j. This is the delay term in the overallexpression. Each exponential term includes a temperature sensitive component, KT. T represents the temperature of thechromophores in degrees Celsius and the eight is indicative of the narrow biological range of this variable. C•T is equalto 0.002 seconds and the term, kd, is a scaling factor carried as a matter of convenience. This equation is shown inFigure 7.2.4-2 with typical values for the variables.

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129Cattell, J. M.(1886) The influence of the intensity of the stimulus on the length of the reaction time, Brainvol 8(4), pp 512–515 Alternately, Mind vol 11(41), pp 220-242 via JSTOR130Green, C. (undated) Classics in the History of Psychology http://psychclassics.yorku.ca/Cattell/Time/

Figure 7.2.4-2 Theoretical responses to an impulse as predicted by the photoexcitation/de-excitation equation. Thelatency is shown explicitly, by the departure from the baseline, as a function of the peak flux density, F, inphotons/micron2-sec. For other temperatures, the time scale can be multiplied by the appropriate value of KT. The valueof σ is appropriate for perpendicular illumination, or a stack of individual disks. The Hodgkin Solution (σ•F•τ = 1.000)occurs at F = 12.

Note that the P/D Equation is a first order equation that departs from the baseline abruptly following a delay (latency)given by the imaginary term in the equation. Note also that the value of the equivalent resistor, r or rn in Figure 7.2.4-1,must be reasonable if a reasonable value for the time constant is to be obtained.

Each waveform exhibits a different absolute delay (latency), a different peak amplitude, and a different slope associatedwith its leading edge. The simultaneous changing of all three of these parameters is the primary cause of difficulty forprevious investigators attempting to find an empirical solution to the P/D Equation.

Cattell is credited with first observing the delay as a function of stimulus intensity in 1886129. Green haspresented the paper in modern form as part of his “Classics in the History of Psychology130.”

Equation 7.2.4-1 is formidable. However, the delay term is well behaved and can be omitted while looking at theremainder of the equation. The most important feature is the fact that the amplitude response involves the differencebetween two exponentials. As shown by its derivative, such an equation exhibits a continually varying slope that is noteasily described by a single exponential function.

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Eq. 7.2.4-2

This response as a function of time, t,remains a function of multiplevariables. These variables include theincident flux, F, the absorption cross

section, σ, the time constant, τ, of the de-excitation process and a constant, KT, related to the temperature. Theappearance of several of the parameters at multiple locations in the equation accounts for many of the problems ofinterpreting the laboratory data using a far simpler equation. This equation also includes a singularity for the productof σ, F & τ equal to 1.000. Under this condition, the solution of the differential equation takes the form shown inEquation 7.2.4.3 and discussed below.

By taking the Laplace transform of the general solution shown above, it is seen that the function contains two poles inthe frequency domain. One pole is the result of a conventional time constant, defined as τ. The second pole is moreunique. It is defined by the product of σ times F. The fact that the second pole, σ•F, is a function of the flux is whathas caused problems for many earlier investigators. They have attempted to introduce a fixed filter in the transmissionchannel to provide a fixed pole equal to this variable pole.

7.2.4.2.2 The Hodgkin Solution to the P/D Equation for σ •F•τ = 1.00

For the values shown in Figure 7.2.4-2, the singularity at σ•F•τ = 1.00 occurs for a photon flux of 12 photons/μ2. shownin the above figure, the product of the flux, the absorption cross section and the time constant is 1.875. At thediscontinuity, the mathematical form of the P/D Equation changes significantly. The complete form at the singularityis shown in Equation 7.2.4-3.

Eq. 7.2.4-3

where τ is the same time constant of the de-excitation process as found in the complete equation and KT remains the thermal coefficient at a given temperature.Again, the imaginary term is well behaved and can be omitted during the following discussion.

Although based on a more complicated process than the Poisson Distribution of statistics, the P/D Equation at σ •F•τ= 1.00 is identical to the equation of the Poisson Distribution for the trial value, ν = 2.

Hodgkin apparently recognized the similarity in the waveforms of the experimental data of Fuortes & Hodgkin to the

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131Fuortes, M. & Hodgkin, A. (1964) Changes in time scale and sensitivity in the ommatidia of Limulus. J.Physiol. vol 172, pp 239-263132Baylor, D. Hodgkin, A. & Lamb, T. (1974) the electrical response of turtle cones to flashes and steps of light.J. Physiol. vol. 242, pp 685-727133Baylor, D. Nunn, B. & Schnapf, J. (1984) The photocurrent, noise and spectral sensitivity of rods of themonkey Macaca fascicularis. J. Physiol. vol. 357, pp 575-607

Poisson Distribution. He attempted to correlate the two in 1964 with little success131. Without knowledge of the delayterm, he had a problem with the trial value when attempting to correlate the Distribution with the measured data. Hearbitrarily assigned ν the value of 10 on page 252 and found a range of 5<ν<14 in Table 1. He intuitively associatedthe value of ν = 10 with an impedance-isolated ten-stage filter in the visual signal chain. This parameter appears as bothan exponent and in a factorial term in the complete Poisson Distribution. It does not relate to any variable in theunderlying process of vision. The best that can be said is that the P/D Equation and the Poisson Distribution share acommon special case. The Poisson Distribution cannot be used to describe the P/D process of vision, except in thespecial case of σ•F•τ = 1.00.

7.2.4.2.3 Other attempts to obtain a P/D Equation

Later, Lamb writing in Baylor, Hodgkin & Lamb132, approached the photoexcitation/de-excitation problem from adifferent statistical direction and derived an “independent activation equation.” This equation was based on theassumption that the initial detection process was inherently linear and related to a photoconductor. The equationremained similar to the Poisson equation but avoided the factorial in the denominator. Being a statistical derivation, theproblem of the factor ν remained (Lamb labeled it the number of “reactions” in quotation marks and assigned it the valueof six). However, by varying the exponent representing the number of observations, and the other parameters, theequation could be made to fit nearly any individual recorded response. As noted in figure 4 of the article, the equationdid not track a series of responses as a function of incident flux unless the variable ν was adjusted arbitrarily for eachresponse. The best fits involved varying the putative time constant of individual “reactions” in a set of six or seven“reactions.” The formulation originating in the above Baylor, et. al. paper does not correlate well with a set of responsesrepresenting the photoexcitation/de-excitation mechanism of vision. Nor does the formulation correlate with anycombination of that mechanism and any subsequent mechanism. In the final section of the above paper, and insubsequent papers, Lamb has concentrated on using a Michaelis (logistic) equation to describe only the rising phase ofthe waveforms related to the P/D mechanism.

As recently as 1984, Baylor, Nunn & Schnapf have recognized the limitations of these earlier efforts to employmultistage filters133. They said on page 581 while discussing the falling phase of the measured waveforms: “This feature,evident in the response of figure 3 [ Figure 7.2.4-3], and even more prominent in responses of other cells, could not befitted by any adjustment of the time constants in the multistage filter models.” The dashed line shows the excellent fitprovided by the P/D Equation in this region. This figure is discussed in greater detail in Appendix A.

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Figure 7.2.4-3 Response of in-vitro macaque outer segment at 36 Celsius. Data was collected using a 0-50 Hz filter.500 nm light stimulus was applied perpendicular to the long axis of the outer segment. Each point represents averageof 264 flashes of light. Note the 0.1 pA (peak to peak) correlated noise at ~20 Hz. Light was introduced perpendicularto the long axis of the outer segment. Flashes were nominally 0.58 photons/micron2 at 500 nm and 11 ms duration. Theintegrated exposure was 53 photons/sec-micron2. Thin line is impulse response of six identical RC filter stages in seriesadjusted to give a peak response at 200 ms following excitation. Heavy dashed line gives predicted responses based onthe P/D Equation for σ•F•t - 0.53 & T = 36 Celsius. Data points from Baylor, et. al., 1984.

7.2.4.3 The dynamics of excitation/de-excitation (large signal case)

The small signal analysis leading to the P/D Equation assumed the absorption cross section of the chromophoric materialremained constant. This is the condition encountered for low level stimulation under full dark adaptation. No bleachingof the chromophoric material is observed. For higher stimulation levels or significant background levels, the constantabsorption cross section is not maintained. There is not a sufficient number of unpaired and therefore excitable groundstate electrons associated with the chromophore pool. Therefore, the absorption cross section is reduced in proportionto the total pool minus those electrons that are still in the excited state at a given time.

Figure 7.2.4-4 shows the quantum efficiency as a function of the current through the emitter (dendritic structure) of thesensory neuron under prescribed conditions. The conditions are:

C The graph applies to steady-state conditions and the large signal case.

C The figure does not apply to the L–sensory channel due to the fact that a 2-exciton phenomenon is employed in thischannel.

C A wavelength of 532 nm is used as a reference point for the center of the M –channel receptor. A correction has beenmade for the number of photons compared to the 555 nm of the SI standard.

C A 2 micron diameter outer segment is assumed for each PC.

C The irradiance applied to a single outer segment is axially oriented and collimated following the lens action associatedwith the inner segment of the PC.

C The protein based material of each opsin-based disk is essentially transparent at the spectral wavelengths applicableto a given PC.

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C The conversion of the irradiance described in terms of the candela is expressable in photons per watt using the 1979International Standard (Section 17.1.3) even though the wavelength of 555 nm chosen is not related to the actualmaximum spectral sensitivity of the human eye (the wavelength is relatable to the peak perceived sensitivity).

C Any attenuation related to the stage 0 optical system is ignored (typically about 10 percent, Section 2.4.2).

The resultant calculations can only be considered an order of magnitude estimate because of the status of the standardsetc. Under these assumptions, the human eye is only operating at 10–8 or less of peak quantum efficiency under photopicconditions. Similarly, Crawford carried out his scotopic experiments at a few percent peak quantum efficiency. Finally,peak quantum efficiency is reached at about 10–6to 10–7 candela/meter2, suggesting that the human eye is able to detectindividual photons as reported sporadically in the vision literature (although it is not always clear the statisticalramifications of that claim are always elucidated adequately). The ramifications include the slowing of exciton velocitywithin the excited state associated with one liquid crystalline layer of one disk (Section 17.2.7.3).

Section 16.4.1.2.2 reports on the data of Baylor, Nunn & Schnapf in 1984. They established a maximum collectorcurrent of 34 pA for their single isolated sensory neuron when stimulated using transverse irradiation at 500 nm.

Section 17.6.1 provides the behavioral (operational) aspects related to the dark adaptation and light adaptationcharacteristics of the human eye. That section also introduces the “exposine,” an expression foreign to the previousvision literature. It describes the response of a 3rd order dynamic system to a short pulse of stimulation. It is the productof an exponential function and a sine function.

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The figure illustrates two major findings; how large the dynamic range of vision is and how it is provided by thedynamics of the chromophores of vision. Under photopic conditions, the outer segments are highly bleached, leavingonly about one part in 108 of the individual chromophore molecules of vision in a sensitive state. Even at the high endof the scotopic region, only about one part in 103 of the available chromophore molecules are sensitive to light. Onlyunder the lowest light conditions does the retina absorb all of the light striking it, appear totally black due to this totalabsorption and not exhibit any bleaching.

Figure 7.2.4-4 The idealized quantum efficiency of a photoreceptor cell as a function of irradiance and with the currentcapability of the 1st Activa of the PC (the adaptation amplifier). Brief references in the literature suggest 30–50 pA isthe nominal current capability of the adaptation amplifiers. The figure only applies directly to the M –channel. It canbe used for the UV– & S–channels by adjusting the horizontal scales. See text. The L–channel follows a different setof loci.

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The total number of chromophore molecules per outer segment is approximately 4A1010 (Sec. 4.3.5.3.5)

- - -

The candela is now defined in terms of monochromatic light at 555 nm (or 540x1012 Hz) and whose radiant intensity inthat direction is 1/683 Watt (4.092"1017 photons) per steradian. At a wavelength of 532 nm, the number of photons persteradian would be reduced proportionally, to 3.922@1017 photons/ per steradian. For UV– and S–channel performance,the horizontal scales should be adjusted to recognize the lower number of higher energy photons per watt at either 342or 437 nm. The conversion between radiant intensity in cd/steradian and irradiance in cd/m2 is not usually addressedin the vision modality literature. The assumption is that the source is sufficiently far from the pupil that the energyarriving at the pupil is collimated and its radiance can be described in terms of watts per steradian. The radiance isusually reported as measured using a calibrated meter and using a white card (with a reflectance assumed to be 100%rather than the more likely 90-95%) at the location of the pupil.

In human vision, the transition between the photopic and mesotopic regions is usually taken as 3–5 cd/m2 measured atthe pupil of the eye.. The transition between mesotopic and scotopic is usually taken as 10–3 cd/m2 (Section 17.2.6).Crawford used an irradiance of 3 x 10–5 cd/m2 for his scotopic measurements (Section 17.2.6.1.1).

- - - -

The reduction of the quantum efficiency of each PC with irradiation is a direct result of the quantum-physics of thechromophores discussed in Section 5.4. The excitation of the chromophoric layers of the outer segment of a PC are theresult of irradiance through the pupil of the eye. The excitation of the chromophoric layers remains essentially constantover time in the absence of de-excitation in the transfer of acoustic energy from the chromophoric layers to the 1st

amplifier of the associated Activa (the adaptation amplifier). In the large signal case, the result of these activities followsthe equation,

irradiant flux (photons in) x quantum efficiency = emitter (dendritic) current (electrons out) nQ<nQmax

where the irradiance is measured at the entrance aperture of the outer segment. For purposes of this discussion, the totalirradiant flux for a 2 micron diameter outer segment will be taken as the irradiance in cd/m2 at 532 nm (3.99@1017

photons/sec) reduced by a factor of π@1012, or 1.27@105 photons/sec.

[xxx make consistent with the figure above ]At very low irradiances, the quantum efficiency of the individual outer segment remains near 100% as the emitter currentis able to de-excite all of the excitons in real time. This condition can be described as the scotopic irradiance region.

As the irradiance level rises, the limit for emitter current (nQmax) is reached. Without complete de-excitation, thechromophores remain partially excited. At the molecular level, the molecules that remain excited are transparent to theincident radiation, thereby lowering the effective quantum efficiency of the outer segment. This condition remains truethroughout the mesotopic and photopic regions. At hypertopic irradiation levels multiple mechanisms limit theperformance of the stage 1 sensory neurons.

It is suggested that the product of the average quantum efficiency times the incident flux level (σCF) remains nearlyconstant over a considerable range based on a nearly constant average emitter current.

- - - -

As calculated in Section 5.4, the absorption per layer of chromophore in the fully configured outer segment to radiationapplied axially is about 0.0004. While this number may appear low, there are two layers per disk and about xxx disksper outer segment. Appendix L proposes the standard PC outer segment incorporates 2000 disks, each with two coatedsurfaces of chromophoric material. This suggests that essentially all of the irradiance applied to the aperture surface ofthe PC outer segment is absorbed under the most severe scotopic conditions; the gross quantum efficiency would be100%.

- - - -

The significant change in the quantum efficiency of the PC with light level is the key to understanding of the greatdynamic range of the visual modality with respect to incident irradiation. This change is not directly measurable at thistime. Two parametric phenomena are commonly associated with the reduction in quantum efficiency of the PC’s, the

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134http://physics.nist.gov/cuu/Units/candela.html

bleaching of the retina (observable by the ophthalmologist) and the processes of light and dark adaptation (observableby the biophysicist).

- - - -

The relationship between the Candela and power in Watts is a tenuous one, although recent activity within the bio-physics community has given it a more solid foundation (Section 17.1.3). The principle problem is it is defined at only2042 Kelvin (the freezing point of platinum under a high pressure) as of 1979. At that time, the Candela was transformedfrom a broad spectrum source at 2042 Kelvin to a narrow spectrum source at 555 nm (540 x 1012 Hertz–the presumedpeak in the human photopic visibility function, Vλ). The blackbody radiation spectrum at 2042 Kelvin is notoriouslyinsufficient in the blue region. whose radiant intensity in that direction is 1/683 Watt (4.092"1017 photons) per steradian.

See US National Institute of Science & Technology definition.134 The definition of the ampere is considerably simpler.one ampere is approximately equivalent to 6.2415093×10 18 elementary charges moving past a boundary in one second.

7.2.5 The dynamics of transduction to a current

The mechanism employed to obtain a determinate current in the neural system of an animal in response to excitation ofthe chromophores by light has been defined in Chapters 4 and 11 of this work. The mechanism is somewhat morecomplex than shown in the above figure. The liquid crystalline structure of each disk is in physical contact with at leastone microtubule (that is actually a dendrite like structure) of the photoreceptor cell. This allows the energy of the excitedstate of the chromophore to be transferred to a suitable structure in the dendrite. This latter structure is the hydroniumliquid crystal forming the base of the Activa within this structure. Figure 7.2.5-1 illustrates the overall situation. In part(a), the energy band diagrams are shown for both the liquid crystal of the OS and the hydronium crystal. The ellipse ismeant to illustrate the coupling in which the de-excitation of an electron in the liquid crystal results in the excitation ofan electron into the conduction band of hydronium crystal. This electron is swept out of the hydronium crystal bytransistor action and becomes the initial free electron current of the neural system. For this process to work, the energyassociated with the exciton(s) must exceed the energy necessary to elevate an electron to the conduction band of thehydronium crystal. Here one quantum of energy, Ed, in the chromophore is exchanged for one free electron in thehydronium at the expense of the energy, En.

In (b), an equivalent circuit is shown consisting of two parts. The left side is the equivalent circuit used earlier todescribe the photon excitation & de-excitation process in the chromophoric liquid crystal. The circuit shows tworesistors, corresponding to the de-excitation of excited electrons by thermal means (also known as “internal conversion”in some texts) and by transfer means. rtrans is smaller than rtherm and therefore dominates in this circuit. This equivalentcircuit is still a model of an energy state process. The quanta, q, do not relate directly to free electrons in an electricalcircuit until they reach the conduction band, represented by the capacitor, cn.

Part (b) of the figure shows the extension of the earlier circuit to recognize the creation of this new current. Here, rtrans.represents an equivalent conductive path for the excitons as they become de-excited. The conductive path, rthermrepresents any other loss path within the liquid crystal. Normally, this term is negligible when the Outer Segment of acell is in contact with the microtubules of the cell. The subscript n is used to indicate an electrolytic element of theneural system. The values Cn and rn are only shown as place holders for a more complex circuit to be introduced later.The purpose of this figure is to show how each exciton of the P/D process generates a single, potentially free, electronin the conduction band of the first neuron of the visual system.

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Figure 7.2.5-1 The circuit diagram of the combined P/D and transduction process. The capacitance and resistance onthe right are only shown for illustration, the processes remains entirely quantum mechanical in this figure.

The transfer of energy between a liquid crystal and a nerve can be likened to a physical impact. Similar situations arediscussed in terms of phonons with properties similar to acoustic phenomena. How the energy is transferred betweenthe crystal and the nerve is not important here. However, properly modeling the process is quite important.

In the neuron portion of this figure, the conduction band is quite wide; therefore, an electron can have a wide range ofenergies and still transition from the valence band to the conduction band. The principal criterion is that it has an energygreater than En. The band gap, En, is approximately 2.0 electron volts in a photoreceptor neuron at mammalian bodytemperature. Therefore, it would be expected that an excited electron in the liquid crystal would require this minimum

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135Williams, R. Piston, D. & Webb, W. (1994) Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry. FASEB Journal, no. 8, pg. 804(also Laser Focus World, Dec. 1997, pg. 77-82)136Gutmann, F. Keyzer, H. & Lyons, L. (1983) Organic Semiconductors: Part B Malabar, FL: R. E. KriegerPublishing Co. pp. 61-87137MacLeod, D. Williams, D. & Makous, W. (1992) A visual nonlinearity fed by single cones. Vision Res. vol.32, no. 2, pp 347-363138Burton, G. (1973) Evidence for non-linear response processes in the human visual system . . . Vision Res. vol.13, pp 1211-1225

energy to exceed the threshold of the neuron. In fact, two or more lower energy quanta in the liquid crystal can combinetheir energy in order to achieve the minimum energy threshold of the neuron--the same effect observed in silver halidephotography. In this quantum mechanical situation, the energy of two quanta acts as one and the resulting transfercharacteristic exhibits a “square law” characteristic as will be shown.

In this model, the quantum generator, creates one quantum in the neuron for each n quanta in the liquid crystal havingthe necessary minimum energy, En. n = 1 in all photoreceptor channels except those sensitive to the long wavelengthspectrum. For the channel sensitive to the long wavelength spectrum, n=2. n=3 and n=4 do occur in photography, butapparently not in vision. The value of n is directly relatable to the function, “gamma,” in both photography and vision.Gamma is the exponent in the transfer function of the spectral channel.

7.2.5.1 Details of the two-exciton process

The development of the details of this transduction process must allow for or account for the difference found betweenthe process in the long wave chromophoric signal path and the shorter wavelength signal paths. As will be discussedin the next section, the long wavelength channel of animal vision exhibits a “square law” response that is the root of thedifference between the photopic and scotopic spectral responses in vision.

The “two-exciton ” process employed in vision is different from the “two-photon” process employed in the pumpingof flourescent dyes135. The two-photon process in dye pumping involves the addition of two quanta of energy duringthe process of excitation. Conversely, in vision, the two-exciton process involves the summation of two quanta of energyduring the de-excitation of excitons in the chromophoric material.

For dyes, there must be at least two energy levels within the energy state diagram of the dye that are approximatelyequally spaced in energy. The first photon excites an n-electron into the first excited state. The second photon excitesthis excited electron, in the same molecule, into a still higher energy state. The resultant single excited electron thende-excites to the ground level, releasing the total amount of energy associated with that single molecule. This amountof energy is frequently associated with an ultraviolet wavelength photon.

In vision, and photography, the first photon excites an individual n-electron into the π* excited state. The second photonexcites an additional individual n-electron associated with a separate molecule into the π* excited state. However, thesetwo molecules are associated in the same liquid crystalline structure. Their energies are associated with a common cloudof excited electrons. De-excitation in vision involves transfer of the combined energy of these two moleculessimultaneously to a separate third material. There is no requirement for the individual molecules of the chromophoricmaterial to exhibit a sufficiently high energy state to excite the third material. The subject of exciton clusters, both bi-excitons and higher order exciplexes, are discussed in Gutmann, Keyzer & Lyons136. The nonlinearity in the L-channelof vision due to the requirement to use the two-excition mechanism has been amply demonstrated in the spatial frequencydown-conversion experiments of MacLeod, Williams and Makous137. Their experiments were limited to the L-channeldue to the use of a 632.8 nm laser. Such a conversion requires a nonlinear process within the first stages of thephotodetection process. A repeat of these experiments using the 441.6 nm laser of Metha & Lennie would show whethersuch a nonlinearity was present in the S-channel of vision. A repeat with a light source in the 532 nm region wouldprovide similar data for the M-channel. If a nonlinearity of similar magnitude is found in these channels, this work willrequire revision. Burton has also provided background on the non-linearities in the initial stages of the visual system138.

The dual-oxygen forms of the Rhodonines are known for their unique stability after excitation. Under biologicaltemperature conditions, they do not de-excite through fluorescence or thermal means. This feature is believed to be dueto the special properties of the triplet states of Oxygen.

7.2.6 Analysis of the excitation equation

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The excitation equation describes the combination of the P/D process with the process of transduction, of the quantummechanical signal of the OS, into the electronic signal of the nervous system. The result describes the electrical currentsfrom the dendrites of the photoreceptor cells in response to photon excitation, measured within the IPM, without relyingon any hydraulic flow of molecules through various putative gates suggested by some analysts. The equation is entirelydeterminant. There is no need to invoke any statistical processes (other than those previously discussed relating to thetransport of excitons within the excited state of the chromophores). This section will only discuss the short wavelengthspectral region to avoid the complexity of the two-exciton process described above. Fortunately some of the bestexperimental data available was acquired using transverse illumination of individual Outer Segments. Transverseexcitation of Outer Segments insures that only the intrinsic isotropic retinoid absorption spectrum will be active.

In all but the long wavelength spectral channel of vision, the process of transduction from an exciton in the chromophoreto a free electron in the conduction band of hydronium base material of the first Activa is a linear process. Theefficiency of the process is very nearly equal to 100%. Because of this fact, this section will be primarily concerned withthe P/D Equation.

7.2.6.1 Parametric analysis of the P/D equation

The P/D process involves six primary variables when discussed in terms of its impulse response,

+ the flux density, F, applied to the Outer Segment of the photoreceptor, + the absorption cross section, σ, of that Outer Segment, + the time constant, τ, associated with the time between excitation and de-excitation at a given temperature, + the temperature coefficient, KT, (or in the expanded form, k and the denominator of the temperature argument takenhere as equal to 8),+ the slowly changing secondary flux parameter, Fd, and + the temperature.

Each of these parametric values can be determined independently in the laboratory. Both the flux and the temperatureare controllable variables. The other four are all experimental variables. Knowing the theoretical form of the P/DEquation, each of the variables can be evaluated by systematically varying the experimental conditions.

7.2.6.1.1 Effect of temperature and incident flux on the delay in the response

The temperature coefficient, KT, and the flux parameter, Fd, can be determined unambiguously by repeating a singleexperiment, on a single in-vivo photoreceptor, to measure the delay between the impulse and the beginning of theresponse waveform. Although such experiments have been performed in the past, the experiment needs to be performedagain because of the inconsistent methods of defining the time delay in those experiments. For precise measurement,the delay must be measured to the start of the response waveform, not at the 10% amplitude point and not at the peakof the response.

The preferred graphical format is to plot the delay as a function of incident flux with the temperature as a parameter.Figure 7.2.6-1 shows a sample of the available data. The data was collected by many investigators over more than 50years. The data was collected using a variety of animals, light sources, delay criteria and methods of temperaturemeasurement. An alternate plot format would be to use an Arrhenius Plot with the flux as a parameter. Such a plotmight aid in the precise determination of the temperature coefficient. Baylor, et. al. have provided such a plot for theturtle. However, considerable scatter exists in their data (+/-13%) and they did not recognize the parametric nature ofthe flux in their graph. The mechanism underlying this data is not a chemical reaction. The primary delay mechanismis related to the transit velocity of the excitons within the chromophores of vision. Attempts to calculate an activationenergy from such a plot, based on an assumption of chemical kinetics, should be avoided. This is particularly so becausethe curves move as a function of flux level on this plot, causing what would be called the pre-exponential factor to bea variable with light level. See Appendix A.

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Figure 7.2.6-1 Collage of delay data versus flux level and temperature. The dashed lines are drawn for a delay givenby the incident flux raised to the one-sixth power. The data points deviate from these dashed lines because of theinconsistency in defining the flux used and in characterizing the delay interval. See Appendix A for details.

7.2.6.1.2 Determination of the effective absorption cross section of a photoreceptor

If the derivative of the complete P/D Equation is taken and evaluated at the time the response departs from the baseline,the slope of the function is found to be σ•F•KT. With F known and KT determined from the previous paragraph, the valueof the absorption coefficient, σ, is easily determined. This is an important variable in vision and should be determinedunder a variety of conditions for a variety of animals to surface any performance variables related to the structure of theirphotoreceptors. The importance of specifying the orientation of the radiation used in the experiments must be stressedsince different results can be expected as a function of wavelength for transverse versus axial illumination. Transverseillumination will generally give an absorption coefficient that is the same for all photoreceptors whatever their functionalspectrum. The measurement should be made at the nominal peak of the isotropic absorption spectrum near 500 nm.Only axial illumination will provide an absorption cross section applicable to the functional absorption spectrum of thechromophores of vision. The axial measurements should be made at the nominal absorption peak of the functionalchromophore under test, either at 342, 437, 532 or 625 nm.

7.2.6.1.3 Determination of the effective time constant

The determination of the time constant of the P/D Equation is more difficult than in the above case. However, a uniquecondition is available that simplifies the task. For the condition where σ•F•τ = 1.000, the complete P/D Equationsimplifies to the special case of Equation 7.2.4-4 xxx. If the measured data is examined carefully, the flux level mostclosely matching the Hodgkin Equation can be determined. The slope of the response at the point where the function

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leaves the baseline defines the desired time constant. Under this condition, the slope of the response is equal to KT/τ andKT is known from above. For this special case, both the time constant and the absorption coefficient are determined sinceσ•F•τ = 1.000.

In the P/D Equation, the primary and secondary processes, using the terminology of radiation chemistry, occur withinvery short time intervals (less than 10–12 seconds) relative to the overall time constant. The dominant factor in the timeconstant is the travel time of the excitons between their point of excitation and their point of de-excitation.

7.2.6.1.4 Effect of the experimental configuration on the time constant

The time constant discussed above represents the time constant of an intact and functioning photoreceptor cell asrepresented by [Figure 7.2.5-1]. For other situations, the measured time constant is likely to be much longer and be moreproperly represented by [Figure 7.2.4-1]. The difference is in the value of the effective resistance shunting the effectivecapacitance in this figure. This resistance can be considered formed by the value of four separate resistances in parallel.These resistances would represent the four different paths an exciton might take to de-excitation. They can be definedas, and there effective value given as below:

+ Rflour ~ infinity: A resistance related to the fluorescence of the chromophores when in the liquid crystallinestate. This impedance would be expected to be very high for the Rhodonine chromophores due totheir excitons being in the triplet energy state. A transition from this state to the singlet ground stateis not allowed in the Rhodonines.

+ Rphos ~ infinity: A resistance related to the phosphorescence of the chromophores when in the liquidcrystalline state. This term would be expected to be very high for the Rhodonine chromophores. Aphosphorescent transition is not allowed by the molecular symmetry of the Rhodonines.

+ Rtrans ~ finite. This is the lowest value term and dominates in the intact and functional photoreceptor cell.It is related to the contact of the dendrites of the neural system to the disks of the OS. This circuitelement is usually destroyed during extraction experiments in the laboratory, either by breaking theOS from the IS or by chemical attack on the chromophores and conversion from the liquid crystallinestate.

+ Rtherm > Rtrans This term related to thermal decay of the excitons is the predominant term after thedestruction of the Rtrans term in the laboratory. The resulting relaxation time constant of the chromophoricmaterial is usually measured in hours.

The observation of phosphorescence in the laboratory is usually an indication that the chromophores have beenchemically attacked and are no longer symmetrical with respect to oxygen at the molecular level.

7.2.6.2 Comparison with the literature

Although data related to the response of the basic transduction process could not be found in the literature, some veryrelevant data is available related to the electrical output from the outer segment as a “total” entity. The data is excellentfor a variety of animals:

Investigator Year Animal Probe Illumination

Fuortes ‘59 LimulusTomita ‘65 CarpBortoff & Norton ‘67 NecturusToyoda ‘67 ScallopToyoda ‘69 Necturus &

GekkoPenn & Hagins ‘69 RatBaylor et. al ‘73-79 Turtle intracell flashBaylor et. al ‘79 Toad contact flashTorre et. al. ‘86 Salamander contact flashBreton et. al. ‘94 Human ERG flash

These were primarily exploratory studies, with the exception of Baylor et. al. in 1974. They attempted to find an

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139Lamb, T. (1996) Gain and kinetics of activation in the G-protein cascade of phototransduction. Proc. Natl.Acad. Sci. USA 93, pp. 566-570140Baylor, D. & Hodgkin, A. (1974) Changes in time scale and sensitivity in turtle photoreceptors. J.Physiol. vol. 242 pp. 729-758141Baylor, D. Lamb, T. & Yau, K. (1979) The membrane current of single rod outer segments J. Physiol. vol288, pp. 589-611

Figure 7.2.6-2 Fundamental current paths in a photoreceptorcell. See text and Section 11.1.5 for details.

appropriate equation without solving the photoexcitation/de-excitation problem. Lamb continued this curve fittingapproach and presented his analysis in 1996139. Several investigators used simple electrical circuits to illustraterelationships but all of the models were found to diverge from the data--always in significant respects. No modeladequately accounted for the fall in the trailing edge of the response or accounted for the initial time delay that is clearlya function of the applied radiation level (or impulse level, F•T).

Baylor & Hogdkin140 made the greatest effort toward a theoretical solution. They made the assumption that the detectionprocess was related to a photoconductor in the wall of the photoreceptor cell membrane. They examined many equations.However, the tone of the discussions was reminiscent of the days before the discovery of Planck’s Distribution Law ofRadiation for the black-body. They could get the rise time right but the decay characteristic eluded them. At one point,their model had 16 degrees of freedom. They finally made the interesting comment that “Our tentative conclusion is thatany model with n=6-7 [i. e. 6-7 degrees of freedom] can be fitted to the results provided that we allow sufficientdispersion of time constants.”

This team also introduced the “suction pipette recording” technique that provides very well defined data without thefrequent corruption by adjacent signals.

The basic problem in the work since 1970, besides failure to analyze the photoexcitation/de-excitation problem, has beenthe concentration on a simple equation that does not support a discontinuity in the response upon the application of lightand does not allow a falling response after a peak is attained. The focus has been on the so-called Michaelis (or Logistic)Equation. This simple algebraic equation was so named at the turn of the last century and does not relate well to thecomplex responses recorded for the OS.

Interestingly, the form of the equation for the photoexcitation/de-excitation problem is very similar in form to the PlanckDistribution Law.

7.2.6.2.1 Detailed comparisons

In 1979, Baylor, Lamb and Yau141 performed a series of very sophisticated tests that are most informative and verydisciplined. They operated entirely under infrared illumination except for the test light exciting the photoreceptor undertest (and a subtle comment about during “initial pithing and enucleation”). They used a suction technique to draw asingle photoreceptor outer segment (OS) into the entrance to a pipette while it was still attached to the IS and the restof the retina. They were able to operate in the current mode and to place the OS/IS junction at the entrance to the pipette.Thus, they were able to measure the current passing from the OS to the IS under optical stimulation by pulsed light, longpulse light and with or without background light. Theyconfirmed most of their earlier work but at a muchgreater degree of precision and control. Their figures 3a,10, 12 & 13 are highly recommended and will bediscussed in this work. Because these curves exhibitconsiderable saturation, which is related to processesfollowing the actual transduction, the responses theyobtained are complex. The details of the circuits leadingto the response they obtained will be developed in PARTC, Chapter 12. For convenience, Figure 7.2.1-1reproduces [Figure 10.8.7-3] from PART B. It will bereferred to in the following discussion.

Baylor, Lamb & Yau prepared a special micropipettedesigned to act as a Faraday Cage. This pipette wasslipped over a single Outer Segment assembly. Theassembly included both the disks and the associateddendrites (microtubules). The current emanating from

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the OS assembly was collected as a function of the position of the lip of the cage. The resultant current represented thatfrom terminal (a) of the photoreceptor cell in the figure until the lip of the cage reached the OS/IS interface. The cagethen began to collect the net charge from terminal (a) minus that from terminal (b). The net current they collected underhigh illumination was shown in their text-figure 6. The net current under variable illumination and before the currentfrom terminal (b) became relevant was presented in their text-figure 3(a).

Figure 7.2.6-3 compares the theoretical equation developed in this work (Section 7.2.4 and Appendix A) with two ofthe curves from the above text-figure 3(a). The solid curves are for a toad in darkness following a 20-msec flash. Thecurves represent only the response of the outer segment after filtering by a 6-pole filter with a cutoff at 20 Hz. Thetemperature was not specified. The dotted curves are from the P/D Equation using the parameters listed in Table 7.2.6-1.

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142Smith, C. (1989) Elements of Molecular Neurobiology. NY: John Wiley

Figure 7.2.6-3 A comparison of the theoretical and measureOS currents. See text for specific parameters.

TABLE 7.2.6-1Measured by | Theoretical parameters from this work

Baylor, et. al. | σ F τ σ•F•τ θ scalephotons/μm2 | unit areas quanta/ msec. msec. factor

unit area*timeupper set 0.7 | 0.028 7600 8.8 1.873 0.3 20 lower set 0.35 | 0.03 3800 5.4 0.677 0.3 20

The delay term was set arbitrarily in the theoretical curves to agree with the measured data. Note the first order breakwith the quiescent level exhibited by the theoretical curves. The outward current is taken as positive.

The currents are those measured at terminal (a) of the circuit diagram. The illustrated low photon flux curves shownegligible distortion due to the operation of the adaptation amplifier. The theoretical waveforms do not include anymultistage or variable parameter filter as usually required by other proposed explanation for these waveforms.

Figure 3a of Baylor, et. al. is shown in Figure 7.2.6-4(left) along with a smoothed set of selected curves fromthe same figure in 4(right). These curves represent thecurrent at terminal (a) of the above figure under a widerrange of conditions. The measured curves, up to 15 pA,in this figure track the theoretical curves of [Figure7.2.6-1(d)] precisely.

Note: Smith, lacking a detailed model, attributed thecurrent recorded by Baylor, et. al. at terminal (a) to thecurrent at terminal (d) for pedagogical purposes. Heapparently did this under the assumption that theimpedance (4) was linear and that no current flowed intothe orthodromic circuit142. This was a bad assumption.It does not show the amplitude compression associated with the actual impedance of the output Activa circuit of thephotoreceptor cell.

Figure 7.2.6-4(b) is annotated to explain the nature of the curves in (a). First, the horizontal line represents the hardsaturation of the equivalent input Activa at roughly 22 pA. It represents the maximum current capability of thedistributed Activa incorporated into the microtubules of the OS. Since no noise associated with the photon flux appearsin this saturation current, the noise shown in the figure can be attributed to the test set. Since the random noise appearsto be uniform, whatever the photon flux elsewhere in the figure, it appears the test set is the predominant noise sourcein the measured data. Second, the slopes of the rising waveforms and their point of departure from the horizontal axis(their delays) are both seen to be functions of the excitation flux. This is in accordance with the P/D equation. Finally,the falling waveforms are seen to all be exponential in character (outside the saturation area) and to exhibit a similar timeconstant. The actual time constants are a combination of the time constant of the P/D process, shown in TABLE 7.2.6-1and the time constant of the input Activa in its role as the adaptation amplifier of vision, See Section 12.5.3.

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143Lamb, T. (1996), Op. Cit.

Figure 7.2.6-4 CR The dynamic characteristic of the current collected from the OS. Left frame from Baylor, et. al. 1979.Right frame smoothed and annotated to show operation of the adaptation circuit of the photoreceptor cell. Note the hardlimit at 22 pA due to saturation in the Activa. Note also the variable delay before the rising portion of the waveformleaves the horizontal axis and the variation in the slope of the rising waveform, both a function of the flux level. Outsideof the saturation area, the falling waveforms exhibit a constant time constant.

The Baylor school, and subsequently Lamb working with others, has proposed a variety of equations to describe the P/Dprocess. These equations have not described the P/D process completely without introducing putative (and generallyvariable) circuit elements that are not found in the visual system. Baylor, et. al. used simple, as opposed to complex,algebra. As a result, their solution does not include a term for the time delay. Furthermore if Baylor’s equation (4) isreplaced by the P/D equation, a redrawn Text-fig. 11 in that paper will result which is a much better representation ofthe data. The situation near the bottom of this figure requires special attention. The irradiance is so high that thecomplete P/D equation may be required. Further, the duration of the light pulse is no longer considerably shorter thanthe response time. A finite pulse width model (as opposed to the impulse model) may be required in the forcingfunction. Appendix A provides further details in this area. More recently, Lamb has only modeled the rising waveformsof the P/D equation. These models are not based on the actual biological processes and circuits.

Although, Baylor did not characterize the time delay, td between the applied impulse and the beginning of the response,Lamb did143. Lamb shows the delay is clearly a function of the applied impulse (and probably the radiation level inthe wide pulse case) although he continued to use an equation with a fixed delay. He merely noted the different valuesof td. In (A), the response clearly saturates at high signal levels. In (B), saturation is not as evident. Note the significantdifferences in time scale. Notice that the Michaelis equation has great difficulty tracking an exponential function in (A)and fails completely to account for the downturn in the waveforms of (B), which that author truncated to avoidemphasizing the difficulty. It should also be mentioned here that the data collected by Torre was based on a current fromthe rod; whereas, the work of Breton measured a voltage (with a return lead attached to the sclera/cornea). It shouldalso be mentioned that the dynamic radiant level used by Breton may have avoided the saturation region, i. e. if asignificant background level was present during or before the impulse, the impulse may have equaled a small fractionof the average light level. Lamb’s experiments were based on “Ganzfeld (full-field) stimulation (with very brief whiteflashes, . . . )” Using this technique would essentially avoid the saturation region of the adaptation amplifier completely.

The data collected in the Baylor and the Lamb work is excellent, however the proper interpretation of that data clearlyrequires the P/D equation and the more complete model of the photoreceptor cell presented in this work.

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144Baylor, D. Lamb, T. & Yau, K-w (1979) Responses of Retinal Rods to Single Photons J Physiol vol 288, pp613-634145Stone, J. (1983) Parallel Processing in the Visual System. NY: Plenum Press pp 190-192146Martinez-Conde, S. & Macknik, S. (2008) Fixational eye movements across vertebrates: Comparativedynamics, physiology, and perception J Vision vol 8(14), paper 28, pp 1–16 http://journalofvision.org/8/14/28/

7.2.7 Noise measurements of Baylor et al.

Baylor, Lamb & Yau144 have provided data on the noise performance of single sensory neurons in-vitro from the toad.However, they did not provide a schematic of the neurons they were investigating. Their values and assertions appearsubject to alternate interpretations. A key factor suggesting this position is in their assertion, “The procedure was to firstmeasure the mean number of quantal electrical events induced by dim 520 nm flashes. The light intensity was thenincreased and the transmitted flux was measured with the quantum photometer at 520 and 580 nm both before and 30-60see after the end of a bright 60 see bleaching light.” No calibration relating to the dark adaptation occurring after thebright flash was provided and the bright flash itself was also not adequately specified. Their 520 nm stimulation waspolarized and presented perpendicular to the axis of the outer segment. See Section 7.2.4 and Section 16.4.1. [xxxexpand if time allows ]

7.3 Dynamics of the physiological optics of vision

The material to be reviewed in this section and sections 7.4 and 7.5 becomes ever more speciesspecific as it proceeds. While the functions associated with the awareness mode of vision are sharedamong a variety of higher chordates, and particularly the higher primates, this does not hold for theanalytical mode. The capabilities associated with the analytical mode of vision vary significantly,even among the higher primates145. This makes confirmation of the performance defined herein moredifficult because it becomes difficult to employ surrogates. When looking at the phylogeny of thehigher primates, an orderly increase in performance, peaking in the human, can be seen. Sections1.2.1.5.3 through 1.2.1.5.5 attempt to outline these differences within Anthropoidea. Martinez-Conde& Macknik have recently surveyed the available data for a broader range of species146. Their paper,and conclusions, are important. They suggest, “ocular tremor is possibly ubiquitous to allvertebrates.” Conversely, they say, “Fixational eye movements, and microsaccades (minisaccades)in particular, appear to be most important in foveate vs afoveate species.” They support the position,“Animals lacking fixational eye movements, such as afoveate frogs and toads, may be incapable ofseeing stationary objects.” They may mean tremor here, since frogs do exhibit some large fixationaleye movements (which may involve movement of what might be called the eye socket). The lack oftremor leads to long term inability to see stationary scenes.

There are significant differences in the brains of the great apes and man, compared to the brains of thelesser apes and monkeys. The difference is primarily in the midbrain. The midbrain is also the leaststudied and most difficult to study. Chapter 15 will show that the thalamus, and particularly theperigeniculate nucleus and pulvinar of the midbrain, are far more developed in man than in any otherspecies, family, super-family, etc. They are key elements in the ability of man to read and analyze finespatial detail in object space. Only a few of the great apes, the Gorilla, Gorilla gorilla, and theOrangutan, Pong pygmaeus, can approach the human in these areas. When studying reading and theanalysis of fine detail, the lesser apes and monkeys are not homologous with humans. Even thechimpanzee, Pan troglodytes, appears inadequate in these areas. Within the context of this work, itappears the hierarchy based on visual performance are Humans, chimpanzees, orangutans, gorillas andthen monkeys (Section 1.2.1.5). Significant differences in performance can be defined between thesespecies.

The primary visual cortex and the lateral geniculate nuclei play negligible roles in the higher levelvisual functions associated with the analytical mode, such as stereopsis and reading.

Without understanding the purpose and operation of the ocular system, understanding the operation of the visual systemas a whole is impossible. The ocular system is the only part of the visual system involving closed loop servomechanisms.It is also the only part of the visual system that employs external feedback.

7.3.1 Background

7.3.1.1 The literature of the physiological optics

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147Davson, H. (1962) The Eye, Vol. 3 NY: Academic Press pp. 4-151148Rashbass, C. (1961) The relationship between saccadic and smooth tracking eye movements (and two othertitles) J Physiol vol. 159, pp 326-364149Held, R. Leibowitz, H. & Teuber, H-L. eds (1978) Perception NY: Springer-Verlag150Krishnan, V. & Stark, L. (1977) A heuristic model for the human vergence eye movement system IEEE TransBiomed Eng vol. BME-24, no. 1, pp 44-49151Records, R. (1979) Physiology of the Human Eye and Visual System NY: Harper & Row152Schor, C. & Ciuffreda, K. eds (1983) Vergence Eye Movements: Basic and Clinical Aspects London:Butterworths153Keller, E. (1991) The brainstem In Carpenter, R. ed. Vision and Visual Dysfunction. Boca Raton, Fl: CRCPress Chapter 9154Leigh, R. & Zee, D. (1999) The Neurology of Eye Movements, 3rd ed. NY: Oxford University Press155Hung, G. (2001) Models of Oculomotor Control. London: World Scientific156Hung, G. & Ciuffreda, K. eds. (2002) Models of the Visual System. NY: Kluwer Academic/Plenum Press157Tyler, C. (1975) Stereoscopic tilt and size aftereffects Perception vol. 4, pp 187-192158Semmlow, J. & Hung, G. (1983) The near response: Theories of control In Schor, C. & Ciuffreda, K. edsVergence Eye Movements: Basic and Clinical Aspects London: Butterworths Chap 6, pg 185

The dynamics of the ocular system and its control by the brain has been an underappreciated aspect of vision. WhileDavson devoted a volume of his work to this subject, it is quite old147. The modern era of work in this field began withRashbass and Rashbass & Westheimer in 1961148. That material is written in simple language that can also be interpretedby someone versed in control theory. The serious reader should not overlook these papers. Their conclusions are stillpertinent, although they can be stated more succinctly using the language of modern control theory and an adequatemodel. They provide many definitions of terms used in the field to this day. These, and other, definitions will becollected in Section 7.3.2. A compendium was published in 1978 that summarizes the state of the art up to that time149.Much of the modern work in the field bears the stamp of Professor Emeritus L. Stark. His brief 1977 paper begins witha heuristic view of the field150. The paper shows the very simple instrumentation used in that day. Many teams workingin the various fields addressed in this section have arisen via the tutelage of Professor Stark. 1979 saw the appearanceof a compendium by Records151. In 1983, another compendium appeared152. While covering the subject area extensively,it is remarkable that all of its Chapters remain conceptually based. Keller provided an extensive and in-depth reviewof the physiology and gross morphology of the brainstem as it relates to eye movements153. It very clearly defines thestate of knowledge at that time regarding the level of detail knowledge available concerning each neural engine. Leigh& Zee provided an excellent compendium of eye movement data in 1999154. Hung has offered a short monograph155.It is designed to provide basic concepts understandable by both engineers and non-engineers. Recently, a newcompendium of work in this area has appeared that summarizes much of the recent literature156. It will be discussed inSection 7.3.9. On the surface, this volume appears comprehensive. However, from a broader perspective, it is largelylimited to the optometric aspects of physiological optics.

Reviewing the literature up to today shows the field remains in an exploratory phase. This is due to one major limitingproblem, the lack of a viable model of the operation of the visual system. Such a model is particularly important tounderstand the fundamental signals used in the pointing (version), convergence (vergence) and focus (accommodation)functions. The aperture control system appears to operate largely independently of the other systems. However, theliterature of the lens, aperture and vergence subsystems are so intertwined that they are frequently spoken of as a triad.

7.3.1.2 Overview of the dynamics of the physiological optics

The physiological optical system has generally been studied from two perspectives, pointing or version, and all otheroptimization procedures. These other subsystems include vergence, accommodation (focus) and aperture control. Thesehave been outlined by Tyler157. Tyler discussed these subsystems individually and from a static perspective. In practice,it is necessary to consider these perspectives “en semble” and under dynamic conditions. This approach leads to theelimination of some of the first order concepts previously proposed that are based on less dynamic conditions.

These subsystems all rely on the same sensory channels and many neurological elements of the midbrain. As a group,these channels and elements are known as the Precision Optical System, POS. Portions of the POS have previously (andinappropriately) been labeled the auxiliary optical system, AOS. Except for the focus and aperture control subsystemsthese subsystems use the same oculomotor plant.

The empirical data show clearly that the operation of the pointing system and the triad are interrelated (Section 7.4.9).However, the conceptual models of how they are intertwined leave much to be desired (see Semmlow & Hung158).

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159Hung, G. (2001) Models of Oculomotor Control. London: World Scientific, pg 112160Patel, S. Ogmen, H. Whilte, J. & Jiang, B. (1997) Neural network model of short-term horizontal disparityvergence dynamics Vision Res vol. 37, no. 10, pp 1383-1399161Sethi, B. (1986) Vergence adaptation: A review Docum Opthalmol vol. 63, pp 247-263162Fuortes, M. & Hodgkin, A. (1964) Changes in time scale and sensitivity in the ommatidia of Limulus. JPhysiol vol. 172, pp 239-263

Specifically, they do not develop the source of the signals input to the servo loops. The way they are interrelated canbest be understood by considering the morphological and neurological elements of the Precision Optical System, POS,as a physical layer (using computer-speak). The accommodation, vergence and pointing servosystems can then beconsidered operating layers overlaid on this physical layer. The physical plant (using control theory speak) of thephysiological optics is found in the physical layer. This plant supports all of the above subsystems. Hung notes thiscommonality of the physical layer with respect to the “plant.”159 However, the plant receives its instructions from theneurological portion of the physical layer. Conceptually, this portion is defined as the controller. Anatomically, it isknown as the precision optical system, POS. This controller has been labeled the auxiliary optical system in theliterature. This POS includes the perigeniculate nucleus, PGN, the pulvinar, and a major portion of the superiorcolliculus. The PGN is frequently labeled the pretectum in lower animals. The POS also includes a group ofmorphologically isolated neural complexes generally known as the oculomotor nuclei. Both the PGN and the pulvinarare elements of the thalamus.

It will be shown that the controller is considerably more complex than shown in the previous literature. This is evidentin the recordings of eye movements in humans. The physical layer exhibits two operating modes related to derivingsignal information from targets in object space and two operating modes associated with the motions of the eyes. It alsoprovides a blanking signal that the TRN uses to suppress signals to the other elements of the thalamus and the occipitallobe during large saccades.

One other major factor should not to be overlooked when modeling the physiological optical systems. The accumulationof signals used to provide spatial coordinates of a target in object space varies with position within the retina. Thisaccumulation, and low-level processing, of information by morphologically identifiable means has been given the namecomputational anatomy.

The physical layer incorporates an enhanced Type I servomechanism. Outside the foveola, it operates as a simple Type0 servomechanism due to the limited resolution of the lens group at off-axis locations. It operates to bring the target tothe line of fixation using only angle location data derived from the illuminated photoreceptors and computationalanatomy within the retina. The precision of this tracking loop is better than 0.1 degrees (six arc minutes). Within thefoveola, the physical layer operates as a Type I servomechanism. It operates in a velocity tracking mode in responseto tremor signals generated within the POS. This velocity tracking offers a precision of better than 6 arcsecond. SeeSection 7.3.3.2.

The controller exhibits two distinct operating modes related to physical tracking, accepts initial conditions from otherportions of the brain, and performs a considerable amount of computation. The latter rely upon Boolean algebra. Thiscomputational input to the servomechanisms of the physiological optics has not been considered previously in theliterature. A hallmark of this computational capability is the fact that the overall physical layer, exhibits autonomouscontrol over both saccadic and smooth motions.

The intertwining of the pointing, convergence and focus functions is well recognized but not well understood. Thereis considerable discussion regarding precedence regarding the triad. A variety of conceptual models have appeared thatsuggest significantly different operating modes within the triad. The exploratory nature of the previous work has ledto considerable difficulty with the nomenclature. A particular problem has been the claim that the system is nonlinearwithout a clear definition of the term. This pervasive problem will be addressed in Section 7.3.2. The challenge ofdescribing the operation of these subsystems based on the exploratory state of the field was highlighted recently by Patel,et. al. in their introductory remarks concerning the human visual system (HVS)160. “Various studies have shown thatthe HVS is nonlinear and adaptive (Sethi, 1986161). Therefore, analytical tools from linear time-invariant system theorycould not be directly applied to study the dynamics of the HVS.” This work will show that the system is definitelynonlinear in the use of logarithmic and transcendental processing (the latter due primarily to mechanical geometries thatintroduce trigonometric factors). However, it will also be shown that the functions are not nonlinear in the differentialequation sense. Neither are they adaptive in the conventional control theory sense. They can be considered adaptivein the sense that information from long-term learning (and stored in memory) is introduced into the servomechanismloops through computational support. The primary reason they have been called adaptive is the same one that has heldup the photodetection community since the time of Fuortes & Hodgkin162.

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163Ono, H. (1983) The combination of version and vergence In Schor, C. & Ciuffreda, K. eds (1983) VergenceEye Movements: Basic and Clinical Aspects London: Butterworths Chap 11164Owens, D. & Leibowitz, H. (1983) Perceptual and motor consequences of tonic vergence In Schor, C. &Ciuffreda, K. eds (1983) Vergence Eye Movements: Basic and Clinical Aspects London: Butterworths Chap3, pg 29165Julesz, B. (1978) Global stereopsis: Cooperative phenomena in stereoscopic depth perception In Held, R.Leibowitz, H. & Teuber, H-L eds Perception NY: Springer-Verlag, Chap 7166Moon, P. & Spencer, D. (1943) The specification of foveal adaptation J Opt Soc Am vol 33(8), pp 444-456

The protocol used by the vergence community and Fuortes & Hodgkins can be simply stated. If youcannot find the precise mathematical solution associated with a phenomenon, adopt a family of similarmathematical functions, or a serial expansion, and define the phenomenon as adaptive. It must belabeled adaptive because it switches between the various members of the mathematical family duringits operation.

The community studying the absorption spectra of chromophores has adopted a similar protocol. Thisvariant says, if you cannot find the precise mathematical solution associated with a phenomenon,adopt a serial expansion of related form and then empirically determine the coefficients of the chosenexpansion. If later work produces different responses, merely change the coefficients in theexpansion.

This work will show that the conclusion drawn by Sethi, even recognizing that few investigations based on control theorymodels had been performed, is inappropriate. With the correct functional and mathematical models, the system is linear,in the differential equation sense, and time-invariant in the control theory sense.

Authors in the field continue to look to Donders (1864), Hering (1868) and Maddox (1893) for guidance regarding theoperation of the pointing system and the triad. This is unfortunate. First, the frequent use of the cyclopean (equivalentunitary eye), based on the Theory of Binocular Eye Movement of Hering, in both pedagogical and research activities,has contributed to the simple use of linear relationships. This has masked the trigonometric relationships critical tounderstanding the operation of the pointing and convergence systems. Second, the reliance on the Theory of equalinnervation of Hering is also self-limiting. It postulates that the two eyes move as though there was only one. Ono hasprovided an analysis of these first order hypotheses, which he cautions against describing as laws163. The need for a thirdset of eye muscles to compensate for the non-orthogonal arrangement of the first two pairs of muscles is a good exampleof an exception to the simple rule.

Owens and Leibowitz have addressed problems with the Maddox baseline164. They make particular note that “laterresearch has also led to fundamental revisions of Maddox’s model of the vergence system. Most notably, the oldunidirectional model of vergence control has been rejected in favor of an opponent-process model.” This marked thebeginning of the introduction of control theory to vergence research. This modification also marked the recognition ofthe tonic nature of the signals controlling the eyes (even though they are encoded and transmitted in pulse code over thestage 3 projection neurons within the POS).

The reliance on angle-measuring to explain the functions of vergence and stereopsis165, as opposed to temporalmeasurements (based on ocular tremor), has left the field related to human vision in a stagnant condition for the lastquarter of a century. Section 7.3.9.1.1 will analyze one analogy to vergence in vision that appears to fail the test ofrationality. The overt dismissal of ocular tremor in the literature, as a significant factor in the operation of the auto-focus,vergence and analytical modes of vision has contributed greatly to this situation. This dismissal of tremor as a desirablephenomenon has even led to its description as a disease, physiological nystagmus166.

While the lower animals may rely upon angle-measurement to achieve vergence and possibly auto-focus, it is quite clearthe higher chordates rely upon a higher performance method to achieve their high visual acuity. This method is foundin the higher primates and probably in many of the predator birds. These animals achieve their high visual acuity in thefoveal region by making angular velocity and position measurements based on ocular tremor. This mode achieves veryhigh temporal precision within the vergence servomechanism and contributes to the capabilities of the analytical mode(such as reading).

It is likely that the awareness mode of vision defined below relies upon angle-measurement in the periphery of the humanvisual system and on angular-velocity-measurement in the foveola. In this sense, vergence in the human visual systemis a two-stage mechanism.

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Dynamics of Vision 7- 89This work moves far beyond a heuristic approach. Sufficient data is now available to provide a much more detailedmodel of the opto-neuro-mechanical operation of the visual system. As in many other parts of the vision literature, muchof the reported data is not accompanied by an adequate report on, or control of, the associated variables affecting thedata. Typically, Krishnan & Stark did not discuss control of the brightness or contrast of their scene generating display.It will be shown that both parameters directly affect the performance of the opto-neuro-mechanical system of vision.This limitation in the database forms a major limitation on how far the model of this work can be extended.

7.3.1.3 Subsystems of physiological optics

The complete schematic drawing of the visual system shows the ocular system includes five separate subsystems;

+ The lens control subsystem

+ The aperture control subsystem

+ The 1st shutter, the eyelid on humans

+ The 2nd shutter, the nictating lens in many animals

+ The pointing subsystem (both pointing and vergence)

Each of these subsystems plays a crucial role in the operation of the visual system. The importance of a given subsystemis directly related to the position of the animal on the phylogenic tree. Simple and compound eyes do not use many ofthese subsystems. They use the musculature of the body segments to point the entire head instead of just the eyes. Thecomplex eyes of Mollusca are not designed to use a separate pointing system. However, the squid has evolved a pointingsystem adequate for its purposes. Many chordates use all these subsystems. The human is one of the few chordates thatdoes not use the 2nd shutter, although it is claimed to be vestigial in man.

Besides the obvious importance of the lens and aperture control subsystem in high performance visual systems, the 1st

shutter and the pointing system play required roles in the proper operation of the complex eyes of the chordates. Therole of the 1st shutter in chordates is an important one. Besides preventing damage to the eye, in the absence of the 2nd

shutter, it is nearly--although not totally-- opaque. It is used primarily as an adjunct to the data processing system of thebrain. While the brain is commanding the pointing subsystem, it also commands the 1st shutter closed. This preventsthe brain from formatting and transmitting data to the brain that is not useful. In this role, the 1st shutter is an integralpart of the short term memory clearing function.

The pointing system performs more functions than are normally discussed in the literature. One of the most importantis normally not discussed at all. The pointing system is obviously used to establish a line of sight as desired by the brainin response to its cognitive activity. This pointing usually involves an initial “large saccade” to establish a line offixation to an object of interest. Once the coarse line of sight is established, the eye may make a series of smallersaccades to explore a complex scene by imaging individual scene elements onto the foveola. The eye is observed topause intermittently for a short period usually described as a gaze. During a gaze, the system actually operates in a finerscanning mode, involving much smaller saccades, associated with recognition of the detailed characteristics of theportion of the scene included in the gaze projected onto the fovea. This last scanning operation is by far the mostimportant in chordates. The obvious gaze is frequently subdivided into subgazes that may not be clinically observable.

One function of the pointing system is to transform the chordate eye into an imaging system. The purpose is to enhancethe capability of the eye to sense danger when the animal is stationary. This is accomplished by the rapid vibration ofthe instantaneous line of sight about the nominal line of sight. This function is performed by the unique muscles attachedto the ocular globe and is described by the label ocular tremor (or just tremor in this work). Without this capability, theeye would only be sensitive to rapid changes of illumination level on individual photoreceptor cells. It could not perceivestationary threats.

An understanding of the operation of the pointing and shutter system leads to an understanding of the spatial encodingby the retina and subsequent decoding by the cortex. This spatial coding provides spectacularly effective transfer ofinformation and the excellent spatial discrimination capability to be performed using only the limited number of neuralfibers found in the optical nerve bundle. This capability relies on two separate techniques; a short term memory storagecapability, similar to the full frame memory storage used in modern digital television transmission, and an encodingsystem of the n-ary type. The specifics related to this subject will be found in Section 14.8.

7.3.1.4 Block diagrams of the physiological optical system

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Figure 7.3.1-1 Top level block diagram of the visual system of Chordata, particularly of man

Figure 7.3.1-1 repeats the top level block diagram of the visual system. It is used as a starting point for discussionthroughout this work. The details associated with specific parts of this figure will be found in the relevant chapters ofthis work. For purposes of this chapter, a simpler figure can be extracted. It focuses on the physiological optics and thesignal processing support for these subsystems, the Precision Optical System, POS. The POS was formerly known bythe ambiguous name of the Auxiliary Optical System. This name illustrated a lack of understanding of its role.

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167Pansky, B. allen, D. & Budd, G. (1988) Reveiw of Neuroscience, 2nd ed. NY: Macmillan, pp. 136-155168Borostyankoi-Baldauf, Z. & Herczeg, L. (2002) Parcellation of the human pretectal complex: achemoarchitectonic reappraisal Neurosci vol 110(3), pp 527-540

Figure 7.3.1-2 Simplified top level schematic of Chordata focused on vertical oculomotor functions.

Figure 7.3.1-2 is the same figure as used elsewhere in this work. It focuses on the servomechanisms of the physiologicaloptics but is drawn to highlight the vertical motion of the eyes. The vertical performance of the two eyes is virtuallyidentical except under pathological conditions. An alternate representation focused on the operation of the visual systemin the horizontal plane will be presented below. It is more useful when discussing vergence and stereopsis. However,it is necessarily more elaborate.

The association of the various terminal nuclei and the pairs of ocular muscles is unclear in the morphological literature.The arrangement shown is based on Pansky, et. al167. Borostyankoi-Baldauf & Herczeg have recently claimed thearrangement is different from that shown. They assert the LTN (or lateral terminal nucleus) is associated with thevertical motion of the eyes, which implies the LTN is connected to the superior and inferior rectus muscles168. Theyassert the DTN (or dorsal terminal nucleus) is associated with the horizontal motion via the medial and lateral rectusmuscles. Separating the lateral terminal nucleus from the lateral rectus muscles appears questionable although thedesignations may relate to different frameworks. They did not discuss the role of the MTN.

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Figure 7.3.1-3 The dual nature of the pointing system seen from above. See text for details related to the nomenclature.

Figure 7.3.1-3 illustrates the dual nature of the pointing system when viewed from the perspective of the horizontalplane. For small motions of the eyes, less than one degree, the system operates as a closed loop servomechanismincorporating the perigeniculate nucleus as its major functional unit. This unit extracts the servo loop error signals anduses them to drive the oculomotor neurons. An alternate source of signals driving the oculomotor neurons is theperturbation generator shown at lower right. Both sources are related to the analytical mode of operation. Two additionalsignal sources drive the oculomotor plant. Instructions from the LGN (as part of the alarm mode) and the highercognitive centers (as part of the volition mode) drive the superior colliculus. The lookup table within the superiorcolliculus is responsible for converting these high level instructions into more elaborate command sets for driving theoculomotor neurons. The switching between these signal sources is under the supervisory control of the thalamicreticular nucleus (not shown).

Note the nearly complete independence of the left and right neurological and physiological plants. Theoretically, theeyes can operate independently in the horizontal plane (as they do for the salamander). However, the signal commandgeneration structure for most chordates is less flexible. The eyes are coordinated. This coordination takes two principalforms. When the eyes rotate in the same direction, the motion is called versional. When the eyes rotate in oppositedirection, the motion is called verginal. Failure of the eyes to operate in a coordinated manner related to these twomotion types is a pathological condition (Chapter 18).

The use of the cyclopean concept (a single equivalent eye) when addressing the exterior geometry of the visual processwill not be addressed in this research oriented work. The concept is convenient in lower level pedagogical and clinicalsettings. However, it obscures the facts required to understand the complete operation of the visual system. Byeliminating the cyclopean stimulus category, the terms local versus global can be used in non-stimulus related contextswithout confusion. Howard & Rogers provide caricatures of the “cyclopean” visual geometry. They define the referencepoint as the midpoint of the arc between the two eyes (drawn with the Vieth-Muller circle passing through the centers

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169Howard, I. & Rogers, B. (2002) Seeing in Depth, vol 2, Depth Perception Toronto, Canada: I Porteous, pp8-11 & 67-100

of rotation of the eyes169. While resting on some logic, this is an unconventional representation as shown in Section7.4.1. More sophisticated analyses of this concept discuss whether the cyclopean eye can be defined relative to a fixedpoint. It appears that different experiments suggest the location of the putative eye may vary.

The details related to the versional and verginal motions of the eyes will be addressed in separate sections below.

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170Rashbass, C. (1961) Op. Cit. pg 327171Pettigrew, J. (2001) Searching for the switch: Neural bases for perceptual rivalry alternations Brain Mind vol.2, pp 85-118

Figure 7.3.1-4 The luminance, chrominance and appearance channels of the eye of normal and aphakic humans. TheUV channel is partially blocked in normal humans. However, the O-chrominance channel is functional. See Section17.1.4 for details of the nomenclature.

Figure 7.3.1-4 also appears in several chapters of this work (Section 17.1.4). It describes the signal processing usedto create the various signaling channels of the visual system and begins to define the appropriate parts of the braininvolved in processing the information delivered over those channels. Of particular interest in this Section is theoperation of the direct channels associated with the individual photoreceptors of the foveola. Each of thesephotoreceptors connects to a direct and exclusive neural channel to the perigeniculate nucleus, PGN, of the thalamuslocated in the midbrain. It will be confirmed that the operation of the servomechanisms associated with the physiologicaloptical subsystems does not depend on inputs from (or even the existence of ) the visual cortex. In fact, the routineoperation of these servomechanisms does not require the existence of the cerebral hemispheres. In discussing eyemovement tracking, Rashbass put it slightly differently170. “It is not clear whether the cortex is necessarily involved inthese movements.” Pettigrew has recently come to a similar conclusion171. The cerebral hemispheres do play a role inthe operation of these servomechanisms via the volition mode of visual system operation.

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172Fisher, D. Monty, R. & Senders, J. (1980) ; Eye movements : cognition and visual perception. Hillside, N.J.: Lawrence Erlbaum Associates pg. 251173Alpern, M. (1970) Muscular mechanisms. In The Eye, 2nd ed. vol. 3. Davson, H ed. NY: Academic Press,pp 1-252174Alpern, M. (1973) Eye movements. In Handbook of Sensory Physiology, Vol VII, No. 4, Jameson, D. &Hurvich, L. ed. NY: Springer-Verlag, pp 304-326175Dell’Osso, L. & Daroff, R. (1999) Nystagmus and saccadic intrusions and oscillations. In Glaser, J. ed.Neuro-ophthalmology, 3rd ed. Chapter 9, pg 340

7.3.2 Terminology

7.3.2.1 Classification of the rotational motion of the eyes

The term ballistic occurs frequently in the oculomotor literature. It usually occurs without definition in a non-technicalcontext with technical overtones. Technically, ballistics is the study of projectiles and particularly the flight path ofprojectiles. The first order flight path of a short range projectile is characterized by its parabolic trajectory. Frictiondue to the air only enters into the problem in the second order. Mathematically, a ballistic curve (describing the positionof an object) is a parabola formed by the action of a single constant force (gravity) operating continually on a single mass(the projectile) given an initial velocity by an impulse ( the firing mechanism).

A motion describable by a parabola can be created in many ways. However, these motions are not ballistic in themathematical or physical sense. In vision, the motion of the eyes is controlled by opposing pairs of muscles operatingon a mass partially immersed in a liquid medium. The muscles can be represented by a source of tension and an elasticelement. While the resulting motion (velocity) of the eyes can be described as parabolic in the casual use of the word,it is not truly ballistic. This is clearly demonstrated by the second derivative of the position of the eyes (the firstderivative of the velocity of the eyes). It is not a constant with respect to time.

Other authors have attempted to describe the motion of the eyes as one of constant velocity following an initial impulseand terminating in a nominally equal and opposite second impulse. Here again the derivative of the velocity is a variableas a function of time. Thus, the analogy to a bang-bang type of motion is not a precise one. Tole & Young havegraphically compared the idealized bang-bang approach with the actual biological saccade172.

Recognizing that the motion of each eye is complex, and generally the result of a pair of muscles working in a push-pullmode in each of two (nominally) orthogonal planes, is best. Because the two pairs of muscles are not physicallyorthogonal to each other, a third pair of muscles is used to compensate for this physical inadequacy in the architectureof the system.

Discerning a pattern in the literature to the description of the various movements made by the eyes is difficult. The termsused clinically show little correlation to those used in research. Alpern has provided a review through 1970173 and alsoa briefer summary of the research literature174. Dell’Osso & Daroff have provided a more recent text and a summarytable of both eye movements and latencies prior to movement175. While recognizing the requirement for tremor to avoidblindness within a few seconds, they do not explore the functional significance of tremor. They provide a variety ofconceptual block diagrams of the oculomotor systems. Unfortunately, they stress the role of the cerebrum (labeled thecortex-- as opposed to the midbrain in many of their figures) excessively. Simultaneously, they note the overwhelmingevidence that the oculomotor, vergence, accommodation and light control mechanisms are substantially if not completelyautonomous (page 328). The cerebrum plays no role in most of the autonomous oculomotor functions of the eyes. It onlyparticipates in the volition related aspects of some of these mechanisms. They also include several external neuronfeedback paths (a so-called efference copy) that has not been found necessary in this work. Such a path would be theonly external neuron feedback path known in the visual system.

Dell’Osso & Daroff do discuss the dual mode of the command generator of the oculomotor subsystem. They describeconjugate eye motions as controlled by the version command generator and disjugate movements associated withconvergence as controlled by the vergence command generator (page 328). This work treats the command signalsdifferently. It treats them as entirely formed within the superior colliculus with individual oculomotor neural commandscontaining both conjugate and disjugate components. The superior colliculus is relied upon to obtain the necessaryvergence control signals from the LGN (coarse) and PGN (fine). These are the sources of autonomous (“reflexive” inthe words of Dell’Oso & Daroff) steering commands while the volition (“Voluntary) steering commands are sent fromarea 7a of the cerebral cortex. The superior colliculus also requires reference information from the vestibular system.See Section 15.2.4, 15.2.5 & 18.8.5.2.2. The figures in those sections differ fundamentally from those of Dell’Osso &Daroff.

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176Martinez-Conde, S. (2006) Fixational eye movements in normal and pathological vision Prog Brain Res vol154, pp 151-175177Engbert, R. (2006) Microsaccades: a microcosm for research on oculomotor control, attention, and visualperception Prog Brain Res vol 154, pp 177-192178Collewijn, H. & Kowler, E. (2008) The significance of microsaccades for vision and oculomotor control JVision vol 8(14) http://journalofvision.org/8/14/20/ 179Steinman, R. Haddad, G. Skavenski, A. & Wyman, D. (1973). Miniature eye movement. Science, vol 181,pp 810–819.180Spauschus, A. Marsden, J. Halliday, D. M. Rosenberg, J. & Brown, P. (1999). The origin of ocularmicrotremor in man. Exp Brain Res vol 126, pp 556–562.181Findlay, J. (1971) Frequency analysis of human involuntary eye movement. Kybernetik. vol. 8 pp 207-14.

Figure 7.3.2-1 A conceptual framework for discussingsaccade amplitudes and temporal frequencies. Solid circledata points are from Robinson, 1964. Crosses are fromWestheimer in 1954 and 1958. Open squares are equivalentfrequencies obtained from data of Becker, 1991. Solidsquare is a tremor point computed in Section 7.3.7.

The start of the 21st Century has seen a resurgence in interest in ocular motions with Volume 154 of “Progress in BrainResearch” devoted to such motions, their purpose and consequences. Papers in that volume by Martinez-Conde176, theeditor of the volume, and by Engbert177 are of particular relevance. The nomenclature in these papers differs from thefollowing because their community has not yet resolved the purpose of tremor. Because of that lack, they describe minorsaccades in the two to 60 minutes of arc as microsaccades that are described as minisaccades below.

Volume 8, number 14 of the The Journal of Vision was devoted to eye motions. The articles generally follow the abovedescriptions using microsaccades to refer to motion amplitudes approaching one degree. Most of the articles also ignoretremor as irrelevant to visual performance. Collewijn & Kowler follow this approach but provide a good review of theliterature as a database178. They cite the recent work of Steinman in saccades in general179. They also cite the work ofSpauschus et al180. in “microtremor,” the tremor of this work. They concluded, “Spectral peaks were observed at low(up to 25 Hz) and high (60-90 Hz) frequencies. A multivariate analysis based on partial coherence analysis was used tocorrect for head movement. After correction, the signals were found to be coherent between the eyes over both low- andhigh-frequency ranges, irrespective of task, convergence or fixation. It is concluded that the frequency content of oculardrift and microtremor reflects the patterning of low-level drives to the extra-ocular muscle motor units.

Figure 7.3.2-1 is offered to present a common ground for discussion. The diagonal expresses the general relationshipbetween the amplitude of a saccade and the frequency associated with it presented by Finlay in 1971181. Specifying thebandwidth of a saccade is difficult. Whatever technique that is used will generate a sloping line as shown but it may bemoved horizontally. Two data points are shown fromRobinson and three from Westheimer. The Westheimervalues were from different times and different methodsof calculation. The classification of saccades is based ontheir size compared with the diameters of the fovea andthe foveola as observed in object space. Large saccadesare generally larger than the diameter of the fovea andmay be much larger. Small saccades are generallysmaller than the diameter of the fovea but larger than thediameter of the foveola. Minisaccades, or flicks, aregenerally observable motions typically smaller than thediameter of the foveola. The finest saccades are notnormally observable without special equipment. Theyare used to support the detailed analysis of fine detailsuch as letters in text. They are generally less than 100arc seconds in amplitude and exhibit fundamentalfrequency components above the fusion frequency of thevisual system. Their range is typically greater than 40and less than 150 Hertz.

To help organize later discussions, saccades greater thanthe diameter of the foveola will be considered majorsaccades. This term combines the large and smallsaccades which are readily observable clinically.Saccades smaller than this diameter will be grouped asminor saccades. This term includes the minisaccades andthe microsaccades which are difficult to observe

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182Engbert, R. & Mergenthaler, K. (2006) Microsaccades are triggered by low retinal image slip PNAS vol 103,pp 7192-7197183Rolfs, M. Kliegl, R. & Engbert, R. (2008) Toward a model of microsaccade generation: the case ofmicrosaccadic inhibition J Vision vol 8(11), pp 1-23, http://journalofvision.org/8/11/5/, doi:10.1167/8.11.5.184Zuber, B. Stark, L. & Cook, G. (1965) Microsaccades and the velocity-amplitude relationship for saccadiceye movements Science vol 150, pp 1459-1460185Leigh, R. & Zee, D. (1999) The Neurology of Eye Movements, 3rd ed. NY: Oxford University Press, pg 4

clinically. Engbert & Merganthaler have recently published using the term microsaccades to represent the minisaccadesrange shown here182.

For most major saccades, the velocity profile as a function of time closely approaches a parabola. Noting that the largestsaccades are characterized by velocity profiles that are no longer parabolic is useful. This deviation would suggest aform of saturation or loss of linearity in the system (See Section 7.3.4.1.3). Making the assumption that the parabolicresponse can be considered half of a sine wave, an equivalent frequency for the oculomotor motion as a function of angleachieved can be calculated. These rough estimates are shown as open squares in the figure, based on Becker (1991).These values fall along a “main sequence” using the nomenclature of Rolfs, Kliegl & Engbert183 based on Zuber, Stark& Cook of 1965. The Zuber, Stark & Cook data only extended down to 2 minutes of arc in amplitude. The early dataof Westheimer is called into question by the other data and the concept of a main sequence.

Figure 7.3.2-3 presents a parallel framework expandedfrom Zuber, Stark & Cook184. Their data is shown in theupper right quadrant and exhibits a saturation describedmore fully in the data of Becker in Section 7.3.4. Thestraight line is drawn to represent a nominal “mainsequence” for major and minisaccades (including flicks)..These motions are typically autonomic but are undervoluntary control when the individuals attention isconcentrated on them. The microsaccades are not undervoluntary control. They generally occur as briefsequences of binocular motions where the vertical andhorizontal components are generally in quadrature withrespect to time (except when analyzing diagonal sceneelements). These motions generally exhibit afundamental frequency in the region of 30 Hertz. Thesebrief motions are difficult to analyze using Fouriertechniques since they only last for a few cycles whenexamining complex scene elements. The use ofwindowed, or Fast, Fourier Techniques generallyassociate harmonics with these waveforms that are afunction of the width of the temporal window used in theanalysis. The + mark at 50 degrees/sec and 18 arcseconds amplitude represents a microsaccades sequenceat 30 Hertz as calculated in Section 7.3.7.

7.3.2.1.1 Classification of eye movementsyndromes or complexes

Clinicians are generally not interested in individualsaccades and are rarely instrumented to observe minorsaccades. They use a series of global definitions relatedto saccadic responses that involve large parts of theoverall visual system. The following list is modifiedfrom Leigh & Zee185.

Figure 7.3.2-2 A conceptual framework for saccade angularrates and amplitudes based on earlier empirical work. Theupper right quadrant is from a 1965 report using laboratoryequipment of limited sensitivity. The diagonal shows thenominal performance for a linear critically-damped impulse-driven oculomotor system elements of the tonal type. Thearea to the left shows the potential area of oculomotorperformance associated with the twitch type oculomotorelements also operating as a linear critically-dampedimpulse-driven oculomotor subsystem. See text.

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186 Leigh, R. & Zee, D. (1999) The Neurology of Eye Movements, 3rd ed. NY: Oxford University Press, pg 91187Newell, F. (1986) Ophthalmology, 6th ed. St. Louis, MO: C. V. Mosby, pg 105

Clinical definitions of eye movement syndromes

Class of Eye Movement Main Function

Vestibular Holds images of the world steady on the retina during brief head rotationsVisual fixation Holds the image of a stationary object on the foveaOptokinetic Holds images of the world steady on the retina during sustained head rotationSmooth pursuit Holds the image of a small moving target on the fovea; or holds the image of a

small near target on the retina during linear self-motion. In the presence ofoptokinetic responses, aids gaze stabilization during sustained head rotation.

Nystagmus quick phases Reset the eyes during prolonged rotation and direct gaze toward the oncoming visual scene.Saccades Bring images of objects of interest onto the foveola.Vergence Moves the eyes simultaneously in opposite directions so that images of a single object

are placed and held on both fovea.

7.3.2.1.2 Classification of clinically observed eye movements–saccades

Several authors have categorized the motions of the eyes. The following table is modified from Leigh & Zee186. Anotheruseful set of classifications is discussed in Newell187. However, the terms are not directly associated with the neuralsystem.

Classification of clinically observed Saccades

Classification Definition

Volition saccades Elective saccades made as part of purposeful behaviorPredictive, anticipatory Saccades generated in anticipation of or in search of the

appearance of a target at a particular location.Memory-guided Saccades generated to a location in which a target has been

previously present.Antisaccades Saccades generated n the opposite direction to the sudden

appearance of a target (after being instructed to do so)To command Saccades generated in response to a cue

Reflexive saccades Saccades generated to novel stimuli (visual, auditory or tactile) that unexpectedly occur within the environment.

Express saccades Very short latency saccades that can be elicited when the novel stimulus s presented after the fixation stimulus has disappeared

(gap stimulus)Spontaneous saccades Seemingly random saccades that occur when the subject is not required to perform any particular behavioral task.Quick phases Quick phases of nystagmus generated during vestibular or optokinetic

stimulation or as automatic resetting movements in the presenceof spontaneous drift of the eyes.

Note: many of the above terms require a prearranged external stimulus or participation by the subject in a trainingprogram as part of the evaluation.

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188Tusa, R. (1988) Cortical control of eye movement Chapter 14 In Kennard, C. & Rose, F. PhysiologicalAspects of Clinical Neuro-Ophthalmology Chicago, Il: Year Book Medical Publishers pg 220189Ogle, K. (1950) Researches in Binocular Vision. London: W. B. Saunders, pg 42190Ashe, J. Hain, T. Zee, D. & Schatz, N. (1991) Microsaccadic flutter. Brain vol. 114, pp. 461-472191Shakhnovich , A. (1977) Op. Cit. pg. 23-24

Tusa has provided a similar list to the above188. He uses “remembered target saccade” as a synonym for memory guidedvolition saccade. It could also be labeled a proximal saccade through its association with the term proximal vergence.

7.3.2.1.3 Classification of clinically unobserved eye movements–flicks and tremor

Many critically important fundamental eye movements are not normally observable clinically. These are the minorsaccades consisting of flicks, minisaccades and microsaccades. Ogle has labeled these motions physiologicalnystagmus189. Flicks tend to be faster and larger than the minisaccades that are occasionally noted by a clinician.However, smaller minisaccades and microsaccades are generally not observable without specialized instrumentation.

Distinguishing among the variety of uses of the above terms (particularly) in the clinical literature is important. Ashe,et. al. describe “microsaccadic flutter” as in the range of 0.1-0.5° in amplitude at a frequency of 15-30 Hz. They describeocular micro tremor as a “near sinusoidal oscillation” about 0.008° in amplitude at a nominal frequency of 100 Hz190.The term “near sinusoidal oscillation” obscures the more complex nature of this phenomenon. They also compare theirterm microsaccadic flutter with the term microflutter used by Carlow and by Sharp & Fletcher (both in 1986) for thisrelatively gross amplitude phenomenon. Shakhnovich reviews the amplitude and frequency range of phenomenadescribed as tremor, drift and saccades by various investigators191. Describing any motion exceeding a minute of arcusing the prefix micro does not appear appropriate.

7.3.2.2 Classification of the temporal characteristics of the motion of the eyes

The temporal frequency characteristics of the eyes have not been carefully documented in a comprehensive manner. Afew investigators have recognized and explored the high frequency motions of the eyes (frequencies greater than 20 Hz).However, most investigators have not achieved sufficient sensitivity in their test equipment to encounter such highfrequencies. As a result, they have generally assumed the temporal frequency of the motions of the eye are limited toless than 20 Hz. This is unfortunate for they have failed to recognize one of the most important operationalcharacteristics of the eyes. The eyes rely upon these higher frequencies to perform two critical procedures. The highfrequency tremor is used to change their operating mode from simply that of a change detector to that of a quasi-imager.What is more important, the high frequency tremor is used to scan the fine detail in the image projected onto the foveola.This scanning is a critical part of the detailed analyses involved in recognizing shapes and characters, such as those foundin writing.

7.3.2.3 Defining the operating modes within the physiological optics subsystem

7.3.2.3.1 Framework for discussions of pointing and the triad

Defining the operation of the two eyes begins with the realization that the two eyes are physically and neurologicallyindependent regarding both their plant and their oculomotor nuclei. Functionally, they operate independently. It is onlythrough the neurological signal processing and command generation functions within the POS that the eyes arecoordinated. Pathological nystagmus is a clear example of the failure within the signaling system between the plant andthe computational centers of the POS. The symptoms are frequently that of a high performance servomechanism inwhich the feedback path has been broken at a point of high impedance. The result is large angular excursions in responseto poorly defined “noise” inputs.

When operating as a pair, rotation of the eyes in the same direction is described as conjunctive. Rotation of the eyes inopposite directions is described as disjunctive. First order eye motions are usually algebraic summations of bothdisjunctive and conjunctive motions.

A large and specialized vocabulary has arisen to describe the spatial orientation of the eyes compared with the desiredspatial condition. This vocabulary attempts to describe the location of a target in object space relative to the axes of thetwo eyes. A sub vocabulary has arisen in the clinic attempting to describe the location of a target with respect to oneequivalent eye (the cyclopean eye). This vocabulary is needed to support the description of the mechanisms andphenomena encountered within the signal processing of the visual system.

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The visual system employs two distinctly separate servomechanisms to control the eyes. The outer or coarseservomechanism is designed to rotate the line of fixation of the eyes to the location in object space of an object ofinterest. This system operates as two distinct servomechanisms. One controls the vertical orientation of the eyes. Thesecond system controls the horizontal orientation of the eyes. The inner or fine servomechanism is designed to supportthe analysis of the object presented to the foveola after its image has arrived at the point of fixation. Both the horizontaland vertical orientation of the eyes are controlled simultaneously (and coherently) within this servomechanism.

Because the two eyes are in a horizontal line compared with the typical environment, and with respect to the motionavailable to the eyes, their vertical spatial orientation is geometrically simpler than their horizontal orientation. In a firstapproximation, the two eyes rotate in the same direction (in conjugation) in the vertical plane. However, because of theseparation of the two eyes relative to the vertical plane separating them, the motion of the eyes in the horizontal planeis much more complicated. While their gross motion may be considered conjugate, a significant disjunctive motion (theeyes moving in opposite direction) is required to cause both eyes to converge on an object at a specific distance fromthe head. The conjunctive motion of the eyes is generally described using the term version. The disjunctive motion isgenerally described using the term vergence.

The goal of all eye movements is to bring objects of specific interest to the point of fixation of both eyes so their spatialcharacteristics can be analyzed (and their nature identified). To do this effectively requires the eyes to both focus at thedesired target distance. It also requires that both eyes achieve the required version and vergence angles to allow fusionof the images provided by the two eyes within the visual system. A mechanism called stereopsis is associated with themidbrain. This mechanism leads to the phenomenon of fusion (the merging of the two images with respect to lateralspatial position or eccentricity). This mechanism also leads to the perception of depth in a perceived image. While thevisual system is capable of depth perception for images not at the point of fixation, this capability decreases rapidly inquality with distance from the point of fixation. The quality decreases so rapidly outside the foveola (a 1.2 degreediameter area of the fovea surrounding the point of fixation) it is considered qualitative in the remainder of the retina.Within the region of the foveola, the depth perception is considered quantitative. Within this region, the precision ofthe depth perception is so good, it is frequently labeled verdicial (or linear).

Under unusual conditions, the images presented to the two eyes may not merge properly within the signal processingengines of the midbrain. Under this condition, the visual system perceives two conflicting images. The resultingsituation is described as diplopia. The two images may appear to compete for attention in what is described as imagerivalry. The temporal characteristics of this rivalry are poorly understood at present. It appears the rivalry is related tothe motions of the eyes usually used to analyze a larger scene than can be imaged onto the foveola at once. In thissituation, the POS causes the eyes to perform a saltatory scanning of the entire scene. The time scales of rivalry andsaltatory scanning are similar.

When evaluating the pointing performance of the eyes, defining two different null conditions is common. The mostcommon is to speak of the angle formed between the lines of fixation of the eyes when they are resting in the dark (thedark vergence or tonic vergence). The eyes tend to converge at a point of fixation at least one meter from the linebetween the principal points of the eyes (points slightly behind the cornea of the eyes and related to their opticalperformance). Unfortunately this distance exhibits a large variation among individuals. The other reference is with theeyes pointed to infinity (with their lines of fixation parallel).

When the two eyes are converged on a target in object space, the angle between the two lines of fixation is called thevergence angle. In the clinic, this angle is frequently described as the binocular disparity. When evaluating theperformance of the servomechanisms associated with vergence, it is common to describe two different vergence angles.The first is the theoretical vergence angle associated with the target (the target vergence). The second is the actualvergence angle achieved by the two eyes (the eye vergence). The difference between these two angles is called thevergence disparity angle or the vergence disparity error. This angle is actually a measure distance. It is the differencein distance between the point of mutual fixation and the location of the actual target.

Retinal disparity is another important term. It is used to describe the disparity of an object in the field of view of thefoveola while the eyes are optimally aligned on another target. This is the angle used by the stereopsis mechanism todetermine the relative lateral position and the relative depth of individual targets in the fused image of the scene.

Another important term is proximal vergence. This is the vergence adopted by the eyes initially when they arecommanded to acquire a target image. This value is normally stored in the superior colliculus (memory) and is basedlargely on experience.

A rarely encountered term is cyclovergence. Since the oculomotor muscles are attached to the ocular globes in a slightlynon-orthogonal arrangement, introduction of a small rotary correction is necessary for targets close to the eyes. This

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192Schor, C. & Ciuffreda, K. (1983) Vergence Eye Movements: Basic and Clinical Aspects London:Butterworths

Figure 7.3.2-3 Mirror stereoscope used in disparityvergence experiments. The perceived range and angle to thetarget is controlled by the lateral position of the two stimulion the monitors. See text for discussion. A standard eyespacing is shown.

component is known as cyclovergence. It is influenced by the oblique oculomotor muscles. When viewing object atinfinity, the cyclovergence angle is considered zero.

Many other terms related to vergence and disparity have appeared in the literature. Schor & Ciuffreda review many ofthese in Chapters 7 & 8 of their text192.

Many experimentalists have used a simple projection screen for introducing vergence disparities into the visual system.They typically place the screen 1-3 meters from the subject. Frequently, rear projection is used to simplify theconfiguration. Two separate sources are used to project different stimuli to the eyes. The light from the two projectedstimuli are isolated so only one image reaches each eye. The use of color selective filters or polarizers is most common.The use of color selective filters frequently leads to difficulties with the calibration of the light levels employed. Thenet illuminance must be calculated from the combination of the spectral responses of the photometer and the filter. Morerecently, gate controlled glasses (as used in stereo-cinema presentations) have been used. These can introduceundesirable temporal effects into the information to be processed within the visual system.

An alternate test arrangement uses a mirror stereoscope. Figure 7.3.2-3 describes a mirror stereoscope frequently usedin disparity vergence studies (compare with Ono variant xxx). As shown, with all fixed mirrors, the system can produceperceived targets at any apparent depth and directionrelative to the centerline perpendicular to the plane of theeyes. Note that disparity is created without significantchange in accommodation. The system can introduceimages from beyond infinity from a vergenceperspective, but not with respect to accommodation. Thedistance to the real scene is virtually constant regardlessof the perceived distance. This system introduces nospectral filters or polarizers into the optical path.

Variants of the mirror stereoscope with movable mirrorshave been used to study the dynamics of vergence andversion under conditions of apparent target motion.

7.3.2.3.2 Defining precedence within thephysiological optics subsystem

The literature in this area is descriptive of a commonquandary during exploration. “Which came first, thechicken or the egg?” Authors have even debated overaccommodation driven vergence versus vergence driven

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193Schor, C. & Ciuffreda, K. eds (1983) Vergence Eye Movements: Basic and Clinical Aspects London:Butterworths194Hung, G. (2001) Op. Cit. pp 49-50195Fry, G. (1983) Basic concepts underlying graphical analysis In Schor, C. & Ciuffreda, K. Vergence EyeMovements: Basic and Clinical Aspects London: Butterworths pg 404

accommodation193. The subject can be addressed more rationally if the description of the physical plant and the POSare considered the physical layer of the combined systems. Accommodation and vergence are only overlay functionsperformed using this physical layer. The discussion gains even more traction if the major role memory plays in theoperation of these functions. They rely heavily upon the information acquired from the awareness channels of visionand the volition channels of vision. This information is used to set the initial conditions applicable to theservomechanism involved. In the volition mode instructions, the initial conditions are already present in the saliencymap of the subject.

When a human opens her eyes in the morning, the eyes are normally prefocused based on theinformation stored in the saliency map. It does not matter whether she is looking across the room orat the alarm clock. The saliency map provides the nominal focus and convergence information.

Under this scenario, the servomechanisms operate open-loop initially, to carry out the commands containing the initialinformation. Subsequently, the closed loop performance of these servomechanisms is used to optimize performance.The initial commands contain the proximal vergence and proximal accommodation values provided by the superiorcolliculus. Hung has noted how the “proximal vergence,” and the similar proximal accommodation, have “frequentlybeen omitted or only vaguely referenced in a qualitative manner such as an ‘injection’ input term.194” His position is that“Recent objective evidence demonstrates that in the absence of visual feedback of target blur and disparity, proximitycould drive the accommodative and vergence system substantially.”

The above scenario introduces a different perspective into the discussion of precedence. Clearly, the initial step is todraw upon the salience map or the awareness signals for the initial information supporting pointing and the triad. Thisdata normally brings the system very near nominal performance for any scene viewed. Whether one member of the triadprovides fine update information to the others, and in what sequence is largely academic.

7.3.2.4 The Law of Equal Innervation

The control of bilaterally symmetrical functions from a central point suggests that the signals sent to each bilateralmechanism would be symmetrical (of equal size but either the same or opposite sign). Hering is credited with makingthis observation first (1868). As a first order proposition, it is defendable. However, the geometry of the muscle systemsand other mechanisms of vision suggest symmetry is lost when the signals are examined in detail.

Fry has described Hering’s proposition in an expansive form195. As he notes in a footnote, the original proposal appliedonly to the disjunctive and conjunctive eye movements. However, it is frequently extended to describe the symmetricaloperation of the accommodation and aperture control functions as well.

7.3.2.5 Defining the motor unit

When crossing disciplines, interpreting concepts in the literature concisely is frequently difficult. The so-called motorunit of the anatomist is one of these concepts. A careful distinction should be made between a motor unit and thecomponents of the unit. These include both neural and muscular components.

7.3.2.5.1 A functional description of the oculomotor muscle

Many investigators have spoken conceptually of the muscles as sources of electrical signals. This has primarily beenwhen discussing oculomyography. Occasionally, the muscles have been considered to include an electrical batterycomponent discharged during contraction. Particularly when speaking of the twitch fibers of muscles, investigators havealso spoken conceptually of the action potentials developed by the fibers. These discussions frequently includestatements that the twitch fibers can reproduce the action potentials of the associated neurons. When describing thetension versus time characteristic of those fibers, recognizing that the electrical action potential of a muscle cell isseparate and precedes the contractile response of the cell is important.

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Dynamics of Vision 7- 103Ocular muscles are usually categorized as smooth muscles. Individual fibers are found able to exhibit sustained (tonic)and twitch (phasic) responses. Some appear able to produce intermediary responses between these two classes.

7.3.2.5.2 Defining the fatigue factor in the oculomotor response

Several authors have provided excellent data on the fatigue characteristics of the eye muscles. However, their focus hasbeen on the long term fatigue effects (minutes to hours). Differentiating between long-term and short-term effects isimportant. Individual muscle fibers are not generally able to sustain their contraction over an extended interval. Byassimilating a large number of fibers whose responses are not precisely correlated in time, a sustained, or tonic, responseis obtained. However, the individual fiber has acted like a leaky integrator and has relaxed after a very short time. Itsmetabolic system returns it to operational condition in a very short interval and it is then prepared to respond to anotheraction potential from its associated neuron.

7.3.2.6 Glossary

Accommodation–The process of adjusting the power of the physiological optical system to focus on a given elementin object space. See also proximal accommodation

Agonist–A contracting muscle that is resisted or counteracted by another muscle, the antagonist.

Antagonist–(See agonist)

Attention searchlight– A synonym for the angular beam in object space projected onto the foveola of each eye.Nominally 1.2 degrees in diameter centered on the point of fixation. A concept taken from the ancient Greek whereinlight radiated from the eyes.

Binocular disparity– A less precise term than stereoptic disparity. Used widely in the clinic. Generally, the anglebetween the two lines of fixation when the eyes are fixated on a target. Equal to the target disparity under closed loopconditions. Associated almost totally with stereopsis and the limited field of view associated with the foveola.

Binocular view– the view obtained using both eyes. It is normally merged by the POS if the target is imaged onto thefoveola.

Binocular visual direction– The direction of a target in object space relative to the intersection of the vertical andhorizontal planes of the subject (see Figure 2.2.1-1). (Schor & Ciuffreda , ‘S & C’ pg 200)

Sensory binocular processing– (S & C pg 200)

Command– A neural message executable by the PNS (including the oculomotor subsystem) and generally originatingin the superior colliculus and associated structures. Usually using a bit-serial word format and transmitted over a single(or redundant) neuron. See Instruction.

Conjunctive motions– motions where the two eyes rotate in the same direction.

Corresponding points– See Cover points.

Cover points– Points in the two retinas that would be overlaid if the two retinas were juxtaposed.

Cover region– A region of the foveola in one eye that is within the coherence distance of the spatial correlator of theperigeniculate nucleus with regard to a point in the foveola of the other eye.

Crossed Disparate– A descriptor for a scene element located within the Vieth-Muller circle. It has a larger targetvergence than the point of fixation. Equivalent to the term convergent when discussing relative disparity. See alsouncrossed disparate.

Cyclofusion– The mechanism leading to fusion of quasi-parallel lines presented to the eyes dichoptically. Consists ofboth a physical component (a limited rotation of the eyes) and a neurological component. (220 & 330, S&C) Cyclopean– Or cyclopian.

Used variously according to Tyler & Scott, 1979.1. (Julesz, 1971) The stereoscopic information first present at a binocular level in the cortex.

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(This work) The stereoscopic information first present within the thalamus of the midbrain.2. (Hering, 1858) The position in the head from which binocular visual direction is perceived.

Cyclovergence– The angular correction required in vergence due to the non-orthogonality of the vertical and lateralocular muscles. (214, S&C)

Dia-stereopsis– A term used in cyclopedean analyses in the clinic. Term is equivalent to diplopia in other environments.

Dichotic stimulus– The presentation of the same stimulus to the corresponding points (areas) of the two retinas.

Dichoptic– Condition where different stimuli are projected onto corresponding regions of each retina. The differencesmay relate to spatial, spectral or any other dimension of vision.

Diopter– 1. A unit of ophthalmic lens power; one diopter focuses light from infinity at a distance of one meter. 2. Basicunit of accommodation and vergence. The reciprocal of the distance from the eyes to the point of interestin meters.See also prism diopter

Dioptic stimulus– a single object seen in essentially the same way by the two eyes.

Diplopia– 1. A failure to merge the images from the two eyes when the target is within the normal region of fusion.2. Similar images falling on non-corresponding retinal points, and therefore projecting to different visualdirections; non-fused images; “double” vision.

Disjunctive motions– motions where the two eyes rotate in opposite directions.

Double-duty linkage– An expression recognizing the effect of the common parameter of the correlator of the PGN, thelocal correlation range, on both the fusion and depth perception phenomenon of vision.

Electromyography (EMG)–A coarse investigative technique used primarily in the clinic, and of limited precision andtherefore of questionable value in current research. The technique records the voltages encountered by inserting a probeinto the ocular muscles. Similar to probing the S-plane of the retina in that a variety of signals result depending on whatsection of the muscle is probed. Reviewed from both the clinical and research perspective by Breinin, pgs 27, 36-52 &134-135.

Essential tremor– A clinical term for postural tremor associated with the skeletal motor system and believed to becaused by a CNS abnormality. Not directly associated with vision or ocular tremor.

False targets– Extraneous images of elements of a scene in object space putatively generated within the signalprocessing mechanisms of vision and illustrated using a Keplerian projection. Also, described as ghost images in theliterature. Largely a spurious concept when the vergence angle associated with the Keplerian projection is held to lessthan 12 degrees.

Fronto-parallel plane– A geometric construction based on the Gaussian assumption of paraxial optics. A plane drawnthrough the point of fixation in object space parallel to the line drawn between the nodal points of the eyes. Assumedto match a similar plane drawn through the point of fixation on the retina. The nodal points are not defined under widefield of view conditions. The principle points should be used. The fronto-parallel plane does not project a focused imageonto the retina under wide field of view conditions.

Fusion– The concept of merging the images acquired by the two eyes within the PGN of the midbrain. Haplopia.

Fusional range– The angular range (average disparity in vergence between the scene and the eyes) inwhich a subject can maintain a fused image acquired using both eyes.Sensory fusion– xxx

Ghost images– See false targets.

Heterarchy– A term coined by Tyler & Kontsevich to represent the opposite of a hierarchy. An arrangement ofcomputational elements that do not exhibit a hierarchal structure, such as a star network in computers.

Hierarchy– A grouping of elements defined in terms of their importance, power, age, etc. Usually pyramidal in form

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Dynamics of Vision 7- 105as in a human organization. See also heterarchy.

Horopter– Used variously.1. The locus of points that have zero binocular disparity is known as the horopter (the “horizon ofvision”). A term attributed to Aguilonius, 1613.2. Nonius horopter– named using the Latinized version of Nune, a Portuguese mathematician andinstrument maker. First described by Wells in 1792 (pg 57).3. A device for measuring the disparity in vergence, in multiple planes under specific conditionsbetween the theoretical and actual vergence of the eyes. The most common are designed tomeasure horizontal disparity. (S & C pp 204-216)

HVS– Human visual system

Instruction– A neural message not executable as a command by the PNS. Used to direct the actions of the superiorcolliculus and thalamic reticular nucleus. Typically found in the alarm mode, volition mode and other channels withinthe CNS. Usually encoded as a bit-parallel word and transmitted over a group of parallel neural paths. See Command.

Interp– A message in vectorial form created by the PGN/pulvinar couple (Pretectum) of the POS in response to theinterpretation of a symbolic input imaged on the foveola during a single gaze. See also percept.

Law of innervation– An archaic (first order) law useful in the absence of a complete understanding of the POS. It isonly applicable to the low frequency characteristics of the oculomotor system. It is reviewed in detail in Breinin, whereits limitations are described.

Motor unit– A motorneuron plus the muscle fibers that it innervates, is the basic functional unit of skeletomotor systems.

Ocular tremor– See tremor.

Panum’s area– A description of the area in X,Y coordinates in object space at the point of fixation associated with thelimits of fusion in normal vision. More precisely, a projection of the maximum effective dimensions of the associativecorrelator of the perigeniculate nucleus.

Panum’s limit– Used variously in the literature. Generally, the edge of Panum’s area as defined at the associativecorrelator of the PGN.

Percept– An accumulation of interps, in vector form, that are presented to the higher cognitive centers. It may relateto a message conveyed by a written sentence or clause. Alternately, it may represent a recognized object. See alsointerp.

Paresis– Partially-paralyzed extraocular muscle.

Phoria– (clinical) A description of the state of deviation of the eye (inward, outward, upward, downward orcyclorotatory in nature) in the fusion free state (typically either with one eye occluded or with prismatic disassociation).A latent strabismus revealed only when the eyes are disassociated (when no fusible stimuli are in view).

Esophoria– An inward lateral deviation of the eye in the fusion-free state.Exophoria– An outward lateral deviation of the eye in the fusion-free state.Orthophoria– Lack of deviation of the eye in the fusion-free state.

Plant– In control theory, the spatially dynamic portion of a servomechanism as opposed to the control portion.

Primitives-- A synonym for features in a scene. Usually used to focus on a specific (but frequently conceptual and openended) list of features.

Prism diopter– A unit of ophthalmic prism power, one prism diopter deviates light from infinity by one cm at 1 meter;1.745 prism diopters equal 1 degree.

Proximal accommodation– initial accommodation assumed based on knowledge of the distance to the target.Nominally the accommodation stored in the saliency map of the subjects environment and available as an initialcondition. The existence of this effect has been questioned. (S & C pg 82)

Proximal convergence– See proximal vergence

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Proximal vergence– “knowledge of nearness,” frequently described as prior knowledge of nearness. Presumably basedon values stored in the saliency map.

RDS– Random dot stereogram

Recruitment– A coarse term describing the typical number of individual muscle fibers innervated by a given axon.Usually with a value of several hundred for neurons supporting the low frequency operation of the oculomotor musclesand about five to ten for the tremor related (twitch) muscle fibers.

Retinal disparity– The geometric angular difference at the eyes between any object in the visual field and the point offixation. Separable into horizontal (lateral) and vertical components.

Reyem’s Loops– The complement to Meyer’s Loops between the LGN and area 17 of the cerebrum. Reyem’s loopsare described by the variable axon distance between the various ganglia of the retina and the lamina cribosa. Actionpotentials travel relatively slowly over these unmyelinated sections of axons.

Rivalry– The commonly observed situation (under laboratory conditions) where the visual system will continue tochange from one perception of a dichoptic scene to another because of the difference between the two images provided.

Saccadic latency– The interval between the change in a test stimulus and the initial movement of the eyes to realign theline of fixation to the new location.

Scene element disparity– Distance, in three dimensional coordinates, between a point in object space and the point offixation within that object space. Sometimes separated into longitudinal and lateral components. The lateral componentis sometimes separated into horizontal and vertical components. See retinal disparity.

Scotoma– A relative or absolute blind area of the visual field (in perceptual space).

Stereopsis– The mechanism within the POS that merges the two images from the foveola of the two eyes. Themechanism results in the phenomena of fusion and depth perception. These phenomena are degraded by verticaldisparity. Tyler takes a narrow view and claims stereopsis is observed under and is independent of the conditions of bothfusion and diplopia. (S & C pg 200) Ogle differed and defined the following

Patent stereopsis– Stereopsis within a range of up to 10 minutes of disparity, roughly aligned with therange of fusion.Qualitative stereopsis– Between 10 and 15 minutes of disparity, where subject still perceives relativedepth position but without veridical relationship.

Strabismus– An anomaly of binocular vision in which the visual axis (line of fixation) of one eye fails to intersect theobject of interest.

Tremor– The arc-second to arc-minute level motions of the eyes of Chordata and some higher members of Molluscadesigned to provide detailed analytical capability to the visual system. Also described as physiological tremor oroculomotor tremor. This tremor in not related to the term “essential tremor” as applied to the postural system.

Uncrossed Disparate– A descriptor for a scene element located outside the Vieth-Muller circle. It has a smaller targetvergence than the point of fixation. Equivalent to the term divergent when discussing relative disparity. See also crosseddisparate.

Vergence– The disjunctive rotation of the eyes to obtain a fused image of an object within the stereoscopic field of viewof vision.

Target vergence– the angle between the lines joining the center of rotation of each eye with the targetstimulus.Eye vergence– the angle between the fixation lines of the two eyes at a given time. Accommodative vergence– vergence angle assumed by the eyes in response to a well-illuminated targetin object space. Performance degrades under reduced illumination. (S & C pg 32)Dark vergence– (see Tonic vergence).Morbid vergence– vergence angle following death or under heavy sedationTonic vergence– vergence angle assumed with the eyes open but in the dark. The quiescent state.

Disparity error – the difference between target vergence and eye vergence under operational conditions.

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196Guyton, A. (1976) Textbook of medical physiology. Phila. PA: W. B. Saunders pp. 818-825

In closed-loop operation, the residual error between target and eye vergence.Accommodative vergence– (S & C pg 101 & 114)Proximal vergence– initial vergence assumed based on knowledge of the distance to the target.

Nominally the vergence stored in the saliency map of the subjects environment and available asan initial condition.

Veridical– Used infrequently to describe the condition where, if the distance of an object at zero disparity is perceivedat its true distance, then the change in distance for a given disparity is also correctly perceived. (S&C 238)

Version– The conjunctive rotation of the eyes, generally used to cause the line of fixation to pass through the locationof an object in the field of view.

7.3.3 The physiology of the pointing subsystem

The pointing subsystem is a very important but little understood part of the visual system. It is a complexservomechanism employing three different sets of muscles per ocular globe and exhibiting several different modes ofoperation. These modes can be grouped by those serving to rotate the two ocular globes in the same direction and thoserelating to stereoscopic vision where the globes are caused to rotate in opposite directions. These modes are associatedwith the term’s version and vergence (along with stereoscopic vision). In this work, these modes will be consideredfunctional overlays on the more fundamental pointing system and will be discussed separately in Section 7.4.

The three primary operating modes of the pointing servomechanism associated with each eye can be discussed fromseveral different perspectives. Concerning their use, the following sequence is appropriate:

+ The static mode, no muscular activity; the eye is in the non-imaging mode (used in many lower chordates).

+ The tremor mode, the overall visual system is in the imaging mode (used routinely in most chordates).

+ The large saccadic mode, a transient mode under both voluntary and autonomous control, depending on thecircumstances.

+ The small saccadic mode, a transient mode normally not under autonomous control.

A variety of hybrid operating modes can be described that use a mixture of these individual modes. They may use theindividual modes in different sequences and sometimes in combination. They can also be used to different degrees.

Guyton196 provides an excellent discussion of the various motions of the human eye, the neural paths involved and thegeneral characteristics of the individual motions. His figure 60-9, which also appears in Chapter 2 of this work, showsthe muscles of the ocular globe and the nerves serving those muscles. His figure 60-10 is quite informative concerningthe various neural pathways associated with vision. It illustrates the close proximity of the neurons from the retinaterminating in the pretectal nuclei and the neurons emanating from the oculomotor nucleus. His figure 60-11 illustratesmost of the motions of the eye as they relate to the motions of the retina in tracking a point source of light.

7.3.3.1 Basic operating scenarios of different species

The operating scenarios available to a given animal are highly dependent on its morphology, (including the shape of theocular globes) and its ecological niche (which largely determines its vision requirements). The following paragraphswill highlight these differences. Besides the modes listed below, inducing oculomotor-based oscillations into the visualsystem is possible. These may be pathologically based or artificially induced. The latter have been useful in evaluatingthe performance parameters of the various closed loop servomechanisms. The former can frequently be traced to aspecific break in the signaling path associated with that type of oscillation.

7.3.3.1.1 Static mode

Many animals do not stalk their prey but remain with their head and eyes in an essentially fixed position while they awaitthe presence of food in their field of view. For these animals, the background within their field of view is a distraction.Therefore, they avoid it. The visual system of these animals normally operates in the static mode, although they mayhave complex eyes. The system may operate in a more dynamic mode on occasion if morphology permits.

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197Yarbus, A. (1967) ibid pp. 113-115

The typical insect operates in the static mode for purposes of defense. Any significant change in the illumination patternassociated with its field of view initiates flight.

The typical stationary fish or frog, operates in the static mode for purposes of finding food. As the food moves throughits field of view, its cognitive abilities determine the size, color and trajectory of the potential food. If thesecharacteristics fit a specific template, the animal reacts in a distinctly predatory manner.

7.3.3.1.2 Tremor mode

An animal that needs to search for its food, but is limited in its locomotion capabilities, needs to be able to examine ascene without traversing over every inch of it. The tremor mode provides such a capability. It converts the eye froma change detector to an imaging device. The resulting background scene can be examined cognitively to determine theprobable sources of food in the field. It can then react accordingly. This mode requires that the ocular globe be able atleast to vibrate about the line of sight. In chordates, this is the principal reason for the morphology of the ocular globeand its mounting arrangement. Only a very simple muscle system is needed to accomplish this objective as the systemneed only vibrate at an amplitude approximating the angular field of one photoreceptor.

It is worth noting the success of the squid in converting a body mounted complex eye to an eye withsufficient freedom to use tremor. The result is a mollusc that can continually image the world aroundit.

Tremor is extremely difficult to measure in the laboratory because of its small angular magnitude and the necessity ofisolating this motion from other cardiovascular, pulmonary or intentional motions of the subject.

7.3.3.1.3 Modified tremor mode

The cat family is frequently noted for its unusual predatory performance and the atypical characteristics of its eyescompared with similarly sized animals. These observed characteristics are principally the result of the operationalcharacteristics of the ocular pointing system. Felines can control the modes of operation of their ocular servomechanismbetter than most other chordates. This provides it several capabilities desirable in its environmental niche. The cat cansit still for significant periods while watching for the presence of prey in its field of view. By reverting to a staticoperating mode, the recognition of prey is greatly augmented. In this mode, it can calculate the parameters of any motionin its field of view. By matching these parameters with a variety of templates, it can categorize the object as food, apredatory animal, or the motion of leaves, grass etc. Clearly, its response is dependent on this classification. It willattach, or begin to stalk prey. It will attempt to elude a predatory animal and it will ignore wind or water related motions.

When the cat enters the browsing mode, its eyes are commanded to use the normal tremor mode. However, the catadopts an intermediate mode when stalking. Under this condition, its computational capabilities associated with thestatic mode can still be used effectively. As a result, the animal seems to exhibit accentuated spatial capabilities to trackits prey. This hybrid mode of operation has attracted the interest of many scientists. They have tried diligently to definea “hard wired” spatial filtering structure either within the signal processing of the retina or in the signal processing ofthe cortex. It appears this capability is actually a cognitive one in conjunction with the control of the servomechanismsof the pointing system.

7.3.3.2 Fixation motion

7.3.3.2.1 Continuous Tremor

[[ Guyton gives continuous tremor as 30-80 cycles per second, no amplitude ]]

The data on continuous tremor is sparse in the literature and contains a large “noise” component since it originates witha variety of investigators. Yarbus197 provides some of the most explicit measurement data; the amplitude of the tremoris 20-40 seconds of arc (1.0-1.5 times the diameter of the photoreceptors in the fovea), the frequency is 70-90 Hertz(much higher than the critical flicker frequency of flicker fusion). For purposes of later calculation, a nominal tremorfrequency of 80 Hertz ( 0.0125 period) will be assumed. The amplitude of the tremor is slightly different in the verticaland horizontal plane (one may recall that the muscles are not aligned with the vertical and horizontal planes), resulting

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198Liston, D. & Krauzlis, R. (2005) Shared decision signal explains performance and timing of pursuit andsaccadic eye movements J Vision vol 5, pp 678-689199Yee, R. Schiller, V. Lim, V. Baloh, F. Baloh, R & Honrubia, V. (1985) Velocities of vertical saccades withdifferent eye movement recording methods. Inv. Ophthal. Vis. Sci. vol. 26, no. 7, pp. 938-944200Adler, S. Bala, J. & Krauzlis, R. (2002) Primacy of spatial information in guiding target selection for pursuitand saccades J Vision vol 2, pp 627-644201Rashbass, C. (1961) The relationship between saccadic and smooth pursuit eye movement J Physiol vol 159,pp 338-362

in a the point of fixation traversing an ellipse in the object plane. Guyton also shows that the neurons controlling themuscles driving the ocular globe originate from different oculomotor nuclei. Yarbus also stresses the care required inmaking measurements of the continuous tremor, to the point of using an inertially stable platform to constrain thesubjects head and measuring the extraneous head motion using a small mirror attached to an incisor tooth so that thismotion can be subtracted from the measured tremor of the eye. Care must also be taken not to disturb the “tuned”mechanical response of the eye to muscular commands. The eye is essentially a critically damped mechanical structure;if an additional structure is attached to it, such as a contact lens with a mirror attached to it, care must be taken that thefrequency or amplitude of the eyes motions are not changed by the test apparatus.

7.3.3.2.2 Slow Drift

7.3.3.2.3 “Flicking movements”

7.3.3.3 Saccadic Motion

See Yee et. Al. In Inv. Ophth. Vis Sci July 85. I have full journal, blue & grey good materialSee Engbert, R. & Mergenthaler, K. (2006) Microsaccades are triggered by low retinal image slip PNAS vol 103,pp 7192-7197

Liston & Krauzlis have recently provided an analysis of saccadic and pursuit motion that included statistical results fromthree subjects198. No physiological model, physical description or description of the servo system was provided.

7.3.3.3.1 Small saccadic mode

The small saccadic mode is used in two distinctly different situations. In many animals, the ocular globe is notsufficiently round to allow significant rotation of the globe. However, a small amount of rotation is available. This isthe case in a great many chordates. As a result, the animal can rotate the globe a few degrees under either autonomousor voluntary control. This motion reduces the need to rotate the entire head.

In the more important small saccadic mode, the saccades are very small and very fast. They follow a poorly understoodmotion. However, it is clearly related to cognition since the motions appear to move the line of sight from corner tocorner when viewing complex shapes.

7.3.3.3.2 Large saccadic mode

The large saccadic motion is limited to a few families of chordates. The higher primates and the chameleons exhibitthis capability since the ocular globe is nearly spherical and large angular changes in line of sight can be achieved. Yee,et. al. have provided velocity information concerning the large vertical saccades199. The paper shows that the saccadesrepresent the motion of the eye operating as an impulse driven inertial body. The peak velocity increases with thedistance to be traversed in order to keep the time of traversal as constant as reasonable. The relationship appears to bebased on simple inertial mechanics.

7.3.3.3.3 Pursuit Motion

Nystagmus [[Guyton pg 820 ]][xxx Adler, Bala et. al. is good material200 02 in file][xxx Rashbass201 1961[xxx Pola & Wyatt only covers slow (smooth) eye pursuit motion ]

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202Sylvester, R. Haynes, J-D. & Rees, G. (2005) Saccades differentially modulate human LGN and V1responses in the presence and absence of visual stimulation Current Biology vol. 15, pp 37-41

[xxx discuss both cues (in Adler, Bala et. al. and distractors]

7.3.3.3.4 Blanking of visual channels during large saccades

To avoid accepting extraneous information into the signal processing system during the positioning movements of theeyes (as opposed to the signal collection movements associated with tremor), it is necessary to suppress the signalsgenerated by the retina during the duration of these movements. As noted earlier, these positioning movements areperformed open loop. The xxx subsystem of the POS generates a variety of scanning waveforms that are sent to theoculomotor subsystem under the supervision of the TRN. During the positioning movements, the TRN directs a blankingsignal, derived from the signal generator, to the relevant elements of the thalamus, primarily the PGN and LGN. In thismode of operation, the elements of the system prior to the PGN and LGN operate the same regardless of the motions ofthe eyes. The PGN and LGN use the blanking signal to suppress extraneous inputs during the positioning movementsto the pulvinar (foveola related) and area 17 (periphery related). As a result, any signal manipulation enginesorthodromic to these bodies are shielded from extraneous signal information. However, the blanking signal creates adifferent signal level during the blanking interval. This difference in signal level may be measured within later stagesof the visual system. This difference in signal level caused by blanking signals has been measured by Sylvester, et. al.using MRI techniques202.

Sylvester, et. al. make another important observation in their supplemental material. They describe the LGN as locatedwithin a cluster of hot spots associated with the thalamus. This observation suggests that they observed signals relatedto the PGN and pulvinar but did not interpret them.

The eyelids are normally closed briefly during a large oculomotor positioning. This closure may be in support of theexternal lubrication of the eye or it may be part of the blanking system. A question remains whether the commands forclosing of the eyelids also generate a blanking signal or whether closing of the eyelids during an oculomotor positioningis initiated by the blanking signal.

It should be noted that the open loop suppression of imagery during positioning signals to the oculomotor system is notperfect. In the case of a strobe light on an aircraft flashing during the period of blanking, and a dark adapted eye, thesensing photoreceptor may generate a generator potential that lasts beyond the end of the blanking interval. In this case,the subject will observe a flash of light at the position in the far field calculated by the POS following the rotation of theeyes. The actual source will be at a location prior to, or along the path followed during the, repositioning.

The literature associated with blanking is described in Section 15.3.5.1.

7.3.3.4 Operating modes of the visual system associated with the physiological optics

Major operational differences are found between the servomechanisms associated with the analytical, alarm and volitionmodes of vision. The major differences are associated with three situations. The first is the significant reduction in off-axis spatial performance of the lens system (Section 2.4). The second factor involves the limitations of the oculomotorplant (Section 7.3.2). Because of these limitations, the correlator formed by the LGN has not evolved to thesophistication found in the correlator of the PGN. It appears the LGN correlator calculates local means for individualobjects in the binocular visual space but does not calculate the deviations from the mean.

As discussed elsewhere, no indication has been found of any capability of any component of the CNS to performmathematical manipulations in the spatial frequency domain. Where appropriate, calculations related to periodicity ofa stimulus may be made in the temporal domain via the convolution integral.

Recognizing the critical role played by memory in the operation of the visual system is difficult. Investigatorsoverwhelmingly consider the visual system as based on the eyes as imaging devices. They are clearly not imagingdevices at the fundamental level. They are fundamentally change detectors. The continuous perception of the outsideworld is a result of the brain maintaining a saliency map of the complete environment exterior to the subject. Thiscapability allows a subject to describe the wall behind him in considerable detail without turning his head (as long as

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Dynamics of Vision 7- 111he was allowed to study the wall in detail previously). The maintenance of a complete saliency map greatly reduces thedata processing load on the visual system. The system needs only process current changes to that saliency map.

The role of memory is obscure primarily because the laboratory investigators have not yet been able to interpret thesignaling code used within the multiple memory and higher cognitive centers of the brain. Thus, the pulvinar, thesuperior colliculus and cerebellum are some of the least understood areas of the CNS. They are understood more fromthe flow of signals they are associated with than for the function they actually perform. They are primarily large capacitymemory elements. Each appears to contain multiple lookup tables. The element(s) of the CNS hosting the saliency mapis yet to be isolated and identified.

As noted below and in Section 15.2.2, the saliency map is contained within a general database, similar to that found ina modern computer. It does not contain an image of the outside world. The database is based on spatial positioninformation. It does not contain spatial frequency information. When needed, such information is determined from thespatial-position-oriented database.

Because of the above differences, the analytical mode of vision will be closely associated with the spatial domain of thefoveola and the operational domain of the PGN/pulvinar couple. The awareness and alarm modes will be associated withthe remainder of the retina and the operational domain of the LGN/occipital couple. See Section 15.6.5 for details ofthese operational configurations.

7.3.3.4.1 The coarse, type 0, (& autonomous) awareness mode

Because of limitation in the spatial resolution of the eye caused by the aberrations of the lens group, theservomechanisms associated with the peripheral (non foveola) retina cannot perceive the motion of the eyes related totremor. Because of this limitation, the peripheral servomechanisms operate as type 0, or position servos only. Thetemporal signals within this servoloop do not contain phase information. The signals report the location of changes inbrightness in object space on a frame by frame basis (the frame interval is about 33 milliseconds) but do not report thedirection of that motion. The precision of the location information is better than 0.1 degrees but far from the few secondsof arc achieved by the analytical mode servomechanism. The direction of the motion is determined by a separatecalculation within the CNS. The processing of awareness mode signals is largely autonomous and the subject is largelyunaware of the processing.

7.3.3.4.2 The coarse, type 0, (& semi-autonomous) alarm mode

The alarm mode operates in the same manner, and under the same constraints, as the awareness mode, although it isassigned a different functional task. Its task is to detect changes in brightness related to vision as they occur in theawareness mode (covering the overall field of view). The information transmitted to the midbrain is limited primarilyto location within object space defined by angles relative to the line of fixation. No information concerning range isprovided. Because of the coarseness of the information, these signals are labeled instructions in the above figures. Theyare converted to more detailed pointing instructions by the superior colliculus. Similar changes are reported to thethalamic reticular nucleus by other sensory systems. The thalamic reticular nucleus filters these reports (and can discounttheir importance based on training and experience). When deemed important, the TRN instructs the POS (and the restof the skeletal system when necessary) to reorient the eyes to bring the location of the change into alignment with thepoint of fixation. This action prepares the system to enter the more precise analytical mode of operation. The controlexhibited by the TRN over the alarm mode signals demonstrates the more limited semi-autonomous nature of thischannel.

7.3.3.4.3 The fine, type 1, (& autonomous) analytical mode

As new scenes are aligned with the point of fixation, the visual system employs the analytical mode of the visual systemto ascertain the detailed properties of the objects in those scenes. The images projected on the foveola exhibit a spatialresolution at least one order of magnitude higher than for typical scenes imaged onto the periphery. This resolutionallows the analytical mode to resolve small changes in the image introduced by the physiological tremor of the eyesinteracting with contrast edges in the scene. These changes are transmitted to the midbrain synchronously with respectto the signals generating the tremor. By synchronously detecting these signals, the POS can detect both position anddirection information with respect to these changes. In this sense, the POS operates as a type 1, or velocity,servomechanism. Using the two eyes in a synchronous mode provides additional information related to the distance tothe objects in the scene. This information allows the POS to create a stereo-optical map of the scene through themechanism labeled stereopsis.

7.3.3.4.4 The (sympathetic and instruction oriented) volition mode

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203

Brodkey, J. & Stark, L. (1967) Accommodative convergence– an adaptive nonlinear control system IEEE TransSystems Sci Cyber vol. SSC-3, no. 2 pp 121-133

The higher cognitive centers can access the saliency map of the external environment and command the visual systemto point to a previously examined object by issuing the appropriate instructions. These instructions are basically thethree-dimensional coordinates of the object maintained in the saliency map. These minimal instructions are passed tothe superior colliculus. The superior colliculus interprets these instructions and issues a more complete set of commandsto the POS. Besides the necessary angular (version) information, these commands include the additional informationrequired to cause the eyes to focus (accommodation) and to converge (vergence) at the prescribed distance.

The volition mode operates essentially open loop. It can only be considered part of a closed loop in the sense that theoriginal data for the saliency map was obtained through earlier operation of the awareness, alarm and analytical modes.This data may have been stored for a very long time before any volition instructions were issued.

The TRN exhibits considerable control over the order of implementation of volition and alarm mode instructions andanalytical mode commands.

7.3.3.4.5 Accommodation, a fixed reference controlled servomechanism

The accommodation subsystem appears to be fundamentally different from those associated with version and vergence.The performance of the subsystem appears to rely heavily on historical information stored in the memory associated withthe superior colliculus. The accommodation values stored there appear to have been optimized over a long period of timeand be tied quite closely to the associated vergence values. It appears that the receipt of a pointing command in the formof an alarm or volition instruction generates an accommodation signal obtained from the superior colliculus. Subsequentoperation of the POS in the analytical mode may further optimize the accommodation function and provide updatedvalues for storage in the superior colliculus.

Brodkey & Stark appear to have provided the best and most extensive data on the operation of the accommodationsystem203. However, their nomenclature may be dated. The system they describe in detail appears to be a linearservomechanism within its typical operating range. It does exhibit mild nonlinearity at the extremes of this range (theirfigure 21). Their discussion defines the limits of their investigation and their assumptions. The last line of their abstractrequires modification when one recognizes the sampled but un-clocked nature of the projection system (stage 3) usedin the neural system. While the system appears to be continuous at low stimulus frequencies, it is clearly sampled. Thedriven nature of the sampling mechanism makes it possible to operate at sample intervals of less than 0.01 seconds. Thisis well below the resolution of the Brodkey & Stark test set. The sampling becomes obvious at higher stimulusfrequencies. Fatigue was found to be a significant factor in their protocol.

Brodkey & Stark review several models capable of explaining their data. In each case, they caveat that the model doesnot contain any memory element. On the other hand, they note the apparent adaptability of the system, a sure sign ofa memory function (or some other computational capability).

7.3.3.4.6 The critical role of memory in POS operation

As suggested in the above paragraphs, memory plays a major role in vision. Short term memory is used to detectchanges within a scene on a short term basis, typically 33 milliseconds to a second. Longer term memory is used torecord the salient features of a scene on a permanent basis. The existence of such a permanent (though up-datable)saliency map, in collaboration with the long term memory of the superior colliculus, is obvious. It allows a subject toreturn to a dark room after intervals of more than twenty years and reach for the light switch with a precision of less thanone inch.

Within the precision optical system, POS, short term memory is used extensively to perform the 2-dimensionalassociative correlation functions required by the stereopsis mechanism. The long term memory capability associatedwith the pulvinar is then used to compare recent information with previously stored information. This allows the contentof a scene to be recognized, labeled and stored in the saliency map. The details of this activity are developed in Section15.6.6.

7.3.3.5 The pointing system in humans

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204Bach-y-rita, P. & Collins, C. (1971) The control of eye movements. NY: Academic Press205Leigh, R. & Zee, D. (1999) 3rd ed. Op. Cit. pgs. 175, 195 & 206. Also pgs. 150 & 237 in the 2nd ed.206Young, L. & Stark, L. (1962) A sampled-data model for eye-tracking movements. Quart. Progr. Rep. Res.Lab. Electr. M.I.T. vol. 66, pp. 370-384207Stark, L. (1971) The control system for versional eye movements. In Bach-y-rita & collins, op. Cit. Ppp.363-393208Yarbus, A. (1965-Rus., 1967-Eng.) Eye movements and vision. NY: Plenum Press209Shakhnovich, A. (1977) The Brain and Regulation of Eye Movement. NY: Plenum Press210Ditchburn, R. (1973) Eye-movements and visual perception Oxford: Clarendon Press

7.3.3.5.1 The general scenario

The pointing system of humans uses all of the above modes of operation except the static mode. Although the staticmode is not normally used, it is easily induced pharmacologically. Its effect can also be canceled in the laboratory byseveral means. It may be shown in future experiments that the human can reduce the significance of the tremor whenstaring into the distance. The human visual system is very sensitive to small motions in the far field. This feature wouldbe further accentuated (but only marginally) if the tremor were suppressed in favor of trajectory calculation as found inother animals.

It is worth noting that the tremor is not known ever to cease in a conscious human. In fact, it is usedby medical doctors as one of the vital signs of life. This is typified so frequently in the movies by thedoctor lifting an eyelid of the subject to see if he is still alive. The features of the ocular globe aremuch more prominent when the globe is stationary.

The typical operating scenario for the visual system is being impacted by modern technology, which places additionalstress on the system. However, the fundamental biological scenario is similar to that of other animals. The system isnormally recognized as in the tremor state until something in the far field moves or changes luminosity. The locationof this change is n-ary encoded with respect to location within the field of view and transmitted to the brain. The braininterprets the alarm type of signal and commands a large saccade to establish a line of sight between the unknown eventand the fovea. Upon establishment of the line of sight, the brain commands a series of small saccades to scan the objectand it proceeds to use its cognitive powers to determine the nature of the object. Interspersed among these activities area series of commands to the shutter to close during major saccades to avoid inappropriate data acquisition and resultantconfusion. Many investigators have collected data on the large and small saccades. A much smaller group has studiedthe tremor.

This work will not explore the large and small saccades. They have been studied extensively and the characteristics ofthe servomechanisms associated with them have been detailed204. Fuchs, in Bach-y-Rita & Collins, has illustrated thedifficulty with semantics in this area. He states that a saccade is the most rapid movement of which the oculomotorsystem is capable. This is only true for large angle motions.

7.3.3.5.2 Alternate models of the oculomotor portion of the POS

Several electronic analogs of the servomechanisms related to the oculomotor system have been prepared. However, mostof these appear to be less flexible than the actual system. Those in the literature are conceptual in nature and do notappear to reflect the contributions of investigators trained in servomechanism theory. Most of these conceptual systemshave been defined in terms of continuous, or analog, servomechanism theory205. Young & Stark206 presented a moresophisticated sampled data type analog. However, according to Fuchs, “miniature fixation movements” were consideredas disturbances. The Bode Diagram presented in Stark’s later paper207 shows a maximum frequency of only four Hertz,clearly far below the tremor frequency (however, this is the correct value for the low frequency part of the overalloculomotor system). The actual oculomotor system is very sophisticated and incorporates both a sampled dataservomechanism and a significant computational capability within its servo loops. A more versatile model of theoculomotor servomechanism, capable of performing in the different modes and to the accuracies found in the humansystem, is still needed. Such a model will be presented in Section 7.5.4.

7.3.3.5.3 Data related to physiological tremor

Reviewing the data regarding tremor is important. The most important and comprehensive data in this area has beencollected by Yarbus208 and Shakhnovich209 in Russia and by Ditchburn210 in England. Additional data has been collected

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211Riggs, L. Ratliff, F, Cornsweet, J. & Cornsweet, T. (1953) The disappearance of steadily fixated visual testobjects. J. Opt. Soc. Am. vol. 43, no. 6, pp. 495-501212Krauskopf, J. (1963) Effect of retinal image stabilization on the appearance of hetero-chromatic targets. J.Opt. Soc. Am. vol. 53, no. 6, pp. 741-744213West, D. (1967) Brightness discrimination with a stabilized retinal image. Vision Res. vol. 7, pp. 949-974214Kelly, D. (1979) Motion and Vision I & II. J. Opt. Soc. Am. Vol. 69, no. 9, pp.1266-1279 and vol. 69, no.10, pp. 1340-1349 215Eizenman, M. Hallett, . & Frecher, R. *1985) Power spectra for ocular drift and tremor Vison Res vol. 25,no. 11, pp 1635-1640216Kalesnykas, R. & Hallett, P. (1996) Fixation conditions, the foveola and saccadic latency. Vision Res. vol.36, no. 19, pp. 3195-3203217Zinchenko, V. & Vergiles, N. (1972) Formation of visual images. NY: Consultants Bureau218Findley, J. (1971) Frequency analysis of human involuntary eye movement. Kybernetic vol 8(6), pp 207-214219Putnam, N. Hofer, H. Doble, N. Carroll, J. & Chen, L. (2004) The fixational stability of the human eyemeasured by imaging the cone mosaic J University of Rochester vol 2(2), pp 26-29220Yarbus, A. op. cit. Pg. 127221Ditchburn, R. Fender, xx. & Mayne, XX (1959)

by Riggs, et. al211., Krauskopf212, West213, Kelly214, Eizenman, et. al215. and Kalesnykas &Hallett216. Noting that thequality of the instrumentation improves rapidly after the 1950's is important. This was due primarily to the introductionof transistorized equipment. However, significant information is found in many of these papers. With each newgeneration of equipment, more specific parameters have been quantified about tremor. Zinchenko & Vergiles217 havedeveloped a new equipment using an accelerometer in the eye cap in which they report components up to 200 Hertz asclearly visible. They also show an angular sensitivity to five seconds of arc. They did not provide more informationon tremor as their main goal. That goal was to study the relationship between cognition and the small saccades relatedto image scanning. The use of a reiterative signal processing system, which is now available, to improve the signal-to-noise ratio and then find the spectrum of the angular displacement should lead to more definitive information. Findleyprovided a broad analysis of tremor and proposed a linear second order system driven by white noise to account for it218.The system had time constants of 0.02 and 0.002 seconds.

Putnam et al219. have recently obtained statistical values for tremor using the Rochester adaptive optics ophthalmoscopeof 2003. Their precision was much greater than any previous measurements. However, their technique did not readilydefine the maximum frequency of the highest frequency component of tremor incorporated in their measurements. They describe the standard deviations for the fixation point when using a site at an eccentricity of 1.25 degrees from thefixation point along the horizontal meridian as 1.92 arc min horizontal, 2.86 arc min vertical and 20.7 arc min rotational.They used a photoreceptor diameter of nominally 0.50 arc min (3.2 microns using a focal length of 22.28 mm).

At the current time, the best estimates of the parameters of tremor are:

Size of high frequency tremors--20-40 arc seconds in object field, 1-2 photoreceptor diameters in fovea. The standarddeviations of the total tremor are on the order of 2 arc min in the horizontal and 3 arc min in the vertical. Frequencyspectrum of high frequency tremors--fundamental in the 30-60 Hertz range with harmonics up to 150 Hertz. The testtechniques used to measure the frequency of the tremor would suggest the above amplitude is an RMS value.

Yarbus220 says, “the lowest or fundamental frequency is over 40 Hertz. Natural tremor is characterized by a frequencyhigher than the critical frequency of flicker. Low frequencies during fixation should be classified as drifts.” The premiseof this work would suggest that the fundamental, or mean frequency is significantly higher, probably near 90 Hz, andthe sidebands extend down to 40 Hz and up to 130 Hz, Ditchburn, et. al221. report on experiments where they introducedan artificial tremor. They found, for tremor amplitudes greater than 18 arc seconds, the fraction of time for which thesubject saw the test object increased. This corresponds well with the diameter of a photoreceptor in the fovea.

7.3.3.5.4 Effect of stabilization

Two major discoveries have been made related to the investigation of the tremor associated with the ocular system. Thefirst is the fact that:

The eye becomes blind in a matter of seconds in the absence of tremor, or other change in the objectfield relative to the line of sight. This change can involve anything that causes a change in theluminosity of a specific pixel in object space.

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222Kelly, D. op. cit. pg. 1348223Yarbus, A. (1967) Op. Cit. pp 59-102

The second is equally important and profound.

The retina need not transmit information concerning a uniformly illuminated region to the brain.Transmitting the shape of the perimeter of that field and the color of that field along the perimeter isquite adequate. The brain will use a “paint” program to uniformly color the area in perception spacedetermined by that perimeter.

An accuracy parameter is associated with the term “uniformly.” Unless a sufficient non-uniformity exists to cause asignal in the luminance processing channel, the chromatic perception apparatus will not perceive a change in the colorof a region.

7.3.3.5.4.1 Contrast performance of the eye in the static mode

Many of the above authors have reported experiments involving the stabilization of the image presented to the eye. Thedegree of stabilization has been varied occasionally to gain more information. However, the degree mostly involved theamplitude of the feedback while using an amplifier of more than sufficient bandwidth.

Riggs et. al. carried out experiments, using a mirror on a contact lens and large dove prisms. This configuration allowedthem to vary the degree of compensation in steps from 0% to 100% and then 200%. At 200%, they obviouslyovercompensated for the tremor. They were primarily interested in the time to recognize narrow lines. They noted thatthe lines disappeared with time in proportion to the width of the lines when full compensation for tremor was employed. Under the accentuated condition, the resolution of the eye was actually enhanced.

West found that a stabilized image faded. He also showed the pattern of fading if the total field was larger than the fovea.Generally, but not always, the fading started farthest from the fovea and proceeded inward. This feature suggests adifferent time constant for different zones of the eye. He also reported data on the effect of color on the fading and thescene contrast. His minus blue filter excited both the L- and M-channel photoreceptors.

Kulikowski pointed out that stabilizing an image to better than 25 to 40 arc seconds is quite difficult. Yarbus went togreat lengths to stabilize his images, using a head rest and a bite bar mounted on a seismic block.

Yarbus (pg. 61) also demonstrated that the retina reported a null condition in the absence of motion. This null conditionwas neither black nor white. This was accomplished by repeating the stabilization experiments and then moving a blackobject through the field. The subject reported the object as black against a null field. In television terms, the visualsystem has no black level restoration capability, a common occurrence in cheaper black and white television sets. Allcolor sets were found to require a restoration circuit or the customer would be exposed to bright blank fields betweenscenes.

The principal finding is that approximately three seconds after initiation of the stabilization system, the observer reportsgoing functionally blind. Without a change in luminosity of an element of the scene, the retina reports a null conditionto the subject, neither black nor white. Kelly said it well: “Our results suggest that retinal image motion is the sine quanon of vision.”222 Unfortunately, no curve was found that could be used to determine a more precise time constant forthis effect.

7.3.3.5.4.2 Chrominance performance of the eye in the static mode

Several of the above authors have also explored the appearance of various colored shapes within a larger field. Yarbushas explored this area intensely using primitive techniques compared with those available now223. He has consideredall of the permutations of a large field surrounding a smaller field in which each field is either stationary or movingrelative to the retina. His general conclusion is that a perimeter, no matter how large or small, must be moving relativeto the retina to be perceived. The color of the inside of the perimeter will be perceived correctly if the perimeter ismoving. This perceived color will be an average of the color perceived along the inside edge of the perimeter itself.If the perimeter is not moving, the perceived color of the area within the perimeter will be that assigned to the areaoutside of the perimeter but inside a larger perimeter that is moving relative to the retina. It there is no perimeter withinthe field of view that is moving relative to the retina, the eye will be functionally blind and no color will be perceived

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224Yarbus, A. op. cit. pp. 100-101225Ditchburn, R. (1973) Op. Cit.

within its field of view. He defines such a field of view as an “empty field.”

7.3.3.5.4.3 Conclusions from experiments by Yarbus

To avoid introducing uncertainty in wording, the following paragraphs are taken verbatim from the English translationof Yarbus224.

“We may draw the following conclusions from the results of the experiments described in Chapter II.For optimal working conditions of the human visual system, some degree of constant (interrupted oruninterrupted) movement of the retinal image is essential. If a test field (of any size, color, andluminance) becomes and remains strictly constant and stationary relative to the retina, it will becomeand remain an empty field within 1-3 sec.

Very often, conditions of steady illumination arise on certain parts of the retina during perception.Such conditions arise during the perception of large and uniform surfaces and during small movementsof the eyes. If the illumination continues to be constant for more than three seconds, an empty fieldappears inside this uniform surface (or surfaces). The empty field always takes the color of thesurroundings and, in ordinary conditions, is never seen by the human subject. In other words, thevisual system extrapolates the apparent color of the edges of the surface to its center. According toelectrophysiological findings, I suggest that in man constancy and immobility of the retinal image willbanish impulses entering the optic nerve from the eye or will sharply reduce their number. In thesecircumstances, absence of signals from a certain part of the retina gives the visual system informationthat this area corresponds to a uniform surface, which does not change and is equal to the color ofits edges.

It may be concluded that the visual system ‘identifies’ the empty field arising in artificial conditionswith the empty field arising in natural conditions. For this reason, the empty field arising in artificialconditions always appears to the subject as a uniform background (all visible contours disappear insidethe field), and the apparent color of the field is always the color of its surroundings.

Two essentially different processes are found in the work of the visual system: the first, a fast processof disappearance of all contours in a stationary test field; the second, a slow process which usually iseasily detected by means of afterimages. The fast process may evidently be associated with theappearance of impulses in the optic nerve in response to a change in the intensity of light (the on- andoff- effects familiar from electrophysiology). The second, slow process is evidently associated witha change in the state of the retina--with its adaptation.

A definite delay is found in seeing the color of an empty field. This delay enables us, by extrapolatingfrom the edges of a uniform surface, to see this surface unchanged in color when the image of theedges is continuously and saccadically displaced over the retina. The presence of this delaymechanism is essential for us to continue to perceive these edges.”

Similar summaries have been given by Ditchburn225.

Based on this work, it can be assumed that each photoreceptor is a change detector and there is a time constant associatedwith each photoreceptor cell. This time constant defines the minimum change required for a signal to be generated andpassed to the brain. Although not defined precisely in the experiments of Yarbus and others, the mathematical value ofthe time constant is apparently less than one second at one extreme and less than three seconds in the other extreme. Thesource of these values will be explored in Chapter 12.

Yarbus identified two essentially different processes related to the transient performance of the visual system. His fastprocess relates to the time constant of the adaptation amplifier discussed above. The slow process is a similar but longertime constant. This time constant is associated with the cessation of illumination. The significance of these two“processes” will be discussed further in Chapter 12.

7.3.3.5.5 Inertial aspects of pointing

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226Leigh, R. & Zee, D. (1991) The Neurology of eye movements, 2rd ed. NY: Oxford University Press. pg. 150227Robinson, D. (1964) The mechanics of human saccadic eye movement. J. Physiol. vol. 174, pp. 245-264228Cook, G. & Stark, L. (1968) The human eye-movement mechanism. Arch Ophthal. vol. 79, April, pp. 428-436229Clark, M. & Stark, L. (1975) Time optimal behavior of human saccadic eye movement. IEEE Trans. Auto.Control. pp. 345-348230Porter, J. Baker, R. Ragusa, R. & Bruecknere, J. (1995) Extraocular muscles. Surv. Ophthal. vol. 39, no. 6,pp. 451-484231Leigh, R. & Zee, D. (1999) Op. Cit. pg. 327

To allow the high angular pointing capability of the human and primate eyes, the optic nerve must be quite long, typically75 mm. in humans. This long protrusion from the spherical shape of the ocular globe introduces a considerable changein the moment of inertial of the eye and the centroid of that moment. It also requires a considerable volume within theeye socket be available to accommodate the motion of the optic nerve. An optimization has been achieved by sharingthis space between the muscles controlling the eye and the optic nerve. When an eye muscle contracts, pulling on oneof the ligaments of the globe, it also expands in cross section. This expansion simultaneously pushes the optic nervein the appropriate direction. Because of this push, the optic nerve can be considered a lever attached to the ocular globe.By adjusting the ratio between the above pull and the push, the effect on the center and magnitude of the moment ofinertia caused by the optic nerve can be negated.

7.3.4 Modeling the dynamics of the pointing system

This section and Section 7.4 will provide a broader foundation for understanding both the spatial and temporal dynamicsof the oculomotor subsystem and the temporal response characteristics of the overall visual system.Many models relating to the mechanical dynamics of the eyes appear in the literature. Most of them are merelyconceptual, suggesting the path to more sophisticated models yet to be defined. Many do not employ sufficientmathematical rigor and some rely upon a putative efference copy loop226. As an example, the equation shown under theupper frame of figure 4-5 of Leigh & Zee is not descriptive of the block diagram presented in that frame. Robinson hasprovided a carefully constructed model of the mechanical aspects of the POS and compared it with the earlier work ofWestheimer227. The Robinson paper includes considerable data on the physical parameters of the human eye andincludes a useful summary. However, some values are inconsistent and require careful evaluation. The most rigorousmodeling of the dynamics of the eyes has been provided by Stark and his associates228,229. However, neither Robinsonnor Stark, et. al. recognized or considered the high temporal frequency components of the eye’s motions above 50 Hz.Both Robinson and Stark, et. al. support the overdamped interpretation of the low frequency mechanical portion of thePOS.

Porter, et. al. presented a major review of the structure and function of the extraocular muscles in 1995230. It cautionsabout the use of certain analyses in the literature dated before 1982 on page 458 and for a similar date on a differentsubject on page 465. The views of Porter, et. al. appear to be consistent with the recent comments in Leigh & Zee231.Both describe the distinctly different types of muscle fibers found in these muscles. Neither differentiates clearlybetween the parabolic characteristic of ocular motion and true ballistic motion that it resembles. Porter, et. al. alsodescribe motorneurons of the oculomotor system as firing at up to 600 Hz on page 453 but do not give a citation. Thiswork does not support the conclusion of Porter, et. al. concerning the role of efference copies and proprioception in theoperation of the oculomotor system. Although they suggest substantial evidence for the existence of such informationalassets exist, no demonstrated need for or evidence of such techniques could be found in the literature by this author. Themodels developed in this work did not call for these techniques. More than sufficient information was available fromthe operation of the POS to satisfy the requirements of vision.

Neither does this work support the suggestion by Porter, et. al. on page 465 that Jampel was wrong. Jampel proposedtwo separate and distinct modes of control system operation based on a segmentation of function within the muscles.They suggest that the oculomotor muscles are essentially uniform and mono-modal in their activity. The followingdiscussion will show that each of these muscles acts as two distinctly different actuators. Although they can be modeledas operating in series or parallel, only additional histology can explain how this is done. Their discussion based on theelectromyograph is of limited applicability based on the inability of that technique to achieve simultaneously thesensitivity and noise bandwidth required to detect the tremor signals present.

Early in the study of oculometry, a general feeling arose that the ocular muscles were in some way unique in the body.During the middle of the 20th Century, this view was generally denied as unnecessary. Scott & Collins studied the

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232Scott, A. & Collins, C. (1973) Division of labor in human extraocular muscle. Arch. Ophthal. vol. 90, pp 319-322233Leigh, R. & Zee, D. (1999) Op. Cit. pg 327234Noback, C. (1967) The Human Nervous System. NY: McGraw-Hill pp 93-98235Breinin, G. (1962) The electrophysiology of extraocular muscle. Toronto, Canada: University of TorontoPress. pp 26-27

subject in 1973 from a clinical perspective232. Their multi-probe EMG data does not include a vertical scale and appearsto have employed AC coupling or very poor probe compensation. They did not provide a discussion of theirinstrumentation but drew two conclusions. One, there was little division of labor between oculomotor muscles. Second,most muscles showed electrical activity with a frequency proportional to eccentricity. However, beginning in the 1980's,the subject was re-evaluated when it was found that the ocular muscles exhibited a dual character233. They were foundto contain individual muscle fibers that responded in two significantly different ways. One type exhibited a slow (tonic)response following groups of action potentials. Another group exhibited a very fast (twitch) response to individual actionpotentials.

The dual nature of the neurons innervating a muscle is well known234. The neuron serving the twitch function isdescribed as an alpha neuron. It is heavily myelinated to achieve maximum signal propagation velocity and connectsto extrafusal muscle fibers. The neuron serving the tonic function is labeled a gamma neuron. It is more lightlymyelinated and propagates signals at a lower velocity to the intrafusal (spindle) fibers of the muscle.

The twitch fibers have been described as reproducing the temporal action potential, of the neuron exciting them, in thespatial motion domain. Only a very small number, five to ten, of twitch fibers were associated with a single nerve fiberwhereas hundreds of tonic fibers shared a common neural signal path. Through this organization, an individual neuralsignal is used to “recruit” a variable number of muscle fibers. The smaller number associated with the twitch fibersassures a higher degree of correlation among their times of response. This feature leads to a shorter response time forthese fibers as a group. This shorter response time is supportive of a higher potential frequency response for the processassociated with these fibers.

The tonic fibers did not exhibit a phasic response to individual action potentials. They were individually found to onlyrespond to the integrated response of a group of pulses. The larger number of these fibers associated with a single neuralpath also resulted in a lower degree of temporal correlation between the responses of the fibers. The result was that thetonic fibers exhibited a low pass frequency response and as a group represented a signal integrator.

This work has defined the purpose of the tonic and twitch fibers of the oculomotor muscles and the associated controlcircuits within the POS. To provide all of the capability required, the POS operates two distinct servo loops withinitself. The first is the conventional low frequency loop associated with controlling the line of fixation of the eye(s). Thesecond is a higher frequency loop associated with the precision analyses of scene details while the line of fixation is heldnominally constant during a gaze at the scene. Whether the POS operates these two loops in parallel, in series or in timesequence will be discussed below.

Breinin has provided a series of comments concerning laboratory technique that still applies to the current and futureinvestigations235.

7.3.4.1 Developing the model

To understand completely the operation of the servomechanisms of vision requires the application of control systemtheory. This field generally addresses two major subsystems of a servomechanism, the controller and the plant. Thecontroller (usually electrical) senses some aspect of the mechanism to be controlled and instructs the plant (usually agroup of mechanical components) what to do to bring the sensed mechanism into compliance with a desired condition.Control systems are normally divided into distinct types.

Type 0– A servomechanism used to sense a position and respond with negligible relative error in its final position. Itmay respond by pointing at the original position or at any other position, depending on purpose.

Type 1– A servomechanism used to sense a velocity and respond by generating an equivalent velocity, which may beaccompanied by a finite position error.

Type 2– A servomechanism used to sense an acceleration and respond by generating an equivalent acceleration, which

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236Cook, G. & Stark, L. (1967) Derivation of a model for the human eye-position mechanism. Bull. Math.Biophysics. vol. 29, pp. 153-174237Clark, M. & Stark, L. (1975) Time optimal behavior of human saccadic eye movement. IEEE Trans. Auto.Control vol. 20, pp. 345-348

may be accompanied by a finite velocity error.

These types of servomechanisms can be combined to provide any degree of precision in position, velocity andacceleration tracking required. They can also accept initial conditions that essentially pre-position the output of theservomechanism.

The interpretation and modeling of servomechanisms require the use of differential equations. Most of theservomechanism loops of vision are modified forms containing both Type 1 and Type 2 servomechanisms. Such systemsare ideal for changing position as a result of a change in position of a stimulus. They are not ideal for tracking (pursuitof ) a moving stimulus. However, this requirement has been met through evolution. Computational and memoryfunctions have been incorporated into the basic analog servomechanisms. As a result, the servomechanisms of visioncan frequently be described as Type 1 analog servomechanism with computational enhancement.

Many experiments to evaluate the pursuit capability of the system have been documented (Section 7.3.3.3). The visualsystem employs sampled data techniques in its sensing circuits and servomechanisms. Determining whether a “smoothpursuit” is truly smooth, or whether it is represented by a series of small saccades separated by short analysis intervals,is important. There is the distinct possibility that the series of small saccades involve negligible associated latencies buta finite analysis time between them. Such a series of small saccades might seem continuous within the bandwidth ofthe low frequency portion of the POS servo-system.

In a 1967 paper, Cook & Stark developed a conceptual model of the mechanical portion of the oculomotor system236.They assembled a group of partial equations describing their proposed system and assigned a set of boundary conditionsto these equations. However, they did not obtain a complete and simultaneous solution to these equations. In their 1968paper, they wrote a series of partial differential equations and asked a computer to determine the response of the plantportion of the system. They did not actually solve for the underlying equation. This methodology had one drawback.It allowed them to ask the computer to find a best-fit set of parameters matching their prescribed initial and finalconditions, at least one coarse approximation (to the tension function), and a set of independently measured waveforms.It did not require that they solve the equations of the system in closed form. The best-fit computer generated resultsemployed parameters that were considerably different from those originally specified by Cook & Stark. It was (is)difficult to rationalize the differences between the two sets of parameters without the underlying equations in closedform.

Clark & Stark presented a different model in a short paper in 1975237. Their strategy appears to be to incorporate twotime constants in the control portion of the system and to treat the nonlinearity related to the tension source by using aparallel mechanical load. This load was nonlinear in the plant portion of the system. Their figure 1(b)[3] suggests thatthis strategy did not result in an improved model. Clark & Stark take issue with Cook & Stark over the “order” of thesystem. They claim to have constructed a sixth order nonlinear homeomorphic physiological model of some impreciselydefined part of the human visual system. This work will continue to rely upon the definition of order in differentialequations as defined by the highest order derivative contained in the equations. By arranging the system equations ofthe mechanical portion of the POS in closed form, they are seen to conform to a second order system with a non constantforcing function. The nature of the forcing function is determined by the controller of the POS system and will bediscussed separately in Section 15.2.4.3.

7.3.4.1.1 The Cook & Stark model as a point of departure

Solving the equations of a mechanical plant without considerable experience is difficult. As an example, Figure 7.3.4-1shows the composite model developed by Cook & Stark. Although the value of Θ is associated with the arrowsuggesting it equates to position, the model suffers a lack of clarity. The 1968 Cook & Stark paper discuss the meaningof the variables in this figure. Furthermore, their model does not address the rapid motion of the eyes related to tremor.It is in essence a low frequency model representing only part of a broader capability system.

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238Cook, G. & Stark, L. (1968) The human eye-movement mechanism Arch Ophthal vol. 79, pp 428-436239Porter, et. al. (1995) Op. Cit. pg. 454

Figure 7.3.4-1 An initial block diagram of the oculomotorplant in one dimension. From Cook & Stark, 1967.

Figure 7.3.4-2 A caricature of the static push-pull operationof the ocular muscles. This figure is based on Cook & Stark1967, for the house cat. See text for details.

Cook & Stark show their interpretation of the applicabledata from Breinin and from Wilkie and from Hill in theirfigures 3a and 3b. The original Breinin data had datapoints that were remarkably consistent and was for asingle muscle. Cook & Stark made the assumption thatthe data for the oblique muscles of a cat weresymmetrical and used the data points for an inferioroblique muscle twice to create a push-pull configuration.The resulting figure was drawn freehand and wasapparently intended to be symmetrical. It appears thesolid curves were forced to zero at L0/2. It is alsobecoming clear that the pairs of oculomotor muscles arenot truly symmetrical238. Figure 7.3.4-2 shows analternate presentation of the data in Figures 3 and 6 ofCook & Stark. Different conclusions can be drawn fromthis figure. Additional scales have been provided toinsure consistent notation. The upper half of the graphrepresents a lateral or superior rectus muscle (althoughthe data was originally from a lateral oblique). This istaken initially as the agonistic muscle and is representedby a positive tension on the eyeball. The muscle isshown under three conditions of innervation by the solidlines, 0%, 50% and 100%. The lower half is taken as a medial or inferior rectus muscle. It is initially considered theantagonistic muscle represented by a negative tension.

These muscles are not known to become slack ever.When acting in the antagonistic role, they rely on theirelastic properties at zero innervation to maintain aminimum tension239. Cook & Stark noted the finitetension in each muscle at zero innervation and at anominal zero angle for the line of fixation of the eye.The net tension on the eye at zero innervation is shownby the dashed line. It varies with the length of themuscles. This length is related to the angle of rotation ofthe line of fixation by the moment arm of the muscle.

Of greater interest is the net tension on the eye as afunction of innervation and static position. The dash-dotlines show the net tension between the pair of muscleswhen one is at 100% innervation and the other is at 0%.Note the net tension goes to zero at ±67 degrees in thiscaricature. This defines the operational limit of thisservomechanism in the absence of any other stops. Notealso that the peak in the net tension is not at zero anglefor the line of fixation. The system is actually optimizedto provide a stronger initial pull for saccades passingthrough the zero fixation point. However, it is notoptimized for maximum angular swings.

Cook & Stark chose to approximate the maximum tension provided by either muscle as a constant value over its angularoperating range, which they defined by the heavy bar at the bottom of the figure. Using the actual value to compute thenet tension provides a different operating scenario. In this scenario, the initial net tension at the start of a saccadedepends on the line of sight at the start of the rotation. This fact should be considered in any laboratory programinvestigating saccades. Their use of a constant to approximate the muscular tension probably accounts for the variance

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240Leigh, R. & Zee, D. (1999) The Neurology of eye movements, 3rd ed. NY: Oxford University Press. pgs.175, 206, pgs. 150, 237 in 2nd ed.

Figure 7.3.4-3 An expanded model of the oculomotor subsystem for a single plane of the orthogonal system. The modeldisplays the “push pull” nature of the system. The antagonistic portion is on the left and the agonistic portion is on theright. Shown are the components of the eye ball in the center, the low frequency (tonic) components of the system oneach end and the and the high frequency (tremor) components (shaded areas). See text for details.

between their initial parameters and the computer optimized parameters they developed.

By adjusting the initial conditions for the net tension characteristics to more realistic values, the net tensioncharacteristics can be approximated by a cosine wave. This approximation simplifies obtaining the closed form solutionto the equation for the response of the POS plant.

7.3.4.1.2 The expanded oculomotor plant model

Leigh & Zee have provided some gross models of the oculomotor system that include both eye and head motions240.Only a few detailed models of the oculomotor system have appeared in the literature. None of them have addressed thefine tremor (measured in seconds of arc) present in the normal eyes. By reviewing some of the approximations inRobinson in 1964 and Cook & Stark in 1967-68, a more complete model can be described. It is possible to include boththe tonal and twitch servomechanisms in this model. The resulting model is much more complete. An expanded modelis presented in Figure 7.3.4-3 that is intended to represent the general case of the entire mechanical portion (the plant)of the oculomotor servomechanical system. Θ =0 is indicative of the direction of the eye under total anesthesia. Thedefined system is linear and a considerable difference in operating frequency exists between portions of the system.Under these conditions, the system can be separated into two separate systems using the rules of superposition. Byeliminating the gray areas (setting Θ3 = Θ3' and Θ2 = Θ2'), a low frequency system quite similar to that of Cook & Starkis obtained that describes the gross saccades (and drift) of vision. By eliminating the two segments beyond the graysegments (setting Θ3' = Θ2' = 0), a system is obtained describing the operation of the total system in the high frequency,fine-motion, regime related to the actual analysis of symbols by the foveola. To interpret the intermediate operatingrange associated with flicks and drifts associated with the scanning (but not analysis) of textual material may requiresolving the general model.

In this figure, the symbology of Cook & Stark has been maintained but the symbol for some dashpots has been replacedby a sawtooth symbol as a matter of convenience to simplify the artwork. In addition, the symbology for the eye hasbeen modified to more clearly represent the rotary motion involved. Rotation of the eye in the positive Q directioncorresponds to rotation of the eye toward the temple. At this initial stage, some labels have been used duplicatively,

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241Breinin, G. (1962) Op. Cit. pp. 118-122242Deubel, H. & Bridgeman, B. (1995) Fourth Purkinje image signals reveal eye-lens deviations and retinalimage distortions during saccades. Vision Res. vol. 35, pp 529-538 & 2897-2902

partly since the previous works have all assumed the agonistic and antagonistic muscles have been symmetrical. In moredetailed discussions, these labels will be subdivided. Although this figure is complex, it can still be represented by asingle 2nd order differential equation. The forcing function, due to the various tension sources (shown by the circledarrows) associated with that equation may change with operating mode. If the model is decomposed into high and lowfrequency models, simpler individual forcing functions may be applied to each simpler model. This figure describes eachof the four muscle elements involved in the push-pull operation of the eye in one plane. Each muscle is shown ascontaining the theoretical elements of inertia, resistive loss, elasticity and a tension generator. Most authors have treatedthe inertial element of the muscles (shown dotted in the figure) as equal to zero for simplicity. Cook & Stark representedthe low frequency, tonal, muscles as a tension source in series with an elastic element, with the combination in parallelwith a second elastic element. This approach is followed here but an additional resistive element is also shown in parallelwith the source leg. This element will become important later since it introduces a low pass filter into the system. It isbelieved that the nonlinearity introduced by Clark & Stark based on their interpretation of the data of Hill is betterhandled by the configuration shown. The pole in this low pass network is believed to be the source of the denominatorin their expression for the total tension. All of the relevant elastic elements are shown in their real locations. Theelasticity of the ligaments is shown for completeness. They will be considered to have a value of zero in subsequentdiscussions. This network does not include a net elastic term defined by Cook & Stark as KP. Under total anesthesia,at the so-called surgical plane of anesthesia, the net elastic term is the combination of all of the elastic terms shown withthe contractile terms open circuited. The result is mathematically the same but the new model is more precise.

More than sufficient data exists in the literature to describe each oculomotor muscle as consisting of two distinctportions, a slow or tonal portion and a fast or twitch portion. This data will be discussed in Section 7.3.2.4.1.

In this model, the tonic portions of each muscle are represented by a single symbol. The individual elements are notphysically identifiable. The network formed by each group of T, KCONTRACTILE and B are symbolic of the summation ofthe tensions supplied by many individual muscle fibers. The result is a tonal response of limited high frequencycapability. In the absence of a tension, T, the contractile element is disconnected from the circuit. The muscle is thenrepresented by the parallel combination of B and KELASTIC. This representation is passive in nature and can be consideredtonal.

The twitch portion of the muscle is less well characterized at this time. However, it is believed that the contractileelasticity has a nominal value of zero and the dashpot, B, is essentially an open circuit. As a result, the muscle does notexhibit a low pass filter characteristic similar to the tonal portion of the muscle. The muscle can respond to an individualaction potential in a characteristic way.

Breinin has described the response of both the tonal and twitch portions of the oculomotor muscle in considerabledetail241. However, it must be noted that his test set was inadequate by current standards. It was either AC coupled orhe used a very poorly compensated probe. The distortion in the recorded action potentials is considerable. The twitchportion of the muscle exhibits a nominal delay following the stimulus of two msec, a time to peak response of 10 msec,and completion of the response within 40 msec. The first order response suggests that the inertia term was insignificantfor the twitch portion of the muscle as tested. The description of the test was not explicit about whether the eye wasstill attached to the tendon of the muscle under test. Neither the tonic nor twitch data showed any signs of anunderdamped second order system. The tonic waveforms did show some ripple due to the temporal spacing of theinnervating action pulses.

The resulting network, with all inertial terms removed except the moment of inertia of the eyeball, is easily reduced toa second order equivalent network using Thevinin’s Theorem.

Discussion appears in the literature as to the rigidity, and therefore the constancy of the moment of inertia, of theeyeball. The vitreous humor is a gel that generally rotates with the rotation of the eyeball. However, a spring constantand damping factor are associated with this rotation. Similarly, the lens is suspended from the outer shell of the eyeballby a spring and dashpot system242. In detailed analyses, these additional effects need to be included.

The original Cook & Stark figure only addressed the tonic operation of the subsystem and only presented the unshadedareas. The shaded areas are introduced to account for the high frequency operation of the system related to the twitchfibers of the muscles. It is this high frequency operation that is responsible for the introduction of the critical tremor

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243Cook, G. (1967) Derivation of a model for the human eye-positioning mechanism. Bull. Math. Biophysics.vol. 29, pp. 153-174244Cook, G. & Stark, L. (1968) The human eye-movement mechanism Arch Ophthal vol. 79, pp 428-436245Breinin, G. (1962) The electrophysiology of extraocular muscle. Toronto, Canada: University of TorontoPress. pg 53

phenomenon into vision. When defining the electronic analog of a mechanical circuit, two major options are availablefor simple circuits. One option is to equate mechanical force to electrical current. The second is to equate mechanicalforce to electrical voltage. In either case, the relationship between time in the two circuits is arbitrary. This arbitraryproperty allows the design of an electrical analog that operates faster or slower than the mechanical equivalent. Cook& Stark used the force-current analog where the angular position of the eye is represented by the integral of the voltageat a node labeled Θ1. The alternate representation would have equated the angular position of the eye by the charge ona capacitor connected to the node, Θ1. Either approach gives correct results. The force-voltage analog is easier for mostpeople to interpret. This analog provides a DC path between the element representing the position of the eye and theelement representing the tension of the muscles. Thus, the overall circuit can be considered a type 0 servomechanism,e.g., one that can maintain a zero position error. The oculomotor circuit is sufficiently complex that it calls for somegroups of elements to be transformed from what appears to be one mode to the other by using Thevinen’s Theorem. The literature exhibits a continuing rivalry between those who consider the low frequency circuit to be underdampedand those who insist it is overdamped. Care should be taken to differentiate the state of damping of the low frequency(tonic) circuitry and the high frequency (phasic or tremor) circuitry. It appears that significant overdamping of the toniccircuitry would contribute greatly to the independent operation of the two distinct circuit profiles. This mode wouldconsiderably simplify the mathematics required to describe the circuit and its performance. This mode will be assumedin the following analysis. It will be shown that in this formulation, the two end circuits can be considered as shortcircuits at high frequencies as far as the twitch circuits are concerned. Alternately, the twitch circuits appear as shortcircuits to the tonic portion of the overall circuit operating at lower frequencies.

The polarities of the sources in the figure are chosen to conform to the common terminology in the literature whendiscussing only one eye. A contraction of the agonistic muscle generates an upward conventional current and a positiveamount of charge on the capacitance CP representing the mass of the eyeball. This positive amount of charge representsthe angle of the eyeball from the quiescent value of the eye under total anesthesia. Following Cook, this positive chargeis associated with a deflection of the line of fixation in the temporal direction in object space. This deflection is due toa contraction of the lateral rectus muscle243. Maintaining only one convention in this area is important because, thetemporal and nasal oculomotor responses are asymmetrical244. When the orientation of both eyes is being consideredsimultaneously, the convention becomes more complex. The convention adopted by Breinin should be considered inthose situations245.

Cook & Stark noted the earlier work of Hill and of Katz in defining the resistive term associated with the tonic portionof the oculomotor muscle response, represented by GAnt and GAg in the figure. Working in the late 1930's, theseinvestigators defined a “nonlinear” characteristic for these impedances. Their representation was entirely empirical anddid not employ any complex notation. They showed that the “damping loss” or resistive impedance of the muscle variedin proportion to the tension of the muscle. Hill showed that the damping loss of the muscle during contraction was alsoinversely proportional to a sum that included a term proportional to the velocity of the shortening.

Figure 7.3.4-4 extends the previous figure by replacing the simple tension generators by piezoelectric devices morerepresentative of actual muscles and connecting them to their driving neurons to form four motor units. The solid blackrectangles represent the electrostenolytic power sources associated with the cytological aspects of each muscle fiber.The mass of the muscles has been eliminated since they are not believed to be significant to the performance of thesystem. No changes are required in the previous physical model. The neural paths back to the oculomotor controllerare discussed in Section 11.6.3.

In this figure, each muscle fiber is treated as a linear piezoelectric transducer. The cytoplasm of the muscle cell normallyexhibits a potential of -70 mV relative to its surroundings. This potential is created by the electrostenolytic process onthe surface of the cytolemma. When the fiber is excited by its associated neuron, current is injected into the cell at thesynapse, the potential of the cytoplasm is reduced and the cell contracts. The contraction along its long axis generatesthe tension exhibited by the fiber. The contraction is assumed to be a linear function of the potential of the cytoplasmover the operating range of the muscle fiber. The response of either the tonic or twitch portion of each muscle is thenthe result of the summation in time and space of the contraction of the appropriate ensemble of individual piezoelectrictransducers. To insure appropriate contraction with respect to time, the number of fibers recruited by a single neuronis much smaller in twitch portions than in tonal portions of muscle.

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Figure 7.3.4-4 The oculomotor servo plant with driving neurons. All inertial elements have been removed except forthe moment of inertia of the eye. Each tension generator has been replaced by a piezoelectric device representingindividual portions of the muscles. The black boxes associated with each device represents an electrostenolytic powersource attached to the muscle cell. The similar white boxes represent the synapse between the muscle cell and its neuron.

Under this interpretation of a muscle, the attack time constant of the muscle is determined by the combination of thetransducer, the elasticity and the friction associated with the muscle ensemble. The relaxation or deactivation timeconstant is determined primarily by the ability of the electrostenolytic power supply of the muscle to reestablish the restpotential of the cells’ cytoplasm.

Cook & Stark estimated the activation time constant at one msec and the deactivation time constant at 10 msec atnormal chordate body temperatures.

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246Becker, W. (1991) Saccades In Carpenter, R. ed. Eye Movements, vol 8, Vision and Visual Dysfunction.Boca Raton, Fl: CRC Press Chapter 5

Figure 7.3.4-5 The displacement and velocity profile oflarge-angle human optokinetics. Recorded from the left eyeusing a magnetic search coil. The angles to the target were2, 5, 15, 20, 30, 40 & 50°. Note the correction saccadesafter about 150 ms in several cases. Corrective saccades for40° and 50° responses have been truncated to save space.Note velocity saturation above 30°. From Becker, 1991.

7.3.4.1.3 The performance characteristics of the subsystem

Figure 7.3.4-5 presents a graph from Becker246. It is similar to an earlier graph by Baloh, et. al. in 1975.

The significant latency between the appearance of thetarget and the response will be addressed in Section7.4.7. As addressed in the above discussion, the shape ofthe velocity responses is parabolic in the first order.However, they are not related to an underlying ballisticphenomenon which calls for a parabolic displacementprofile. The displacement profile is linear in the firstorder. The causal phenomenon is a push-pullarrangement of the oculomotor muscles and the intrinsicproperties of these muscles.

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247Fuchs, A. F. & Luschei, E. S. (1970) Firing patterns of abducens neurons of alert monkeys in relationshipto horizontal eye movement J Neurophysiol vol 33, pp 382-392248Robinson, D. (1964) Op. Cit.249Schiller, P. (1970) The discharge characteristics of single units in the oculomotor and abducens nuclei of theunanesthetized monkey. Exp Brain Res. vol. 10(4), pp 347-62. 250Westheimer, G. (1954) Mechanism of saccadic eye movements. A. M. A. Arch. Ophthal. vol. 52, pp. 710-724See also; Westheimer, G. (1958) Bull Math Biophys. vol 20, pp. 149-153251Tole & Young also Sheena & Borah, In Fisher, D. Monty, R. & Senders, J. (1980) ; Eye movements :cognition and visual perception. Hillside, N.J. : Lawrence Erlbaum Associates252Becker, W. & Fuchs, A. (1969) Further properties of the human saccadic system: . . . Vision Res. vol. 8, pp1247-1258

While the response shown in the Becker figure can be associated with a damped ballistic system, it is necessary tosupply a holding torque after the ocular has achieved the desired angular deflection. Fuchs & Luschei247 have shownthe action potential firing rate required to maintain a given angular position as shown in Figure 7.3.4-6.

7.3.4.2 Expansion of the Top LevelSchematic of Vision

7.3.5 Measured open and closed loopperformance of the oculomotor system

Robinson has provided extensive mechanicalperformance measurements for the human oculomotorsystem248. He performed a series of isotonic, isometricand high inertial load tests.

Schiller has provided a series of dynamic measurementsfor the cat that are very instructive249. They show the“holding” discharge rate as a function of eccentricityangle of the eye for several neurons in the oculomotornuclei.

7.3.5.1 The low frequency, wide angle(>6.2°diam.), case

This is the region where the saccades are designed toreorient the line of fixation to bring the point of interestinto the foveola. Optimally, the saccades should causethe point of interest to overlay the point of fixation withintens of minutes of arc. The data in the literature generallyconfirms the position that the Oculomotor plant isoverdamped and strongly driven by the controller. Itdoes not support the earlier claim by Westheimer that thesystem was underdamped and oscillatory250. This isparticularly true when the oculomotor system is

recognized as a sampled data servo system. The caricature (no data points) of position versus time on page 81 of Leigh& Zee, 3rd ed. supports this position as do the other two parts of that figure. However, the velocity versus time andacceleration versus time curves have been corrupted by introducing low pass filters into the data reduction scheme. Thevelocity profile should reach a higher value (~ 390°/sec.) and be much more flat-topped if it related directly to theposition plot. The two wings of the acceleration plot should also be larger (peak near 44,000 °/sec/sec) and moredistinctly separated with an obvious plateau between them as shown in Tole & Young251.

Becker & Fuchs have provided very important data on the wide angle saccades of the eyes252. They explored this areawith the eye in the dark and also when viewing illuminated targets. They also provide a good bibliography and brieflydiscuss the effects of fatigue and medication on the oculomotor system response. Data is provided to demonstrate thatthe oculomotor system operates slower and at lower velocities of saccades when no input is received from the eyes.

Figure 7.3.4-6 RECOPY Action potential firing raterequired to maintain an angular position. Measurementsapply to the abducen motor neurons. From Fuchs & Lushei,1970

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253Nemire, K. & Bridgeman, B. (1987) Oculomotor and skeletal motor systems share one map of visual space.Vision Res. vol. 27, no. 3, pp 393-400

Figure 7.3.5-1 Saccadic duration (A) and maximum velocity (B) of human eye movement between well illuminatedfixation points (solid lines) and eye movements in the dark (dashed lines) for a representative subject. Each point is theaverage of at least 10 values with the bars indicating the standard deviation. From Becker & Fuchs, 1969.

They also present data suggesting the larger the subject, the longer the optical signal paths and the slower the responsesof the POS. The conclusion can be drawn that volition mode movements operate slower than alarm mode movements.These subjects will be discussed in Section 7.4.

Their duration and velocity data is shown in Figure 7.3.5-1. While offering more precision, it is similar to the caricatureof Baloh, et. al. Becker & Fuchs point out that most subjects could not make a single saccade of more than 40° withoutrelying on a second corrective saccade. This might explain the bending of the parabola in the Baloh curves at highsaccade angles. For larger angles, they found the subject typically made a saccade of 90% of the nominal value and thenperformed a corrective saccade after a period of error analysis. They considered it noteworthy that the second saccadewas always in the direction of the first. They also found that a subject that typically made two saccades in the light alsomade two in the dark, suggesting action based on programming or earlier training. This suggested to them that such aset of saccades belonged to an operational package used by the POS. They described this “package hypothesis” andfurther experiments to explore it in detail on their pages 1253-55. Finally, they note the ability of the subject to makea saccade of prescribed angle deteriorated with time in the dark.

Becker & Fuchs point out an artifact in EOG recordings not found in competitive methods of oculography. Theyconsistently recorded an 8 ms long pulse waveform representative of a nominal 2° pre- and anti-saccadic motion. Theytreated this as an artifact that was convenient to use as a point of departure.

It is clear from Becker & Fuchs that experiments involving latencies must describe the size of the individuals involvedas this is a variable in the signal projection component of the overall duration of stimulated saccades.

Nemire & Bridgeman have provided some values for the precision of the oculomotor system in bringing the line offixation to a target253. They introduced a target suddenly at 16.5 degrees from the line of fixation in the horizontal plane.They found the response had a mean error of 0.03 degrees but a standard deviation of 3 degrees based on 90 trials. Whilethe mean is excellent, the standard deviation appears excessive. This appears to have been a cumulative error. Thesubject responded by moving a pointer to signify the location of the target. No eyeball tracker was used.

Hebbard has introduced a method of recording wide angle saccades with good precision using an optical levering

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254Hebbard, F. (1988) Photographing eye movements to obtain both high resolution and large amplitude appliedto the experiment of J. Mueller, Am. J. Optom. Physiol. Optics. Vol. 65, no 5, pp 377-382255Shakhnovich, A. (1977) Op. Cit. pg 57-61.256Steinman, R. Haddad, G. Skavenski, A. & Wyman, D. (1973) Miniature eye movement Science vol 181(102),pp 810-819 257Ditchburn, R. (1960) Thomas Young Oration. Proc Phys. Soc (London) vol 73, pg 66 also in Westheimer,G. (1963) Optical and motor factors in the formation of the retinal image J Opt Soc Am vol 53(1), pp 86-93

Figure 7.3.5-2 Spatial orientation of fine movements (<3°)of the two eyes. Monocular fixation in subject N.Z. wascarried out by the right eye (solid lines). The amplitude, ρ,is in minutes of angle. The shades areas are drifts and theunshaded are saccades. From Shakhnovich, 1977.

technique254.

7.3.5.2 The mid frequency, mid angle (1.2°<Θ<6.2° diam.), case

This is the region of oculomotor operation designed to selectively place areas of interest within the foveola for precisionanalysis. Figure 7.3.5-2 reproduces one of the figures from Shakhnovich showing the performance of the POS at thelevel usually associated with the step and repeat type of process such as reading255. It does not address the very finemotion associated with character identification. Only movements from word to word and syllable to syllable wereconsidered. This type of motion is encountered under three conditions, eyes closed and no point of reference, eyes openwith no point of reference and eyes open with one or more points of reference upon which to fixate. The major axes varyunder these conditions, among subjects, and among pathological subjects, as illustrated in Shakhnovich. To the extenta major axis appears in these figures, a dominant phase relationship can be discerned between the horizontal and verticalsaccades. The variation among subjects suggests training plays a role in the operation of the POS at this level.

Although this figure shows all saccades occurring in theupper left quadrant and all drifts occurring in the lowerright, this was an unusual characteristic of this subject.Most subjects exhibit double lobed patterns for theirsaccades.

7.3.5.3 The high frequency, narrow angle(<1.2° diam.), case

This section contains two subsections, the minisaccadesassociated with scene scanning and the microsaccadesassociated with detailed image analysis. Engbert &Merganthaler have provided data for the motionsassociated with scene scanning.

This is the region of oculomotor operation designed toanalyze, in detail, individual symbols imaged on thefoveola. The area of interest still involves approximately23,000 photoreceptors. The motions associated with thiscase have been reviewed in Section 7.3.2.1.3. Many ofthe finest saccades, true microsaccades, have an angularextent of 10-20 seconds of arc. Steinman et al. haveprovided introductory data related to these smallmotions256. Figure 7.3.5-3, from Ditchburn asreproduced in Westheimer, shows the mixed (non-stochastic) character of these fine microsaccades257. [xxxprobably due to Fender in 1956, see below. ]

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258Shakhnovich, A. (1977) The Brain and Regulation of Eye Movement. NY: Plenum Press

Figure 7.3.5-4, from Shakhnovich, shows the bestavailable high frequency data applicable to tremor andmicrosaccades258. A high fundamental frequency of near100 Hz, is clearly seen in the upper traces. Note thedistinctly different character of the traces in the upperand lower pair. These are clearly not random noisewaveforms. The instantaneous difference between thetraces is highly suggestive of the microscanning beingaccomplished to analyze the detailed structure of theimage projected on the foveola.

Figure 7.3.5-3 RESCAN Record of eye movements duringsteady fixation. From Ditchburn, R. (1960).

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259Fender, xxx (1956) xxx 260Kowler, E. (1991) The stability of gaze and its implications for vision In Carpenter, R. ed. Eye Movements,vol 8, Vision and Visual Dysfunction. Boca Raton, Fl: CRC Press Chapter 4261Fisher, D. Monty, R. & Senders, J. (1980) Eye movements : cognition and visual Hillside, N.J. : LawrenceErlbaum Associates. pg 229262Leigh, R. & Zee, D. (1999) Op. Cit. pp 328-330263Collewijn, H. (1991) The optokinetic contribution In Carpenter, R. ed. Eye Movements, vol 8, Vision andVisual Dysfunction. Boca Raton, Fl: CRC Press Chapter 3

Figure 7.3.5-4 Waveforms of tremor resolved into verticaland horizontal components with the upper two traceswrapping around to the lower traces. Note the instantaneousdifference between the two waveforms suggestive of ahigher level of signal processing. From Shaknovich, 1977.

Figure 7.3.5-5 Bandpass recording of tremor in the human.The noise floor is only a few arc seconds. From Fender,1956.

Shakhnovich did not provide the amplitude of thewaveforms in the above figure but they can be inferredfrom the data of Yarbus and Figure 7.3.5-5. This figure,from Fender on a slow time axis and with less than idealbandpass filtering, shows the magnitude and variabilityof the microsaccades clearly259. The noise floor appearsto be less than a few arc seconds.

Kowler has provided a discussion of the utility of the finemotions of the eye260. He discusses a series of simpletasks requiring good visual and motor skills, such asthreading a needle and conclude “no useful role for smallsaccades in either vision or oculomotor control has beendiscovered.” He did not explore targets morecomplicated than a simple point or line target.

Noting that this work does not support the conclusion ofKowler or the aside in Fisher, et. al. concerning the deleterious effects of microsaccades is important261. It is the positionof this work that they are the very key to the performance of the visual system in the higher primates. Their purpose isrelated to tasks more complex than those explored by Kowler.

The high activity rate associated with the oculomotor system has also been described in electromyographic studies byScott & Collins as illustrated in Leigh & Zee262. Using probes described as miniature electrode needles, they showactivity levels of more than 2000 events per second on a routine basis for the orbital and global portions of oculomotormuscles.

Collewijn has provided additional optokinetic datacomparing the eye movements of cat, monkey and humanunder a variety of conditions263. The material applies tothe coarser motions of the eyes.

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264Owens, D. & Leibowitz, H. (1983) Perceptual and motor consequences of tonic vergence, Chapter 3 in Schor,C. & Ciuffreda, K. Vergence Eye Movements: Basic and Clinical Aspects. London: Butterworths, pp 35-37265Hamstra, S. Sinha, T. & Hallett, P. (2001) The joint contributions of saccades and ocular drift to repeatedocular fixations. Vision Res. vol. 41, pp 1709-1721266Taube, J. & Bassett, J. (2003) Persistent neural activity in head direction cells Cerebral Cortex vol 13(1), pp1162-1172267Tweed, D. (1997) Three-dimensional model of the human eye-head saccadic system J Neurophysiol vol77(3), pp 654-666

7.3.5.4 The pointing of the eyes under quiescent conditions

Owens & Leibowitz discuss pointing under dark, low stimulus level and quiescent conditions264. Care must be takenin interpreting their material. Their figure 3.2 shows that their measurements of ocular vergence in the dark were notactually in the dark as specified. A laser-generated stimulus was presented against a dark field.

Because of the limited database, inferring normative values for the quiescent state of pointing at this time is difficult.

Owens & Leibowitz gave data for a group of 60 subjects

Typical range of mean fixation distance in the dark 39-197 cmTypical range of mean fixation distance at morbidity 56-100 cm also under strong anesthesia and

deep intoxication

Typical range of mean focus in the dark -0.25 to +3.0 diopters

They conclude that vergence and accommodation dissociate under low light level conditions. However, it is likely thatmore work is needed in this area for two reasons. Under truly dark conditions, the eyes can adopt a priori values basedon volition. Volition mode activity may also play a strong role in determining the vergence and accommodation valuesassumed under conditions of limited scene input. They also propose that the dark vergence measures represent theresting or tonus position of the vergence system, unbiased by accommodative or fusional convergence. Other authorssay the eyes typically diverge under conditions of morbidity.

7.3.6 Measured Performance of the augmented oculomotor system

7.3.6.1 The interrelationship of saccades, ocular drift and eye position

Several groups have been investigating the relationships between saccades, tremor and drift. Hamstra, et. al. haveprovided a group of interesting graphs265. They were not directly interested in, nor did they record tremor. Theirdefinition of microsaccades (2-28 min. of arc) corresponds to the definition of minisaccades in this work (See Figure7.3.2-1).

7.3.6.2 The optokinetic and vestibular-ocular mechanisms

Taube et al. have performed significant electropysiological studies concerning the interaction of the vestibular systemwith the vergence system266. Their analysis is beginning to show how the POS accepts signals from the vestibular systemand uses them in circuitry reminiscent of the typical man-made servo-mechanism resolver. Tweed has provided a modelof the complete servo system controlling the eyes, head and torso267. He shows how the laws of Listing and Donder’sare satisfied, or approached, under a variety of conditions.

Optokinetic experiments related to the vestibular mechanism center on the ability of the eyes to track an object movingin object space, or conversely a fixed object in object space when the subject is being rotated in a chair. Theseexperiments attempt to define two different mechanisms. The first is the ability of the Type 0 servomechanism of theoculomotor system to track a constantly moving target. The second is the ability of the eyes to track a fixed point inobject space when the subject is rotated. This latter ability is frequently measured in two different contexts. In one, theeyes are open and actively attempt to fixate on an object in space. In the second, the eyes are in the dark, the fixationpoint is imagined and the rotations of the eyes relative to the body are measured. The latter approach providesinformation on the performance of the vestibular-oculomotor system independent of external inputs. The former

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268Baloh, R. Lyerly, K. Yee, R. & Honrubia, V. (1984) Voluntary control of the human vestibulo-ocular reflex.Acta Otolaryngol. (Stockholm). Vol. 97 pp 1-6269Baloh, R. Yee, R. & Honrubia, V. (1980) Optokinetic asymmetry in patients with maldeveloped foveas. BrainRes. vol. 186, pp 211-216270Kennard, C. & Rose, F. (1988) Physiological Aspects of Clinical Neuro-Ophthalmology Boca Raton, FL:Year Book Medical Publishers pg 277271Shakhnovich, A. (1977) Op. Cit. pp. 92-96272Robinson, D. (1972) Eye movements evoked by collicular stimulation in the alert monkey. Vision Res. vol.12, pp 1795-1808273Tarlov, E. (1970) Organization of vestibulo-oculomotor projections in the cat. Brain Res. vol. 20, pp 159-179274Tarlov, E. & Tarlov, S. (1971) The representation of extraocular muscles in the oculomotor nuclei. BrainRes. vol 34, pp 37-52275McGeer, P. Eccles, Sir John. & Mc Geer, E. (1987) Molecular Neurobiology of the Mammalian Brain, 2nd

Ed.. NY: Plenum Press pg xxx

approach introduces another variable into the evaluation process. Much of the clinically oriented exploratory work inthis area has been performed by Baloh and his associates268. Lacking a detailed model, they have not differentiatedbetween the role of the extra-foveola retina in the performance achieved. By studying what are describedmorphologically as afoveate animals, the known directional sensitivity of certain neurons to direction has been examined.However, the role of space and time diversification in generating this directional sensitivity does not appear to have beenconsidered. Those authors used a very simple analog servomechanism block diagram only calling for a velocity inputfrom the vestibular system and relying on an efferent copy of the muscle response to control the performance of theoculomotor system. It also included a symbolic simple neural integrator that they have associated with the pontinereticular formation of the midbrain in an earlier paper269. In that paper, they state that foveate animals consistently havebidirectionally symmetric optomotor responses but they do not quantify or corroborate that statement. They providedan assessment of the pathological asymmetry in the slow phase velocity of the eyes for five patients.

Kennard & Rose have also provided substantial material on smooth pursuit270.

7.3.6.3 Oculomotor signals from the controller of the POS system

The signals generated by the POS controller to control the oculomotor plant are very complex and differ for the differentoperating modes of the system. It appears that the signals controlling the twitch fibers of the muscles are distinct fromthe signals controlling the tonal fibers. This is suggested by the multiple neural paths from the brain to these muscles.Little data could be found in the literature describing the signals generated to control the tremor implemented by thetwitch fibers.

The Superior Colliculus is an area containing at least a million individual neurons and probably more than 1000individual output signals. Since the individual neurons are much smaller than any man-made probe, isolating a specificneural circuit by current investigative techniques is difficult.

Shakhnovich has discussed the nature of the signals applied to the tonal portion of the oculomotor system271.

Robinson has explored the source of oculomotor signals within the Superior Colliculus of the monkey272. Although, heused stimuli consisting of pulse strings of square wave pulses, it appears he only addressed the signals directed to thetonal portions of the muscles. His figures only relate to responses over intervals longer than 30 msec. The pulses wereusually 0.5 msec wide at a rate of 500 pulses/sec. His technique was to probe the Superior Colliculus and observe theresulting saccades.

Tarlov has studied the neural organization of the midbrain of the cat in relation to the oculomotor plant273,274. Thetechnique was to induce lesions and trace the resulting degeneration in the neural paths. A great deal of histologicalmapping was performed. Some of this mapping showed the high degree of overlap in some functional areas.

7.3.6.3.2 Bandwidth of the neural path

Little data was found defining the temporal bandwidth of the neural signals exciting either the tonic or twitch typeoculomotor muscles, but independent of the muscles. McGeer, et. al. have provided data on the bandwidth of a typicalprojection neuron. The data suggests they only measured the tonic oculomotor drive signals275. Their data indicates atypical half-amplitude-bandwidth of xxx

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276Fuchs, A. & Binder, M. (1983) Fatigue resistance of human extraocular muscles. J. Neurophysiol. vol. 49,pp. 28-34277Morgan, D & Proske, U. (1984) Vertebrate slow muscle: ---. Physiol Review vol. 64, pp. 103-111278Shall, M. & Goldberg, S. (1992) Extraocular motor units: type classification and motoneuron stimulation:---.Brain Res. vol. 587, pp. 291-300279Breinin, G. (1962) Op. Cit. pp 40-42280Sparks, D. Holland, R. & Guthrie, B. (1976) Size and distribution of movement fields in the monkey superiorcolliculus Brain Res. vol. 113, pp. 21-34281Sparks, D. & Nelson, J. (1987) Sensory and motor maps in the mammalian superior colliculus TINS, vol. 10,pp. 312-317282Huerta, M. & Harting, J. (1983) Connectional organization of the superior colliculus J. Neurophysiol. vol.49, pp 28-31283Shaknovich, A. (1977) Op. Cit. pp. 1-21

7.3.6.4 Histological features of the oculomotor system (will move to Chap. 10)

7.3.6.4.1 Histology of the muscles of the plant

Several articles have explored the musculature of the oculomotor system in detail. Fuchs & Binder explored the uniquefatigue properties of both the fast-twitch and slow-twitch muscle fibers276. Their regimen was unable to elicit significantfatigue in the oculomotor muscles. Morgan & Proske studied the properties of vertebrate slow muscle in particular277.They struggle with the distinctions between the terms slow, tonic and nontwitch as used in the literature. The statementis made that “true twitch muscle, which is characterized by the ability of the muscle membrane to propagate actionpotentials and the fact the fiber can contract synchronously in response to each motor nerve impulse.” They also stressthe apparent commingling of different fiber types within one muscle. They also provide details on the sizes of musclefibers and on motor neuron propagation velocity as a function of temperature. Shall & Goldberg provided a descriptionand classification system for the extraocular motor units278. Shall & Goldberg appear to use the term motor unit to referonly to the muscle fibers and not the associated neurons. They have provided a useful discussion on the projection ofneural signals along a monosynaptic path from the oculomotor nucleus to a specific abducens nucleus. They have alsoaddressed the subject of recruitment among the muscle types. Their fusion data is significant. It shows that somemuscles can respond at more than 230 Hz (although the normally associated neurons may not).

Breinin discussed the unusual operation of the oculomotor muscles relative to the waking and sleep states279.

7.3.6.4.2 Histology of the controller circuits

Considerable data is available on the organization of the superior colliculus with respect to oculomotor activity. Muchof it predates the fMRI and is based on monkeys. Sparks, et. al. present the size and distribution of movement fields280.Later, Sparks & Nelson provided a set of sensory and motor interconnection maps281. Huerta & Harting have providedorganizational maps of the superior colliculus, by layer, and also an extensive discussion of all related interconnectionpaths282. Their listing includes many references to the pulvinar pathway between the superior colliculus and areas 7 &8 of the cortex. The associated discussion recognizes the unique importance of this pathway regarding “spatial vision.”No material was found differentiating between those neural paths connecting to twitch versus tonal oculomotor muscles.Shakhnovich has provided a comprehensive discussion of the neural paths between the midbrain and the oculomotormuscles that can be mined effectively283.

7.3.7 Definition and measurement of tremor

Traditionally, measuring the fine natural tremor of the eyes has been very difficult, due to the amplitudes and frequenciesinvolved. Equally important is the phase relationship between the tremor waveforms associated with the two orthogonalaxes of the eye. Section 15.2.5.2 discusses the organization of the two-dimensional correlator used in human vision.

7.3.7.1 Potential modes of signal acquisition

The method of signal acquisition at the retina and the architectural design of the correlator found in the perigeniculatenucleus (PGN) are closely tied. No current information could be found describing the precise character of the tremorused to generate the temporal signals at the photoreceptors from the image projected on those receptors. While Ogle

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284Ogle, K. (1950) Op. Cit. pg. 42285Burton, G. (1973) Evidence for non-linear response processes in the human visual system from measurementson the thresholds of spatial beat frequencies. Vision Res. vol. 13, pp 1211-1225286McKee, S. (1983) The spatial requirements for fine stereoacuity Vision Res. vol. 23, no. 2, pp 191-198

Figure 7.3.7-1 Potential scanning modes associated with theanalytical mode.

recognized the characteristics of the tremor284, the last comprehensive work was by Yarbus and by Ditchburn in the 1960-70's (Section 7.3.3.5). A critical relationship not reached by them, due at least partly to instrumentation problems, isthe phase relationship between the tremor signal applied to the horizontal and vertical motions of the eyes. This phaserelationship is critical to the specific design of the circuits of the two-dimensional correlator of the PGN. Because ofthis, the following material must be limited to a discussion of candidate modes of tremor operation.

Only nominal values are available suggesting the tremor has an energy spectrum extending to at least 100 Hz andpossibly 150 Hz. The harmonic content of this spectrum would be very beneficial in understanding the analysis modeof visual operation. The physical plant of the oculomotor system is presented in detail in Section 7.3, along with a fewcomments on techniques for measuring tremor. It is the “twitch” portion of the plant (using a special portion of theoculomotor muscle) that is particularly involved in the analytical mode. The question to be answered is threefold. First,what is the phase relationship between the vertical and horizontal components of the tremor? Equally important, is thephase relationship fixed or a programmable variable? Third, does the plant operate in a linear mode or does it operatein an inertial mode (like the plant used to cause larger saccades)? Figure 7.3.7-1 displays the potential operating modes.

The linear scan patterns would suggest the tremor energyspectrum would be a narrow band near the nominalscanning frequency. Only the phase varies between thecircular, linear and figure eight Lissajou figures shown.A more efficient scan from the information handlingperspective would use a nonlinear drive signal to a linearsystem that was critically damped by the inertia of theeye. In this approach, the eye rotates at a constantvelocity during the emphasized portions of the scancycle. This approach would lead to maximum linearity inthe conversion from spatial position to a temporalwaveform.

The square pattern would suggest the presence of abroader energy spectrum for the tremor, as probablyencountered in practice. It also suggests separate dataframes are collected during each of the four linearizedportions of the cycle. The diagonal approach suggeststhe collection of data during only two intervals associatedwith the movement of the eyes due to tremor. Thecrossover approach would suggest data is only collectedduring the two longer linear intervals. This approachwould not be efficient unless data was also collectedduring the shorter vertical and horizontal intervals. Other feasible scan patterns may exist. These are the simplest.

Burton has discussed the acuity of the human eye to interference fringes and concluded that the eye is most sensitive tohorizontally and vertically oriented patterns285. This would support the assumption that the phase relationship betweenthe two sets of oculomotor muscles was 90 degrees. He also confirmed that the acuity of the eye was not related to thephotoreceptor mosaic. The mosaic showed no recognizable preference for horizontally or vertically oriented patterns.

McKee has discussed the impact of different simple target shapes on stereoacuity286. She concluded that disjointedpatterns (either horizontal or vertical lines) exhibited a lower threshold than did patterns containing junctions. Whilenot relating directly to the phase of the tremor, her results are consistent with the assumption that the tremor operatesin a square (phase quadrature) manner as drawn in the above figure. This pattern exhibits less performance whenexposed to patterns containing junctions rather than separate parallel lines.

Let the baseline for discussion be the square, impulse-driven pattern. This pattern would suggest data is collected in twopairs of time intervals. For a 100-Hz fundamental frequency tremor, each complete data collection cycle would becompleted in 10 msec. This is less time than generally associated with the interval between minisaccades of the eyes

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Figure 7.3.7-2 Caricature of photoreceptors scanning anedge near the visual acuity limit. Photoreceptor cell isscanning a corner of a right angle in the scene near theacuity limit. The maximum tremor amplitude is nominally2.5 times the diameter of the cell entrance aperture.

observed during the study of fine detail by the subject. The process usually involves time intervals of 50-100 msec. Based primarily on fusion frequency data, let it be assumed that the fundamental frequency of the tremor is 30 Hz withovertones extending up to at least 90 Hz. This would suggest the tremor did operate in the inertial mode. Here, the datacollected with respect to each side of the square would be acquired during about 8 milliseconds. This frame intervalwould be sufficient to generate one action potential describing the state of the pixel scanned in one direction relative tothe previous frame interval. For examining fine detail, this is all that is required. The visual system is basically lookingfor edge transitions.

To obtain a nominally square movement of the eyes due to tremor, the underlying signals from the oculomotor nucleiwould be generated in phase quadrature. Either the nuclei, the twitch muscles, or the combination of both, wouldlinearize the signals to provide a constant velocity movement for roughly 70% of the available time. These waveformsare presented in Section 7.3.4 as a function of time.

The caricature in Figure 7.3.7-2 is provided to help visualize the process. In this candidate situation, the individualphotoreceptor aperture is made to scan over a distance of 2.5 aperture diameters. Such a value is consistent with the bestavailable data on the amplitude of the tremor (Yarbus, 1957). By examining the output waveform of the scanningphotoreceptor, the correlator can detect an edge within the time of interval one and another edge within interval three.No edge will be reported in any of the other intervals. Knowing the phase of the signals from the tremor scan generator,it can say that the first edge is vertical and the second is horizontal. However, the adjacent photoreceptor to the left ofthe one shown will report a vertical edge in interval two and a horizontal edge in interval three. The cell immediatelyto the right of the original cell will not report any vertical edge but will report a horizontal edge in both interval eightand interval three. This simple procedure has determined that there is a corner located within the scan pattern of the firstcell. The corner has a vertical line extending up from the corner (beyond the scan pattern of the three cells) and ahorizontal line extending to the right from the corner (beyond the scan pattern of the right cell).

By completing a more extensive examination of themapping achieved by a larger group of photoreceptors,the Boolean logic required to be programmed into thecorrelator can be determined.

The above mode of operation would suggest relativelysophisticated synchronous switching at the input of thecorrelator in the PGN. Each signal received from thephotoreceptors would be in a differential form internallyand bear a specific temporal relationship to the signalsfrom adjacent cells. A primary goal of the correlatorwould be to sum these signals in a way that enhances theratio of signal data to noise while preserving thegeometrical fidelity of the edge determination.Conceptually, this would suggest two possibilities.Either a complex switching of incoming signals from agiven photoreceptor sequentially into various time relatedbins OR the use of additional dimensions in thecorrelator to represent the foveola map at separateintervals of time.

Look briefly at the switched signal approach first. Eachaction potential representing a different time interval, andtherefore spatial position in the foveola. It would need tobe fed into a different time bin at the output of stage 3and the resulting output would need to be switched to oneof four planes of the correlator. Two of the planes wouldstore vertically oriented information (one for the risingscan and one for the descending scan) and two wouldstore horizontally oriented information. The data setwould represent edges detected within the imageprojected onto the foveola. This data would not containany chromatic information. All of the photoreceptors inthe foveola would be treated equally, without regard tospectral sensitivity. This mode of operation is quitecompatible with the well-known loss of color vision atvery fine resolution. The color information would be

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Figure 7.3.7-3 Candidate tremor waveforms for the twoorthogonal oculomotor motions. See text.

derived only from the much coarser awareness channel.

The nominal signal amplitude at each pedicle of a photoreceptor would be the same (in the absence of chromaticadaptation). This is because each of the outer segments of these receptor is of equal size and all of the chromophoresexhibit the same absolute sensitivity in response to an equal photon flux light source (nominally 7053 Kelvin fortrichromats).

Other than the requirement for synchronism, the above switching is quite simple. The requirement for synchronism isnot difficult considering the fixed temporal and physical relationship between the tremor generator and the signalrecovery circuits. A tremor amplitude equal to the diameter of only one photoreceptor can be accommodated. Largertremor amplitudes could also be accommodated when called for by other operating requirements and implemented bythe POS.

The use of additional temporal planes in the multi-dimensional correlator approach replaces the need for theconsiderable switching circuitry associated with each incoming neural pathway with a simpler mechanism. Instead ofswitching neural signals individually, they are collected in parallel and then all of the data associated with a giveninterval of time can be combined with that from adjacent intervals by using a shift-and-sum approach. This is a coreapproach in the architecture of man-made parallel processing computers. The data in one time plane is combined withthat in an adjacent plane by transferring the data of the first plane into the data bin holding the second plane. However,the shift is done along a diagonal that results in a summation in signal amplitude with respect to spatial positionregardless of time slice.

This shift-and-sum approach can be employed using various diagonals as test cases. The amplitude of the variousoutputs obtained can be compared to determine the optimum output amplitude. In similar radar correlators, this step-and-repeat process with respect to the shift-and-sum mechanism can be used to adaptively correct for incorrect estimates ofaircraft velocity introduced into the correlator. As a result, one output of the correlator is a better estimate of theaircraft’s velocity than that available from its own instruments. Other outputs provide an enhanced map of the sceneof interest. The signal-to-noise ratio of individual line elements in the scene can be improved by about 200:1. In vision,one alternate output of the correlator is a signal indicating the degree of convergence between the imagery provided bythe left and right eyes. This signal can be used as a precision vergence signal in the oculomotor control portion of thePOS.

Since both of the above approaches involve multiple signal storage planes, it is probably easiest to implement the shift-and-sum approach. This approach requires the fewest discrete switching circuits. The dendritic trees of neurons, actingas temporary signal storage bins, are particularly adapted to the shift-and-sum approach.

This discussion suggests that a candidate relationship between the two twitch modes of oculomotor operation is that ofFigure 7.3.7-3.

In this figure, the two orthogonal waveforms are shownidealized to provide two out-of-phase linear movementsof the reticle formed by the entrance aperture of the outersegments. The time scale and amplitude are both shownin relative terms. The amplitude appears to have aminimum (for its active portion) approximating thediameter of one photoreceptor within the foveola. Largeramplitudes (particularly multiples of this diameter)appear to be acceptable and the amplitude may be underactive control by the POS. The appropriate periodappears to be about 1/30 second. The available datasuggests the power spectrum of the tremor extends upinto the region of 90-150 Hz. The first three harmonicsof a sine wave produce a creditable sawtooth waveformof the type shown. This would suggest the fundamentalfrequency is in the region of 30 Hz. Under thisassumption, let the period be 32 ms and each portion ofthe active scan occupy 8 ms. These numbers would becompatible with an action potential frequency of about 125 Hz in the stage 3 neurons of the optic nerve associated withthe foveola. Under this assumption, the action potentials cannot actually be considered to have a frequency. Eachinterval of 8 ms is represented by either a pulse or a blank space representing the change sensed by the photoreceptor

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287Harwood, M. & Harris, C. (2002) Time-optimality and the spectral overlap of saccadic eye movements. Ann.N.Y. Acad. Sci. vol. 956, pp 414-417288Xxx (2010) Eye tracking with the adaptive optics scanning laser ophthalmoscope Proc ETRA vol xxx ACMPress289Iscan, Incorporated, 89 Cambridge Street, Burlington, MA. E-mail: [email protected], R. Hammer, D. et al. (2005) Three-dimensional retinal maps with tracking optical coherencetomography (TOCT) SPIE Photonics West, 22-27 Jan 2005.291Deubel, H. & Bridgeman, B. (1995) Fourth Purkinje image signals reveal eye-lens deviations and retinalimage distortions during saccades Vision Res vol. 35, pp 529-538

during the previous sampling interval. The result is a pulse-coded stream of action potentials at a clock rate of 125 pulsesper second.

Under the above assumptions, the average tremor velocity can be approximated using a nominal photoreceptor diameterof two microns. This diameter gives an average tremor velocity of 2.5 cm/sec. If the amplitude is larger than twomicrons, the velocity may be higher or the scan duration may be extended to equal two sample intervals of the stage 3action potential generator. Either change would cause a change in architecture of the two-dimensional correlator ofSection 15.2.5.2.

A small saving in time could be realized if the two waveforms shown above exhibited some rounding of the corners, andthe time interval involving rounding was shared by the two quadrature waveforms. The saving is probably marginal ifthe servomechanism driving the twitch oculomotor responses is highly optimized. No data is available on the subjectof twitch responses at the detail required. Harwood & Harris have recently discussed the operation of the non-twitchportion of the servomechanism primarily with respect to the volition mode of operation287. Their investigations appearto be largely exploratory.

7.3.7.2 Methods of measuring tremor

xxx has provided a graphic comparison of the methods of measuring tremor288. It shows the traditional contact lens withmirror was the highest capability approach until the recent introduction of the scanning laser ophthalmoscope marriedto an adaptive optics system (abbr. AOSLO). The AOSLO can image an edge onto the retina with a positional accuracyof less than one photoreceptor diameter.

The investigator should avoid counting the number of peaks in a recorded temporal waveform of finite durationin order to calculate the mean tremor frequency. This method is far too crude for use when the amplitude of theunderlying data exhibits a 1/F frequency spectrum. The tremor is clearly a broad but band-limited pseudo-randommechanism (frequently described as a random-walk mechanism) that can not be described by a mean frequency.A peak counting approach has been used by many past investigators who lacked a clear understanding of thecomplexity of the problem.

Instrumentation has always been a problem in tremor measurement. Recently, new video cameras have become availablethat considerably simplify the instrumentation and the introduction of optical coherent tomography (OCT) has quickenedthe pace of development of fine trackers.

Iscan, Incorporated is now offering full frame video cameras with a frame rate up to 240 frames per second289. SkalarMedical is offering an IR tracker with a Bode plot showing negligible rolloff prior to 100 Hz and a 3dB point at 185 Hz.

Ferguson et al. demonstrated a new tracking OCT in 2005 designed to 3D image the in-vivo retina of the eye290. Thereason for the tracking function was because of the poor results with the best high resolution OCT because of theinstability of the eye over the image collection interval. Their tracking loop had a closed loop bandwidth of 1 kHz. Theyclaim their system was able to maintain diffraction-limited performance over periods of one minute. Figures 3 & 4 oftheir paper show the output of their servo tracker with the tracker turned on and turned off. The tremor amplitude drivingthis waveform is on the order of a few resolution elements.

During the late 1990's the combining of adaptive optics and the scanning laser ophthalmoscope has added a newcapability to observe individual photoreceptors of the retina over a significant area at frame rates exceeding 100 Hz.The recent paper by xxx [xxx proc etra paper ] has summarized this capability and provided a useful bibliography. Theyshow it is possible to eliminate various extraneous motions from their data and compute the spectral frequency of thetremor in two orthogonal directions with good fidelity. The fidelity is so good, they had to account for wobble in thehuman eye due to motions between the lens and its surrounding/supporting sclera during major saccades291. They

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292Arathorn, D. Yang,Q. Vogel, C. Zhang, Y. et al. (2007) Retinally stabilized cone-targeted stimulus deliveryOpt Express vol 15, pp 13731-13744293Raghunandan, A.Frasier, J. Poonja, S. Roorda, A. &. Stevenson, S. (2008) Psychophysical measurementsof referenced and unreferenced motion processing using high-resolution retinal imaging J Vision vol 8(14), pp1-/11

achieved about one arcsecond (a fraction of a photoreceptor diameter) resolution with their AOSLO. They show theresultant spectra are well represented by a 1/F spectra characteristic of a random walk mechanism as illustrated in theabove single trace recordings. They show this spectra is obtained up to at least 700 Hz but includes some artifacts atmultiples of 30 Hz because of their scanning protocol.

Figure 7.3.7-5. shows their figure 9 representing themean vertical amplitude spectrum of eye movementsduring periods free of recognizable saccades. The datawas obtained with the subjects fixating on a 16 arc minsquare target. 16 arc min is equal to the diameter ofabout 50 photoreceptors at the retina. (Section 19.8.2).Segments 200 ms long were used in the FFT calculation,setting a lower limit for the frequency scale of about 5Hz..

The trace labeled “grid” is obtained using an “artificialeye.” The details related to this trace were not provided.It exhibits a 1/F0.5 characteristic in their figure 9.. In theirhorizontal spectrum, figure 8, the raw “grid” trace showsa horizontal component (1/F0) from 5 Hz to 300 Hzfollowed by a rapid rolloff. This would be the moreexpected characteristic of their artificial eye described asa “plus lens and a piece of paper mounted rigidly to theAOSLO platform.” The rapid rolloff could them beassociated with the diffraction limited performance oftheir lens.

The other traces relate to four normal subjects. Thesmoothed versions of these traces all show a near 1/Fresponse with a potential shift in the gain constant in theregion of 50 to 100 Hz. It is suggested this change isassociated with the change from the tonal muscle to thetwitch muscle systems described in Section 7.3.1. Thisis a different interpretation from the authors suggestion that their data set represents a scale-invariant random walkpattern. As noted by the authors, there is no dominant (sinusoidal) frequency component associated with tremor. Thisis consistent with the model of this work.

The xxx paper provides a good discussion of their artifact removal protocol.

The Matlab FFT transform apparently does not maintain the cardinal numbers of the individual traces used in thecalculation. As a result, a spatial position versus time response has not been recovered from this data. However,Arathorn et al. have recovered such information apparently on the same AOSLO equipment292.

Raghunandan et al. have recently reported AOSLO data using an asymmetrical (3 x 19 arc min) stimulus but focusedon the vertical motion of the eye when viewing this horizontal bar293. The paper provides very useful information butthe discussion is hindered by the lack of a sophisticated model of ocular dynamics and the neural system. Thecomplexity of the mechanisms they are trying to understand requires an equally complex model. In the introduction,they note the earlier postulates that “the functional significance of such retinal jitter is to overcome the fading of retinalimages. . .” using the term fixational jitter when refering to tremor. They did not reference the second postulate thatsuch motion is actually used to extract information from the scene. They proceeded to adopt the position that tremorwas a masking noise (“spurious motion due to retinal jitter.”) relative to the performance of the system. They draw astrong conclusion with respect to efference copies of neural commands or proprioceptor signals reporting the motion ofthe eyes contributing to the servomechanism controlling eye motions.

Figure 7.3.7-4 Amplitude spectrum calculated withMatlab’s FFT function from AOSLO video. Segmentswithout saccades were selected from several videos ofsubjects fixating a 16 arc min square target. The horizontaland vertical sprectra are essentially the same. See text.From xxx, 2009.

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294Schor, C. & Ciuffreda, K. eds. (1983) Vergence Eye Movements: Basic and Clinical Aspects. London:Butterworths295Hung, G. & Ciuffreda, K. eds. (2002) Models of the Visual System NY: Kluwer Academic/PlenumPublishers296Hung, G. (2001) Models of oculomotor control, River Edge, NJ : World Scientific297Howard, I. (2002) Seeing in Depth, vol. 1 Basic Mechanisms Toronto, Canada: I Porteous298Howard, I. & Rogers, B. (2002) Seeing in Depth, vol 2, Depth Perception Toronto, Canada: I Porteous299Lotmar, W. (1971) Theoretical eye model with aspherics J Opt Soc Am vol 61, no. 11, pp 1522-1529300Reading, R. (1983) Binocular Vision. London: Butterworths301Jones, J. (1983) XXX [ correct paper] Parallel Processing in the Visual System. NY: Plenum Press

7.4 Operational overlays on the Precision Optical System

As noted in the introduction to section 7.3, significant differences appear in the performance of thevisual systems of each species within the higher primates and the monkeys. These differences makethe use of surrogates in the exploratory and precision performance laboratories less than ideal. Inmany cases, the use of surrogates is completely inappropriate.

Historically, the evaluation of the performance of the underlying servomechanisms of the physiological optical systemhas been performed by different researchers than those interested in the operational performance of the same opticalsystem. Until recently, both of these groups were performing primarily exploratory investigations and their activitiesdid not overlap significantly. The investigations of operational performance were particularly limited in two ways. First,they generally relied upon non-invasive techniques. Second, they assumed that the physiological black boxes they werestudying contained only linear analog circuitry. The suggestion that these black boxes might contain memory or complexcomputational engines was not found in the literature.

Leading works summarizing prior investigations of the operational overlays include; Schor & Ciuffreda294, Hung &Ciuffreda295, and Hung296. A problem with these compilations is suggested by the title of Hung & Ciuffreda. Thedifferent authors employ a variety of floating models rather than one comprehensive, and consistent, model.

Howard297 and Howard & Rogers298 have completed a massive two-volume work on Seeing in Depth. The first volumeis subtitled Basic Mechanisms. However, the term mechanisms is used in its most general. Its use is similar to the waymany authors have used the word function. Both speak of functions and mechanisms at the conceptual level. In manychapters, they have used the assumptions of Gaussian optics to explain wide angle optical situations. The wide anglesituation requires the use of complete physical optics as shown in Section 2.4 and in Lotmar299. Little discussion isprovided relating their psychological discussions to the physiology of the human visual system. The second volume isbased entirely on psychological investigations and employs many caricatures that have stretched the applicability of theparaxial optical assumption. The second volume also appears to suffer from a lack of editorial review by the publisher.Several inconsistencies appear between the caricatures presented.

Reading has provided a comprehensive text on Binocular Vision aimed at introductory pedagogy300. It goes into moredepth, and provides many more special themes, than in this work.

The question to be addressed in this section was posed by Jones301. “Although all comprehensive theories of fusionrecognize that disjunctive eye movements provide the substrate for sensory unification, this realization does not ‘explain’sensory fusion. It begs the following important question: what is the nature of the sensory process that recognizes retinaldisparity and directs the eyes to eliminate it?

Since the answer proposed here does not build on the previous literature, that literature will be discussed after the maindiscussion (Section 7.4.5).

A key to the understanding of stereopsis and fusion is recognizing the critical role played by physiological tremor in thefunction of these mechanisms. As noted in Section 7.3.3.5.4, the visual system is blind in the absence of relativemotion between the retina and the scene imaged onto the retina. While this fact is well documented, it has largely beenignored in the recent literature. It is this relative motion that is used to convert spatial image information at the retinainto temporal information within the neural system. This temporal information can be processed and projected to otheranatomical sites within the visual system. Without tremor, no temporal information is created or passed from the retinas

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to the CNS.

A second key is the availability of a model in sufficient detail to explain how the perigeniculate nucleus of the thalamusperforms a two-dimensional correlation function over a spatial range of photoreceptor cell signals constituting thefoveola of each eye.

A third key to understanding stereopsis and fusion is to accept the fact that a “merged image” is not formed within thecentral nervous system. There is no need to “eliminate retinal disparity” in the cortical image as frequently suggestedin the recent literature. The data extracted by the thalamus and other elements of the CNS is processed in tabular form.The Thalamus calculates both the mean and deviation associated with each pair of edges corresponding to one edge inobject space. These tabular values are used to provide the perception of depth. They are incorporated into the saliencymap of the visual system and can be recalled by a variety of subsystems (related to the command implementationprocess) of the system.

7.4.1 Framework for evaluating the operational overlays

Attention to detail is mandatory when considering the complex functional overlays to the pointing system ofaccommodation, version and vergence. Regarding the physiological optics, the use of the Gaussian Optics assumptionis to narrow. Only the incorporation of the broader laws of physical optics allows an understanding of the systems.Physical optics introduces the losses in performance related to field angle, aberrations and other effects (such as thevarious Stiles-Crawford Effects). These losses must be accounted for when performing the data analysis associated withperformance of the visual system.

A similar situation occurs regarding terminology. Attention to detail is necessary. Understanding the above overlaysinvolves many complex relationships. Much of the historical work has been at the conceptual level. This has led to theconceptual, and frequently imprecise, definition of many terms. When later investigators have attempted to use theseterms, they have replaced them with their own similarly (but not identically) defined terms. The result has frequentlybeen similar to that found in translating a foreign language. The nuances intended by the original author are lost. Theserious reader is encouraged to seek out original articles whenever possible to avoid being misled.

Figure 7.4.1-1 defines the geometry of vision frequently found in the pedagogical literature. It is based on an earlyconcept associated with Vieth & Muller. This concept was in turn based on earlier ideas of Maddox and Fechner. Itoriginated with Aguilonius in 1613. The Vieth-Muller circle is defined by the nodal points of the two eyes and thenatural fixation point located along a perpendicular bisecting the line drawn between the two nodal points (on the survaceof the sagittal plane). Three major problems with this concept appear at the research level. First, the “natural fixationpoint” is a variable with a high standard deviation among the population. This makes it awkward to define the diametero f t h e c i r c l e w i t h a n y

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302Jones, R. (1983) Horizontal disparity vergence, Chapter 8 in Schor, C. & Ciuffreda, K. Vergence EyeMovements: Basic and Clinical Aspects. London: Butterworth pp 297-303

Figure 7.4.1-1 Geometry of horizontal disparity. Note the Gaussian optics approximation. For large angles from theline of fixation, the rays do not pass through the lens without bending. The fronto-parallel plane (or tangent plane) isshown for discussion. It does not represent a useful concept. See text.

precision. Second, the angles associated with horizontal disparity are usually defined with reference to the lines offixation leading to the “natural fixation point.” Since the fixation point is poorly defined, the angles associated with thelines of fixation are also poorly defined. Jones discusses this difficulty in Schor & Ciuffreda but proceeds with it forpedagogical purposes302.

Finally, the Vieth-Muller circle does not represent actual performance well. The Hering-Hillebrand deviation from thisgeometric horopter is found in nearly every individual (See Records, pg 649 and the more extensive analysis in Ogle,pp 24-49). The deviation is so pervasive that the Vieth-Muller circle can only be considered a first order approximationof the fundamental performance of the human visual system.

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303Jones, R. & Kerr, K. (1971) Motor responses to conflicting asymmetrical vergence stimulus information Am.J. Optom. vol. 48, pp 989-1000304Owens, D. & Leibowitz, H. (1983) Op. Cit. pp 26-46

While pedagogical discussion of vergence are frequently couched in terms of two or more points, it iscritically important to recognize that stereopsis and fine vergence rely on features rather than points atthe locations highlighted. These features are generally larger than a few times the diameter of a singlephotoreceptor of the retina. It is the scanning of this feature by the tremor of the eye that results in timecorrelatable signals from multiple photoreceptors in each eye that can be used to provide fine stereopsisthroughout the receptive field of the foveola.

Jones defined a set of equations based on a proposition of Hering known as the Law of Equal Innervation (Section7.3.2.5)303.

Jones defines the net disjunctive eye movement (of the point A relative to the physiological resting condition) as αL –αR where these angles are measured from the nominal point of fixation. While useful for pedagogy, it has problems atthe research level. Owens & Leibowitz describe these problems in some detail304. Their discussion highlights thetendency of the eyes to diverge under conditions of deep anesthesia and death. The divergence angle is highly variableamong subjects. It has been reported to be as high as 71 degrees at birth. Under physiological conditions, the eyes tendto converge. However, the resting condition, leading to the point of fixation, is also quite variable. Owens & Leibowitzgive the distance to the point of fixation as 39 to 197 cm. These numbers lead to resting vergence angles of 1 to 7degrees. With this kind of variation, the measurement of any angle from the resting vergence angle is poor practice.Determining the resting vergence angle for each subject under a variety of conditions, such as fatigue level, becomesnecessary.

A more precise definition would be given by (βL + αL) – (αR + βR ) = γL – γR where the values of beta represent the angleto the resting position from the collimated condition.

Similarly, Jones defines the net conjunctive eye movement (of a point A relative to the natural resting condition) as αL+ αR. This value goes to zero for any point along the vertical axis through the fixation point. A more precise definitionwould be given by (βL + αL) + (αR + βR ) = γL + γR where the values of beta and gamma are measured from the collimatedcondition.

The terms in these equations can be summarized as,

α = vergence to point A with reference to the physiological (resting) condition.β = physiological (resting) condition with reference to the collimated condition.γ = vergence to point A with reference to collimated condition.δ = anatomical (morbid) vergence with reference to collimated condition.

The angle between the two lines of fixation, 2β, is usually described as the target vergence (or sometimes simply as theeye vergence).

Jones uses these equations to support two measurement regimes. He relates the terms disjunctive and conjunctive asdescriptors referring to eye position in terms of the signals applied to the pointing system. He then uses the termsvergence and version as referring to the physiological responses of that system.

Another obvious problem is the use of the nodal points of each eye as references. The location and the distance betweenthe nodal points change with rotation of the ocular globes. Thus, the Vieth-Muller circle moves relative to the definedcircle of equal convergence.

When discussing vision over wide fields of view, it should be recognized that the Gaussian Optics approximation doesnot hold. The ray passing through the lens at greater angles than a few degrees from the axis cannot be consideredstraight (Section 2.4.1). It is only because the eyes are optically symmetrical that points such as A can be consideredimaged on similar (cover ) points of the two retinas.

The preceding and following figures show a fronto-parallel plane through the point of fixation. Under the Gaussianassumption, such a plane would be imaged as a similar, and parallel, plane at the point of focus on the retina. However,the retina is highly curved to satisfy the physical optics of a wide field of view optical system. Thus, the fronto-parallel

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305Blakemore, C. (1970) The range and scope of binocular depth discrimination in man J Physiol vol. 211, pp599-622306Ogle, K. (1950) Researches in Binocular Vision. London: W. B. Saunders, pg 29

Figure 7.4.1-2 Figure from Blakemore with dashed arcs ofbest focus added. Points show where an object would haveto be placed to appear single during fixation at F. Modifiedfrom Blakemore, 1970.

plane is only imaged on the retina under the Gaussian assumption (that the field of view is less than a few degrees). Toachieve this imaging, the appropriate value of accommodation must be established. This condition is only met for thefoveola, and possibly a part of the fovea. The fronto-parallel plane cannot be used to discuss wide field of view scenesunder the assumption of a fixed condition of accommodation.

For a constant state of accommodation, the point of fixation of the eyes rotates about the point of rotation of the eyesat a constant radius. This radius is much larger than that of the horopter. The locus of constant accommodation fallsbetween the horopter and the fronto-parallel plane at all angles. While the horopter defines a circle of constant vergenceangle, it does not define a circle of constant accommodation.

Blakemore illustrates the problems with trying to use a fronto-parallel plane in his figure 3 reproduced here as Figure7.4.1-2305. In the caption, he asserts “The scale, showing the distance from the eyes, is also appropriate for the fronto-parallel coordinate.” Unfortunately, the distances from the eyes are in radial coordinates while that for the fronto-parallelplane is in rectilinear coordinates. If two arcs of 43.7 mm radius are drawn through the point of fixation representingthe condition of prime focus for each eye, the problem becomes obvious. Both eyes are in optimum focus over only asmall region around the point of fixation. Ogle illustrated this in his figure 13, although he took some license in drawinga “Normal” locus306. The resolution of the eyes also falls rapidly at angles greater than a few degrees from the point offixation. His measured points do not follow the Vieth-Muller circle or his fronto-parallel plane. Nor do the points satisfythe definition for points along the horopter (since their vergence angles are obviously different from those along thehoropter). As he states in his text, they are the locations of points that appear single while the eyes are fixated at F. Theeyes observe these points under conditions of considerable defocus and reduced resolution.

7.4.1.1 Monocular, binocular andstereoscopic domains of vision

When discussing the operational aspects of pointing, e.g., version, vergence and accommodation, it is extremelyimportant to differentiate carefully between the fields ofspatial vision, Figure 7.4.1-3. In pedagogy, theseregions are usually only defined for vision in the far-field(infinite distance). The monocular field of vision is thatangular region of object space observed instantaneouslyby one eye. The monocular fields of the two human eyesare not congruent. However, they do contain a commonangular region described as the binocular field of vision.This field is normally only described for the regiondefined when the two eyes are pointing perpendicular toa line drawn between them (they are looking straightahead). This region has two important features. First, itdescribes a region that includes a series of equivalentareas in the two retinas. These equivalent pairs of areasare sometimes described as covering points (areas) in the literature. The extent of the binocular field of view isconstrained by the physical structure of the nose. Second, the binocular field of vision also describes the range overwhich the line of fixation can be moved while still maintaining a common point of fixation for both eyes in object space.It is this latter feature that is critical to stereopsis. Both foveola must be able simultaneously to observe the same region(within tens of milliseconds) in object space to achieve stereopsis.

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Figure 7.4.1-3 The visual fields of monocular, binocularand stereoptic vision. The stereoptic field is shown incyclopean form for simplicity. Each eye exhibits a similarfield. They are usually convergent at the point of fixation. The fronto-parallel plane is shown for discussion. It doesnot represent a useful concept. See text.

For scenes closer to the eyes than defined above,equivalent areas can be defined. However, more detail isrequired in the wording. The total and binocular fieldsare reduced for off-axis viewing.

A great tendency exists to use the terms binocular visionand stereoptic vision interchangeably in scientificliterature. However, they are operationally quitedifferent. Monocular vision is used primarily in theawareness mode of vision. It is used to providedirectional (versional) signals to the POS. The POS usesthem to align the line of sight to significant areas ofinterest. The required computations occur in both theretinas and the LGN. Binocular vision is used by theLGN to generate coarse vergence signals for use by thePOS. Stereo-optic vision (limited to the spatial regionsimaged by the two foveola) is used within the PGN toextract a precision vergence signal related to the point offixation in object space. Stereo-optic vision is also usedto calculate differential vergence signals describing thelocation of other objects imaged by the two foveolarelative to the location of the point imaged at the point offixation.

While the narrow field of view mechanism of stereopsiscan be directed anywhere within the wider field of viewof binocular vision, these two concepts are quiteindependent and separate.

Interpreting the above definitions carefully leads to anunambiguous description of how the operational overlays to the pointing subsystem work. It also explains how stereo-optic vision is achieved within the analog domain of the PGN without using a large amount of computational power. When exploring questions concerning fusion and stereopsis, Section 7.4.1.1 will show that only the region of the Vieth-Mueller circle (the horopter) imaged instantaneously by the foveola is involved in precision stereopsis. Under theseconditions, the relevant angles associated with retinal disparity are very small, less than 1.2 degrees, and theapproximations associated with Gaussian Optics can be used. Outside of this small area, only coarse performancestereopsis can be achieved.

Within the field of view associated with the foveola, the normal eye can perceive a relative disparity of ten arc-secondsor 0.0028 degrees. The best trained observers can achieve two arc-seconds (0.00056 degrees) at a 75% discriminationlevel. These numbers suggest that differences of 0.001 inches can be discerned at ten inches and differences of two milescan be discerned at the horizon (S&C pg 238). Better documentation is needed to confirm these values. Figure 7.4.1-4provides a summary of the functional capabilities of the human visual system relative to object space.

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307Tyler, C. & Scott, A. (1979) Op. Cit. pg 645308Sperling, G. (1970) Binocular vision: a physical and a neural theory Am J Psychology vol. 84 pp 461-534309Richards, W. & Kaye, M. (1974) Local versus global stereopsis: two mechanisms Vision Res vol. 14, pp1345-1347

Figure 7.4.1-4 A summary of the on-axis parameters of vision in object space. The vertical dashed line separates finedepth perception related to the foveola and the analytical mode of vision from the coarse depth perception related to theperipheral retina and the awareness/alarm mode of vision. The latter depends heavily on scale cues and angle-rateinformation.

When discussing depth perception, two conditions are frequently described. The First is stereoptic depth perceptionwhere depth perception is based on a fusion of the images from the two eyes. The second is diplopic depth perceptionwhere depth perception is estimated without fusion of the two images. Finding a statement that “Depth is perceived inthe region of both fusion and of diplopia” is common in the pedagogical literature307. Section 7.4.5 will discuss thesignificant differences between these two domains in the character and the mechanism generating the perception ofdepth.

7.4.1.1.1 Global, local, fine & coarse in discussing functional overlays

The terms global, local, fine and coarse have been used in many ways in the literature of functional visual performance.Most of the usage has been at the conceptual level. Adopting more formal and precise terminology in this area is useful.

Sperling defines two distinct neural binocular fields (NBF)308. He defines these NBF’s as internal three-dimensionalrepresentation of the external world. Although not stated specifically, these representations appear to be based onindividual planes representing different distances from the subject. He defines “a primary NBF for the fine-detailfunctions of binocular vision, and a secondary NBF for coarse-detail functions. The interaction of these two systems iscrucial for many phenomena of binocular depth perception.” He does not elaborate on the spatial extent of the NBF’s.

Richards & Kaye describe stereopsis as occurring within two domains309. One domain is small and corresponds wellwith the foveola defined in this work, although it may extend to the diameter of the full fovea. They note that this arearequires a high degree of binocular scene similarity and yields fusion. Their second domain does not require as high adegree of similarity in scene elements and generally does not result in fusion. Their criterion was based primarily ondisparity values. They provide a graph of relative perceived depth versus stimulus disparity but placing it in context ishard. It can be compared with the graphs of Section 7.4.5.

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310Julesz, B. (1978) Global stereopsis: cooperative phenomena in stereoscopic depth perception, Chapter 7 InHeld, et. al. ed. Handbook of Sensory Physiology, Vol VIII, NY: Springer-Verlag311Tyler, C. & Julesz, B. (1980) On the depth of the cyclopean retina Exp. brain Res. vol. 40, pp 196-202312Richards, W. & Kaye, M. (1974) Local versus global stereopsis: two mechanisms Vision Res. vol. 14, pp1345-1347313Tyler, C. (1991) The Horopter and Binocular Fusion. In Regan D. ed, Vision and Visual Disorders. Vol. 9,Binocular Vision. NY:Macmillanpp. 19-37 http://www.ski.org/CWTyler_lab/CWTyler/TylerPDFs/Tyler_HoropterCh1991.pdf

Julesz defined fine and coarse in his 1978 paper by painting a scenario310. He said “The stereopsis of narrow bars (orsmall dots) will be called fine stereopsis, while stereopsis of wide bars (or large dots) will be called coarse stereopsis.”He went on to conceptualize that “fine stereopsis is carried by the high spatial-frequency disparity detectors and coarsestereopsis by the low spatial-frequency disparity detectors.” The two types of disparity detectors were not definitizedfurther. Tyler & Julesz311 suggest that Richards & Kaye312 used local and global to mean the same as the fine and coarseof Julesz. Tyler expanded on the theory of the horopter in 1991313. See Section 7.4.5 where the label precision is usedinstead of fine.

Julesz (1978) went on to define global and local stereopsis much as in this work. Paraphrasing, he said, a global processis needed that evaluates different sets of corresponding element pairings (local stereopsis) and selects one set of pairingsfrom the many pairings in a scene as the dominant element. This work proposes the global stereopsis process calculatesa nominal point of fixation for the scene based on a mean of all the element pairings. This mean is then used as areference for describing each corresponding element pairing (local stereopsis).

There seems general agreement in the literature that there is a fine depth perception mechanism associated with thefoveola and a coarser mechanism associated with the outer retina. Richards & Kaye referenced several other authorsand defined the disparities associated with local stereopsis as occurring within the range of +/– 0.5 degrees. They claimlocal stereopsis customarily yields fusion and requires a high degree of binocular similarity of the disparate images.They again reference several authors and define global stereopsis as accepting less similar targets in the two eyes. Theysay these targets are generally not fused but appear diplopic. Their global stereopsis occurs for disparities much largerthan +/– 0.5 degrees. They build a two-mechanism model around the differences in performance associated with thesetwo zones. They show that their experiments did not support such a separation into two distinct mechanisms.

Figure 7.4.1-5 shows the plan view from above of the optical system of the right eye. The plan view of the left eye issymmetrical with this image (the optic nerves both exiting on the nasal side of the ocular). The optical rays in this figureare symmetrical about the vertical axis. The optical system of the human eye is highly anamorphic in the language ofopticians. Note, the optical rays cannot be represented as straight lines passing through a single nodal point for raysbeyond 0.6 degrees from the optical axis. For larger angles, it is appropriate to employ two principle points, one (P1)near the projection of the external rays at 0 and 90 degrees and a second (P2) at the intersection of the internal opticalrays near the external surface of the lens. While not important when conceptualizing version, vergence and fusion, thisoptical diagram shows conclusively that the angles relating to two points on the external horopter do not correspond totwo similar points on the retina of each eye. The two images projected onto the two retina can not be overlaid in anyrealistic sense as is frequently assumed in conceptual discussions (whether flattened or not). The process of fusing thetwo images occurs entirely in the signal processing (mathematical domain) of stage 4 of the neural system. Even thesignal processing related to precision stereopsis must rely on stage 4 signal processing (within the PGN-pulvinar couple)to merge the two images, except within a few photoreceptor diameters of the point of regard of the two images.

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Figure 7.4.1-5 Plan view from above of the right ocular. The optic nerve exits on the nasal side of the ocular. Beyond0.6 degrees from the central axis, the optical rays are not represented well by straight lines. The center of the foveolais about 5 degrees from the central axis, well beyond the field angle compatible with the simplified optical systems ofLeGrand and others. See text. From Lotmar, 1981.

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314Richards, W. (1971) Independence of Pamum’s near and far limits Am. J. Optom. vol. 48, pp 103-109

Tyler & Julesz also define two distinct mechanisms associated with depth perception based on their definition of acyclopean “retina.” The cyclopean retina of their terminology appears to be a conceptual retina within the cortex perJulesz, 1971. Their first mechanism employs a “binocular cross-correlator.” Their second mechanism is less welldefined. They suggest it is associated with four distinct, but relatively abstract, features. Their binocular cross-correlatorappears to be quite similar to the parallel processor described within the perigeniculate nucleus of this work (Section15.6.3). Their figure 4 shows a distinct transition between their two types of depth discrimination. However, the datais quite sparse and a marginally higher value is possible. A conflict appears to exist between their figure and their text.The horizontal scale of the figure is given as area. The break point is described as near 0.5 square degrees. For sucha circular area, its diameter is 0.8 degrees. In the text, the area is described by the dimensions of 0.5 by 0.5 degrees.The 0.8 degree number is in better agreement with this work. They continue the confusion in their claim that “the spatialintegration area of 0.5 degrees is specific to the depth discrimination system.” They go on, “Consequently, the finedisparity system seems to have a rather restricted spatial integration area, in contrast to the coarse disparity system, forwhich no spatial integration limit was found up to about 100 times this area.”

Based on these, and other ideas in the literature, this work will propose that two distinct mechanisms support depthperception in human vision. The first mechanism is limited to the diameter of the foveola, nominally a 1.2 degreediameter, centered on the point of fixation True stereopsis, and image fusion, is achieved within this area by means ofa two-spatial-dimension parallel processor (cross-correlator). This correlator is associated with the analytical mode ofvision and is found within the perigeniculate nucleus of the thalamus (Section 15.6.2).

The correlator of the PGN is more than just a single 2-D cross-correlator. It is more properly called a two-spatial-dimension associative processor. It can cross-correlate information within regions smaller than the total extent of thecorrelator space, as well as correlate over the entire space. The first leads to what will be discussed below as localcorrelation and the latter will be described as global correlation.

The two-spatial-dimension associative correlator plays a major role in version, vergence and accommodation. It is atthe very heart of the precision optical system, POS. Defining the performance of a specific element within this multiple-closed-loop servomechanism, is difficult. Therefore, defining the performance of the correlator alone, with respect toone of its major tasks, is difficult. Similarly, defining its overall performance is extremely complicated. Theperformance of the individual loops containing the correlator is somewhat easier. Different aspects of the performanceof the 2-D associative correlator of the PGN will be developed at several places within this work.

The limiting performance with respect to version precision is better than 0.1 degrees. The limiting performance withrespect to vergence precision is better than one second of arc. The limiting performance with respect to accommodationprecision is less well defined.

The second mechanism is associated with the peripheral retina and its projection to the LGN of the thalamus (andpossibly the further direct and retro projections to the occipital lobe of the cerebral cortex, see Section 15.6.5). Thespatial area associated with this mode exceeds ten degrees and probably includes all of the binocular field of view.Section 17.4.4 will show the quality of depth perception is one or more orders of magnitude poorer than for the stereopsisregion.

The spatial demarcation between the first and second mechanisms is generally related to Panum’s Limit (although thislimit may need further definition as suggested by Richards314). Tyler & Julesz describe a significant difference inlimiting noise performance with respect to these two mechanisms. They also describe a different relationship betweenstimulus size and disparity for these two mechanisms.

These considerations lead to the definition of coarse and fine regions of depth perception and both local and globalregions of stereopsis as defined in the above figure. The fine region of depth perception relates directly to the mechanismof stereopsis and is associated with the analytical mode of vision. The coarse region of depth perception does not relyupon stereopsis and is associated with the awareness (and alarm) mode of vision. Within the region of stereopsis, theglobal region relates to the overall extent of the three-dimensional field that can be processed by the two-dimensionalcorrelator of the PGN. This region is limited by the field of view of the foveola. The local region of stereopsis refersto the range of correlation associated with a specific point within the spatial range of the two-dimensional correlator.It is directly associated with the precision of depth perception achievable by the visual system. In the mathematics ofstereopsis, these terms have a different connotation. The global value of the stereo-optic function describes the meandistance to the point of fixation of the foveal field of view. This function is the sum of the integrals associated with eachof the individual local stereo-optic integrals associated with each element of the foveal image.

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315O’Shea, R. & Corballis, P. (2003) Binocular rivalry in split-brain observers Invest Ophthalmol Vis Sci (inpress)316Pettigrew, J. (2001) Searching for the Switch: Neural bases for perceptual rivalry alternations. Brain Mindvol. 2, pp 85-115317Laing, C. & Chow, C. (2002) A spiking neuron model for binocular rivalry J Comp Neurosci vol. 12, pp 39-53

The precision of depth perception falls rapidly as the selected point approaches the edge of the stereopsis space due tothe limited correlation range available near the edge. This function is shown in [Figure 7.4.5-2]. Beyond the edge ofthe foveola, the precision of depth perception is quite low and difficult to measure.

7.4.1.1.2 Fusion & rivalry differ in foveola and peripheral vision

The phenomena of fusion and rivalry have been widely studied. However, the studies have been largely psychologicallybased and have not involved physiology directly. The studies have generally followed the assumption that fusion andrivalry were centered in the occipital lobe of the cerebral cortex. More recently, these studies have begun to focus onfusion and rivalry as phenomena associated with the midbrain315. Pettigrew confesses to a recent epiphany regardinghis thoughts on rivalry316. His article is quite extensive and defends his new position that rivalry is not centered on theoccipital lobe as he so forcefully argued for more than thirty years. However, he did not describe the physiology of thehuman visual system, or the portion of the retina to which his discussions relate. His figure 2 provides a histogramdescribing the rivalry alternation rate in Hz for a few “bipolar patients” (manic depressive disorder) and many normals.Typical values are between 0.25 and 0.8 Hz (4000 to 1,200 msec). The lower value does not differ greatly from thetypical quiescent interval between saccades during reading (Chapter 19).

The findings of the above investigators agree with the model of this work developed in the following sections and inChapter 15. In this model, stereoptic fusion and stereoptic rivalry relate to the the analytical channel of vision, thefoveola and the perigeniculate nucleus (PGN). Binocular fusion and rivalry occurring outside the foveola relate to theawareness channel, the peripheral retina and the lateral geniculate nuclei (LGN’s). The role of the occipital lobe infusion and rivalry outside the analytical channel is not addressed in this work.

Of specific importance is the fact that fusion and rivalry are phenomena related to two different fundamental mechanismsassociated with the foveola (analytical channel of vision) and the peripheral retina (awareness channel of vision).Designing any laboratory investigation to account for these differences is very important. In the O’Shea & Corballisstudy referenced above, the stimuli were applied outside the foveola. However, the authors did not express any distinctreason for adopting that test configuration. They review several extant theories regarding binocular rivalry. They alsostudied two subjects who had their corpus callosa severed for medical reasons. While they expected their results on splitbrain subjects to point clearly to rivalry within the cerebral cortex, their conclusions were that the cerebral hemispheresdid not play a major role in binocular rivalry. They concurred with the suggestions of several other recent researchersthat rivalry was a phenomenon of the midbrain. They noted that their conclusions, and those of others, placed theirexperiments outside the scope of current rivalry theories. Section 15.2.7 shows the presence of a corpus principia thatwas not severed in the subjects examined. That section also discusses the role of the thalamic reticular nucleus in suchrivalry phenomena.

Current methods of studying rivalry can be described as traffic analysis studies. That is the term used by cryptoanalystswho initially study traffic patterns to learn the source, intermediate points and terminal points of radio traffic. In mostpsychophysical experiments, a stimulus is applied to the retina and a signal is sought in the cortex that relates to thatstimulus. No information is collected concerning any other locations between the retina and the occipital lobe wherea similar signal might be obtained. Thus, no assurance can be given that the signals were not processed at anintermediate location such as the PGN or LGN. In such cases, the occipital lobe may only act as a receiver of processedinformation and not as a feature extraction engine.

This work will not discuss binocular or stereoscopic rivalry at length. This is a high-level phenomenon that takes onmany guises in the absence of a detailed physiological model. To begin to understand it, the literature must be sortedwith respect to foveola versus non foveola participation. It must then be categorized with respect to the type of stimuliused. Since the data obtained is traffic analysis data, determining the latency of the detected signals relative to the timeof stimulus is also important. The time constants of the various stages of the visual system must be accounted for. Onlythen can the results of various investigators be correlated. Laing & Chow have discussed some examples of rivalry onpage 49 of their largely conceptual and mathematical paper317.

The recent inauguration of fMRI techniques to evaluate rivalry is quite interesting. The experimental protocols reported

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318Polonsky, A. Blake, R. Braun, J. & Heeger, D. (2000) Neuronal activity in human primary visual cortexcorrelates with perception during binocular rivalry Nature Neuroscience vol. 3, no. 11, pp 1153-1159319Tong, F. & Engel, S. (2001) Interocular rivalry revealed in the human cortical blind-spot representationNature vol. 411, pp 195-201320Blakemore, C. (1969) Binocular depth discriminaton and the nasotemporal division J Physiol vol. 205, pp471-497

specifically omit the foveola from the stimulus pattern318,319. This may be because stimulation of the foveola does notresult in any recognizable fMRI pattern at the occipital lobes. Such a conclusion is in accord with the predictions of thiswork. Rivalry, and the accompanying fusion phenomenon, related to the foveola occurs within the PGN/pulvinar couple,not within the LGN/occipital lobe couple.

In the recent fMRI experiments, very complex, and very large dichoptic imagery were used. Checkerboard patterns, withsquares one degree on a side, and sinusoidal patterns, at less than one cycle per degree, were used. These suggest thequalitative nature of signal processing in the peripheral retina. Simpler test stimuli, such as that used earlier by Hubelshould be adequate. They would also provide data that was easier to interpret. However, the resulting signal to noiseratios may be too low for current fMRI techniques. The fMRI technique remains too slow to provide any latency dataconcerning the arrival of signals at the occipital lobe following stimulation. VEP techniques appear to remain the onlynon-invasive techniques able to provide latency information to augment the simple traffic analysis information providedby fMRI.

O’Shea is maintaining a current bibliography on binocular rivalry at http://psy.otago.ac.nz/r_oshea/br_bibliography.html.

Fusion will be discussed in Section 7.4.5 as it relates to the analytical channel of vison, the PGN and the mechanism ofstereopsis. It will not be discussed from the perspective of the awareness channel, the peripheral retina and the LGN’s.

7.4.1.2 General physiology and operating modes associated with binocular vision andstereopsis

This work will only address the framework and first order mechanisms of depth perception. To accomplish the necessaryanalysis, a detailed model of vision is needed.

The most well recognized forms of depth perception involve:

1. Stereopsis associated with fixed objects imaged on the foveola.

2. Mechanisms associated with fixed objects imaged on the retina beyond the foveola.

3. Mechanisms associated with moving objects imaged on the peripheral retina.

4. Mechanisms not involving any of the above mechanisms; cues such as scale changes between familiar objects.

Much of the scientific literature omits discussion of the third category. However, the angle-rate information associatedwith such objects plays a large part in determining their perceived relative distance from other objects in the field ofview. Blakemore has discussed categories 1, 2 & 4 in some detail and taken particular care to avoid cues of the fourthtype320. He introduces some discussion of the neuroanatomy of the visual system. However, he did not recognize thepresence of the foveola, and any elements associated with it, when discussing the performance of the visual system. Hedid incorporate many ideas of Ogle in the discussion.

The most important cues generally involve context, scale and angle-rate information. Clearly, a red spot in a generallyuniform green field is a context worth investigating. It might be food.

The following discussion will depend heavily on the material of Sections 15.3, 15.6, 15.7 and 17.8, and particularly[Figure 15.6.5-8 ]. Figure 7.4.1-6 is a greatly simplified form of that figure. It is focused primarily on the responsesof the system to changes in stimuli in object space. Although eliminated from this figure, the crucial role of time delayalong the various paths should not be overlooked in the following discussion.

As reviewed in Section 7.3.1, the visual system supports a variety of operating modes. Some are autonomous and some

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Figure 7.4.1-6 A simplified pointing schematic based on the revised Functional Diagram of human vision, ca 2002, inSection 15.6.4. It shows the TRN in its role as the central control point of vision. It also stresses the paired nature ofmany functional elements of the visual system. Signals from the retina are separated into three groups. Those relatedto the foveola pass to the Analytical Channel. Both monocular and binocular signals from the peripheral retina pass tothe LGNs. The figure shows information signals passing to the right through the TRN. It also shows instructionspassing down through the TRN and control signals passing to the TRN. The heavy lines from the PGN/Pulvinar couplepassing through the Superior colliculus and the Oculomotor couple to the eyes represent signals within the PrecisionOptical System. The diagram is compatible with dual mechanisms of depth perception and shows only abstractinstructions being transmitted to the SC/cerebellum for implementation as commands.

are sympathetic.

In this figure, the chiasm is shown in two places for convenience. The two nerves from the chiasm labeled binocularare meant to represent the combined output from both eyes that represent their common field of view in one field. Thetwo nerves from the chiasm labeled monocular are meant to represent the output of the one eye that has no counterpartfrom the other eye.

In this figure, each occipital lobe consists of two areas, the dorsal area above the calcarine fissure and the ventral areabelow the calcarine fissure. The resulting signals passing to the parietal cortex via the TRN consist of five distinctcommissure representing the four quadrants of the peripheral retina and the one high acuity region of the foveola.

The fact that the photoreceptors of the foveola are not processed within the LGN/occipital lobe couple is confirmed bythe work of Polonsky, et. al. and Tong & Engel referenced above. The signals from the foveola are not passed to theoccipital lobes in high acuity form. To measure responses in the occipital lobes using fMRI techniques, stimuliilluminating the peripheral retina was necessary.

7.4.1.2.1 Major features of the Functional diagram and schematic related to version andvergence

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The figure shows that the visual field is divided into three classes of object space. It also seeks to show the signalprocessing is organized similarly. The field imaged onto the foveola is very small. The information from this field isprocessed at high spatial resolution within the analytical channel by the PGN/pulvinar couple. The phenomenon offusion is a feature of the processing carried out in the PGN/pulvinar couple. The large binocular field in object spaceis processed within the two portions of the awareness channel. These areas merge the images from the two retinas.However, the merging mechanism is different from the fusion mechanism of the PGN/pulvinar. Finally, the peripheralmonocular areas are also delivered to the LGN/occipital couple. These areas are entirely independent of each other. Theinformation from the monocular, binocular and foveola areas are passed to the parietal lobe. The signals from thePGN/pulvinar to the parietal lobe are by far the most complex and are represented by multiple signal lines in parallel.These lines project complex percept vectors associated with each object in the field of view of the foveola. These vectorsdescribe many properties of the individual objects, such as position in three dimensions, orientation, and detailed shape.Whether the saliency map is stored within a specific region of the brain or is distributed within it is unknown at present.This question will probably be answered within a few years using the new imaging techniques now available.

A feature not normally found in diagrams of this type is the thalamic reticular nucleus. This thin layer virtuallysurrounding the thalamus is being recognized as most likely the primary control mechanism of the neural system, at leastin higher primates. It plays both a supervisory and control role. The supervisory role involves observing the signalsbeing passed through it. The control role involves switching the paths that signals follow based on instructions from thehigher cognitive centers. Further discussion of this role will be found in Section 15.6.

The superior colliculus, and for more complex signals the cerebellum as well, act primarily as coding and decodingcenters for the brain. The decoding role is emphasized in this figure. They are primarily involved in receiving brief highlevel instructions and converting those into more detailed commands that can be distributed to the muscular-skeletalsystem for implementation.

7.4.1.2.2 Key features of the Precision Optical System

The figure highlights the elements of the POS by darkening the lines on the left side of the drawing connecting them.To achieve maximum performance in a variety of tasks supported by the POS, it does not include any elements of thecerebral cortex. The delays related to the projection of signals to these parts of the CNS are inordinately large.

The POS includes the photoreceptor elements of the foveola connected directly to the PGN/pulvinar couple withoutsignificant processing within the neural circuitry (stage 2) of the retina. The PGN/pulvinar provide pointing instructionsdirectly to the superior colliculus for decoding into pointing commands. These pointing commands are delivered directlyto the oculomotor nuclei. The nuclei in turn deliver them directly to the appropriate oculomotor muscles. This signalflow provides the minimum possible delay within the POS servoloops. When examining reading, and other highlystylized visual functions, it can be shown that even these minimal delays are a hindrance. To reduce the delay further,a set of default actions is programmed into the repetitive functions related to these tasks (Section 19.8.2).

The PGN contains a unique two-dimensional correlative cross-correlator used in many feature extraction andidentification operations. This correlator provides raw signals related to the primitive features of images projected ontothe foveola. After passing to the pulvinar, these primitives are interpreted (in real time) into signatures previouslyassociated with recognizable objects through training (experience). The presence of primitives that cannot be recognizedcauses the POS to enter a default training loop. This loop is much slower than the normal process loop and frequentlyinvolves the cerebral cortex in the training exercise.

7.4.1.2.3 Signal paths associated with version and vergence

The figures of Section 7.3.1 show the signal paths and plant accepting version and vergence inputs from the neurologicalsections and operating modes associated with pointing. The gross instructions intended for purposes of pointing the linesof fixation are generally represented in conjugate form. The pointing system accepts these instructions and generatesthe appropriate commands in the same conjugate form. These commands cause the eyes to rotate in the same direction.The degree of rotation can be quite large.

The instructions intended for purposes of converging the lines of fixation at a given distance from the subject aregenerally represented in disjunctive form. The pointing system accepts these instructions and generates the appropriatecommands in the same disjunctive form. These commands cause the eyes to rotate by small amounts in oppositedirection.

What is not shown in the figures of Section 7.3.1 is the extensive use of memory in supporting these functions. Theprevious figure and Section 15.6.5 develop the important role of memory associated with the LGN, the PGN and the

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321Howard, I. (2002) Seeing in Depth: Volume 1, Basic Mechanisms. Toronto, Canada: I. Porteous322Howard, I. & Rogers, B. (2002) Seeing in Depth: Volume 2, Depth Perception. Toronto, Canada: I. Porteous

superior colliculus. The importance is so great that these individual elements are redefined within individual couplescontaining a feature extraction element and a memory element.

Significant elements of very short, short and long term memory are involved in the operation of the version, vergenceand accommodation functional overlays. The saliency map and much of the memory associated with the pulvinar,superior colliculus and cerebellum are obviously long term memories. However, the pulvinar and possibly the superiorcolliculus also appear to incorporate short term memory elements associated with assembling interps and percepts.

7.4.1.3 Forms, cues and protocols of depth perception

Depth perception has been studied intensely for a very long time. The literature is immense. It includes considerableminutiae collected under less than precise circumstances and often difficult to place in proper context. Howard321 andHoward & Rogers322 have recently provided a massive compendium on the subject of depth perception. However, theiruse of the word mechanisms is quite different than here. Their mechanisms are largely conceptual and based on non-invasive observations of a very complex “black box.” In this work, the term is used only when describing much moredetailed operations based on physiology and electrophysiology.

It is difficult to separate the forms of depth perception, the cues found in depth perception and the test protocols neededto describe various phenomena distinctly because of their complexity and intertwined relationships. Several authors haveattempted to organize this group of materials. Howard has provided a framework separating cues based on monocularand binocular vision. Based on this work, a better framework contains three classes of depth perception based on thefield of view related to monocular, binocular and foveola vision. Noting that this three level framework is hierarchaland not exclusionary is important. Most monocular aspects of depth perception also occur in binocular vision. Similarlythose cues found in monocular and binocular vision are not constrained from being present in foveola vision. Notingthe great loss in spatial performance with angle from the line of fixation due to the wide angle lens group is important.This is a particular problem in human eyes.

Figure 7.4.1-7 provides an alternate to the figure of Howard (vol. 1, pg 5) using as much of his terminology as practical.However, the term stereopsis is used more restrictively here. Stereopsis is the term used to describe the perception ofdepth within a scene in object space projected onto both foveola (and only the foveola) simultaneously. This scene isperceived by the two eyes as one. It is said to be fused. The perceived depth of various individual objects in the sceneis represented veridically. An object represented veridically is perceived to have a depth relative to a reference surfacein the field that is proportional to its difference in vergence relative to the same surface. Objects in the scene imagedonto the remainder of each retina from areas observed binocularly are not observed veridically. In fact, the quality ofthe perception of depth is typically two orders of magnitude or more, lower than for stereopsis within the foveola. It isso poor it is usually described only as qualitative depth perception. Because of this feature, this work describes theimages obtained binocularly as being merged within the neural system rather than being fused. Finally, the monocularfields associated with each eye can evaluate a variety of cues, but only at a qualitative level. This level is even lowerthan for the binocular field. The loss in performance is due to the further decrease in performance of the optical systemat angles greater than fifty degrees from the axis.

The various types of cues are discussed extensively in Howard and Howard & Rogers. See pages 3-5 and section 4.6.5in Howard and chapters 24-29 in Howard & Rogers. Their presentations are based primarily on psychological testingand analysis. A single framework encompassing all of the terms used to define cues could not be found in this material.As a result, the lower classifications of cues are not mutually exclusive, appear to overlap significantly, and appeararbitrary in their classification. They will not be discussed in depth here.

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323Tyler, C. (1983) Sensory processing of binocular disparity, Chapter 7 in Schor, C. & Ciuffreda, K. ed.Vergence Ey Movements, London: Butterworths

Figure 7.4.1-7 A Re-classification of cues found in depth perception from Howard. Veridical depth perception is at leasttwo orders of magnitude more precise than qualitative depth perception. The subtitles show considerable overlap dueto their largely conceptual definitions. See text. Compare with Howard, 2002.

Personal observation is that qualitative depth perception relies as much, or more, on cues than it does on the processingof local vergence values associated with an object in the image. Improvements in the classification of cues could leadto considerable improvement in the protocols used to evaluate the response to these cues.

7.4.1.4 Overview of theories of binocular and stereo-optic vision in the literature

It is difficult to discuss other theories of binocular and stereo-optic vision in the absence of a firm combinedphysiological and psychophysical basis. As a result, most of the discussion of the literature will be delayed until Section7.4.5.4.1.

Tyler has provided a brief discussion of the various theories of binocular and stereoptic vision found in the literatureca 1983 in Schor & Ciuffreda (S&C)323. While he does discuss binocular (S&C pg 216), stereoptic (S&C pg 244) and“other” (S&C pg 250) theories of depth perception, he does not differentiate clearly between the binocular and stereopticmodes with respect to retinal fields of view. He briefly discusses the previous conceptual theories of binocular vision.Three of these were developed in the 19th Century and one dates from 1935. Tyler noted the exploratory nature of thevarious theories of stereopsis and fusion (pg 245, first line). He pointed out that “great plausibility” and “explanatoryrange” are predominant features in the published analyses of stereopsis. These features are shared with the lack ofdefinition between binocular depth perception and stereopsis within the foveola.

Tyler makes four points related to his general discussion of stereopsis.

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324Tyler, C. (2004) Binocular vision In Tasman, W. & Jaeger, E. eds Duane’s Foundations of ClinicalOphthalmology Chapter 24325Schwartz, R. (1994) Vision: Variations on some Berkeleian Themes. Oxford: Blackwell326Berkeley, George (1709) An Essay Towards a New Theory of Vision http://psychclassics.yorku.ca/Berkeley/vision.htm 327Pizlo, Z. (2008) 3D Shapes. Cambridge, MA: MIT Press

1. Neurophysiological experiments point strongly to the existence of special-purpose mechanism supporting thisfunction.

2. There is substantial psychophysical evidence for the existence of these special-purpose mechanisms.

3. Special-purpose mechanisms are an efficient method of network operation.

4. Current models of non-stereoscopic cortical function also strongly point to the existence of special-purposemechanisms.

The conceptually defined series of special-purpose mechanisms defined by Tyler, in his figure 7.2.2, appear tocorrespond to the feature extraction engines of this work. Their output is stored in the saliency map developed in Section15.2.2. The model portrayed in that figure and attributed to Nelson is entirely open loop. Such a model cannot explainthe origins of the neural signals found in the visual system. Nor does an open loop analysis lead to the mechanism offeature extraction used in the visual system.

Tyler has recently prepared a new chapter on the various aspects of stereovision aimed at a clinical audience324.

7.4.1.4.1 Recent papers on stereo vision from psychology laboratories

The psychology community appears to have struggled to avoid physical facts, particularly with regard to the physiologyof the visual modality in its entirety.

Schwartz provided a very learned but nearly incomprehensible volume in 1994 focusing entirely on the geometry ofthe stationary eyes (no tremor or microsaccades)325. The entire volume was his interpretation of the thesis of Berkeley,an early 18th Century philosopher of wide scope but very little depth with regard to vision. Relying upon the staticgeometry of the eyes and the eyes in conjunction with multiple targets at different positions in the external field of view,Berkeley hypothesized that the human could not determine the distance to an object immediately326, “It is, I think, agreedby all that distance, of itself and immediately, cannot be seen. For distance being a Line directed end-wise to the eye,it projects only one point in the fund of the eye, which point remains invariably the same, whether the distance be longeror shorter.” In subsequent assertions he asserts that the system can estimate distance to an object by determining thevergence angle of the two eyes. He did not consider the challenge of determining the distance to multiple objects inobject space during the time the vergence angles of the two eyes remains constant. While a rational position for the 18th

Century, the introduction of tremor and the computing power of the brain into the discussion provides an entirelydifferent hypothesis that is more viable (Sections 7.4.5 & 7.4.6). No physiologist or neurologist participated in or wascited in the preparation of Schwartz’s book.

Pizlo and colleagues have presented a variety of papers from a purely psychology laboratory perspective. These havegenerally ignored completely the physiology of the visual modality and the immense importance of memory in humanvision.

Pizlo presented a book in 2008 based entirely on the concept of “recovering” 3D imagery from a single 2D imageprojected onto a single retina327. While possessing two PhD’s in engineering, he notes in the introduction, “I did notinclude a treatment of the neuroanatomy or neurophysiology of shape perception.” That was followed by “The textconcentrates on the discussion of the main concepts; technical material has been reduced to a minimum. This makes itpossible to tell the ‘story of shape’ without interruption.” His six goals stated farther down page xii appear difficult toachieve based on the above constraints. The opening paragraph on page xiii seems highly implausible based on theabove framework. While Pizlo did cite one paper by McKee (from 1990), he did not cite any of the work of Tyler.

He distinguished between recovering information about the 3D image from “reconstructing” the 3D image in perceptionspace. His discussion was entirely geometric and employed “symmetrical” objects. He did not introduce any operationalfeatures of the visual modality other than to note the hyperacuity encountered in 3D vision compared to the expectedacuity based on the physical size and spacing of the photoreceptors of the retina (and no field lens due to the curvatureof the outer retinal surface). His figure 3.13 is incompatible with the hyperacuity he encountered. He does explore the

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328Li, Y. Pizlo, Z. & Steinman, R. (2009) A computational model that recovers the 3D shape of an object froma single 2D retinal representation Vision Res vol 49, pp 979–991329Pizlo, Z. Li, Y. et al. (2010) New approach to the perception of 3D shape based on veridicality,complexity, symmetry and volume Vision Res vol 50, pp 1–11330Li, Y. Sawada, T. et al. (2011) A Bayesian model of binocular perception of 3D mirror symmetricalpolyhedra J Vision vol 11(4), pp 1–20

work of Gibson and the work of Marr but primarily in conceptual language. Pizlo did not address the horopter of humanvision, any aspect of retinal image motion due to tremor, or the photoreceptors as change detectors. Interestingly, hedid not address the high percentage of people who are essentially naive and untrained with respect to stereopsis. Hisreconstructions relied upon a Simplicity Principle (page 37). “The Simplicity Principle is incorporated in perceptualmechanisms in order to make up for information lost due to (i) the projection from the distal to the proximal stimulusand (ii) the presence of noise in the visual system.” He explains this principle further on page 171, “According to this(Gestalt) principle, the shape most likely to be perceived is the simplest possible interpretation of the ritinal shapeproduced by a 3D object ‘out there’.” There is no guarantee (or even high probability) such a shape is veridical withthe actual distal shape. Even to support the simplicity principle, it was necessary to adopt the “figure-groundorganization” of page 27. Figure-ground organization “refers to the fact that closed contours establish special closedregions in the percept that correspond to objects in the visual scene. These regions which were called ‘figures’ areperceived as lying in front of the ‘background.’” A corollary to this figure-ground organization is that the contoursalways belong to the objects (figures), never to the background.” An additional concept introduced by Pizlo involves“shape constancy” (page 3). “Formally, ‘shape constancy’ refers to the fact that the perception of the shape of a givenobject remains constant despite changes in the shape of the objects’ retinal image.” Shape constancy in this definitionis strangely unassociated with the learning and memory functions of the human neural system that contributes so greatlyto the overall perception process. His assertion that “Shape constancy has profound significance because the perceivedshape of a given object is veridical (the way it is ‘out there’) despite the fact that its shape on the retina . . .has changed.”is undoubtedly true but the number of hidden variables and mechanistic processes within the overall shape constancyconcept is quite large.

Pizlo did address the difference in definitions and standards encompassing the words theory, model andexplanation over the years (his section 3.3.1).

Li, Pizlo & Steinman328 presented a paper in 2009 that also focused on the projection of a 3D image onto a single retinaand attempted to show how a recovered 3D perception could be obtained through purely geometric computations. Theystress the veridicity of the results in their assertion that the subject perceived the object as “out there” in space.Veridicity is commonly found in the psychology literature as a synonym for veracity when applied to a perceived visualimage. Their computational model contains no elements of the physiology or electrophysiology of the visual modality.As in the book by Pizlo, their recovery of a veridical perception relied upon a simplicity principle.

Pizlo, Sawanda et al329. presented another paper, labeled a mini review, in 2010 that was primarily a bridge to their 2011paper, Li, Sawada, et al330. This paper adopted a different thesis, based on the use of both eyes, and described two majorexperiments. The first employed physical objects. The second employed images prepared on a 3D class flat screen HDtelevision monitor of large size. As a result, the subject actually scanned across a wide field in order to make judgementsabout relative distances to various points of light or object features. These investigators again noted the hyperacuity oftheir subjects compared to the expected resolution of a fixed retinal matrix. The importance of this hyperacuity isdiscussed in the following section based on the findings of Yarbus.

They noted that all of their subjects had “normal vision” and that only one of their subjects was naive about thepurpose of the tests. There was no discussion of, or data confirming, what they considered normal vision. Touse knowledgable subjects in a series of experiments so dependent on human memory seems unusual. Even thenaive individual had a wealth of experience in 3D imaging defined by his age.

Their experiments involved dot separations on the order of three degrees. This value suggests their experiments wereoutside the range of the normal human horopter for optimum disparity measurements and/or the subjects were allowedto scan a large flat field in order to perceive the dots separately. Their summary and conclusions discuss multipledifferences between their results and those of others based on similar experiments. Neither set of experiments wereachieved using adequate protocols based on the known physiology of the human visual system.

The above works suggest the deductive nature of the current vision work in the psychology community related tostereopsis. While the concepts discussed above can be described as rational they appear largely irrelevant; they lack

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331Harris, L. & Jenkin, M. (2011) Vision in 3D Environments. NY: Cambridge Univ Press

any foundation in the physiology of vision available from more inductive analyses. They also fail to make a distinctionbetween stereopsis based;C entirely on relative motion in the peripheral field of view,C entirely on parallax–based vergence calculations and C higher level neural calculation based on time differences derived from tremor.

The latter form of stereographic vision is defined as true stereopsis in Section 7.4.5.1. McKee makes specific note ofthis difference in his 1983 paper discussed in that section. Stereopsis provides the high precision disparity values anddisparity range found only within the 1.2 degree diameter field associated with the foveola.

Harris & Jenkin edited a book based on a workshop in Toronto in 2011331. The organization of the work is well detailedon page 5. Two summary figures (fig 1-2 & 1-3, are provided with little supporting detail. They are reproduced below. While the work is an excellent source of examples of binocular vision and stereopsis, it is bereft of physiological detailsof the biological systems of vision. The attendees were primarily psychologists and those working in machine vision.Many geometric drawings are used to explain binocular vision. However, none of the papers reference either Yarbusor Ditchburrn and those investigators do not appear in the extensive index of cited authors.

An important indication of the maturity of the field as viewed by Harris & Jenkin is given on page 1, “the problem ofperceiving 3D shape and layout is a classic example of an ill–posed and under constrained inverse problem.” Aftermaking these assertions, they carefully caveat their individual statements concerning them. Their position is clearly theanalog of an inadequately educated audience in front of a magician. In the general case, biological 3D vision performsadequately within the normal environment. If the environment is abnormal; poor lighting, carefully obscured placementof mirrors, etc., the audience may fail to perceive the obvious.

The papers in Harris & Jenkin generally fail to address realistically the physiology that the authors claim to befamiliar with. They routinely rely upon the paraxial simplification of the optics of the eye introduced by LeGrandand by Gulstrand (Section 2.4 and particularly Figure 2.4.1-4) without realizing this simplification only appliesfor scene elements occurring at angles of less than 0.6 degrees from the point of fixation. The simplificationdepends on the approximation, sin(x) . x. They also fail to recognize the significant spatial non-linearity of theprojection of the external field onto the curved retinas of each eye (Section 2.4.2 & Section 15.5.3). Further, theyfail to recognize the major spatial transform introduced between the retinas and the striate cortex of the occipitallobe (Section 15.6.5). Most of these papers must be considered inadequate without a more robust descriptionof the physiology they claim they are attempting to emulate. Section xxx describes the net result of the spatialtransforms between the exterior field and the striate cortex of the monkey. A similar transformation appears tobe intrinsic to virtually all mammals,

Jenkins & Harris (page 1) describe the inverse problem as, “how to build a three–dimensional representation from suchtwo–dimensional patterns of light impinging on our retinas or the cameras of a robot.” Under constrained, the term theyemploy, is clearly associated with a lack of knowledge concerning all of the variables, and neural mechanisms, associatedwith the problem. From this conceptualization of the problem, they proceed to a discussion of how difficult the problemis. The text ignores any fine motion of the oculars associated with tremor, thereby implicitly ignoring any fine motionbetween the image projected on the retinas and the retinas themselves. Figure 7.4.1-8, their figure 1.3, illustrates thisimplicit assumption. No data points are provided and the area of most significance in human vision, distances on theorder of 0.5 meter, has been marginalized. The terms are not defined in this introductory figure in Harris & Jenkin. Themaximum just-discriminable depth threshold is recognized to be highly dependent on lighting conditions and the sizeand surface character of the individual figures in object space. Relative thresholds of less than 0.005 (fraction of meandisparity distance representing the minimum change in disparity recognizable) are seldom reported.

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Figure 7.4.1-9 has been significantly expanded from their figure 1.2. It now includes material from their psychologyschool on the right and an alternate description of 3D information extraction on the left based on the physiology of thevisual portion of the neural system. This physiology model is addressed extensively in this work. It is important to notethis psychology school focuses its attention initially on a single monocular representation of 3D object space. Thus, thedisparity between the two retinal images (a “hidden” variable) and disparity calculations using disparity are largelyoutside of the realm of psychology–based hypotheses of 3D information extraction. Figure 5.11 in Pizlo (2008) diagramsthe conventional thinking associated with this school. Only later is the disparity between the two 2D images projectedonto the retinas of the eyes during 3D operation, considered: see Chapter 2 in Harris & Jenkin (2011).

There is no physiological evidence for stage 4 signal manipulation (information extraction, such as identifyingfigures in a figure–ground conceptuallization) occurring within the stage 1 and 2 engines of the retina.

Figure 7.4.1-8 The just–discriminable depth threshold (detectable difference in depth as a fraction of viewing distance)for information provided by various cues. The area under each curve indicates when that information source issuprathreshold. Some annotation added; see text. From Cutting & Vishton, 1995, as redrawn by Harris & Jenkin, 2012.

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Figure 7.4.1-9 An overview of 3D Information Extraction from two schools of thought. There is a large amount ofpsychology literature addressing 3D information extraction from a 2D image presented monocularly. It does not addressthe disparity between the two images presented in the binocular situation. The physiology literature is smaller but morerecent. It identifies the engines of disparity calculations and oculomotor optimization in detail. See text. PsychologySchool portion of figure from Harris & Jenkin, 2011.

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332Adamovic, J.(2004– ) Optical Illusions http://brainden.com/optical-illusions.htm 333Qian, N. & Andersen, R. (1997) A physiological model for motion stereo integration and a unifiedexplanation of the Pulfrich like phenomena Vision Res vol 37(12), pp 1683–1698

Pizlo describes a number of “principles” developed within this school to explain how 3D images are analyzed by amonocular view of the 3D object space (Section 7.xxx).

This psychology school has identified a large number of cues within a static 2D image that can be used to infer thecharacteristics of a 3D scene, as identified by Harris & Jenkin in this figure.. These cues cannot be relied upon however;reliance upon them leads to many illusions332 and misunderstandings that provide professional magicians with anexcellent living. These cues are heavily dependent on learning and memory (as suggested by the comments of Pizlo,page 45, relating to the maturation of the visual system in a young child who was maintained in a controlled environmentuntil about the age of 19 months when that level of control became impractical).

Another psychology school does address the subject of disparity between the two images presented to two retinasbinocularly. However, its analyses largely ignore the physiology of the visual system. The analyses are fundamentallygeometric optics. It has also largely restricted itself to analyses based on the narrow-field (less than one degree)representation of vision implicit in its use of the thin lens model of the visual system. This has resulted in a poorunderstanding of the location of the loci of the theoretical Vieth-Muller circle.

A third psychology school suggests it is providing a physiological model, but is actually proposing numerical modelsbased on a linearity assumption and complex correlation integrals outside the realm of neural computation333. Qian &Anderson note regarding their 1994 model, “while the spatial receptive fields of cortical simple cells can be modeledaccurately by Gabor functions the temporal responses of the cells are clearly not Gabor like. The integrated model wedeveloped using spatiotemporal Gabor filters is therefore not completely physiologically realistic.” They then presentseveral complex double integrals purported to represent the amplitude of the signal at “simple cells” found in theoccipital cortex (without any discussion of the neural paths leading to these simple cells. See Section 7.4.5.1.1.

Incorporating the physiology of the visual modality, and particularly the electro–physiology of the modality, leads toa much different model of 3D vision than that achieved to date based on the various psychology schools. The left portionof the figure describes the computational mechanism leading to cognition of 3D imagery. Upon recognizing that thephotoreceptors act as change detectors, and not imaging detectors, the only other pertinent stage 1 feature is the delayas a function of illumination associated with the complete P/D equation (Section 7.2.4). This delay, normally presentand equal in both eyes, is not particularly important except potentially in the case of the Pulfrich Effect due to thestimulus intensity reduction in one eye. The stage 2 signal processing is of limited concern, except to recognize that theO, P & Q chrominance difference signals and the R-channel luminance summation signals are created in stage 2. Thesesignals are passed independently to the initial engines of the thalamus (sometimes labeled morphologically the pretectum)where they are processed separately in the lateral geniculate nuclei (LGN)and in the perigeniculate nuclei (PGN) insupport of foveal (qualitative) binocular vision and precision (stereoptic) binocular vision respectively. All of theprocessing between the disparity calculations and the information extraction operations occur within stage 4 signalmanipulation.

It is in the LGN that the disparity calculations are most obviously performed. The R–, O–, P– & Q– channel signals fromthe two left ocular fields and the two right ocular fields are processed pair–wise. The pair of R–channels are aligned withthe O–, P– and Q– channels so that any calculations can be readily compared between the layers or transferred to theother layers (Section xxx). It is at this stage that the coarse level mean disparity associated with a 3D object space isinitially determined. This mean disparity signal is used to optimize the ocular parameters associated with coarseconvergence, coarse accommodation and myosis (aperture control if appropriate). Subsequent to this coarse disparitycalculation and coarse oculomotor optimization, the PGN performs a similar calculation of precision mean disparityusing the signals from the foveola. These calculations provide a fine or vernier signal to the ocularmotor optimizationmechanism.

To minimize the analog calculation load, the oculomotor engines employ preset parameters, selected from thequiescent condition, or from a previous (a matter of tens of milliseconds) signal manipulation cycle.

Upon optimization of the ocular parameters (in an open loop mode), the calculation of the final binocular disparityparameters and the differential disparity parameters are calculated for each significant element (figure) in the 3Dfield.(within an accuracy determined by the signal to noise ratio of the individual channels). With these values in hand,

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334Cumming, B. & Parker, A. (2000) Local disparity not perceived depth is signaled by binocularNeurons in cortical area V1 of the macaque J Neurosci vol 20(12), pp 4758–4767335Prince, S. Cumming, B. & Parker, A. (2002) Range and mechanism of encoding of horizontal disparityin macaque V1 J Neurophysiol vol 87, pp 209–221336Prince, S. Pointon, A. Cumming, B. & Parker, A. (2002) Quantitative analysis of the responses of V1 neuronsto horizontal disparity in dynamic random-dot stereograms J Neurophysiol vol 87, pp 191-208

the LGN and PGN are able to fuse the various O–, P–, Q– and R– images and attach lateral and depth disparity values(as tags) to the signals describing the elements in the fused images. It is at this point that the visual information can beconsidered cyclopean (but with both lateral and depth disparity information attached to the amplitude informationassociated with a figure). The fused and tagged signals are then passed to the stage 4 engines responsible for furtherinformation extraction and delivery to the saliency map for access by the stage 5 cognition engines. The signals fromthe LGN are passed to the area 17, a.k.a. V1, of the occipital lobe (over relatively long and time consuming neural paths)while the signals from the PGN are passed to the adjacent pulvinar.

As confirmed in the conclusions of Cumming & Parker334, the process of binocular fusion has already occurred by thetime the cyclopean information reaches the occipital cortex (V1) from the LGN. They continued their analyses of V1signals without reaching a significantly different conclusion335. Subsequently, they transitioned to random dot patternanalysis and invoked and described in some detail the energy model of Ohzawa et al. (1990)336. They continued toconclud that much more work was required to demonstrate a role for V1 in binocular vision information extraction. Theydid not provide any schematic of how the signals from the retinas propagated to V1. Cumming & Parker did not arriveat any value for the range of qualitative (fovea–based) depth perception or precision (foveola–based) stereopsis basedon their studies. Results in this area will be discussed in greater detail when addressing the work of Allison & Howardin Section 7.4.7.4.

Information extraction at this point in stage 4 operations involves much more than just 3D perception. The informationstill exhibits a degree of scene-optic organization, although in a cyclopean format. Additional information is extractedin both V1 and in the pulvinar relative to the shading, texture, etc. are cues that are transferred to appropriate memorysites for future comparisons with other figures in 3D object space images (as suggested by the arrow pointing to the listof static cues on the right). Note, the term familiarity at the extreme lower right is a synonym for prior learning andmemorization and not a cue in itself. It should be noted that the quality of these cues extracted in the pulvinar areconsiderably better than those extracted in V1. The thalamic reticular nucleus (TRN) compares the signals returned fromthe pulvinar and the occipital lobe and transfers the best quality information to the saliency map associated with theparietal lobe.

In many cases, the information extracted in the pulvinar is transferred to the saliency map of the parietal lobebefore the original information even arrives at the occipital lobe for processing (a well documented oddity notexplained by earlier discussions of visual modality operation, Section xxx).

It is proposed that the inductive process of the physiological school, relying upon both the physiological andelectro–physiological databases to develop the details of the signaling chain leads to stronger null hypotheses andprotocols than the deductive approach of the psychology school based primarily on observation and behavioral studies.As noted, the focus on a monocular presentation, essentially eliminates disparity from any discussion of binocular visionand stereopsis.

The fact that the two images projected on the retinas contain different information, particularly regardingdisparity, is readily seen by observing a 3D HDTV presentation without using the required stereo-glasses. Thedepth disparity information is clearly observed to be represented by differential lateral disparities.

Interestingly, chapter 8, by Allison & Howard, introduces the concept of the change in disparity but only as applied tothe “cyclopean domain.” They define an interocular velocity difference (IOVD) signal as a change in disparity (CD)related to a single object moving in object space. They then introduced a binocular presentation, Figure 7.4.1-10, ofconsiderable utility to the discussions below. The information was introduced dichoptically, separate sources for eacheye using 45 degree semi–silvered mirrors (a Wheatstone stereoscope). There was no discussion of the linearity of thepresentations created using a pair of Tektronix 608 oscilloscopes. The nominal diameter of the foveola associated withprecision stereopsis and the diameter of the fovea associated with qualitative binocular vision are shown the the dashed

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overlays. Obviously, this protocol was not designed taking the physiological parameters of the retina in mind.Specifically the area of maximum stereopsis was not included in the test protocol except for purposes of maintainingvergence and convergence. The experiments with this presentation are discussed in greater detail in Section 7.4.7.4.

[xxx put words to this display Be sure it matches the caption of figure 8.2 ]The basic protocol is to present a stationary set of random dots to each eye in the upper half of the image whlemaintaining fixation on a single point and simultaneously presenting a set of correlated dots to each eye in the lowerportion of the field of view. The sets of dots projected to each eye in the lower portion can be moved about using adichoptic optical system. When correlated, the “opposed to-and-fro motion,” or lateral motions of the images projectedinto the two eyes are perceived as changes in depth of the merged dot sets.

Many experiments were performed using variants of this display. It is useful to note the expanse of this display. Thehorizontal width indicates no preference was given to the foveola as the region concentrating on stereopsis. The factthat only the fixation point and the two nonius lines were imaged on the foveola, suggests the experiments are not useful

Figure 7.4.1-10 Basic stimulus arrangement of Allison & Howard. The observer fixated the binocularly visible dot inthe center of the stimulus and monitored fixation via adjacent nonius lines (the left eye sees one line and the right eyesees the other). In one half of the stimulus (top in this example) was the test display, moving in opposite directions inthe two eyes at a given frequency and vlocity. For experiments using matching tasks, the oscillation of the correlatedcomparison image (bottom in this example) was adjusted by the observer to match the motion in depth of the teststimulus. The dashed circles have been added to signify the size of the foveola (1.2 degree circle) and fovea (8.7 degreecircle) in this non rectilinear representation. Modified from Allison & Howard, 2012.

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337Shipley, T. & Rawlings, S. (1970) The Nonius horopter– I. History and theory and II. An experimental reportVision Res vol. 10, pp 1225-1262 & 1263-199338Howard, I. & Rogers, B. (2002) Seeing in Depth. Toronto, Canada: I Porteous, Chapters 20, 24 & 25339Ogle, K. (1950) Op. Cit. pp 14-49

for evaluating precision binocular vision (stereopsis). The individual experiments will be addressed later in Section 7.4.5on stereopsis.

Recently, Pizlo called for a conference in 2013 to “help move our field forward, because substantial progress in any fieldis not possible without formal theories.” He called for a “focus on the role of mechanisms (vision algorithms)” instereopsis.

The work of the psychology community would be better served by protocols more firmly based on the physiology of thehuman visual modality as developed in Sections 7.4.5, 7.4.6 & 7.4.7 below. Recognizing the role of the photoreceptorsas edge detectors (Section 15.1.4.6) and the role of the perigeniculate nucleus/pulvinar couple (Section 15.6.3.5.1) increating the 3D perception within the brain would also be useful. An explanation of hyperacuity is readily availablebased on these roles. 7.4.1.4.2 The Yarbus Test as a critical hurdle for theories of fusion and stereoptic vision

An important criterion for any description or caricature related to vision is whether it passes the Yarbus Test. Yarbus,Ditchburn and others have shown that the visual system of chordates (demonstrated with humans) is blind in the absenceof motion between the retina and the scene in object space (Section 7.3.3.5.4). Such motion is generally provided bythe mechanism of tremor, the microradian amplitude angular vibrations produced by the eye muscles.

The requirement for such motion is due to the adaptation amplifier found in each photoreceptor cell. These amplifiershave a zero at zero frequency in their frequency response. That is, they cannot transmit a signal that is not changing withtime.

The result of the circuitry within the adaptation amplifiers is that the retina is not an imaging device. It is a changedetector. Thus, any light imaged on the retina must be either moving spatially or changing temporally if a signal is tobe generated at the output of the individual photoreceptor cells. The Yarbus Test incorporates these requirements.

The theories of fusion and stereoptic vision discussed in the above section do not pass the Yarbus Test and can generallybe disregarded for purposes of research. They will be examined in greater detail in Section 7.4.5.

7.4.1.5 Alternate interpretations of the horopter

The following material will be brief. The literature is so convoluted in this area that only a significant effort couldproduce a useful discussion here. Any serious reader of the following material should first read the history and theoryof the horopter of Shipley & Rawlings337. They claim “that investigators in this area have often been unclear as to whichaspects of their analyses were immutable physiological, contingent physiological, purely hypothetical and analytical,or empirical.” [emphasis in original] It appears this is just as true today. As an example, the 2002 text by Howard &Rogers, editors, titled Seeing in Depth, contains entire chapters based on the so-called paraxial approximation, orGaussian optics of the most elementary form338. The authors of those chapters fail to appreciate that the use of thisapproximation is limited to scenes within 1.2 degrees of the point of fixation. The simple form used also fails toincorporate Snell’s Law of optics. That law accounts for the differences in the optical index of refraction on the twosides of a lens. As a result, most of the figures in those chapters are only useful for pedagogical purposes at theundergraduate level. Much of the earlier material in the psychological literature suffers from these same shortcomings.

Ogle has presented a major discussion of the horopter as a phenomenon and as an instrument339.

Shipley & Rawlings go on to focus on another problem. “We see here the very core of the problem. Unlike the othersenses, it was felt that vision “exteriorizes: projects sensations outside of the self.” The fundamental geometry ofvergence discussions is based on the archaic Keplerian model that assumes that optical rays emanate from the eyes. TheKeplerian model completely ignores the laws of physical, and physiological, optics.

Schreiber, Tweed & Schor have provided an interesting analysis of the horopter that is entirely mathematical (and relies

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340Schreiber, K. Tweed, D. & Schor, C. (2006) The extended horopter: quantifying retinal correspondenceacross changes of 3D eye position J Vision (on-line) vol 6, pp 64-74341Tyler, C. & Scott, A. (1979) Binocular vision, Chapter 22 in Records, R. ed. Physiology of the Human Eyeand Visual System NY: Harper & Row. 342Howard, I. & Rogers, B. (2002) Seeing in Depth, Volume 2, Depth Perception. Toronto Canada: I Porteous,pp 20-26343Solomons, H. (1976) The three-dimensional space horopter Ophthalmol Opt pp 101-111

upon an approximation)340. Their field angles appear to be much larger than those associated with the fovea and theregion of high quality stereopsis of primary interest in vision.

An additional shortcoming in the psychological literature is the complete absence of any material reflecting findings inthe physiological literature of the last forty years. Because of the paucity of physiological models in the psychologicalliterature, investigators have adopted the policy of introducing a great variety of less than precise unique definitionsrelating to vergence, stereopsis and fusion.

7.4.1.5.1 The horopter as a physiological characteristic EXPANDxxxThe concept of the horopter is an ensemble of points in space where each point subtends an equal angle at the eyes. Thisdefinition includes the Vieth-Muller circle and a vertical line through the point of fixation.

The physiological horopter is a largely conceptual, and difficult to portray, characteristic. Most portrayals of the horopterare greatly simplified geometrical caricatures. They ignore the physiological characteristics of the eyes and therequirements of physical optics. The discussion of Tyler & Scott is one of the best for pedagogical purposes341. Howard& Rogers have also provided a readable description of the horopter342. A more theoretical discussion appears inSolomons343. While Tyler & Scott open with a definition of a horopter, their second paragraph discusses a range ofdifferent horopters based on details related to the definition. Their opening definition is a geometry “in whichcorresponding points on the two retinas are defined as being at the same horizontal and vertical (or monocular visualdirection) from the center of the fovea of each eye. (The rotation of the eyes must be taken into account, but may beconsidered identical when the eyes are in the primary, straight-ahead position.)” This definition is based on the Gaussian(or paraxial) assumption in optics. It completely disregards the actual conditions of physical optics (Section 2.4).

Howard & Rogers probably give the clearest definition of the horopter. They first define the point horopter as “the locusof points in space that project images onto corresponding points in the two retinas.” This definition is compatible withthe actual optics of the eyes but is incomplete. It should be extended to require the eyes to be fixated on a point in themedian plane of the head. They go on to subdivide this horopter into a horizontal (or longitudinal) horopter and avertical horopter. The horizontal horopter is limited to those points in space lying in the horizontal plane of regard. Thevertical horopter is limited to those points in space lying in the median plane of the head.

The caricatures defining the horopter invariably show various principal rays as straight lines between a point in objectspace and a point on the retina. Such a case is patently wrong, except within less than one degree of the line of fixation.However, the eyes are sufficiently symmetrical and the points of correspondence between the two retinas can still bedefined. [As an aside, there is evidence that the retinal arrangement of photoreceptors does not exhibit mirror symmetryas in most of the body of a bilateral animal. It appears the mosaics of photoreceptors in the two retinas can be overlaidat a very fine level of detail.] The caricatures also invariably fail to show the resolution capability of the physiologicaloptical system. At more than one degree from the line of fixation, the resolution capability of each eye declines rapidly.Additionally, the caricatures fail to delimit the portion of the Vieth-Muller circle describing the binocular field of view.Beyond about 51 degrees from the fixation point, the circle is irrelevant. Finally, as Tyler & Scott alluded to in the abovequotation, the conventional point horopter only applies to points of fixation along the perpendicular bisector of a lineconnecting the 1st principal points of the two eyes. As the eyes rotate, new Vieth-Muller circles must be drawn

With the above understandings, Figure 7.4.1-11 illustrates the geometry of a simplified longitudinal horopter useful forpedagogical purposes. Being an ensemble of points, it is formally known as the point horopter in the horizontal planeof regard. The figure does not show the rays from the point of fixation passing through the lens to the retina. They arenot straight extensions of the rays in object space except within about one degree of the point of fixation.

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344 See Ogle, K. (1950) for a discussion on the value and limitations of nodal points.

Figure 7.4.1-11 A horizontal horopter showing effect of accommodation and rotation of the eyes. The horopter is onlydefined within the binocular field. Note the significant difference in the surfaces of best focus of the two eyes. Notealso the difference in distance to the target, resulting in different magnifications in the images. These problems areaggravated for off-axis positions. Only the regions of the Vieth-Muller circle projected onto the foveola remain in goodfocus. This is the field of view where stereopsis and fusion occur. The center of the Vieth-Muller circle has moved withthe rotation of the eyes.

The caption to a similar figure by Tyler & Scott is instructive,

“For convergence at any distance other than infinity, all points that do not lie on the Vieth-Muller circle or the verticalhoropter line project to the retina with either a vertical disparity or both a vertical and horizontal disparity. Dashed linesshow geometric horopter for symmetric fixation. Dotted lines are construction lines. Full lines represent relevant lightrays. The vertical disparity arises from the differential magnification occurring when the point is closer to one eye thanthe other, as must occur with all points off the vertical axis. The three-dimensional point horopter is therefore not asurface, but two lines in space.”

Their comments were aimed at a horopter such as shown on the right when they say that the dashed lines only apply to“symmetrical fixation.” Tyler & Scott go into considerably more detail concerning asymmetrical fixation.

Several types of empirical measurements designed to confirm the theoretical point horopter have shown consistentdeviations. Tyler & Scott provide a good introduction to these problems.

7.4.1.5.2 The horopter as a test instrument

The basic non-invasive instrument for studying the operational performance of the POS and the physiological opticalsystem is the horopter. The general horopter is defined primarily conceptually. Conceptually, it derives from the Vieth-Muller Circle shown in [Figure 7.4.1-1]. This is a circle drawn through the 1st principal point (1st nodal point344) of thetwo eyes and “the natural fixation point” on an axis perpendicular to, and bisecting the line drawn through the twoprincipal points. The horopter is an instrument used to determine the disparity between scene elements. Thesedisparities describe the location of points in 3-D object space relative to a reference point. Such disparities can be theactual disparities associated with a scene or pseudo-disparities associated with a pseudo-scene created by an optical

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345Johnston A. (1971) Clinical horopter determination and the mechanism of binocular vision in anomalouscorrespondence Ophthalmologica vol 163, pp102-119 (DOI: 10.1159/000306329)

Figure 7.4.1-12 A simple horopter test set. Because of the scale involved, the “rods” are frequently replaced by taughtthreads. A handle is provided for moving each rod. The null position of these handles is randomly arranged in depthto avoid providing cues to the subject. The pins are ink pens that can be brought into contact with the paper to recordthe position of the rods.

instrument. They can also be the disparities determined by the visual system and found by measurement of the angularrelationships between the eyes when observing the actual scene (or pseudo-scene). More specific, and limited, horoptersare defined sufficiently to be fabricated and used in the clinic and laboratory.

Ogle has described a variety of horopters. Most of them are focused on the longitudinal (or horizontal) horopter. Thesecome in two distinct variants. The first is the simple (non reflecting) horopter. The second is the reflecting horopter orhaploscope (as defined originally by Hering). In general, the first type is so crude mechanically that it can only be usedfor qualitative measurements related to the peripheral retina. The second is better suited to measuring veridical disparityassociated with stereopsis. However, the instrument must be made with considerable precision if it is to providereproducible measurements at the arc-second level. Figure 7.4.1-12 shows one of the simplest non reflecting horopters.Its accuracy is limited as shown by the practice of using thin rods as test targets until the precision provided by thinthreads is required. Even the size and reflective properties of the threads cause accuracy problems. Because of thelimited capability of this type of test set, it is usually used initially to determine an apparent field of constant perceiveddepth. This parameter is usually labeled, rather inappropriately, the apparent fronto-parallel plane. The surface definedis never a plane. As shown earlier [Figure 7.4.1-2], this surface is not normally planar. It is not planar with respect tofocal conditions or depth conditions. The visual system is based on spherical geometry. Ogle attempts to define thisplane precisely. However, he resorts to two footnotes to incorporate all of the caveats in the definition. He also notesthe necessity of avoiding cues in the scene or test set that would skew the data. He even points out the necessity ofrandomizing the position of the handles used to adjust the rods used to establish the plane. Following adjustment of allof the rods by the subject, the platen could be raised to mark the position of the rods on graph paper.

The horopter shown can be modified by introducing a series of apertures immediately in front of the subjects eyes.

The description of a modern clinical horopter, used to measure steropsis performance, is difficult to locate in theacademic literature. Johnston provided some information345. Earlier equipments were usually based on the Howard-Dolman apparatus of the early 1900's, a simple viewing box able to measure the ability of a subject to establish hishoropter relative to the theoretical Vieth-Müller Circle. Both eyes have uninterrupted view of all of the test objects. Theangular field of view has never been standardized but tests beyond a 15 degree total field of view are unusual.

The Nonius Horopter is more sophisticated. It separates the view of the two eyes, and presents two separate sets of

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346Howard, I. & Rogers, B. (2002) Op. Cit. pp 20-40

Figure 7.4.1-13 A typical empirical horopter frequentlyused in pedagogy, with the so-called fronto-parallel plane(X,Y) defined. Frequently called a fusion horopter anddrawn without scales. The Vieth-Muller circle is drawnincorrectly. It should pass through the coreas of each eye.The 1.2 degree fields of view of the foveola have beenadded.

vertical lines to the subject. He is asked to align the upper set of lines viewed by one eye with the lower set of linesviewed by the other eye. See Shipley & Rawlings cited above.

The literature has not provided a concise list of definitions describing the many potential horopters. Howard & Rogersprobably provide the best overview and guide to the literature of simple horopters346. Most of these units candemonstrate the presence of qualitative depth perception under conditions of merging of the two images. This binocularmerging is not synonymous with fusion in this work.

The modern computer controlled horopter used for screening as part of a general eye examination provides a very narrowfield of view, estimated at 1.5 degrees or less. It effectively determines the subject’s depth perception on–axis, i.e. usingonly the foveola.

7.4.1.5.3 Representations of horopter data

Measurements designed to confirm the theoretical horopter generally do not. Significant systemic deviations appearrelative to the fundamental assumption on which the horopter is based. These deviations are frequently labeled theHering-Hillebrand deviations. Figure 7.4.1-13 shows the frequently reproduced conceptual figure of the empiricalhoropter dating from at least Ogle (1950). The deviation of the horopter from the Vieth-Muller circle is shown. Thefields of view of the foveola have been added for clarity. Describing the Hering-Hillebrand deviations precisely usinggraphs at this scale is difficult. It is also a bit embarrassing to point out that the versions of the figure by Tyler & Scottin Record (pg 656), by Tyler in Schor & Ciuffreda (pg 222), and in Howard & Rogers (pg 27) are drafted improperly.They all have the Vieth-Muller circle passing through the point of rotation of the eyes and the point of fixation. Sucha circle is more commonly known as the circle of equal convergence. The Vieth-Muller circle is defined with respectto the 1st principal point of each eye and the point of fixation. Although it is usually reproduced without attribution, theconcept appears to go back to Alhazen in the 11th Century (Howard, pp 50-52). Interest in it was only revived by Heringin the 19th Century. As usually reproduced, it is drawn without scales and any definition of the criteria used to draw it.Tyler, writing in Schor & Ciuffreda, notes that the form of the empirical horopter is not as shown in the figure undermany conditions. He demonstrated that it even changed in local areas depending on the nature of the stimulus used.

Tyler discusses the empirical horopter in terms ofPanum’s area. He then concluded with, “the traditionalconcept of Panum’s area as a fixed property of a givenretinal region must be abandoned.” This is clearly thecase. The situation will be discussed in greater detailbelow. The description of the empirical horopterdepends greatly on the geometry of the stimulus used, thecriteria used to define the limit, the light level andwhether the stimuli are presented dichotically ordichoptically. Failure to account for these parametersleads to much of the conflict found in the literatureconcerning Panum’s area.

Howard & Rogers lists fusion range (the range in x,ydimensions defined by Panum’s area), mid-fusional-zoneand maximum stereoscopic acuity as criteria for definingthe empirical horopter on pages 26-33. Ogle discussedfour criteria but only described them in contexts andprotocols (pp 29-49). One was the maximum differentialstereoscopic sensitivity. A second involved the sameprimary subjective visual direction (along the z-axis) fortwo threads in a horopter. He discussed several protocolsfor meeting this criterion. A third criterion involved thematch of the horopter to the apparent fronto-parallelplane. The fourth criterion concerned the center of theregion of “binocular single vision.”

Ogle (1950) proceeded to derive an additional

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347Tyler, C. & Scott, A. (1979) Binocular vision, Chapter 22 in Records, R. Op. Cit. pp 650-656348Tyler, C. & Scott, A. (1979) Binocular Vision, Chapter 22 in Records, R. Op. Cit. pg 649

Figure 7.4.1-14 Theoretical framework for displayingempirical horopter data. The Vieth-Muller circle is drawncorrectly and a series of ellipses from Ogle are also shown.The limits on the field of binocular vision are shown and thearea imaged by the foveola is highlighted. The potentialshift in the vertical axis of the horopter is also shown. Seetext.

mathematical framework for evaluating the empirical horopter against these criteria. His derivation employed twoparameters that describe the horopter when it is allowed to become a conic section rather than only a circle. The first,H, described the asymmetry of the Vieth-Muller circle. The second, R0, is always small and defines the difference inmagnification between the two eyes in the horizontal meridian. The precision in discussing the empirical longitudinalhoropter is greatly enhanced using his equation. It introduces a series of geometric horopters of which the Vieth-Mullercircle is only one.

Figure 7.4.1-14 provides an extended theoretical framework based on a correct Vieth-Muller circle, the equations ofOgle plus several other additions. Ogle’s equations introduced a series of ellipses transitioning from the Vieth-Mullercircle to the horizontal axis of the fronto-parallel plane through the point of fixation. With the parameter H = 0.0, theVieth-Muller circle is obtained. If H = 2a/b, where a is the inter-pupillary distance and b is the distance to the point offixation from the mid point of the inter-pupillary line, the horizontal axis is obtained. Intermediary values of H equateto intermediate ellipses as shown. One of these ellipses is particularly important because it corresponds to the surfaceof best focus for an equivalent “cyclopean eye,” or the actual eyes where a is much smaller than b. This ellipse will beimportant when looking at the data. The impact of the depth of focus of the visual system on horopter measurementssuggests the data in the literature may be skewed toward the ellipse of best focus unless precautions are taken.

Little data is available on the precise shape of the focalsurface of the human visual system in object space. Thevariable focal length with field angle of the design couldintroduce unexpected variations in the shape of thatsurface. Because the off-axis resolution of the systemdecreases so rapidly, the subject is largely academic. Itwill be assumed here that the eye is in optimum focus forall field angles when focused at infinity and that anyaccommodation changes the focal surface proportionallyfor all field angles.

The figure also includes the approximate limits (thedashed lines intercepting the ellipses) of the empiricalhoropter based on the binocular field of view. Finally, adeviation from the true vertical axis is shown. This smalldeviation of zero to two degrees is due to the Volkmann-Helmholtz Effect. This Effect is due to the relative tilt ofthe vertical axis of the eyes when they converge347. Thisis due to the non-orthogonal motions introduced by theoculomotor muscles. When aligned for vision at infinity,the Effect is negligible. At near distances, the Effect cancause the empirical horopter to tilt away from the eyesfor points above the horizontal by up to two degrees.

Finally, the figure includes the small circular area imagedby the foveola. This small area is the only area involvedin stereopsis. By expanding the image, this small area is clearly the only area of the horopter that lies in the fronto-parallel plane. It is also the area of maximum spatial performance of the physiological optics.

The data in chapter 4 of Ogle show that the actual horopter of an individual does not correspond to the Vieth-Mullercircle or the fronto-parallel plane. His figure 11 would suggest the “typical” empirical horopter at 40 cm correspondsalmost exactly with the ellipse of best focus (H = 1/b) rather than the Vieth-Muller circle. The data for several otherdistances to the point of fixation for this observer are shown in his figure 16. Tabulations of the value of H are alsoprovided for a group of subjects using a variety of test criteria. Tyler & Scott summarized this data but chose not to showthe data for six meters range, probably because it would have required more discussion348. The empirical horopterreversed curvature and became hyperbolic at six meters for the subject tested. While such a situation is not addressedin the simple conceptual horopter, the Ogle equation supports it for values of H greater than 2a/b.

The data clearly shows that the theoretical Vieth-Muller circle and fronto-parallel plane generally circumscribe, but do

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349Clement, R. (1985) The geometry of specific horopters Ophthol Physiol Opt. Vol 5(4), pp 397 -401,

Figure 7.4.1-15 Caricature of an empirical horopter basedon stereoacuity or on maximum to minimum distance ofperceived depth perception, relative to the point of fixation.See text.

not bound the empirical horopter. Their utility is mostly in introductory pedagogy. Ogle has shown that the empiricalhoropter can vary significantly with the precise parameters of the subjects eyes. Differences in the phoria of the subjectscan lead to significant differences in performance, at least using the Nonius (vertical bars arranged vertically anddisplaced horizontally) method of measurement (his figures 16, 22 & 23).

Ogle provides a definitive answer to the question of the median location of the empirical horopter but he says very littleabout the diameter of the horopter as suggested by the caricature in [Figure 7.4.1-9]. His figure 27 shows the regionof “binocular single vision” as expanding from about 5 mm about the point of fixation at 40 cm to about 7.5 mm at 12degrees from fixation. However, his table 5 suggests the mean variations of setting defining the empirical horoptervaried about seven to one for the two observers measured. This would suggest that the horizontal tube shown in thereferenced figure should flare to a much larger diameter near its ends than shown.

The question remains, what parameter can the empirical horopter display that will best describe the depth perceptionperformance of the visual system? One answer would be to describe the angular precision obtained by measuring thestereo-acuity of the subject. This would produce a grossly different empirical horopter from the conventional caricature.It would focus specifically on the difference between qualitative depth perception and stereopsis. Figure 7.4.1-15 showsa caricature of an empirical horopter that can illustrate two criteria. When based on the best available data and thecriteria of stereo-acuity, the tube drawn along the Z-axis has a length approximately 100 times the diameter of theempirical horopter drawn along the ellipse or the vertical axis. The range is similar when based on the criteria ofmaximum distance from the point of fixation to the edge of the perceived field of depth perception. The depth ofperceived depth perception is much greater within the field of the foveola than outside it. This figure provides a clearrepresentation of the difference between the region of stereopsis and the region of qualitative depth perception. Thevariation in depth perception outside the foveola using these criteria are so small, compared with that of the foveola, theycannot be shown easily on the same graph.

The above figure provides a framework for displaying arange of empirical horopter data. It also shows the greatdifferences involved in discussing stereopsis andqualitative depth perception. It clearly shows the fronto-parallel plane plays no role in qualitative depthperception for fields beyond the foveola. It also shows,along with [Figure 7.4.1-7], the importance of selectingdistances to the point of fixation compatible with thedepth of focus of the lens group.

7.4.1.5.4 Parameters important in horopterprotocols

The depth of focus of the lens group and thus the f/# ofthe lens group, and ultimately the light level in thelaboratory are major limitations on the quality ofhoropter data collected. It is important that the lightlevel and color temperature of that light emulate daylightwhen collecting data of high quality, particularlyconcerning stereopsis.

Similarly, it is important that the effect of target disparityangle on the overlapping of the surfaces of best focus ofthe two eyes be controlled, or at least noted. Whencollecting high quality stereopsis data at the edges of the foveola fields, the inter-ocular distance should be smallcompared with the distance to the point of fixation.

The phoria of the subject should be determined before making horopter measurements.

Clements has provided data on the criticality of the plane of the horopter versus the horizontal plane of the head349.

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7.4.1.5.5 A more realistic horopter for discussions of stereopsis EMPTY

Figure 7.4.1-16 presents a horopter applicable to discussions of stereopsis. It clearly defines the area of precisionstereopsis compared to the much broader extent of initial coarse stereopsis. The Vieth-Muller circle is shown for H =0.00, see chapter 4 of Ogle for important values of H. The fixation point is in the sagittal plane of the head and the eyesare converged at equal angles. The region of precision stereopsis and optimal fusion is defined by the 1.2 degree visualcone associated with each eye (Figure 7.4.1.4-14). If the eyes are significantly rotated to fixate on a point outside thesagittal plane, the quality of the image focused on the retinas will suffer. from rotation of the oculars about the lines ofsight (Figure 7.4.1–10). Some investigators define a tangent board,” typically a vertical panel with a horizontal linealigned with H = 2a/b and a vertical line aligned with the sagittal plane.

Note the only optical rays that are straight lines between the external environment and the retina are those satisfying thesimplification, sin x . x. These rays are within 0.6 degrees of the optical axis of the lens. These are not the rays leadingto the fixation point or center of the foveola of each retina. The angles, αL and αR are the most useful in discussing thestereoptic field and the phenomenon of fusion. However, they do not correspond to the equivalent angles within theoculars for large angles where sin x … x.

As will be developed in Section 7.4.5.xxx, it is not necessary that the object at the point of fixation, or at other locationssuch as A, do not need to be multidimensional objects, they may be multidimensional features of a multidimensionalobject of greater extent. The feature can extend beyond a single or few photoreceptors at each retina. However,stereoptic performance will improve if the feature extends over more than a few photoreceptors in dimension (the signal-to-noise associated with the stage 2 through 4 signal processing will be higher.

The most important distance in the figure is the distance to the fixation point from the midpoint between the nodal pointsof the two oculars (the nodal point of the mythical

7.4.1.6 Description of Panum’s area, depth perception and the fusional horopter

7.4.1.6.1 Panum’s area relates to the X & Y axes of object space

Panum’s area, or Panum’s fusional area, is a convenient concept used inconsistently in the literature. This makes itextremely difficult to define the term precisely. Panum reported on his work beginning in 1858. It has been discussedconceptually by many authors. Conceptually, it has long been considered a relatively constant area defined in terms of

Figure 7.4.1-16 The optimal horopter for stereopsis discussions ADD. See text.

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Dynamics of Vision 7- 171a small difference in visual angle relative to the point of fixation. Within this area, points of light presented to the tworetinas will fuse into a single perceived image. Howard gives a simple illustration of the concept on page 51 and refersto a fuller discussion on pages 272-282. These more complex discussions quickly become generic and revolve aroundthe concepts of fusion and diplopia. They get into the question of whether the area is measured under dichotic ordichoptic conditions, how the area varies with eccentricity from the point of fixation, etc. The subject of hysteresis isalso introduced. As two dichoptic points are moved farther apart, fusion is lost at a definable disparity angle. However,the angle at which this occurs is different from that where two widely disparate points fuse as they are brought closertogether. The subjects of scene contrast and brightness must be dealt with. In addition, the relevant temporal factorsmust be considered. The problem is further complicated by the use of the term spatial frequency when the targetsinvariably consist of only two discrete objects separated by a finite space (interval).

In 1979, Tyler & Scott writing in Records said flatly “the traditional concept of Panum’s area as a fixed property or agiven retina region must be abandoned. Instead, the fusional extent is strongly dependent on the stimulus used to measureit.” They went on, “Hence, the fusional horopter (frequently) presented (in the literature) must be taken only as anindication of the fusional range in the real world, which will expand and contract according to the objects present in thefield and the optical characteristics of the eyes viewing them.” This position appears strongly influenced by Tyler’papers of 1973 and 1975. These papers introduced the apparently ultimate simple variable to evaluate fusion andPanum’s area simultaneously. They used various permutations of a straight line, a wavy line and dashed versions ofstraight and wavy lines in their experiments. However, his methodology introduced cues related to both eccentricity anddepth. No comment was found saying a goal was to challenge and evaluate the performance of the correlationmechanism of the visual system. Others have used even more complex shapes to study fusion and rivalry. However,these variations usually lead to a more complex explanation or set of rules to explain the phenomenon observed, ratherthan a simplification of the basic mechanisms underlying the phenomenon.

The first challenge here is to decide whether Panum’s area refers to a two or a three-dimensional phenomenon.

Tyler, writing in 1983 in Schor & Ciuffreda, (pages 220-227) begins by defining the binocular visual direction asapplying to the x,y position in the “frontal plane.” He discusses Panum’s area as a two dimensional plane and cautionsabout the importance of separating the fusion task from the depth perception task. He summarizes by saying, “Insteadof a fixed fusional region there is a strong dependence of fusion on the local stimulus characteristics. Panum’s area isa dynamic entity that is continually being adapted to the prevailing features of the stimulus environment.” As notedearlier, He also cautions that “the fusional horopter presented above is not a fixed range around the point horopter andthe conventional depictions of figure 7.11 must be taken only as an indication of the fusional range in the real world,which will expand and contract according to the objects present in the field and optical characteristics of the eyesviewing them.”

Howard discusses the area as an ellipse on page 272 to account for the difference in vertical and horizontal performance.He also notes that “one must ensure that subjects are judging fusion rather than apparent depth between the disparatestimuli. This is a severe problem with the forced-choice procedure because subjects tend to rely on apparent depth ifthat is the only difference they see [emphasis added].”

The term Panum’s limit occurs occasionally in the literature to describe the boundary of Panum’s area. This limit variesas a function of the specific stimulus configuration. Section 7.4.6 will show that Panum’s area is more directly relatedto the effective dimensions of the correlator of the PGN than the physical dimensions of the foveola.

7.4.1.6.2 Depth perception involves the Z-axis

The expression depth perception is nearly self-defining. It is the perception of different distances to objects in the visualfield of view. As discussed in Section 7.4.1.3, a variety of cues can contribute to the perception of depth. Some provideonly a qualitative perception while others provide a quite distinctive perception defined as veridical.

7.4.1.6.3 The maximum range of fusion and depth perception

Section 7.4.6.2 develops the relationship between the phenomena of fusion and depth perception and shows they sharean underlying mechanism. As a result, Panum’s area, describing the x,y region of fusion in object space, and theequivalent range of depth perception, along the z-axis in object space, are plastic regions. They are both derived froma more fundamental expression of Panum’s limit associated with the associative correlator of the PGN. This Panum’slimit defines the maximum effective spatial range of the correlator when implementing the mechanism of stereopsis.In this correlator space, Panum’s limit refers to a combination of the eccentricity and depth, relative to the nominal pointof fixation in object space, that can be processed by the correlator.

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350http://webvision.med.utah.edu/book/part-viii-gabac-receptors/space-perception/

This broader limit in 3-dimensional space can be described as Panum’s volume limit. The generally egg-shaped spaceenclosed by this limit can be described as Panum’s volume (although he did not study the depth perception aspect). Itreduces to Panum’s limit in x,y space for z = 0. The area enclosed by this limit is known as Panum’s area. This limitcan also be expressed by the maximum value of z for the condition x = y = 0. This limit describes the maximum rangeof depth perception relative to x0,y0,z0. For other values of x,y,z, a volume can be defined that is conceptually equivalentto Panum’s area. It defines the combined range of fusion and depth perception achievable by the subject.

7.4.1.6.4 The fusion horopter involves the X,Y & Z or θ, φ, ρ axes

While much of the early literature describes stereopsis in terms of X, Y & Z coordinates, this is not the systemused within the stage 4 saliency map. To accommodate, hearing inputs as well as visual inputs, the saliency mapof the external environment is almost certainly maintained in a gravity oriented inertial framework using θ, φ,ρ coordinates. The inertial framework in healthy humans is biased so that the φ = –90° axis is parallel to thegravity vector when standing or sitting.

[xxx what does it say?]The definitions of Panum’s area cited above relates to the X,Y plane perpendicular to the (Cyclopean) line of sight.When combined with the idea of depth perception providing the third or Z-axis, a different Panum’s volume would bedefined. This volume would consist of a torus, as frequently drawn to represent the “fusional horopter.” The torus wouldconsist of a series of laminates or curved planes orthogonal to the line of sight (not the line of fixation) and varying intheir vertical size with their distance from the 1st principal point of each eye. Each plane consists of a series ofoverlapping ellipses representing Panum’s area at each specific eccentricity. The variation in vertical size with depthis controlled by the change in size of Panum’s area with radial distance from the point horopter. The variation inhorizontal size with depth also varies with radial distance from the point horopter. However, this dimension is obscuredby the merging of adjacent ellipses to form the horizontal extent of a single laminate (plane). This merging is similarto the row of shields on the side of a Norseman’s medieval sailing ship merging to define the outer surface of the ship.As noted by Tyler, the specific size of the fusional horopter is highly dependent on the precise nature of the stimulus usedand the characteristics of the subjects eyes.

The online text, Webvision, sponsored by the University of Utah provides additional material related to Panum’s areafor the undergraduate350. Webvision as an introductory text does not appear designed to be accurate at the theoreticallevel.

7.4.2 The version control subsystem: pointing

First order version eye movements are by definition conjunctive. Rashbass and Rashbass & Westheimer have provideda series of papers shedding light on the version control subsystem. See references in Section 7.3.1.1.

The version control subsystem calls upon the underlying pointing system to operate over an extended range of anglesand velocities as discussed in Section 7.3.

Delineating between the operation of the version control system for large signals (and those originating outside thefoveola) from those smaller signals associated with the foveola (and originating within the precision optical system) isimportant. The former is generally associated with the awareness and alarm modes of vision. The latter is generallyassociated with the analytical mode of vision. The analytical mode employs a different type of servomechanism thando the others. In fact, the differences extend to differences in the actual muscles supporting the two servomechanismtypes. Because of the complex interplay between these servomechanisms (and the role of memory in their operation),describing them individually in-toto is difficult.

An introductory description of the operation of the version subsystem can be provided. The alarm mode of visionprovides instructions to the TRN relating to the angular location, from the point of fixation, of any changes in theexternal environment detected by the awareness mode subsystem, the LGN/occipital couple. These changes occuroutside the view of the foveola by definition. These instructions are passed to the superior colliculus where they areconverted into detailed commands for implementation by the pointing and accommodation subsystems. Similarly, thecognitive portion of the HVS can provide instructions via the volition mode channel to the TRN for implementation.Here again, the signals are passed to the superior colliculus for conversion into implementable commands that can beacted upon by the pointing and accommodation subsystems. The precision optical system can detect and respond

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351Adler, S. Bala, J. & Krauzlis, R. (2002) Primacy of spatial information in guiding target selection for pursuitand saccades J Vision vol 2(9), pp 627-644352Liston, D. & Krauzlis, R. (2005) Shared decision signal explains performance and timing of pursuit andsaccadic eye movements J Vision vol 5, pp 678-689

autonomously to changes occurring within the field of view of the foveola. However, these actions may be subject tooverride by the TRN.

7.4.2.1 The type 0 version control servomechanism (related to awareness)

The version control servomechanism associated with the awareness and alarm modes of vision have the primaryresponsibility of keeping the organism current on the state of its environment. This is a particularly important role withrespect to changes in that environment. The organism maintains a complete saliency map of its environment in memoryand does not rely upon the awareness mode for static information. The awareness servomechanism is tailored to detectchanges in the environment and report the location of those changes to the thalamic reticular nucleus (TRN) for action.It is the TRN that forwards the coordinates provided by the alarm mode channel (primarily from the LGN) to theoculomotor functions within the POS for implementation. Following that implementation, the awareness and alarmmodes re-evaluate the environment. Thus, closed-loop operation is achieved. The fact that the awareness and alarmmodes only deliver position information to the TRN during any single cycle of the servomechanism defines it as a type0 servomechanism. Information related to the spatial velocity of changes is only extracted over the long term. Thiscapability is limited by the time involved.

7.4.2.2 The type 1 version control servomechanism (related to analysis)

The analytical mode of vision employs the much higher spatial resolution of the combined foveola and associativecorrelator of the PGN. It also relies upon the twitch capability of the oculomotor subsystem and the tremor generator.With these aids, it can compute both location and velocity information within the response time associated with the tonicportion of the oculomotor subsystem and also within the response time of the accommodation subsystem. In this sense,the analytical mode provides the capabilities of a type 1 servomechanism.

7.4.2.3 Smooth pursuit versus salutatory motions EDIT

The awareness and alarm modes of vision are primarily responsible for causing the visual system to redirect the line offixation to specific locations within object space. They are generally not involved in the pursuit function, the trackingof moving objects. The analytical mode of vision is primarily responsible for tracking a moving object. For an objectmoving within the field of view of this mode at a low rate, the type 1 servomechanism of that mode is able to providetracking signals to the POS. With these, the POS and the oculomotor subsystem can provide a pseudo-continuoustracking capability (the two images remain fused within the correlator/pulvinar circuits of the PGN). This mode ofoperation is called smooth pursuit. For targets moving faster than the type 1 servomechanism can process, the TRNcauses the system to go into a salutatory tracking mode. The eyes will be redirected to a new calculated point of fixation(new version, vergence and accommodation values) different by more than the diameter of the foveola from the previouspoint and a new correlation cycle will be initiated. Rashbass has concluded that the smooth pursuit capability extendsup to 10 degrees/second (pg 338). The capability of the analytical mode is usually degraded under salutatory trackingconditions due to the short integration times available.

7.4.2.4 Data related to smooth and salutatory pursuit

A team at the Salk Institute of San Diego has been active recently in the psychophysics of target acquisition, recognitionand tracking.

Adler, Bala & Krauzlis have provided data built around two experiments351. [xxx add more here ]

Liston & Krauzlis352 have provided good psychophysical data related to salutatory pursuit (based on Rashbass’s criteriaof 10 degrees/second). However, their conceptual model, discussed only in words, is not compatible with that of thiswork. They offered no schematic of the oculomotor system supporting their conclusion that the motor elements aredifferent for the saccadic and pursuit phase of operation. Thus, their proposed operation of the oculomotor system andthe conclusions drawn are not supported and should be examined critically by the reader. The frequent use of the wordsmight and could in their discussion is suggestive of the firmness of their findings. However, their discussion andreferences related to neural activity associated with the reticular formation is very interesting.

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353Green, D. & Swets, J. (1988) Signal Detection Theory and Psychophysics. Los Altos, Ca: Peninsula

Liston & Krauzlis used two moving windows on a kinescope monitor and monitored the motion of the eye with aninfrared tracker to a precision of ~0.1 degree and a 1kHz interrogation rate. Each window was filled with a spatiallystationary pseudo-noise pattern. Their test criteria was based on a sensitivity criteria developed by Green & Swets353.Horizontal scene motion was limited to 14.2 degrees/second. The eye was required to jump 2 degrees from a point offixation and then track the motion of the stationary noise pattern within the moving window. The protocol includedoperations during two modes of vision.

Awareness Mode• a period of fixation on a 0.5 degree diameter cross• a random interval• the appearance of two moving windows, one above (2°) and one below (-2°) the fixation point and spanning the full width of the 45° field of view framed by the monitor.C an analytical interval while the brightest window was determined.

Analytical ModeC a vertical saccade of nominally 2° to bring the brightest window over the foveola.C a period of analysis while the character of the pattern applied to the foveola was determined.C a subsequent time while the POS determined and instituted a predictive sequence of pursuit saccades.

When exploring the performance of the POS, it is useful to categorize and document the time delays associated with theindividual functional elements.

Type Stage Nominal Value CommentC Sensory neuron delay (without adapt.) 1 Varies with avg. light levelC Sensory neuron delay ( adaptation) 1 up to 25 ms2 Varies with delta light levelC Peripheral signal processing delay 2 Xxx ms in humansC Afferent signal propagation delay 3 Typically xxx ms (human)C POS signal processing delay 4 Optional based on protocolC Cognitive signal processing delay 5 Optional based on protocolC Volition/Command generation delay 6 Optional based on protocolC Efferent propagation delay 3 Typically xxx ms (human)COculomotor plant delay 6

2 Ritter & Gegenfurtner. Probably includes all sensory delay.

The sensory delay varies with light level as shown in Section xxx. It is typically xxx ms under photopic illuminationconditions.

DeValois has used 50 ms as the typical cumulative delay recorded at the LGN. As seen from the above table and thisdiscussion. The 50 ms appears to apply to the output side of the LGN.[xxx add additional comments here]

7.4.3 The vergence control subsystem: coarse convergence via the LGN

In this section, noting two situations related to nonlinear mechanisms versus nonlinear analyticaltechniques will be important. Differentiating between a nonlinear biological mechanism beingmodeled by a mathematical equation that is also nonlinear; and a piecewise linear model that resultsin a nonlinear output will be important. The piecewise linear model relies upon linear mathematicalequations over individual intervals of a larger interval. It may or may not represent the actualmechanism being modeled. Differentiating between circuits that are actually parallel in themathematical model of a servomechanism and circuits that are drawn in parallel but are active onlyindividually (under the control of some form of switch) will also be important.

As stated in Section 7.3.3, the vergence system is an overlay on the pointing subsystem. While it may only be a single-stage system in most lower animals, who do not exhibit the ability to analyze fine detail, it is a distinctly two-stage

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354Schor, C. (1991) Effects on the resting states of accommodation and convergence. In Grosvenor, T. & Flom,M. Op. Cit. pp 310-317355Del’Osso, L. & Daroff, R. (1999) Eye movement characteristics and recording technique. In Glaser, J.Neoro-ophthalmology, 3rd ed. NY: Lippincott Williams & Wilkins Chapter 9, pp 327-344356Gamlin, P. (2002) Neural mechanisms for the control of vergence eye movements. Ann. N.Y. Acad. Sci. vol.956, pp 261-272357Pierrot-Deseilligny, CH. Ploner, C. Muri, R. Gaymard, B. & Rivaud-Pechoux, S. (2002) Effects of corticallesions on saccadic eye movements in humans. Ann. N.Y. Acad. Sci. vol. 956, pp 216-229358Hung, G. & Ciuffreda, K. (2002) Op. Cit.

servomechanism in humans and a few of the higher primates. The precision achieved by the coarse system, employingthe LGN, is much lower than the remarkable capability achieved by the precision optical system (the POS) and the PGN,described in Section 7.4.5.

The performance of the opto-mechanical systems of the human eye has been studied primarily by four distinct groups.The optometric community has studied the subject using primarily non-invasive techniques. The morphologicalcommunity has studied the optics primarily as a physical structure. Only recently has either of these two groups studiedits parameters associated with the wide angle optical performance of the system. A third group, the medical surgeonshave studied the physiological optics from a perspective outside the scope of this review. The fourth group of surgicallyoriented physiologists have studied (disparity based) coarse stereopsis using electrophysical techniques after initialconvergence has been achieved.

The optometric community has studied the opto-mechanical systems primarily by evaluating the performance parametersresulting from a stimulus applied to a black box. They have not dissected (in the intellectual sense) the system into abroad description of its internal components and evaluated them individually. The dissection that has occurred has beenlargely limited to the separation of the system into three components. The first is a physiological optical component(s).The second is a muscle system (frequently described as the plant based on servomechanism terminology). The third isa mathematical description of the overall circuitry required to realize the performance measured.

7.4.3.1 Review of vergence models in the literature

Schor has provided a brief summary of the various states of convergence in the visual system354. Dell’Osso & Daroffhave provided information from the clinical perspective, of the vergence system355. The block diagrams are suggestivebut not in agreement with the diagrams of this work (See Chapter 15). Their diagrams concentrate on the volition modeof signal processing to the near elimination of the more automatic modes of awareness and analysis concentrated in themid brain.

Gamlin has recently discussed the vergence system in non-human primates. Although his block diagram contains manyquestion marks, the data appears useful356. Pierrot-Deseilligny, et. al. have discussed similar eye movements in humansdue to lesions in the volition mode circuits357. Several block diagrams and time lines are presented. However, the focusappears to be on the volitional High-level commands generated in the cerebrum almost exclusively. Jiang, Hung &Ciuffreda have recently provided a major chapter on vergence and accommodation models and interactions. Thecharacteristics of these models were discussed in Section 7.3.1 above. They represent early floating models that havenot been integrated into a system model compatible with the physiology of the visual system. While of great value toan analyst attempting to create a more comprehensive model, they will not be discussed in detail here.

Recently, a large compendium of work associated with the opto-mechanical systems of human vision has appeared358.It was edited by Hung & Ciuffreda. This compendium exhibits the characteristics just enumerated. By exhibiting thesecharacteristics, it simultaneously defines the state of the art in the field. While titled, “Models of the Visual System,”it is largely focused on individual floating models of various parts of the opto-mechanical systems of vision. Littleattention is given to the other aspects of the visual system. The volume does provide an excellent summary of the largenumber of floating models developed by different teams. Many of these teams had short lives while under the tutelageof Professor L. Stark. His name appears in a secondary position on the author line of many important papers in this areaof the literature. One of these papers will be adopted as a starting point in developing the pointing subsystem underlyingthe operation of the focus and vergence subsystems (Section 7.3.4.1).

While the performance of the system is generally recognized to exhibit large signal performance (and therefore generallynonlinear) properties, the system modeling techniques used to date have been largely limited to the small signal regime.Alternatively, they have adopted piecewise linear models to achieve a nonlinear mathematical model of an underlyingphysiological mechanism (whether that mechanism is linear or nonlinear). This is clear from a review of the papers inHung & Ciuffreda. The papers have provided a great deal of useful experimental data along with a wide variety of

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359Patel, S. Ogmen, H. White, J. & Jiang, B. (1997) Neural network model of short-term horizontal disparityvergence dynamics Vision Res vol. 37, no. 10, pp 1383-1399, quote on pg 1384

floating models. The papers in even this recent volume appear to reflect the limited formal training in servomechanismsof many individual authors. In general, each model attempts to rationalize the performance data collected. While thesemodels are all different, they do provide excellent source material for an analyst with a broader background inservomechanism theory and circuit realization techniques. Be carefully examining the data, and the individual modelsand equations, it is possible to synthesis the underlying, and more fundamental, equation of the overall process. Oncethis is done, the mathematical model can be converted to a circuit model using realization techniques compatible withthe physiological and neurological limitations of the visual system. This consolidation of the largely conceptual modelsinto a single comprehensive model (rich in features not shared by linear models) will mark a major advance in the stateof the art.

The papers in Hung & Ciuffreda are generally limited to the small signal regime (in the mathematical context). As aresult, the formal structure of the papers is limited to the linear case. It is interesting that at least six different modelsare provided to describe the vergence servomechanism of the visual system (their Section 9.2). A progression of modelsis also provided related to the saccadic aspects of the oculomotor system. The papers generally provide estimates of thes-plane characteristics of the underlying servomechanisms required to achieve the measured temporal responsecharacteristics. Only a few papers alluded to the use of root-locus or other sophisticated (but linear) servomechanismanalysis techniques. They do introduce a finite, but lumped, time delay into the overall performance model. They alsorecognize a “dead space” in the response associated with the accommodation system. Some graphic models incorporatea range limiter, shown as a graphic symbol, but do not introduce the same constraint into the equations. Only in a veryfew cases have the potentially discontinuous nature of the signal processing elements been suggested. None of theincluded papers has recognized the intrinsically sampled-data characteristics of the system. Thus, no reference to Z-plane, or other higher order servomechanism modeling techniques, were noted. Progress in this field will be slow untilthe transcendental and exponential properties of the opto-neuro-mechanical systems of physiological optics areintroduced into these models along with the time delay and dead-zone characteristics noted above.

Several papers in Hung & Ciuffreda incorporate multiple parallel signaling paths in their models. However, most ofthese paths are only active sequentially. The switch required to arrange the sequential operation is not always apparent.This notation is introduced to satisfy the nonlinear operation by using a piecewise linear model in the analysis. Whileeasy to draw, confirming this mode of operation within the neurological networks of the brain is difficult. It is likelythat recognition of the logarithmic processes used in the neural system (and the transcendental processes in the plant dueto geometry) will eliminate the need for this method of analysis in all but the largest saccadic motions.

The various plant models presented in Hung & Ciuffreda vary from early systems with constant gain characteristics tosecond and third order systems. These models represent attempts to more closely match the performance data of thesystem based on better test design and instrumentation. Many plant models in Hung & Ciuffreda assign a time constantof about 160 milliseconds to the plant associated with oculomotor response. This value will be used here for the nominalslow time constant of the tonic portion of the oculomotor plant. However, an entirely different time constant must beassociated with the twitch component of the oculomotor plant (Section 7.3.4.1.3).

A vast majority of the papers in Hung & Ciuffreda show the physical plant in the forward path of the servomechanism,with conceptual outputs taken from the output of the plant. These are generally labeled vergence or vergence response(VR) and accomodative response (AR). No example was found of any signal being extracted from the models andprojected to the higher neural centers of the brain. In Section 10.4 of Hung & Ciuffreda, Pola briefly refers to a potentialextra-retinal signal used in the higher neural centers. He then asks a question. “What is the source of this signal?” Hisonly response is to mention a putative efference signal that has appeared occasionally in the literature.

Several papers in Hung & Ciuffreda attempt to explain the interaction between the vergence and auto-focus(accommodation) systems (their section 9.3). However, the presentations are largely conceptual and based strictly onfloating mathematical models. They typically treat the input signals to these two systems as independent, as if they didnot arise from the same photoreceptor cells. They then introduce cross-linking between the two subsystems in an attemptto rationalize the common elements of the output performance seen in the two systems.

As noted in Patel, et. al., these models do not address the source of the neural signals in the real retina359. They say thefollowing. “For example, most control theory models of the HVS [the human horizontal vergence system] use disparityas input and vergence eye-position as output without specifying how disparities are computed from retinal activities andhow motoneurons are driven to generate the desired disjunctive movements.” Based on this lack of adequateunderstanding of the signal generation process, the model presented by Patel, et. al. is more conceptual than other recent

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360Bodis_Wollner, I. (2002) Beyond classical retinotopy: striate cortical mechanisms associated with voluntarysaccades and attention In Hung, G. & Ciuffreda, K. eds (2002) Models of the Visual System. NY: KluwerAcademic/Plenum Press Chapter 7.361Julesz, B. (1978) Global stereopsis: cooperative phenomena in stereoscopic depth perception Chapter 7 InHeld, R. Leibowitz, H. & Teuber, H-L. Handbook of Sensory Physiology NY:Springer-Verlag362Julesz, B. (1971) Foundations of cyclopean perception Chicago, Il: Univ. of Chicago Press363Tyler, C. & Julesz, B. (1980) On the depth of the cyclopean retina Exp. Brain Res. vol. 40, pp 196-202

models reviewed in Hung & Cuiffreda.

An intriguing aspect of the literature is its complete lack of association of tremor with the operation of the opto-mechanical (more properly opto-neuro-mechanical) aspects of the visual system. The term tremor does not even appearin the index to Hung & Ciuffreda. Neither does the fact, that the visual system becomes blind within about three secondsin the absence of tremor, appear in their text (See Section 7.3.3.5.4). This lack of appreciation of the critical role oftremor has prevented the optometric research community from associating their measured data with the actual sourceof the signal processing within the visual system. It has also prevented the psychological community from makingsignificant progress in how animals analyze the imagery in a scene. This work will show the focus and vergence systems(as well as the ability to analyze, including read) are critically dependent on the tremor introduced into the oculomotorsystem for their performance.

The neurophysiology of the visual system appears only peripherally in Hung & Ciuffreda (their Section 10.2.3). Thismaterial does not differentiate the operating modes of the visual system. Without such differentiation, providing a formaldescription of the neurophysiological description of the visual system is difficult. A clearer differentiation of this areais provided in this work (Sections 11.1, & 15.2).

This work will provide a broader conceptual foundation for the opto-neuro-mechanical model of the physiological optics.The foundation is compatible with the larger overall model of vision presented in this work. A single broaderservomechanism model will be introduced that serves all of the vergence, accommodation, analysis and pointingfunctions of the visual system. It is based on accepting only a single complex signal from the overall retina, withmaximum emphasis in processing place on the portion from the foveola. It will output neurological signals to bothhigher neural centers and the multiple motor “plants” associated with the ocular. The oculomotor, the accommodation,and the pupil control plants will be shown in separate feedback paths of the common servomechanisms. The delayassociated with the systems will be subdivided into the transport delays associated with the stage 3 projection neurons,processing delays associated with the neural system and plant delays associated with the musculature.

Bodis-Wollner has provided a recent discussion of some neural aspects of saccades and attention360. While this materialtouches on the opto-mechanics of the visual system, it is brief. It will be reviewed further in Chapter 15.

The references listed here and in Hung & Cuiffreda have provided excellent data. However, interpreting that data bythe investigators or others is quite difficult. Interpretation is more difficult than the original investigators assumedbecause they had no appreciation of the actual disparity signal generation mechanisms. Because of this situation, thenext two sections will develop the appropriate model of the vergence mechanism before the data of the literature isreviewed.

7.4.3.1.1 Models of the physiology of the vergence control system

Julesz presented a caricature representing depth perception in a discussion labeled “Ambiguities in Stereopsis” in 1978361.It was a reproduction of a similar figure of 1971362. A more complex but similar caricature appears in Tyler & Julesz363.Related caricatures have also appeared in two different articles in Leibovic. One is by Dow (pg 111) and one is byWildes (pg 341). The latter is attributed to Grimson. These caricatures have all suffered from several problems. First,they are all drawn without any scales and place the eyes farther apart than the objects in the scene. This causes theconvergence angles to far exceed those achievable by any human, other than a young child. It also causes principal raysdrawn between adjacent objects and the two eyes to appear to intersect. Julesz uses these intersections to define“phantom targets.” He proposes that these phantom targets, which do not appear in more realistic geometries, must beeliminated by undefined neural processing. Second, they invariably employ the Gaussian optical approximation thatsuggests that all optical rays passing through the lens of the eye travel in straight lines. This is entirely incorrect forangles larger than a few degrees. Third, they are all based on a time invariant geometry. This leads to the assumptionthat the visual system operates on spatially static information.

Because of the above caricatures, the community has limited its discussions of depth perception to such a degree it hasnot moved beyond the conceptual realm. In recent times, it has discussed the phantom targets of Julesz under the name,

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364Anderson, B. & Nakayama, K. (1994) Toward a general theory of stereopsis: binocular matching, occludingcontours, and fusion Psychol Rev vol. 101, no. 3, pp 414-445

Figure 7.4.3-1 Caricature of depth perception at a bowlingalley.

the “false target problem.” Anderson & Nakayama have recently written “The severity of the false target problem hasbeen the primary theoretical constraint that has shaped virtually all extant models of stereopsis.” They then asked thequestion, “Is the false target problem a false problem?364” They conclude it is not a real problem based on theirassumptions and analysis. Specifically they say, “we believe that the fundamental mistake that has been made in thestatement of the matching-noise problem (an element of the false target problem) is the confusion of a method of stimulusconstruction with a theory of visual perception.” The conceptual method of stimulus generation adopted by thecommunity has long been a basic problem. The next paragraph will show the dynamics of the eyes relative to any fixedscene results in a totally different interpretation of the stereopsis mechanism. It shows the false target problem is totallyspurious.

Figure 7.4.3-1 provides a caricature using more realistic geometries than those found in the literature. It contains threeviews. The left view represents an overhead view of a four-lane bowling alley with the subject playing in lane C. Eachlane is sixty feet long and 42 inches wide. The pins are 4.75 inches in diameter and arranged in an equilateral trianglewith the closest pin to the subject spotted 34.73 inches from the farthest edge of the lane. The size of the pins causesconsiderable overlap in their images. This aids the subject greatly in perceiving their relative position in depth. To allowfor gutter lanes, the lanes are on seventy two-inch centers. The head and eyes of the subject are still shown seven timesactual size to be identifiable at this scale. When the line of fixation of the eyes is convergent on pin #1 in lane C, theback row of pins extends over an angle of 3.35 degrees. When the line of fixation of the eyes is convergent on pin #1in lane C, the principal rays passing through the center of the far end of lane B, and lane D, are at an angle of 5.73degrees to the line of fixation.

Several propositions are offered. The typical subject cannot see the individual pins in lanes A, B & D when fixated onpin #1 in lane C. Each pin group could be replaced by a triangular cardboard box and the subject could not tell thedifference if his line of fixation is restricted to pin #1 in lane C. This is due to the significant aberrations in thephysiological optics of the eyes. Furthermore, the principal rays drawn between the pin sets in adjacent lanes do notintersect among themselves or with the principal ray to pin #1 of lane C. Thus, no “phantom targets” are created in thisconfiguration. This is also true with regard to the pins in lane C alone as can be seen in the middle view of the figure.Looking at a different case, the caricature of Dow suggests phantom targets could occur (at his location C) if the targetswere at significantly different distances relative to the horopter. However, this is unlikely. The accommodationmechanism would cause the potential phantom target to be considerably out of focus and poorly resolved. No phantomtargets occur under realistic conditions of human vision.

The middle view expands the left view by 5:1 to illustrateadditional details. The nominal view imaged by thefoveola of each eye is shown by the 1.2 degreedimension. To image the full set of pins within thefoveola requires the instantaneous line of fixation bemoved to three positions, the central position andpositions 1.2 degrees each side of that position. This isthe conventional situation. The visual system is normallyrequired to scan a scene to perceive the relative distancesto all of the objects in the scene (Section 7.5.2). Whencentrally fixated, the foveola can observe the equilateralarrangement of pins #1, 2 & 3. However, the foveola isunable to provide high quality depth information relatedto the outer pins at #4, 7, 6 & 10.

The right view highlights the difficulty in obtaining ahigh degree of depth perception related to pins #6 & 10when the eyes are fixated on pins #4 & 7. In fact, mostpeople can only determine which pins are in front bytheir overlapping images. If smaller diameter “duckpins” are used (diameter, 4.125 inches), bowlingbecomes a much more difficult game. In duck pins, nooverlap occurs between images of the pins and mostpeople cannot discern any depth perception related to pins #6 & 10 when fixated on pins #4 & 7. They rely on looking

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Figure 7.4.3-2 A caricature introducing tremor to explainthe mechanism providing stereopsis. The vergence angleshown is at least twice, and typically ten times, that usuallyused in human vision. See text.

at each pair individually, determining their relativepositions and then computing their relative positions asa group. This information is stored in their saliency mapof the scene (the technical name for the memory portionof the conceptual cyclopean retina of Julesz).

The dashed lines in the above figure are drawn with onlyone apex, essentially the cyclopean eye of Hering. Thereis no hint in this static figure of how stereopsis is actuallyachieved. Figure 7.4.3-2 provides an answer to thisquestion using a simpler configuration involving onlythree pins that fall well within the 1.2 degree field ofview of each foveola. Each nominal foveola has adiameter of 175 nominal photoreceptors (pixels for thisdiscussion). The figure shows the instantaneous field ofview of only nine pixels (-4, -3 . . . 0, . . . +3, +4)selected from the center of each field of view. Theinstantaneous fields of view are shown as parallelbecause of the distance to the 1st principal point of eacheye. Each instantaneous pixel field is only 2 arc secondswide. The vergence angle between the two lines offixation is also highly exaggerated. The vergence angleis twice what it would be for a real person looking at ascene only 30 cm (11.8 inches) from his eyes. If drawnto scale, there would be virtually no crossing of the fieldof view of non corresponding pixels for targets at morethan 30 cm. Because of this situation, the so-calledcorrespondence problem is a minor problem at best. Thecorrespondence problem will be discussed further afterthe following thought experiment is defined.

Let the two eyes be converged on the central dot in thefronto-parallel plane of the eyes. Now, introduce atremor into the line of fixation of each eye and let themotion caused by the tremor be conjunctive. Assume theeyes are scanning from left to right as shown. Themagnitude of the tremor induced motion is not importantas long as it is greater than one pixel diameter. Thisrequirement is due to the fact the pixels act as edgedetectors and the interpretation is simpler if the pixelscross edges (or dots) in the field of view completely.

As seen, any dot found in the fronto-parallel plane will appear in the corresponding pixel channels of the two eyesrelative to the 0 numbered pixels. This is not true for any dot not located in the fronto-parallel plane. The dot on theleft appears in pixel -3L and -4R. As the eyes sweep across the scene, a signal will be transferred to the midbrainrepresenting this single dot. The signals would be deposited in the cells of the associative correlator of the PGNaccording to their foveola pixel number. Similarly, the right-hand dot would generate signals in cells +3L and +4R. Thecentral dot (located at the point of fixation) would obviously generate signals in channel 0L and 0R.

The function of the correlator is to calculate the mean location of each dot in the scene as well as the deviation from thatmean location represented by the above differences in cell location. The mean location gives the true location of theindividual dot in x,y space and the deviation (which is sign-sensitive) gives the location of the dot in the z-dimension.With this information for each dot (or edge) available in mathematical form, the part of the complete saliency map relatedto spatial position of objects in the scene can be prepared.

7.4.3.1.2 The practical solution to the correspondence problem

Look more closely at the correspondence problem. Based on the near parallel nature of the instantaneous fields of view of the corresponding and near corresponding pixelsof the eyes, very few, if any, false targets (or ghosts) are introduced into the spatial domain of the associative correlatorwhen a scene is at a reasonable level of complexity. At a reasonable level of complexity, the scene can be analyzed bythe pulvinar without difficulty. This is the situation in reading, except for the occasional highly illuminated first

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character of a paragraph opening a chapter. It is also the case in most other analytical situations. If, on the other hand,the scene is quite complex, the correlator may report many potential pairings that are not relevant. This situation willrequire more time for the pulvinar (and possibly higher cortical centers) to interpret the scene content satisfactorily.Alternately, the complexity of the scene may result in a very low contrast ratio in the signal channels related to thedifferent pixels. High contrast signals rely upon distinct edge crossings. Under these conditions, the TRN may instructthe eyes and muscular-skeletal system to establish a different view of the scene to allow easier analysis. This might evenresult in the reliance upon a microscope or other aid.

7.4.3.2 Comprehensive model of the horizontal vergence system

This section on the horizontal vergence system (HVS) may appear out of place. It will rely heavily upon the models ofthe brain developed in Section 15.2. The performance of the model, and that of the actual horizontal vergence system,will be shown to be similar to spatial contrast functions of the visual system as a whole (described in Section 17.6.3).The delay aspects of the vergence system, along with those of the pointing system overall, which are dominated byprojection delays in the stage 3 circuits, will be discussed in Section 7.4. The material will focus on the human HVSbecause it is significantly higher in performance than that of most other animals. This higher performance is needed toallow the analytical mode of operation to achieve the performance level it does (especially in reading). The details ofthe performance achieved by the analytical mode of vision will be discussed in Chapter 19.

Justifying the development of the models defined in Section 7.4.3.1 is possible by using the more comprehensive modelof this work. Highlighting some problems with the earlier models is also possible. The key new feature introduced hereis the fact that the vergence and focus subsystems are entirely dependent on tremor for their operation. This is in spiteof the fact the community has largely ignored tremor as unimportant during the last 40 years. This ignorance hasprevented the community investigating HVS from defining the source of their conceptual vergence disparity signal.

In the absence of tremor, the explanation of how the eyes can converge to a null condition without the underlyingservomechanism becoming unstable has represented a “difficulty” in textbooks.

A major problem is their lack of an appreciation of the importance memory plays in the operation of the pointing system,including the vergence system. It will be shown that the superior colliculus maintains a large memory for convertingcommand instructions, from either the awareness or volition circuits of the brain, into absolute directional commandsrelative to the local skeletal system. This fact is mentioned to suggest that some reported data may suffer in accuracyif the data were not collected using randomized test stimuli.

It is also important to differentiate between the operation of the three major modes of operation of the precision opticalsystem, POS, of the HVS. These are the autonomous mode associated with such repetitious tasks as reading, the volitionmode processing instructions from the higher cognitive centers and the alarm mode processing responses to the detectionof change by the LGN/occipital couple. This distinction will make it easier to interpret papers dealing with thepsychophysical responses of the visual system. These distinctions are most easily made in Section 7.4 when discussingthe time delay related to these different signal paths.

The most comprehensive model of the overall human visual system (HVS), circa 2002, is shown in the figures of Section15.6.4. A slightly simpler set circa 1998 is shown in Sections 15.2. The operating modes of the servoloops forming thePrecision Optical System (POS) are shown in Section 15.3.

The caricature in Figure 7.4.3-3 provides the simplest framework for discussing the operation of the HVS and the originof the (frequently named) disparity vergence signal of the literature. Recognizing that the eyes are continually scanningobject space under the control of the POS. is necessary. When not responding to a pointing command, each eye isresponding directly to the instructions of the tremor generator. Defining a typical operating sequence will aid in thefollowing discussion. This sequence will begin with a large pointing command to the POS from the awareness orvolition signal paths. If the eyes should fail to bring the desired target in object space to within about two arc minutesof the line of fixation, a second pointing command may be generated. This rarely happens. The next step in the sequenceis for the POS to both focus and converge the eyes on the target. It might be assumed that this focusing and convergenceprocess begins from scratch following each major saccade. However, this does not seem true. The operating commandsprocessed by the superior colliculus appear to contain an estimate of the required focus condition and degree ofconvergence appropriate to the estimated target distance. For the instruction received via the volition signal, this estimateis contained in the saliency map that already exists. For the alarm signal instruction, the information may be insertedby the superior colliculus. Thus, the focus and convergence circuits appear to work routinely in more of an optimizationmode. In this mode, the eyes are focused and pointed generally as required when they first observe the target in thefoveola. However, an unacceptable error may be contained in the overall response. Because an edge of the target isencountered earlier in one eye than in the other due to scanning, a temporal vergence error is measurable at the PGN.

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365Krishnan, V. & Stark, L. (1977) A heuristic model for the human vergence eye movement system IEEE TransBiomed Eng vol. BME-24, no. 1, pp 44-49366Pobuda, M. & Erkelens, C. (1993) The relationship between absolute disparity and ocular vergence BiolCyber vol. 68, pp 221-228367Semmlow, J. Hung. G. & Ciuffreda, K. (1986) Quantitative assessment of disparity vergence componentsInvest Opthal Vis Sci vol. 27, pp 558-565

Figure 7.4.3-3 Caricature of vergence control problem.

The PGN creates a vergence error signal proportional to the temporal width of this error signal and transmits it to theoculomotor neurons. This signal can occur under two conditions, first where the left eye is leading and second wherethe right eye is leading. It is likely that these two error signals are transmitted to the oculomotor neurons over separatesignal paths. Depending on which signal is dominant, the error is used to drive both of the eyes nasally or temporallyto achieve convergence. Following the above action, the POS continues to create signals such as those shown in thefigure until the spatial vergence error is forced below an acceptable threshold value.

The complete pointing and vergence servomechanism is shown in block form in [Figure 15.3.1-3]. Note the multipledelay terms in this figure associated with the projection neurons connecting the various signal processing engines. Byexpanding this figure to a circuit level, [Figure 15.2.4-3] is obtained. This figure can be compared with the mathematicalmodel of figure 6 in Krishnan & Stark of 1977365. This model contains four major components, three of which appearedin that paper. The analog elements before the delay term correspond directly to the analog circuitry of the photoreceptorcells (stage 1). The delay term corresponds to the summation of the individual projection delays plus the computationaldelays associated with each signal processing engine and the delay associated with the plant. The plant corresponds tothe more mature plant shown in [Figures 7.5.3-3] and [Figure 7.5.3-4. It is interesting that the complete P/D Equationfor a step change in contrast of Section 16.4.1 and 16.4.2 describe precisely the form of the data of figure 5 in Krishnan& Stark. It is only necessary to overlay the two figures to determine the time constants of this model based on their data.The P/D Equation shows a variable amount of overshoot depending on the prior state of adaptation of the photoreceptorsand the brightness and contrast of the vergence test stimuli. This is typical of what Krishnan & Stark describe as anintegral-derivative controller. It is more commonly called a lead lag network. However, here the “network” representsthe photoexcitation/de-excitation process of the chromophores (without any rapid changes in the state of adaptation ofthe photoreceptors. The rise time of about 0.6 seconds would suggest their 29-year-old subject was looking at a dim orvery low contrast stimulus. It is noteworthy that Pobuda& Erkelens did not follow Krishnan & Stark in their1993 paper366. Without assuming an integral-derivativecontroller, their model did not have a zero in thenumerator. Without a zero, they were unable to accountfor the overshoot they measured easily. Because of this,they proposed a piece-wise linear circuit as a solution.This work confirms that the Krishnan & Stark model isan adequate precursor to a complete and continuousmodel. The properties of the P/D Equation can providethe variations in gain, time constant and overshoot thatboth Krishnan & Stark and Pobuda & Erkelens report intheir data.

Pobuda & Erkelens compared their mathematical model(which lacked any circuit model to define the vergenceerror signal) with the models described in Hung &Cuiffreda up through 1993. This included the two-stagemodel of Semmlow, et. al367. Pobuda & Erkelensconcluded that a two-stage model was unlikely.However, the data in their table 1 appears to support justsuch a two-stage model. When their test disparity wasmore than the diameter of the foveola, their data showeda different gain-time delay relationship than for smallertest stimuli.

While the data of Pobuda & Erkelens is very useful, itsuffers from at least two design difficulties. First, theuse of color filters to separate the signal projected toeach eye from a monitor nearly insures different timeconstants in the disparity signal created from the two P/D environments. This is particularly true since one filter wasdescribed as red transmitting. The filters were not described in technical terms. They also used a technique of partial

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image stabilization to achieve an open loop servomechanism condition without encountering fading of the image asexpected under full stabilization conditions. It does not appear that they accounted for this level of stabilization in detailin their calculations. The partial stabilization of the image would have a significant impact on the temporal bandwidthof the signal passing through the limited bandwidth of the adaptation amplifiers found in each photoreceptor cell. Theconvolution of the signal bandwidth and the bandwidth of the photoreceptor cell could be expected to have a significantimpact on their experiment.

Pobuda & Erkelens discounted all of the models they reviewed, except their piece-wise linear model, based on fourcriteria they developed. They proposed that a successful mathematical model met their hypothesis. The hypothesis wasthat; (1) the vergence loop processes disparity through channels that have low pass filter characteristics; (2) the filter characteristics depend on the amplitude of the disparity input; (3) the vergence loop contains a pure delay of between 80 ms and 120 ms instead of 160 ms as is generally assumed;(4) the vergence loop is insensitive to the rate of disparity change.

Their first criterion is clearly inappropriate. If it were correct, they could have completely stabilized their images toobtain a completely open loop condition. As shown by Yarbus, Ditchburn and many others, the image disappears underthis condition. The mathematical model must contain a zero in the numerator as zero (temporal) frequency. The secondcriterion is appropriate but not for the reason they suggest. The time constants of the P/D signal created within the outersegment of the photoreceptors exhibits a strong dependence on amplitude of the stimulus. The third criterion seemsargumentative for two reasons. First, the individual delay terms of a more comprehensive model were not defined.Second, the method of defining the individual time constants adding to a net value was not given. The leading edge ofthe P/D mechanism is not easily defined using a “rise to 63%” criteria. Third, the net delay is a variable in the P/Dequation. The delay associated with the P/D mechanism is highly dependent on both the luminance of the stimulus andthe state of adaptation of the subject. The eight millisecond value they suggest appears compatible with the long timeconstant of the P/D equation for σA FAτ > 1.00. The nominal value for the Standard Eye of this work was taken as 12.5ms. The fourth criterion appears to also be argumentative. Higher quality data is required to prove the point. Thevergence loop will fail if the product of brightness and contrast falls below a critical threshold. Because of the relianceupon tremor to transform the spatial sharpness of an edge into a temporal signal, the rate of change of the disparity ishighly dependent on the brightness-contrast product.

Noting that the “sine wave response” in figure 3 of Pobuda & Erkelens is actually the response to a sine wave on apedestal (as shown) is useful. This is significant because of the low frequency characteristics of the actual vision servoloop.

The question of a two-stage model becomes one of semantics when the presence of a significant memory componentin the signals delivered to the POS by both the awareness and volition channels of the human visual system. Thisinformation could be introduced from a separate stage or be considered a set of initial conditions for the vergenceservomechanism.

7.4.3.2.1 The perception of 3D by the neural system

(b) of the figure has been expanded to include a second point, R to the right and more distant than F, for the purpose ofdiscussing the mechanism of fusion and depth perception. Fusion is a two–step process beginning with the calculationof a most optimal convergence angle and state of accommodation based on the determination of the dominant elementin object space, taken here as the object at F. This calculation is first performed in the lateral geniculate nucleus (LGN)producing a qualitative signal used to drive both the oculomotor vergence system and an accommodation system. Thecalculation is then repeated within the perigeniculate nucleus (PGN) after qualitative convergence has been achieved.The resulting precision convergence angle is then used to drive the oculomotor vergence and accommodation systemsin vernier mode.

The initial state of convergence and accommodation are set by preset values stored in non-declaratory memory.These presets explain why it is so difficult to see an airplane against a clear blue sky even though it is readilyheard and tracked by its sound to within a few degrees of its location. By looking at another prominent featureat approximately the same estimated distance to establish appropriate presets, and then looking back at theestimated location, the airplane is frequently perceived suddenly.

The process of selecting the dominant element in object space, possibly based on the figure-ground concept,requires additional research.

The diameter of the foveola projected into object space largely determines the size of the fronto-parallel plane

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Figure 7.4.3-4 Block diagram of the complete horizontal vergence system of human vision. No stage 2 analogprocessing is shown following the photoreceptor cells and prior to the analog-to-pulse conversion in stage 3 for signalprojection to the pretectum (consisting of both the LGN and PGN. All stage 4 signal manipulation is believed to beperformed in analog form (with stage 3 sections interspersed between widely separated (>2 mm) engines.

(FPP) of precision binocular (stereopsis) vision..

These calculations are more complicated than indicated above in the case of the precision binocular, stereopsis, case.The calculations lead to a mean vergence angle for the scene and a mean disparity of the scene (taken here to relate tothe point F). They also produce a differential version angle (lateral disparity) and a differential depth disparity valuefor each element in the scene relative to the mean values. These tags associated with every element within the field ofview of the foveola (taken here to be a 1.2 degree diameter in humans) are then used by the LGN’s to prepare a fusedperception for the left and right hemispheres of the binocular field and by the PGN to prepare a fused perception of theprecision field of view.

For a mean disparity distance much greater than the interocular distance, the Vieth-Muller circle can beapproximated by a straight line perpendicular to the sagittal plane of the eyes. The straight line and the 0.2degree tilt of the vertical axis (from a perpendicular to the Vieth-Muller plane) in object space define the so-calledfronto-parallel plane of stereopsis vision. A series of fronto-parallel planes parallel to the mean plane can beassociated with the resolvable depth disparity values.

Following optimum fusion, the resulting preliminary 3D perceptions are passed to the subsequent stage 4 engines withinthe occipital lobe from the LGN and within the pulvinar from the PGN, for additional information extraction. As a resultof the additional tagging, it is likely the information associated with a given scene element is passed to the occipital lobeand pulvinar over address nerves using multiple neurons supporting word-serial/bit parallel encoding.

7.4.3.3 Detailed model of the horizontal vergence system

This work has developed detailed models of each element and circuit used in the HVS vergence system. Theseindividual models have been individually qualified based on the relevant data. By assembling these circuits from othersections of this work, a detailed block diagram of the HVS is shown in Figure 7.4.3-4. To avoid complexity, the two-stepprocess involving both the LGN and PGN is shown as only involving the PGN.

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368Hung, G. (2001) Models of Oculomotor Control. London: World Sceintific, figure 35

This figure is similar to the simpler HVS block diagrams of the literature, but it is greatly expanded. This is particularlytrue with respect to the sensing circuits that lead to the generation of the vergence signal within the common blocklabeled the pretectum (or perigeniculate nucleus, PGN, in humans). Compare it with a similar recent diagram by Hungthat still lacks any description of how the input function is derived368. The PGN is a very complex computational engineof the midbrain. It will be examined more fully below. The PGN accepts an input signal from each eye that describesthe scene viewed by the foveola of that eye. It subtracts the two signals to generate a difference signal. The initialdifference signal describes the difference in arrival time between the signals from the two eyes as shown in [Figure7.4.3-1]. This output may also exhibit a distinct amplitude profile if the signals from the two eyes are not symmetrical.This can happen if the eyes are receiving spectrally different input signals, are operating under different states ofadaptation, or the networks connecting the photoreceptors to the PGN have different gain characteristics. The initialdifference signal is integrated by passing through a low pass filter. The output of this filter is then used to drive thelateral terminal nucleus in the motorneuron complex of each eye. The signal is applied to the LTN’s with a polarity thatcauses the two eyes to rotate in opposite directions. This rotation is counter to the rotation introduced by the pointingcommands. The pointing commands are applied to the LTN’s with a polarity appropriate to rotate the eye in the samedirection. The effect of the vergence signals is to change the angles αR and αL symmetrically such that αR – αL describesthe convergence angle required to converge the eyes. This same signal can be used to focus the visual system at aparticular distance from the eyes.

The signals applied to the PGN are derived from the scene by scanning the line of fixation of each eye across the sceneusing one of the scanning patterns described in the text accompanying [Figure 7.3.7-1]. These patterns are of very smallmaximum angle. For purposes of discussion, this angle will be taken as 20 seconds of arc, about the diameter of three2-micron diameter photoreceptor cells. This scanning is introduced by the twitch portion of the lateral oculomotormuscles in response to the perturbation generator shown in the figure. This twitch signal is introduced into the LTN’swith such a polarity as to cause the two eyes to rotate in the same direction. The result is output signals from the twoeyes that are synchronous but exhibit a difference in time depending on the angular rotation of the eyes from parallelismand the distance to the scene ( the angle αR – αL). This is the vergence disparity (or “disparity vergence”) signal. Whilethis time difference is dominated by the position of the scene relative to the eyes, it can be affected by the absolute delayassociated with the P/D mechanism of the photoreceptor chromophores. This delay depends on the illumination levelapplied to the individual spectrally selective photoreceptors, as will be discussed further regarding the operation of thePGN.

While the time difference between the two signals at the output of the photoreceptor cells is quite stable, the amplitudedifference can be quite large. This is because of three main factors.

1. The operating state of the chromophores of the individual photoreceptor channels can affect thenet signal amplitude. 2. The operating state of the adaptation amplifier within these channels can also affect the net signalamplitude. 3. The logarithmic conversion of the current through the photoreceptors into a voltage by the diodeload, labeled (4), at their pedicles can have a lesser impact on this amplitude.

There may also be an impact on the amplitude of these signals if a test set is used partially tocompensate for the gross motion of the scene. Such compensation changes the frequency spectrumof the incident image relative to the limited passband of the adaptation amplifier as discussed below.

While the twitch mechanism associated with the oculomotor muscles is critical to the operation of the tremor mechanism,it is not significant in the vergence loop performance. Any contribution to the signal loop is filtered out by the limitedhigh frequency performance of the adaptation amplifier and the projection stage neurons.

The most appropriate mathematical model of the vergence subsystem consists of the “integral-derivative” type circuitof the P/D mechanism combined with the bandpass characteristics of the adaptation amplifier and the low passcharacteristic of the oculomotor muscles. The resulting equation has a simple zero and a zero expression in thenumerator and two poles in the denominator.

7.4.3.3.1 A mathematical model of amplitudes in the sensing portion of the vergence system

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Dynamics of Vision 7- 185The complexity of the vergence servomechanism makes discussion of a suitable mathematical model awkward.However, it can be addressed initially in segments. This paragraph will concentrate on the amplitude aspects of thevergence disparity signals. The time delay aspects are addressed in the next paragraph.

Conceptually, the model consists of a differencing circuit, the PGN, driving a plant, the oculomotor neuron and musclesystems, in response to two sources of vergence information. The two sources provide information concerning theirnormal, relaxed, condition. This condition is determined both genetically and through learning, as the morphology ofthe body matures. While the foveola are near the center of the retinas in humans, some animals have displaced, or evenmultiple foveola, that allow them to provide appropriate signals to their PGN (‘s).

The two sources of vergence information are the photoreceptors of the individual eyes. The mathematical modelapplicable to these photoreceptors has been explored extensively in Chapter 12 of this work. The model includesseparate terms related to the P/D mechanism of the chromophores, the variable gain and limited bandwidth of theadaptation amplifiers and finally the logarithmic conversion associated with the pedicles. Without addressing timedelays, and under small signal conditions, the voltage at the pedicles of the photoreceptors in the foveola of each eyecan be described by:

Eq. 7.4.3-1V Ln R E d LnA= ⋅ =∫ ( ) ( )λ λ λwhere R(λ) is the responsivity of the photoreceptor and E(λ) is the radiant flux applied to the photoreceptor.

Subtracting the signals from the corresponding photoreceptors in each eye results in an equation of the form:

log AL – log AR which can be rewritten, Log [AL/AR]. Eq. 7.4.3-2

It is interesting to look at the form of Eqs. 7.4.3-1 and 2 for each source and the logarithmic manipulation illustratedabove. If the two sources are operating under identical conditions, and complete convergence is achieved, all of theterms within the expression, log[AL/AR], cancel. The variation in amplitude at the output of the correlator, due to thesource signals, would be zero. This is the nominal condition. The only output of the correlator is a signal related to thetime delay between the two signals as discussed below. This delay may introduce an amplitude term in the output relatedto the terms AR and AL being shifted in time before complete convergence is achieved. When complete convergencehas been achieved, even the output due to the relative delay between the signals is also equal to zero.

7.4.3.3.2 A mathematical model of delays in the vergence system

The time delays associated with the vergence system can be defined using [Figure 7.4.3-2] and figures in Section 15.2.5which illuminate some of the delays associated with the signal projection circuits of vision.

The following analysis will not discuss delays arising in the awareness and volition portions of the visual system. Thesedelays are distinctly external to the closed loop performance of the vergence system. As noted earlier, these inputs canbe considered a separate stage in the overall performance of the vergence capability, or as establishing the initialconditions within the closed loop vergence servomechanism. These additional delays have been discussed in Section15.2.5. That discussion is consistent with the delays associated with the signaling paths presented in Section 7.4.

Major delays arising within the vergence servomechanism are:

1. The delay (relative to an arbitrary reference) in the light from an edge (or other feature) sweeping across the profileof a given photoreceptor.2. The delay in the reporting of that edge sweeping across the outer segment of the photoreceptor due to the P/Dmechanism. This delay is a function of the excitation state of the chromophores.3. The delay associated with transferring the signal generated by the chromophores to the pedicles of the photoreceptors.This delay varies with the length of the axons, which vary with position of the photoreceptors within the foveola.4. The delay associated with the transfer of the signals from the pedicles, through the stage 2 and stage 3 neural circuits,to the output of the stellate cells connecting directly to the nodes of the PGN.5. The computational delays associated with the PGN and other neural processing within the POS.6. The delays associated with the transfer of neural signals from the output of the PGN to the oculomotor muscles.7. The delay inherent in the muscles of the oculomotor system.8. The delay due to the inertial properties of the ocular globes.

The above forms an impressive list. Seeing why a nominal delay of 160 ms is commonly reported in the literature iseasy. However, only a few of the terms are variable. Terms 1, 2, 5 and 8 are the dominant variables. The others are

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nominally fixed. The goal of the vergence system is to minimize term 1. Term 2 is a direct function of the illuminationlevel falling on the photoreceptors. This term is under the complete control of the scientific investigator. It can rangefrom less than 1.0 milliseconds to large fractions of a second under laboratory conditions. Whether the value for term5 is a variable is not currently known. It undoubtedly varies with the complexity of the scene. Term 8 is welldocumented (Section 7.3.4 through 7.3.6). Under closed loop conditions, terms 1 and term 8 are driven to zero, subjectto the limits on loop performance introduced by the other delays (and any compensation provided by other cognitiveprocesses).

By accumulating the fixed delays due to terms 3,4,6 & 7, accounting for 120 to 150 ms is easy. Terms 4 & 6 are roughlyone or two ms each. Term 3 can be much larger. The remaining delay appears to be associated with the computationaltime required by the PGN, term 5. The average value of term 5 is not currently known. It could be 750-125 ms. Forfurther details regarding these delays, see the appropriate sections of Chapter 13, signal processing, Chapter 14, signalprojection and Chapter 15, higher signal processing. Under closed loop conditions, the remaining delay due primarilyto the P/D mechanism brings the total delay into the 160-ms region generally reported in the literature.

7.4.3.3.3 A mathematical model of the plant portion of the vergence system

The plant associated with the vergence servomechanism is the same as that discussed regarding pointing in Section 6.35& 7.3.5. The only difference is that here the plants associated with each eye are driven differentially rather than intandem as in pointing. Because the geometry of the ocular globe and muscles introduce transcendental factors(trigonometric terms), this mode may introduce some second order effects when discussing vergence at high anglesrelative to the rest position of the eyes. However, under closed loop conditions, the net effect will be small. The modelfrom the above sections will be adopted in whole for the discussion in the next section.

7.4.3.3.4 Discussion of the overall mathematical model of the vergence system

Using the definitions in Section 7.3.4, the vergence servomechanism can be described as a Type 2 servomechanism withcomputational enhancement. This designation applies under normal operating conditions. It exhibits near zero error(noise limited) for fixed objects in the scene. It will exhibit a fixed spatial error when tracking a moving scene. Itsability to track accelerating scene elements is distinctly limited. Through training, the subject can learn to introduce“Kentucky windage” to maintain convergence and focus on objects moving along unusual trajectories. This capabilityis analogous to that available within the pointing servomechanism.

The servomechanism uses the same stage 1 circuits associated with the photoreception process. It uses a separateG–channel (Y–channel) that involves the direct transfer of signals from the photoreceptors to the mid brain. This channeldoes not involve any stage 2 signal processing although it still relies upon stage 3 signal projection mechanisms. Thesystem involves a differencing technique within the PGN that makes the system largely immune to amplitude variationsin the signals used to create the vergence disparity signal under normal operating conditions. However, laboratoryconditions may disrupt this balance and introduce largely spurious (test set generated) amplitude effects. The majorlimitation on the performance of the system is the total delay due primarily to the length of the neural paths within thestage 3 projection paths. A secondary limitation relates to the time delay associated with the PGN, especially whensimple edges are use as test targets. The PGN appears to be optimized for a scene of a specific, as yet un-characterized,complexity. Finally, the performance of the system can be reduced if the scene is not adequately illuminated. Bestperformance is apparently achieved at light levels similar to those prescribed for a drafting room or for performing finehand-eye work such as quality sewing.

The complexity of the servomechanism makes the presentation of a simple mathematical model, such as those in mostof the literature containing less than three variable terms, inappropriate until many test criteria have been established.The partial model associated with just the amplitude response of the photoreceptors of each sensory channel (eq. 7.4.3-1)can be written in expanded form. In expanded form, the amplitude portion of the equation involves a definite integralcontaining at least seven parameters including the simple zero in the numerator. The latency portion of the equationcontains at least four terms containing at least one of these parameters. One parameter appears in both equations andis directly proportional to the absolute intensity of the stimulus at the retina. This dependency makes it very difficultto compare the work of investigators using different test sets.

By insuring that the two sensory channels are treated symmetrically in the design of a test set, many terms containingthese parameters can be made to cancel completely. Here, the output of the PGN is a simple signal describing the timedelay related to the vergence disparity angle, αR – αL. This error signal has a rise time limited primarily by the rise timeof the P/D mechanism. Under conditions of unusual scene brightness, the limit may be due to the passband of theadaptation amplifier. Under the assumption that the subject is either emmetropic, or wearing appropriate glasses, theselimitations are usually encountered before any other channel restrictions. As addressed in Section 7.3.10, the focus

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369Zuber, B. & Stark, L. (1968) Dynamical characteristics of the fusional vergence eye movements system IEEETrans Syst Sci Cyber vol. SSC-4, pp 72-79370Krishnan, V. & Stark, L. (1977) Op. Cit.

Figure 7.4.3-5 Averaged disparity vergence responsesobtained for 2-degree convergent disparity pulses of 100msec and 500 msec. Labels have been added and changedto emphasize these are responses. See text. Modified fromZuber & Stark, 1968.

servomechanism and the vergence servomechanism work in parallel and simultaneously. If the eyes are not able to focusproperly on the object, the risetime associated with sweeping the scene across the photoreceptors of the retina will bedegraded. This will impact the signal-to-noise performance of the vergence servomechanism and its ultimateconvergence capability.

Figure 7.4.3-5 provides disparity vergence responses very similar to those predicted in the above discussion369. Whilethe model presented in Zuber & Stark was not confirmed by their data, the data is in excellent agreement with the theoryof this work. The initial delay of about 200 msecs is compatible with a relatively low light level stimulus. The curvesclearly show the difference between two P/D responses passed through the adaptation and logarithmic conversionprocesses and then subtracted from each other as described by the model of [Figure 7.4.3-2]. Note the long responseexhibits a break at 500 + 200 msec. This is appropriate for a stimulus that is long compared to the impulse response ofthe network under test. The shorter response does not exhibit such a break. The response is the impulse response of thenetwork when driven by a pulse properly described as an impulse relative to the network. The impulse response isessentially the P/D response of the photoreceptor cell. The model also supports similar response data acquired by Jones(S & C pg 300). In the Jones data, Jones appears to overlook the fact that he is using three different types of stimulationand not two. While he uses a step stimulus, a 200-msec pulse stimulation and a 50-msec pulse stimulation. As in theZuber & Stark example, the 50-msec stimulation is actually an impulse, not a pulse, from the perspective of the circuitunder evaluation. The 50-msec interval is shorter than the impulse response of the circuit by itself. This accounts forthe reduction in amplitude of his third waveform without any change in waveshape compared with the second waveform.

The quality of the match between theory and measurement depends on the particular configuration of the test set as thisaffects the balance shown by the signals being differenced. If these are not balanced, the net waveform will reflect thisimbalance. The Jones data clearly shows the 160 msec latency associated with th vergence disparity response (regardlessof the duration of the stimulus duration). It should be noted that averaging the instantaneous amplitude values associatedwith five responses is not appropriate if the intent is topreserve the latency associated with the response. Suchan average will always show a (less than distinct firstorder) latency equal to the minimum latency of the set.

Jones found the Fourier transform of his responsesexhibited a corner frequency of about 1/3 Hertz. Thisvalue is virtually identical to the baseline time constantof the adaptation process of this work. Such a timeconstant gives a frequency response falling as 6 Db peroctave above the corner frequency. Depending on theillumination level of the stimulus, this corner could be adouble corner with the frequency response falling at 12Db per octave above the corner frequency. See similarresponses in Section 17.6.3. The response of a circuit toa pulse with a duration shorter than the time constant ofthe circuit invariably exhibits a peak amplitudeproportional to the pulse duration. This is clearly seen inthe Zuber & Stark figure.

7.4.3.4 The vergence data available in theliterature

It is recommended that readers review Sections 7.4.3.2& 7.4.3.3 before attempting to review the published data.It is presumed that this will provide the reader a greater understanding of the test configuration affecting the data.

The data of Krishnan & Stark form a good starting point370. They describe their model as heuristic. This seems correctfrom both a pedagogical and a problem solving perspective. They provide very little data on the conditions related totheir test equipment (or the test equipment of others they have relied upon in their discussion). Their data in figure 5 and7 is clearly that of a Type I servomechanism exhibiting significant internal delay. The delay is about 150-200 ms. Thedominant time constant is about 1.6 Hz. This value corresponds generally to the time constant of the physical plant, the

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371Pobuda, M. & Erkelens, C. (1993) Op. Cit.

eye muscles combined with the inertia of the ocular globe. They do show some overshoot in their data that leads themto suggest an integral-derivative type of controller. As they show in figure 4, the choice of a conventional integral-derivative controller leads to considerable ringing that is not seen in their data. Under some conditions, the ringing couldbe filtered out by the time constants associated with the plant. The measured overshoot is completely compatible withthe overshoot associated with the P/D mechanism, although other (isolated) pre-emphasis circuits within the neuralcircuits could contribute to the displayed amount of overshoot. The P/D mechanism does not exhibit any ringing. Thetime constants shown in their mathematical model for the controller are quite compatible with the time constants of theP/D mechanism under low photopic conditions. The cumulative delay of 160 ms shown in the model is also realisticfor low photopic conditions, where the P/D mechanism only contributes a few to 10 milliseconds to the total. As notedabove, under higher illumination, the total delay could be reduced by 10-20 ms and the total settling time could bereduced to less than one second. Frame (a) of their figure 5 shows a slight turn of the response away from the zero levelnear three seconds. This is compatible with the low frequency limit of the adaptation amplifier passband in the modelof this work. Their figure 3 is not used in the paper. It is taken from a more extensive model of the plant appearing inan earlier paper. That model appears to have many second order conceptual features.

The data of Pobuda & Erkelens reflects many different test modes371. Their figure 1 suggests the forward bandwidth ofthe vergence servomechanism is less than 0.6 Hz and is similar to that found for the version servomechanism. This valueis much lower than the bandwidth of the oculomotor plant alone.

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372Ogle, K. Mussey, F. & Prangen, A. (1949) Fixation disparity and the fusional processes in binocular singlevision Am J Ophthalmol vol xxx, pp xxx373Ogle, K. Martens, xxx. & Dyer, xxx. (1967) xxx 374Helmholtz, H. (Xxx) Southall translation: Treatise on physiological optics, 3rd Ed. NY: Optical Society ofAmerica375Nakayama, K. (1983) Kinematics of normal and strabismic eyes In Schur, C & Ciuffreda, K. ed. VergenceEye Movements: Basic and Clinical Aspects Boston, MA: Butterworths pp 543-564376Porrill, J. Inins, J. & Frisby, J. (1999) The variation of torsion with vergence and elevation Vision Res vol39, pp 3934-3950

7.4.3.4.1 Transient response of the vergence system

Rashbass & Westheimer have performed a series of experiments designed to measure the forward open loop gain of thevergence subsystem. Their test set did not have the frequency response required to measure the flicks and tremorassociated with the analytical mode. For vegence stimuli applied within the field of the foveola, they recorded datasuggesting the vergence response was bandlimited to less than 0.6 Hertz. This is compatible with the model of this work.

7.4.3.4.2 Vergence deviation as a function of stimulus location

Schor discussed vergence deviation as a function of forced vergence for conditions where the visual field centered onthe point of fixation is blanked out. The discussion centered on the difference in performance between the foveola andthe peripheral retina. It focused on the data in two papers by Ogle, et. al372,373.

7.4.3.5 State diagram for the vergence subsystem RESERVED

7.4.3.6 The role of torsion in vergence and version

Pedagogy usually describes the motions of the oculars in terms of an orthogonal system of axes (Section 2.2.1) andsuggests the muscles attached to the oculars act orthogonally. This is not the case.

Whenever the two eyes are not looking straight ahead (focused on infinity) in the plane of the optical axes of the twoeyes, the two eyes exhibit an independent rotation of their optical axes in the plane of focus. Such rotations wouldprevent the image from the two eyes to be merged into a single composite image except at the very point of convergence.The role of the torsion subsystem is to correct this condition over the largest region of the object field as possible. Inhuman vision, the goal is to correct the image within the region associated with at least the foveola, 1.8 degrees (2.0degrees according to Helmholtz in 1867374, 1.5 degrees according to Nakayama in 1983375).

The geometry of the situation and the operation of the torsion subsystem remains a subject of discussion in the literature. Porrill et al, discuss the history of stereo vision beginning with the simple Donder’s Law that focuses on the plane ofthe horopter and disregards the torsional error. They note Listing’s Law covers the more general requirement376.Contrary to their assertion, this subject has been studied to exhaustion within the field of stereo-photography for aerialand satellite reconnaissance . The subject has been documented extensively in that field where the torsion-angle iscalled the crab-angle. The geometry has been analyzed for both flat, curved and spherical object surfaces and ahead,behind and lateral to the flight path. These conditions completely encompass the equivalent situation in vision. The JetPropulsion Laboratory is the current leader in the correction of stereo-images to remove distortion preventing optimummerging. When using photographic film, that does not stretch easily, an average crab-angle must be used to optimizethe field. When electronic sensors are employed rather than photographic film, correction is possible on an individualpixel basis before merging. The human imaging system is not believed to employ pixel-by-pixel correction within thelateral geniculate nuclei where merging appears to occur.

Porrill et al, have described both the cycloversion and cyclovergence components of the overall binocular torsionparameter. However, they only explored the vergence condition as a function of field elevation. They discuss thepurpose of Listing’s Law as if it is implemented biologically for an unknown reason and constitutes a limitation on theperformance of the system (their section 4.2). In fact, Listing’s Law is implemented in order to optimize the performanceof the system when viewing the real world external to the subject. Figure 9 of Porrill et al, summarizes the situation wellfor the conditions they explored. The achieved performance appears compatible with the theoretical requirement. Amore complete exploration of both vergence and version with variations in elevation should conform to the situationdocumented as above.

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377Ostriker, G. Pellionisz, A. & Llinas, R. (1985) Tensorial computer model of gaze--I. Oculomotor activity is expressed in non-orthogonal natural coordinates NeuroSci vol 14(2), pp 483-500378Morisita, M. & Yagi, T. (2001) The stability of human eye orientation during visual fixation and imaginedfixation in three dimensions Auris Nasus Larynx vol 283, pp 301-304379Ellis, W. (1938). A source book of Gestalt psychology (pp. 71-88) in translation London: Routledge &Kegan

Ostriker et al have provided detailed modeling of the human ocular rotation focusing on the non-orthogonality of themusculatura of the two eyes377. They develop the paths followed by the eyes when commanded to off-axis positions inconsiderable detail but do not concern themselves with the corrections introduced by the torsional pair of muscles toensure the ability to merge the two images during convergence. After discussing the prior tendency within thecommunity to consider the ocular movements as orthogonal for convenience, they note, “In general, reducibility is acharacteristic feature of orthogonal (e.g. Cartesian x, y, z) multivariable systems, but a decomposition of themultivariable CNS, such as the gaze-stabilization apparatus, into single dimensions along horizontal and verticaldirections cannot be taken for granted. Caution is warranted in particular because of the non-orthogonality of both theextraocular motor and vestibular sensory apparatus, and in general because the gaze stabilization involves other systemst hat are even less orthogonal (e.g. neck muscles). Thus, it is preferable to find a general solution for the CNS controlof gaze for any system of coordinates, rather than limiting the analysis to special quasi-orthogonal solutions.”

Morisita & Yagi have recently addressed the stability of the eye as it relates to vergence and version in threedimensions378.

7.4.4 Filling in of a color

Having established in this work that the photoreceptors do not act as an imaging sensor, but instead as change detectorsdependent on relative motion between the retina and the image projected on the retina, how a uniform color field isperceived becomes important. The biological mechanism of color rendition for an area in object space of constantchromatic and luminous intensity appears to be similar to that used in Hollywood to colorize old black and white movies.It involves identifying closed perimeters, or large contrast change contours of figures, and then attaching a specificchromatic parameter to each of them. In the case of the neural system, this process must be achieved withoutintervention by an outside intelligence.

7.4.4.1 The figure-ground concept of psychology

The psychology community long ago developed the concept of figure-ground within a set of Laws of PerceptualOrganization (beginning with the founder of the Gestalt School of psychology, Werthheimer, 1923379).

Closed contours in visual space establish special closed regions in the percept describing that space. These regions arecalled figures and are perceived as lying in front of the “background.”.

The original concept needs updating in a variety of aspects.

C The idea of the retina as an imaging device is false and archaic. The animal retina is a change detector as proved forhumans by Yarbus, by Ditchburn and by others. C The term contour is probably a poor choice of translation from the German. What is meant is either a closed contrastedge or perimeter of sufficient amplitude to be above threshold in stage 4 signal manipulation (information extraction)in the neural system, or a contrast edge forming a closed contour (figure) within a larger ground.. C Such a contrast edge in neural signal space is the result of the motion of the image applied to the retina across theboundary of one or more photoreceptors acting as change detectors.C The contrast edge may be interpreted in luminance space, the R-signal of neural signaling or in spectral space, the UV–,S–, M– or L– signal space. In complex images, the contrast edge in chrominance space is actually evaluated in thechrominance difference, O–, P– and Q–signal spaces.C The basic difference signal is generated as a contrast edge between the figure signal and the ground signal generatedwithin an individual photoreceptor by the image motion (Section 7.3.7).C The basic difference signals are combined and integrated within the lateral geniculate nucleus and the perigeniculatenucleus depending on the area of the retina involved.C The figure-ground concept need not involve a physical edge or border. A contrast change of sufficient amplitude isenoungh.

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380Ditchburn, R. (1973) op. cit. pg. 242

Contrast edges always belong to the figure, never to the background. The concept is cascadable. The smallestidentifiable contrast perimeter, or contrast contour encloses the first figure. If the ground is delineated by a larger closedcontrast perimeter, it becomes a secondary figure surrounded by a larger ground, etc. The identifiable contrast perimetermay be formed within the luminance channel or a specific spectral photoreceptor channel of vision. A contrast perimeteror contour may be more prominent if formed within the O, P or Q channels of vision.

Yarbus describes the same procedure with regard to filling in a color as suggested by Wertheimer, and as is used inmodern computer-based drawing programs. The system first establishes the perimeter of a figure. Once established,a color can be selected from a palette and used to fill in the perimeter. The manner in which the color is selected is veryspecific in biological vision. If the luminance of the interior of a large field remains constant for more than threeseconds, it becomes a null field, in the absence of any other information, the fill color selected to fill that null field isthe same as that of the surround (ground). However, if the photoreceptor signals defining the perimeter indicate a changein luminance or chrominance between the outer edge of the figure and the adjacent edge of the ground, the figure isassigned a luminance and chrominance compatible with the integrated luminance and chrominance differences measuredby those photoreceptors (relative to the surround).

In this work, the notion of Yarbus, that the visual system “identifies” the empty field arising in artificial conditions withthe empty field arising in natural conditions, is not needed. The cognitive and control portions of the cortex haveinstructed the ocular muscles to tremor. The system is an open loop. The cortex has no choice but to assume the musclesdid as instructed. Therefore, the cortex has no way of determining whether the empty field is due to natural or artificialconditions. This realization is probably why he chose to use quotation marks around the word identifies.

The definite delay in filling in a color discussed by Yarbus is interesting. It is not obvious whether this delay is relatedto signal processing in stage 4 or to cognition in stage 5. See the call for additional research in Section 7.4.4.3.

7.4.4.2 Filling in for the blind spot and capillaries on the retina

Ditchburn380 discusses the fact that a stationary image on the retina is not perceived. He points out that this is why theblind spot and blood vessels on the surface of the retina, are not perceived. However, he humanizes the visual systemby saying; “The visual system accepts the fact that no signals are received from certain parts of the visual field.” Thereis no need for this position. The computational and cognitive powers of the visual system work with the informationreceived. Again, the cognitive and control portions of the cortex have instructed the ocular muscles to tremor. Thesystem is an open loop. The cortex has no choice but to assume the muscles performed as instructed. Therefore, theyprocess and evaluate the imagery detected by the retina. It does not happen to include any information about the blindspot or other scotomas. It does include changes in luminance contrast surrounding the blind spot. These changesconstitute a perimeter. Therefore, the cortex assigns a color and luminance to the area within the enclosed perimeter inthe usual way. Ditchburn does point out another important aspect. The cortex does not just assign a uniform color andluminance to the assigned area within the perimeter. It appears to fill the perimeter with a pattern matching that at theedge of the perimeter, again like “wallpaper” in a computer paint program.

Ditchburn also documents the fact, recognized by many people, that the blood vessels may be seen under two specialconditions. If a bright light is shined into the eye from the side of the field of view, the shadow of the blood vessels maymove relative to the retina due to normal tremor. They will be perceived under this condition. Some people willoccasionally perceive the pattern of some blood vessels due to the expansion or movement of some blood vessels causedby the pulse from cardiac activity.

7.4.4.3 Processing luminance versus chrominance values at a perimeter

It appears that color contrast does not play a major part in whether a perimeter is recognized. If the luminance of theinterior of the first perimeter is the same as the luminance found between the first and second perimeters, the firstperimeter will not be perceived. The color of the inner perimeter will be chosen to be the same as within the secondperimeter. The color found at the inner edge of each perimeter is sensed and used to fill in the rest of the interior of thatperimeter. Whether more than one pixel is used to determine this color fill is not clear. However, this technique doesexplain why Mach bands are not seen in daily life except under very special conditions.

7.4.4.4 A uniform field is dependent on the luminance/chrominance at its perimeter

After a 15 year hiatus, Ditchburn & Foley addressed the question of color rendition in a partially stabilized image in two

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381Ditchburn, R. & Foley-Fisher, J. (1985) Effect of imposed step movements and pulse movements of theretinal image on perception of hue with coloured targets Ophthal Physiol Opt vol 5(4), pp107 - 116.382Ditchburn, R. & Foley–Fisher, J. (1985) Effect on perception of hue of imposed oscillatory movements ofa stabilized retinal image Ophthal Physiol Opt Vol 5(4), pp 369 - 382

papers in 1985381,382. The first paper addressed step changes in the position of a stabilized image. In the second paper,they employed a colored diamond on a dark background and repetitive motions aligned to the diagonals of the diamonds.Tests for a possible variation with illuminance were made with red light (Chance’s OR]) at retinal illuminances of 640and 60 id. The results were indistinguishable. It was not therefore considered important to equate the illuminances (forcolours of different spectrophotometric composition) very accurately. Retinal illuminances of 500 td for yellow(Chance’s OY3), 370 td for green (Chance’s OGr l ) , 400 td for blue (Chance’s OBIO) and 320 td for blue (interferencefilter 448 nm) were used. Initially the subject classified the colour appearances into the following 4 grades.Grade 1: Full colour (appearance of the restored image similar to that of the unstabilized image except for somedarkening near the centre). Grade 2: Good colour (the target appeared bright and of the same hue as the unstabilized image but there was anoticeable loss of saturation).Grade 3: Poor colour (the hue was distinguishable and, except when the yellow target was displayed, was the same asthe hue of the unstabilized target. The target appeared pale in comparison with the unstabilized target and veryunsaturated). For yellon the perceived hue was orange-definitely more red than the unstabilized target. Grade 4: No colour (field appeared grey). The results for different hues and for triangular-wave motion are shown ascontour maps of frequency f and peak-to-peak movement M in Figs 2-6. Red gives rather larger areas for “full colour”and “good colour” than green or blue. Green and blue require about the same value of M for full colour but green isrestricted to a narrower frequency range. The results obtained for blue (Chance’s OBIO) and blue (448 nm interferencefilter) are similar except that the interference filter gives good colour at a lower value of M and a narrower range off.The artificial oscillatory movements required to restore vision of the boundaries of a dark target on a white backgroundwere measured by Ditchburn and Drysdale (1977). The curve from their results giving, for each frequency, the movementrequired to enable the subject to see the boundaries 50% of the time is shown on Fig. 2. This curve indicates that themovement required for “good” colour vision is at least 5-fold larger than that required for seeing the boundaries. For “fullcolour” the movement is more than 15-fold that required for seeing the boundaries. Also the frequency range for colourvision is much narrower.

Good graphics were supplied describing these results.

Preliminary observationsIf the target is moved with a fairly large movement ( I 5 ‘ ) and the frequency is varied from 0.1 to I5 Hz,the following sequence is observed with green light at a retinal illuminance of about 1000 td.(i) At 0.1 - 0.2 Hz the edges of the target are seen intermittently and they are seen to move but the hue is uncertain.(ii) At 0.5 Hz, the green hue appears at the edges of the target but the centre is pale.(iii) At 1 .O - 3.0 Hz the appearance is similar to that of the unstabilized image in regard to brightness, hue andsaturation.(iv) At 4.0 Hz the centre goes dark and appears unsaturated.(v) At 6.0 Hz the edges are clear but there is little discrimination of hue.(vi) At 6.0- 10 Hz the edges gradually disappear.(vii) At 12 Hz the edges are not seen but there is a flicker in the field over a vaguely defined area in the region of thecentre of the target.

Effects similar to (vii) and (viii) are obtained with the unstabilized target.

If the movement is suddenly stopped when the target is seen (i.e. with a movement of 1.0 Hz to 4.0 Hz), the targetdisappears in about a second. If the movement is stopped when the target is not seen (13- 15 Hz) the target appears forabout 2 s as though it were a freshly presented stabilized image.

When the frequency is held at 3 Hz and the movement is gradually increased from zero, the edges appear at apeak-to-peak value of about 1 ’ , then colour at the edges of the target ( - 5 ’ peak-to-peak) and finally colour spreadingover the whole target area ( - 10’ peak-to-peak).

Similar results were observed with red and blue targets. Optimal frequencies were not quite the same for all colours.

SUMMARY AND CONCLUSION( I ) There is no significant difference between the effects of sinusoidal, triangular and square waves, provided the

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Dynamics of Vision 7- 193amplitude and frequency are the same. This applies to frequencies of 1 Hz and above.(2) The movements required to give good colour vision are large compared with the movements required for perceptionof a boundary. At luminances in the range 300- 2000 td a factor of 10 is involved.(3) The above movements are also large compared with the movements which remain when a well trained subject fixatesas accurately as he can.(4) The movements required for perception of red are less than those required for perception of green or blue. Yellowrequires even larger movements.( 5 ) Movements of frequencies above about 4 Hz (i.e. periods of 250 ms) are ineffective in regard to perception of hue.

We conclude that, whereas for perception of boundaries it is sufficient to move the boundary through a distance equalto one-inter cone separation, hue perception is obtained only when the boundary sweeps rapidly over many cones.Perception of hue thus involves combination of signals from many cones. Also the signals must be maintained for a timeof at least 100 ms.

The data of Ditchburn & Foley–Fisher is compatible with, and supportive of the distribution of color photoreceptors inthe retina described in this work. The experiments need to be repeated using more detailed protocols and selected narrowband lights in order to discover additional properties of the contrast edge detection (stage 1) and information extraction(stage 4) mechanisms. By using narrower band lights in these experiments, it should be possible to determine the relativeutility of using luminance contrast versus various chrominance contrasts in reading and other tasks. (See Chapter 19on reading.

7.4.5 Mechanism of precision convergence & Stereopsis via PGN-pulvinar

The closely related mechanisms of precision convergence and stereopsis underly the high performance aspects of boththe fusion and depth perception phenomena associated with the foveola. These mechanisms will be discussed beforethese phenomena. Precision convergence and stereopsis are phenomena dependent on the foveola-PGN-pulvinar signalpathway. As of this time, no significant theories of precision convergence and precision stereopsis, fusion, and depthperception have appeared in the literature that successfully explain the operation of the visual system in these areas oralong this signal pathway.

There is a problem with the theoretical derivations in the literature. That is their inconsistent treatment of the relationshipbetween stereopsis and fusion. In some cases fusion is treated as a result of stereopsis, in some stereopsis is treated asa result of fusion and in some fusion and stereopsis are treated as distinct mechanisms. A similar situation exists betweenstereopsis and depth perception. This work will show that a clear difference exists between these concepts. Stereopsisis a specific visual mechanism involving a two-dimensional correlation process performed within the precision opticalsystem and extending over the spatial field associated with the foveola. Both fusion and depth perception are perceivedphenomena that result from the stereoptic mechanism. Stereopsis operates in a three-dimensional signal processingenvironment, x, y & z. Fusion is a perception related to the plane perpendicular to the line of sight and only involvingthe x,y plane. Depth perception is a perception related to distance along the line of sight and only involves the axisperpendicular to the x,y plane, the z plane.

Both fusion and depth perception has been studied for centuries. However, most of the studies have been qualitative.Most studies have failed to differentiate between performance related to the foveola and that related to the rest of theretina. This situation has been partly due to the precision of the instrumentation available. It has also been due to thelack of an adequate understanding of the underlying mechanisms of vision. Recent texts continue to be qualitative,follow the 19th Century investigators Maddox, Fechner, Panum and Hering, and be based on Gaussian Optics. Theyfurther assume the index of refractions of both the aqueous and vitreous humors are equal to 1.000.

Schor & Cuffreda describe depth perception as falling off logarithmically with field angle. However, they do notdescribe how the response reaches a peak near the point of fixation. Neither do they discuss the significant change indepth perception performance at the edge of the foveola. This section will compare the wider literature with a morequantitative model.

The two-dimensional correlation process is performed by the combination of the PGN and pulvinar, components of thethalamus in the midbrain. The two-dimensional correlator found in the PGN is the embodiment of the conceptualbinocular correlator discussed by Lappin & Bell in 1976 and by Tyler & Julesz in 1980. The combination of the PGNand the pulvinar are the physiological embodiment of the so-called cyclopean retina of Julesz. The label cyclopean retinais misleading in that it suggests the existence of an image within the cortex. The information concerning the scene isactually stored in a tabular file and not as a multi-spatial-dimension image. The tabular file corresponds to (at least aportion of) the saliency map of Treisman in 1986 (Section 15.2.2).

The two-dimensional correlator of the thalamus also supports the version, accommodation and analytical function of

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383McKee, S. (1983) The spatial requirements for fine stereoacuity Vision Res. vol. 23, no. 2, pp 191-198

vision. When the correlator and the additional memory functions of the pulvinar are combined, the couple are theprincipal elements responsible for the interpretation and perception mechanisms associated with reading and the studyof images containing fine detail.

7.4.5.1 Background

The psychology community has struggled to understand the extraction of 3D information from the visual system for avery long time under the assumption that the retinas of the visual system are image detectors rather than change detectors.Pizlo has recently presented an entire book attempting to show how the parameters of figures in object space can beperceived as three-dimensional based only on a single 2D image projected onto one retina (Section 7.4.1.4.1). His entirediscussion assumes the implicit operation of the retina as an imaging device. “Existing psychophysical evidence showsthat the human eye is a calibrated camera (page 202).” This statement is patently false based on Yarbus, on ditchburnand on others. His arguments as a group are not convincing at the detailed level. His figure 3.13 can be disregarded.He proceeds to a Neo-Gestaltism and Neo-Empiricism to overcome classical problems found in the psychologicalexplanation for 3D perception (Chapter 2). His discussion in Chapter 5 regarding a new paradigm based on recent workmakes interesting, but largely anecdotal reading. He does present an interesting table in Appendix C comparing the goalsof human vision research compared to the goals of machine vision.

To understand all aspects of 3D imaging and particularly stereopsis, the operation of the visual system as a large arrayof change detectors (each retina) dependent on the relative motion between those detectors and the images projectedseparately onto the TWO retinas is mandatory.

7.4.5.1.1 Precision versus qualitative depth perception

Up through the 1950's, the depth perception of human vision had been assumed to involve only a single mechanism.At that time, Ogle stressed the likelihood of two distinct mechanisms but did not isolate them. He introduced the ideasof a high performance area and a low performance area. However, his criterion was the actual level of depth perceptionachieved rather than a relationship involving different areas of the retina. He defined a high performance area as thatof patent stereopsis (threshold disparity less than 10 minutes of arc) and a lower performance area of qualitativestereopsis (threshold disparity greater than 10-15 minutes of arc). He also discussed areas of central and peripheralfusion (pg 99). With time, the area of patent stereopsis, or central fusion, has come to be called foveal stereopsis. Thisinterpretation is rather loose and includes the area currently labeled the foveola, the fovea and the peripheral retina outto about seven degrees from the point of fixation. The more peripheral area of the retina became known as the area ofambient stereopsis or peripheral fusion. In more recent times, improved instrumentation has identified an area ofsignificantly better stereopsis than the inner area defined by Ogle. The area bounded by the edge of the foveola(nominally 0.6 degrees from the point of fixation) consistently exhibits threshold disparities down to less than fiveseconds of arc.

The area of best disparity threshold could be defined as the area of foveola stereopsis. However, this could easily leadto confusion. It will be shown that this area involves a different mechanism than that used in the more peripheral areas.It becomes easier to speak of the area involving the foveola as the region of true stereopsis and use the alternate term,qualitative depth perception, to describe the performance in the surrounding area. In this way, stereopsis is associatedwith the foveola and the analytical mode of vision (involving the PGN). This leaves qualitative depth perception asassociated with the remainder of the binocular field and with the awareness mode of vision (involving the LGN). Usingthis notation, stereopsis exhibits a linear relationship between disparity and the perception of depth (it is veridical) whilequalitative depth perception does not.

As frequently noted, true stereopsis requires geometric similarity between the images provided to each eye. This is tobe expected since the stereoptic correlator of the PGN operates primarily upon the contrast edges associated with eachobject. The image provided to the LGN is much lower in spatial resolution than that provided to the PGN due to the off-axis performance of the lens group. As a result, the LGN is much less sensitive to the detailed geometric similaritiesof the images provided to individual eyes. The similarity requirement suggests that the term fusion is related primarilyto stereopsis as associated with the foveola. Fusion of dissimilar shapes is a bit of an oxymoron.

The above definitions are supported by the more recent literature. The comment by McKee is probably the most direct.“Fine stereoacuity is a property only of the foveola383.” Depth perception appears to occur outside the foveola. However,

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384Ogle, K. (1953) J Opt Soc Am vol. 43, pp 906-385Tyler, C. (1983) In Schor, C. & Ciuffreda, K. Op. Cit. pg 240386Rawlings, S. & Shipley, T. (1969) Stereoscopic acuity and horizontal angular distance from fixation J OptSoc Am vol 59, no. 8, pp 991-993387Blakemore, C. (1970) The range and scope of binocular depth discrimination in man J Physiol vol. 211, pp599-622

its precision is much less, and judgements rapidly become impossible, see Ogle for details384.

Tyler, writing in Schor & Ciuffreda, has provided a graphical description of stereo-optical performance using a sphericalcoordinate system but without providing any data points385. They also note the performance falls off exponentially withdistance from the point of fixation. Figure 7.4.5-1 illustrates this capability along the horizontal meridian. The squaredata points and the dashed lines represent measurements made by Rawlings & Shipley using point light sources witha diameter of one minute of arc386. They employed a mirror haploscope adjusted for a fixation point at infinity. The largediameter of their sources obviously limited the threshold stereoacuity they could measure. They specifically noted,“There is a specific binocular function, a central process, without which stereopsis simply does not exist.”

Blakemore reported very similar results at about the same time387. He used multiple vertical slits 2.25 minutes wide and2.25 degrees long. He notes that his measurements were limited to about 0.5 minutes of threshold disparity by therelatively low illumination levels used. It was probably also limited by the width of his lines and by scatter from thesurface quality of the mirrors in his haploscope. He separated his measurements into those related to convergent anddivergent disparities relative to the point of fixation. The results showed small but systemic differences between the two.By plotting his results on logarithmic scales, he showed that the disparity did follow an exponential curve for disparitiesgreater than 0.6 minutes of arc.

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Figure 7.4.5-1 Stereoacuity as a function of horizontal offset. See text for details.

The triangular data point and the solid lines represent the data of McKee. She used narrow vertical lines of variablelength generated on Tektronix model 602 monitors using a P4 phosphor (33 msec decay time). Images from the twomonitors were combined using a pellicle. Polarizers were used to isolate the image presented to each eye. A series ofdots was used to form long lines. These lines were used by the correlator in the PGN to improve the stereoacuityreported. The dots on the screens were also about one minute of arc in diameter and spaced at 30 seconds of arc. Thequality of the edges of these lines may have an impact on the performance of correlator within the PGN of the subject.The monitors had a refresh rate of 100 Hertz. The test images were presented for short intervals to avoid voluntary eyemovements during each test. She says this configuration limited the minimum change in symmetrical binocular disparityto 3.4 arc seconds. Her subjects were chosen for their stereoacuity. She says the general population seldom exceeds5 arc seconds stereoacuity under similar conditions.

McKee provides considerable discussion related to the need for a physiological summation process that is compatiblewith the 2-dimensional correlator defined in Section 15.6 of this work. She confirmed that the summation was not basedon the absorbed photon flux but on the information carried by the test structure. She also noted the complicationsencountered when abutting lines were used as a stimulus. Finally, she noted the observation of Westheimer & McKeethat “presenting the target as little as five minutes of arc in front or behind the fixation plane elevates the stereo

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388Westheimer, G. & McKee, S. (1978) Stereoscopic acuity for moving retinal images J Opt Soc Am vol. 68,pp 450-455389Richards, W. & Kaye, M. (1974) Local versus global stereopsis: two mechanisms Vision Res. vol. 14, pp1345-1347

Figure 7.4.5-2 Stereopsis as a function of field angle withinthe foveola.

threshold388.” This latter finding suggests a mathematical description of the stereopsis function (within the region of thefoveola). It appears the threshold of stereoptic vision relative to the point of fixation can be described by an exponentialfunction with a negative exponent.

McKee (1983) and others have frequently discussed the variability in the limit of human stereoacuity amongindividuals. Textbooks generally give the limit as 2–10 sec of arc for “good” eyes. It appears stereoacuity is asignificant function of learning and probably practice.

Richards & Kaye have presented data on perceived depth perception as a function of stimulus disparity.389 Their dataare for crossed (convergent) disparities only. The images were centered on the point of fixation. The data can also beinterpreted as defining the perceived depth perception versus distance from the point of fixation. The perception of depthfalls rapidly when part of the stimulus falls outside of the foveola. For stimuli completely within the foveola, the datashows good agreement with the linearity rule corresponding to the veridical condition (although the use of a logarithmicaxis obscures this relationship). For stimuli at least partially outside of the foveola, the depth perception performanceis only qualitative.

Figure 7.4.5-2 is redrawn from xxx [ not from Richards & Kaye, could be Rawlings & Shipley, 1969, probably McKee,1983 but coord are different. ]

7.4.5.1.2 Block and state diagrams for theprocess of stereopsis

Figure 7.4.5-3 presents a top level block diagram of thevisual modality optimized for discussing stereopsis. It isan expansion of [Figure xxx] that highlights the parallelsignal processing occurring in stages 1 & 2 of each eye.It also highlights the matrixing of stage 3 signals passingalong the optic nerve in accordance with Section 15.2.5.Note the chiasm of the optic nerve is not reproduced asnormally represented because the two LGN are notshown separately as in Section 15.2.5. A secondarybifurcation of the optic nerve is shown here dividing thesignals of the optic nerve between the LGN and PGNengines (Section 2.8.1). The PGN is also called a minorfeature of the Brachia of the Superior Colliculus in themorphological literature, Section 15.1.6.

The arrows shown between stages in this figure represent stage 3 pulse signals (action potentials). In the case of the Qian& colleagues papers, it requires careful reading to determine whether their electronic probing of the striate cortexinvolves sensing pulse signals arriving at the occipital lobe or leaving the occipital lobe. The potential pulse signal pathsassociated with the cerebral cortex are described in Section 14.4.1.

A saliency map, presumed to be located in the parietal lobe of the brain, but potentially of holographic form is shownas a subtitle under the parietal lobe. It is a critical engine between the occipital lobe and the engines of stage 5 cognition.It is presumed, based on discussions in Chapter 19, that the saliency map is initially provided with signals from the LGN-striate signal path and that these are updated by subsequent signals provided by signals from the PGN-pulvinar signalpath.

Nothing has been found in the academic literature expressing how the perceived depth of a feature in the external field

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390Tyler, C. & Kontsevich, L. (1995) Mechanisms of stereoscopic processing: stereoattention and surfaceperception in depth reconstruction Perception vol. 24, pp 127-153, fig. 1

of view is represented in the saliency map or in stage 5 cognition.

The dark band, labeled the TRN represents the non-conscious “command and control” role of the thalamic reticularnucleus of the diencephalon (an outer layer of neurons covering a majority of the thalamus).

A neutral density filter is shown in the optical path between the stimulant and the stage 0 optics of the left eye to supportthe discussion of the Pulfrich Effect in the papers of Qian & colleagues, Section 7.4.5.5.

This figure can be interpreted as a detailed extension of the lower left quadrant of the Schematic of the recognitionfunction, [Figure 19.10.6-1]. The signal path leading to precision stereopsis, the foveola–PGN-pulvinar path, isassociated with the “What” path of that figure. The signal path leading to coarse stereopsis, the completefovea–LGN–Occipital lobe, is associated with the “Where” path of that figure. The regions of the retina beyond 5-8degrees eccentricity are probably not significant to the stereopsis mechanism.

Tyler & Kontsevich have provided a conceptual model of the visual system supporting their conclusions concerning theextraction of several features of a scene, including depth perception. The top level schematics of Section 7.3.1 lead toa much simpler view of the framework for stereopsis and other complex relations within the visual system than theapproach of Tyler & Kontsevich390. Figure 7.4.5-4 is drawn to resemble their figure.

Figure 7.4.5-3 Top level block diagram optimized for stereopsis discussions. The upper left quadrant illustrates theparallelism between the signal path for the two eyes. The upper center illustrates the complex matrixing of the earlystage signal paths into the later stage signal paths. At the extreme left is a neutral density filter intercepting the stimulusreaching one of the complete eyes and important when discussing the Pulfrich Effect. See text.

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Figure 7.4.5-4 A more detailed schematic of the top level block diagram focused on precision stereopsis. The binocularfield of view is reduced at the 12 degree vergence angle shown. The oculomotor subsystem, the PGN and the pulvinarare under the operational control of the POS during the analytical mode of operation.

The plane of vision is shown for a typical viewing distance of not less than 30 cm (10 inches). The fields of view of thefoveola are shown. When optimally converged, the two foveola image a common area of 1.2 degrees in diameter. Theneural signals related to this area are passed over the optic nerves to the PGN of the midbrain. The neural signals fromthe surrounding field of view are passed over the optic nerves to the LGN. These signals can be further segregated intothose related to the binocular field of view and the remaining monocular fields.

The signals related to the foveola are delivered to the PGN acting as a two-dimensional associative cross-correlator. Thecorrelator exhibits an effective diameter equal to that of each foveola. It is typically 175 photoreceptor cells in diameter.Internally, it may exhibit a small multiple of this number of cells to accomplish its mathematical tasks. The main tasksof this correlator are two. The first is to establish a global average vergence disparity error signal for the total image onthe foveola. If the deviation relative to this mean is acceptable (less than the required disparity for fusion), no furtheroculomotor action is required before further analysis. If the deviation is unacceptable, instructions are issued to theoculomotor subsystem, by the POS, to reconverge the lines of fixation. Following this fine tuning, the global mean anddeviation are recalculated.

The second is to establish a local vergence disparity signal for each significant object in the image. This signal consistsof a mean location of each object and a deviation from that mean describing the depth of the object relative to the globalaverage vergence.

The global average disparity for the scene and the local means and deviations for each object in the scene are transferredto the pulvinar. The pulvinar is a large lookup table and general database storing nearly all of the detailed signaturespreviously identified by the subject. It attempts to identify each object in the field of view based on experience. Itsoutput is commonly described as an interp, an initial interpretation of a small fraction of the scene (the followingterminology is drawn largely from the field of reading research discussed in Chapter 19). Multiple interps may berequired before a complete object is recognized at the level of the pulvinar. The result is commonly called a percept.It relates to the content of the instantaneous field of the foveola.

By systematically moving the line of fixation around within the binocular field (Section 7.5.2), a group of percepts areassembled that result in a perception of the entire binocular field of view. These movements involve a series of flicks,and some minisaccades, followed by a period of tremor. The tremor period corresponds to the time the PGN absorbsthe necessary amount of information about the instantaneous scene for it to establish a new interp. This period isfrequently described as a quiescent period between saccades when low spatial and/or temporal resolution instrumentationis used to study eye movements.

The binocular perception is passed to the next higher level of the brain for insertion into an even larger saliency mapdescribing the overall perception of the external environment of the subject. This saliency map also receives informationfrom other visual channels and from other sensory modalities. It is the saliency map that can be perceived and acted

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upon by the higher cognitive centers.

Figure 7.4.5-5 presents a preliminary stereopsis state diagram describing the operation of the stereopsis mechanism asan overlay on the pointing system of the POS. This state diagram will be discussed in terms of analyzing a simple setof geometric primitives combined into a single scene presented to the visual system of a subject. It can also be used todescribe the process of reading. It includes inputs from both the awareness and volition modes of the overall visualsystem shown in the top-level block diagrams. Following the initialization process, the process continues cyclicallyunder control of the precision optical system (POS) controller. Each cycle consists of three steps. The first step involvesmoving the direction of each major subject in the overall field of view into alignment with the line of fixation. Thesecond step involves analyzing the content of the scene presented to the foveola. The third step repositions the line offixation to interrogate the next most significant object in the overall scene. The next cycle occurs after the POS directsthe line of fixation to the next most significant object.

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Figure 7.4.5-5 State diagram for the stereopsis mechanism.

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391Tyler, C. & Kontsevich, L. (1995) Mechanisms of stereoscopic processing: stereoattention and surfaceperception in depth reconstruction Perception, vol. 24, pp 127-153

The steps outlined in the preliminary stereopsis state diagram can be listed in more detail.

1. Initial setupA. Start in rest conditionB. Accept high level a priori instructions (commands) from awareness or volition mode channels.C. Convert a priori commands to operational commands using the superior colliculus lookup tables

2. Implement operational a priori commands for accommodation, vergence and version to center the best images of ascene at the point of fixation for each foveola.

3. Prepare to transfer images of the scene to the midbrainA. Form an image of the scene on each foveolaB. Microscan images using the physiological tremor facilityC. Highlight the edges (contours) by differentiation within the adaptation function of the photoreceptor cells.

4. Transfer foveola images to the two-plane, 2-D associative correlator of the perigeniculate nucleus.

5. Perform vergence optimization on the scene presented to the correlatorA. Compute global vergence value for sceneB. Adjust vergence to minimize the error between computed global vergence and the a priori vergence valueC. Adjust global accommodation value based on corrected vergence value and the lookup table in the superiorcolliculus.

---- ---- FUSION IS OBSERVED HERE ---- ----

6. Compute local (mean) position and vergence difference tokens for each significant edge in the scene using the 2-Dassociative correlator.

7. Transfer all stereopsis tokens to the pulvinar

8. Compare edge tokens with the (experience based) signatures stored in the pulvinar.

9. Assemble the signatures to form an initial interp of the scene

10. Transfer interp of the initial scene to the appropriate cell of the initial saliency map

11. Repeat steps 1 through 10 for each foveola-sized image of the overall scene, under instruction from the POS.

12. Assemble individual interps, stored in individual cells of the initial saliency map, into a more comprehensive visualpercept

13. Transfer the comprehensive visual percept to the overall visual saliency map of the subject.

14. Associate the comprehensive visual percept with signals from other sensory channels to form a comprehensivesaliency map.

15. Make the comprehensive saliency map available to the higher cognitive centers for cognition and action.

The above schematic of stereopsis and state diagrams can be compared with the five-step process offered by Tyler &Kontsevich391. The differences are major because of the basic differences in concept. Tyler & Kontsevich do not addresshow the information from the retinas is transferred to the CNS or where in the CNS it resides.

7.4.5.2 Background specific to stereopsis

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392Leibovic, K. (1990) Perceptual aspects of spatial and temporal relationships Chapter 6 in Science of Vision,NY: Springer-Verlag pg160393Tyler, C. In Schor, C. & Ciuffreda, K. (1983) Op. Cit. pg 239

7.4.5.2.1 Stereopsis as distinct from binocular vision

If as proposed, stereopsis is distinct from binocular vision, and disparity is primarily related to stereopsis, it follows thatthe term binocular disparity should be replaced by stereoptic, or stereo-optical, disparity.

Efforts to define Panum’s Area have been pursued for a long time (Section 7.4.1.6). Leibovic provided a veryconceptual plan view of Panum’s area using a Keplerian Projection392. The figure was reproduced from an earlier paperof his in 1970. The figure exhibits three significant problems. First, it does not conform to the preferred definitions ofTyler and of Howard. They define Panum’s area as a two-dimensional plane perpendicular to the line of sight. Suchan area would appear as a line in Leibovic’s figure, not an area. Second, it does not recognize what is now known aboutthe topography of the occipital lobes and the role of the PGN (and foveola) in depth perception. If the fields of view ofthe foveola are drawn on his projection, a useful relationship appears. The small area around the fixation point (1.2degrees in diameter) associated with the foveola projections is the same area as delineated in the previous figure. Thissmall area is only represented at low resolution in the topography of the occipital lobes as shown in Section 15.2, andespecially [Figure 15.2.4-6 ]. The neurons from the foveola deviate from the rest of the optic nerve going to the LGNand eventually the occipital lobes (Section 2.8.1). These neurons proceed to the PGN and the precision optical system.Thus, the lines of fixation should be accompanied by the field of view of each foveola. The area within these fields ofview does not appear at full resolution in either hemisphere of the occipital lobe. Third, the target vergence angle shownin the figure is much larger than found in the real world. This distorts the proportions of the figure. The Leiboviccaricature also omitted the effect of accommodation and the spatial performance of the optics of the eye. These effectslimit the area of high performance imaging to a small circle surrounding the fixation point. This circle is well matchedto the circle representing the field of view of the foveola.

7.4.5.2.2 The PGN as a general purpose 2-D associative correlator

General agreement is found in the recent literature of stereopsis that a dedicated computational element associated withthe foveola of the retina exists (at least in humans and some higher primates). At this time the literature has not linkedany physiological elements of the HVS to such a computational element. The 2-D correlator of the perigeniculatenucleus and the lookup tables of the pulvinar and superior colliculus appear to provide the necessary computationalcapability and memory to satisfy the requirements of the stereoptic function. These entities are defined in considerabledetail in Sections 15.5 & 15.6. They are also shown to be compatible with the requirements of the more sophisticatedanalytical functions of detail analysis of a scene and reading.

The literature has assigned a variety of conceptual names for the entity that merges the two images into a single “image”in stereopsis. A serious problem exists in associating the term image with an abstract mathematical message that istransferred to a general data base. Thus, while Julesz has used the term cyclopean retina to describe this entity as animage, there is clearly no 3-D spatial image formed within the CNS as part of the stereopsis mechanism. Similarly, Marr& Nishihara have spoken of a 2 ½- D image consisting of a 2-D image surface with attached tokens describing the thirddimension. Here again, the word image implies the storage of information in a reasonably conformal surface somehowrelatable to the input images. This is not likely to be the case. Tyler, writing in Schor & Ciuffreda, refrains fromspeaking of an image in this context and uses quotation marks when discussing the three-dimensional “fovea393.” It ismost likely that the information from the foveola undergo anatomical computation before reaching the PGN and theorganization of the data in the PGN is optimized for feature extraction, not conformal integrity.

Noting that modern commercial and military map-makers no longer maintain a master 2-D map of an area of interest isuseful. Nor do they maintain a physical 3-D map of an area. All of the data is stored in a general purpose database ina digital computer. How the data is stored in the computer varies with ease of accessibility by the computers peripherals.It has absolutely nothing to do with a two-dimensional planar projection. The data base can be used to create imagesof the terrain never before seen by surveyors or anyone else.

The convenience of using random dot stereograms has contributed to the concept that the information processed withinthe CNS is maintained in a recognizable series of planes. It appears from this work that this is unlikely. Even thereconstructed stereographic information appears to be stored as a vector containing a series of tokens. These tokensrelate to the angular location and radial range of the original feature in “spherically specified” object space. In line withthe above paragraph, it may be that anatomical computation is used to arrange the information supplied to the PGN ina more rectilinear coordinate system. If this aids feature extraction, it would surely be done. However, when discussing

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Figure 7.4.5-6 The associative correlator of the PGN in itsrole supporting the version, vergence and accommodationsubsystems. The two loops highlight the ability of thecorrelator to perform local stereopsis in the horizontal andvertical directions. See text.

feature extraction within the 1.2 degree diameter area imaged by the foveola, the question appears moot. The small angleapproximation of trigonometry would suggest minor differences between the two representations.

The ability of the associative 2-D correlator proposed in this work to correlate over local regions as well as more globallyappears compatible with the concept of Tyler & Kontsevich ( pg 130).

The claim by Tyler and Julesz in the last paragraph of their paper appears quite compatible with the model of this work.They are describing the operation of the awareness mode of vision, involving the LGN and occipital cortex. Thiscapability operates without significant inputs from the vergence system and does not use the high quality memoryassociated with the mechanism of stereopsis associated with the analytical mode of vision.

7.4.5.2.3 The general operation of the PGN as an associative correlator

The PGN is discussed more fully in Section 15.6.6. This section will use Figure 7.4.5-6 to describe the operation ofthe PGN in its role of supporting the version, vergence and accommodation subsystems. This engine may be showneventually to be the most functionally complex individual engine in the neural system. It is a two-dimensional, multi-plane associative processor containing some multiple of 23,000 data cells. This number is based on the nominal 23,000photoreceptors within the foveola of each eye represented in each of the input planes of the correlator. It is likely thereare at least three or four times this number of individual cells within the PGN. This larger number would provide a cellfor each signal input and a cell for the sum and the difference signals relative to these inputs. This is the configurationshown in the figure.

It appears that the PGN accepts input from all of thephotoreceptor channels of each foveola without regard totheir spectral selectivity. It also appears that the PGNtreats them all equally. As a result, the PGN can operateat the maximum spatial precision provided by thecomplete retinal array in each foveola. Thismethodology provides the maximum signal-to-noise ratiofor a given scene contrast when the scene is illuminatedby a broadband (white) source. In the above sense, thePGN operates in an achromatic regime but does notemploy the spectral channel weighting found in theluminance, R–, channel (Sections 13.3 & 13.4 ). Thissignaling regime, associated only with the foveola, hasgenerally been labeled the Y– or G–channel (dependingon the context) in this work.

7.4.5.2.4 The detailed operation of the PGNas an associative correlator

[xxxStereopsis is one of many mechanisms implemented bythe perigeniculate nucleus, a part of the thalamus andwithin the precision optical system. The perigeniculatenucleus is organizes cytologically as a two-dimensional,multi-plane associative correlator very similar to theorganization of the lateral geniculate nuclei (LGN). Likein the LGN, the information from the photoreceptors ofeach foveola are inserted into separate planes of thecorrelator. Unlike in the LGN's, where the planes aredivided into pairs to support the luminance andchrominance channels of vision, the perigeniculate nucleitreats all of the photoreceptors achromatically. The PGNuses the remaining planes to hold calculated parametersrelated to the images.

The effective diameter of each plane of the associative memory is proportional to the diameter of the foveola, nominally175 photoreceptors. The data from corresponding points in the foveola are loaded into similar locations within the x,yspace of the correlator. For the PGN, it appears the association process related to stereopsis is largely limited to thehorizontal and vertical directions.

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Dynamics of Vision 7- 205The stereopsis mechanism mathematically merges the information (but not the images)from the two foveola. Themathematical manipulations of the stereopsis mechanism are carried out in two major steps, one of global stereopsisand one of local stereopsis. First, using its associative capability (which is similar to that used in a variety of man-made military computers), the PGNattempts to pair up all significant edges in the two images within the effective spatial limits of the correlator. Thisprocess is called local stereopsis. The scope of this sub-mechanism is illustrated by the vertical and horizontal loopsin the figure. Each loop can interrogate all of the cells in a given row or column related to the nominal cell, xn,yn of boththe right and left planes of the correlator. The long dimension of each loop is adjustable under control of either the POSor the thalamic reticular nucleus (TRN). The correlator can institute a pair of such loops for each nominal location,xn,yn, within the correlator. The individual loop attempts to locate significant edges appearing in both the left and rightplanes of the correlator. When it locates a significant pair, it calculates a mean x,y location for each pair. It alsocalculates a signed difference in location, delta-x, delta-y for each pair. It places the value of this signed difference inthe cell of an auxiliary plane with the x,y address equivalent to the mean calculated value. Having only two eyesarranged in a horizontal plane, the vertical signed difference in the above calculation is usually quite small relative tothe horizontal signed difference.

Second, the PGN then calculates the 2-dimensional centroid of all the means found above. This establishes the nominalcoordinate of the center of the information, x0,y0. This is the first part of the global stereopsis process. It then calculatesthe mean of all of the differences associated with the above pairs (where the sign of the differences is important). Thisvalue is taken as z0.

The original means and differences calculated above are now readdressed relative to the centroid x0,y0,z0. The meanlocations become xn,yn and the differences become zn. These values are assembled into a vector called an initial interp.It describes all of the significant edges in the small portion of the original scene imaged on the foveola. This interp isdelivered to the pulvinar for further correlation and conversion into an initial percept of vision.

The values xn,yn,zn, obtained in the above process, constitute the mathematical equivalent of the cyclopean imagedescribed by Julesz. The value of the centroid, x0,y0,z0 corresponds to the error between the actual target location inobject space and the a priori location the eyes were directed to by the POS. The x 0,y0 value corresponds to theeccentricity error and z0 corresponds the disparity error. If either of these errors is excessive, the POS may command asaccade or a change in vergence before proceeding.

The mathematical values xn,yn correspond to the "fused" image of each significant edge in the scene imaged on thefoveola. The value z0 describe the distance, the local disparity, of each "fused" edge relative to z0.

The purview of the correlator is circumscribed by Panum's limit in correlator space. This limit reduces to Panum's limitin x,y space for z = 0. The area enclosed by this limit is known as Panum's area. This limit can also be expressed bythe maximum value of z for the condition x = y = 0. This limit describes the maximum range of depth perception relativeto x0,y0,z0. For other values of x,y,z, a volume can be defined that is conceptually equivalent to Panum's two-dimensionalarea. It defines the combined range of fusion and depth perception achievable by the subject.

As a two-dimensional correlator, the PGN can increase the signal-to-noise ratio of its output signal by correlating overa larger area than that represented by a pair of photoreceptors, one from the same nominal position in each foveola.Thus, the length of the edge projected onto the foveola is important in determining the performance of the PGN, bothin vergence signal generation and other signal extraction operations. Further, being a two-dimensional correlator, it cancorrelate differences over the entire area of the foveola. This explains the ability of the visual system to improve itsperformance using gratings, even sine-wave gratings, and other patterns relative to its single edge performance. It caneven obtain vergence information from a series of dots placed within the object space viewed by the foveola. If the dotsare not in the same plane, neural confusion, and even vertigo, can result. Such dots, and various three-dimensionalpatterns are used in conventional tests of vergence performance in the clinic.

The desire for the photoreceptors of each retina to represent similar positions in object space introduces a condition ofinterest in the literature. Remarks that the two foveola may not be organized as mirror images of each other appear inthe literature (Section 3.2.2.2). They exhibit swirl patterns that suggest they are anti-symmetrical, e. g., their patternswould overlay each other if projected into object space.

7.4.5.2.5 Putative use of spatial frequency filters and Fourier transform calculations in vision

Discussions and proposals appear repeatedly in the binocular and stereoptical vision literature concerning the likelihood

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of spatial frequency filters occurring in the visual system. Many authors also have speculated on the use of the FourierTransform (and occasionally the La Place Transform) in conjunction with computations within the visual process. Nodata has been uncovered in the physiological or morphological areas supporting the use of such complex transformcalculations in vision. Neither have any physiological structures been identified within the neurology of the visualsystem that could represent multi-section frequency domain filters.

Using spatial frequency patterns, both square wave, sine wave, Gabor windowed and orthogonal, as stimuli in thelaboratory is obviously easy. For waveforms of only a few cycles, the actual frequency of the underlying frequency isonly known precisely because it was generated locally. However, showing any unique response to such patterns thatcannot be explained using simple temporal domain (and spatial domain in the case of the PGN correlator) sum anddifference circuits is very difficult.

As in discussing strings of action potentials, a conceptual problem arises when speaking of “windowed” waveforms ascontaining a specific spatial (or temporal) frequency. The recovery of the underlying frequency of a waveform isdifficult if the waveform consists of less than five cycles. At the level of two or three cycles, the definition of frequencybecomes awkward. Under these conditions, it is more appropriate to speak of time differences between the peaks, orother features, in the waveform.

No evidence of transcendental calculations being performed within the visual system has been documented. In specificcases, computations leading to similar results are accomplished using convolution integrals instead of transforms andmulti-section filters.

While postulating such filters and transform calculations is easy, investigators should refrain from proclaiming theexistence of such circuitry in the complete absence of any supporting physiological evidence.

7.4.5.3 The mechanism of stereopsis

The mechanism of stereopsis is associated with an overlay to the basic pointing system. It is one of the most complexmechanisms in the nervous system. Stereopsis can be described as a control-intensive synchronous mechanism involvingconsiderable neurological computation and memory. It involves the entire Precision Optical System in a variety ofindividual activities. These activities include the computational and memory activities of both the perigeniculate nucleus(PGN) and pulvinar of the thalamus. These two entities, operating in tandem, form the two-dimensional correlator andthe lookup table described conceptually as the cyclopean retina by Julesz. All of these activities are under thesupervision and control of the thalamic reticular nucleus (TRN). These functional relationships are defined in greaterdetail in Chapter 15.

The PGN and pulvinar are feature extraction engines. Their output is abstract information. That information does notform a fused image and cannot be described in terms of a retina. The information does form a tabular description of theinstantaneous three-dimensional scene presented to the two foveola. This tabulation can be considered an instantaneousor fragmentary saliency map. It includes both version, vergence and accommodation values for each element in the sceneimaged on the foveola.

The mechanism of stereopsis is highly dependent on the mechanism of tremor, the continuous, microradian-level,motions of the eyes. Stereopsis involves several individual operational processes. One of these processes calculates aninstantaneous global vergence value for the complete scene imaged on the foveola. A second process calculates aninstantaneous differential vergence value for each significant element in the scene imaged on the foveola. These valuesare used to form the instantaneous saliency map associated with that scene.

The instantaneous saliency maps resemble the interps and percepts defined when discussing reading. In both cases, theselow level perceptual elements can be combined with other similar elements to form a complete saliency map or semanticthought.

7.4.5.3.1 The geometry associated with stereopsis

Figure 7.4.5-7 is an expansion of the right frame of [Figure 7.4.3-1]. It shows an instantaneous field of view similarto that labeled “α” of a bowling alley in that figure. However, the instantaneous field of view has been rotated slightlyto be centered on pin #4. The resulting figure shows the detailed geometry involved in stereo-optically imaging andevaluating an instantaneous scene of 1.2 degrees width (requiring a total of few hundred milliseconds). The exquisiteprecision of the stereopsis mechanism makes it difficult to represent the true geometry of the situation. Therefore, thedistance between the eyes has been expanded in the figure to represent a convergence angle for each eye of four degrees.The dashed sector represents the instantaneous field of view of the left foveola. It consists of an array of about 175

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Figure 7.4.5-7 The geometry of the stereopsis mechanism in object space.

photoreceptors arranged in a one-dimensional fan that is symmetrical about the left line of fixation. The dotted sectorrepresents a similar situation for the right foveola. The two lines of fixation are shown intersecting at the instantaneouspoint of fixation established a priori by the visual system. Note that the two nominal foveola are unable to image thefour bowling pins simultaneously. Pin #1 is unknown to the stereopsis process.

The stereopsis process begins with the two eyes rotating synchronously by a few seconds of arc (microsaccades)according to the discussion of tremor in Sections 7.3.2 & 7.3.7. For purposes of discussion, let the tremor be representedby a linear sawtooth motion. This motion will convert the spatial positions within object space into a time series ofelectrotonic signals that can be passed to the midbrain. On arrival at the midbrain, these signals are placed in the two-dimensional correlator of the PGN (Section 15.4.1). The signals from the left foveola are placed in one surface of thecorrelator and the signals from the right foveola are placed in a second. The correlator subtracts the signals in these twoplanes to learn where and for what distance the signals in each local area (the local correlation interval) of the correlatordiffer. It then performs a two-step process. It calculates an average signal that describes the instantaneous globalvergence error between the scene and the a priori vergence value. With this value available, it calculates a differentialvergence error for each significant object in the image relative to the instantaneous global vergence error. These valuesare illustrated in the lower right frame of the figure. Since the depth of the scene is symmetrical about pin #4, theinstantaneous global vergence error shows the error between the a priori point of fixation and the radial position of pin#4. For the same reason, the differential vergence error for pin #4 is zero. The differential vergence error for pin #7suggests its additional distance from the a priori point of fixation. The differential vergence error for pin #2 suggeststhe fact it is nearer to the subject than both the a priori and instantaneous global vergence values.

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394Sperling, G. (1970) Op. Cit.395Howard, I. & Rogers, B. (2002) Op. Cit. pg 544-549

The ensemble of the a priori vergence value, the instantaneous global vergence error and the differential vergence errorsassociated with each significant object in the image constitutes a complete three-dimensional representation of the spatialfeatures associated with the instantaneous scene. This information can be combined with luminance and chrominancechannel information to provide a complete instantaneous saliency map of this particular instantaneous field of view. Itis proposed that this is a responsibility of the pulvinar. With further manipulation of the data, it can be combined withother instantaneous saliency maps to form a more complete initial saliency map or update any a priori saliency map.Whether the complete saliency map is a responsibility of the pulvinar or a higher cortical center remains uncertain.

Under many conditions, the instantaneous global vergence error computed in the above sequence appears to become thea priori vergence value for the next instantaneous scene presented to the two eyes.

With the two-dimensional correlator of the PGN performing local correlations over a correlation range correspondingto only a small number of adjacent photoreceptor cells, there is no need to employ complex correlation and evaluationcalculations to eliminate extraneous “phantom targets.”

7.4.5.3.3 The local correlation range supporting stereopsis and fusion

Little firm data exists concerning the correlation range of the two-dimensional correlator of the PGN when operatingin the vergence signal extraction mode. Sperling has suggested that correlation occurs over a range of +/– 1/8 degree394.This would correspond to a diameter of about 17 photoreceptors in the foveola. It appears likely that the number is morelikely five, or less, based on known tremor amplitudes. This would correspond to plus or minus two minutes of arc.Such performance would suggest the alarm mode of visual operation should command the line of fixation to alignmentwith a target to within this precision.

7.4.5.3.4 The potential variation in tremor amplitude

In the above analysis, tremor is a free variable. Variations in the amplitude and phase of the tremor signals applied tothe oculomotor muscles can have a major impact on the above correlation process. These parameters are completelyunder the control of the POS itself. The amplitude of the horizontal tremor determines what horizontal range of thefoveola area is overlaid on the two-dimensional correlator of the PGN. Under some circumstances, such as a verycomplex scene, changing the amplitude of the tremor may allow the correlator to concentrate on only the very center ofthe field of view. This would allow the POS to establish a nominal value for an a priori global vergence value. Withthis value in hand, the POS could then proceed with evaluating the remainder of the image.

7.4.5.3.5 Forms of stereoscopes and autostereograms

A variety of stereoscopes have been defined over the years. There are refractive(Brewster’s prismatic), reflective(Wheatstone’s mirror) and polarizing (polaroid projection) stereoscopes. “An autostereogram is a 2-D display thatappears in 3-D without the aid of a stereoscope” according to Howard & Rogers395. They describe a variety of thesestereoscopes and presentations, and how they are created.]xxx

7.4.5.4 Theories of Stereopsis prior to 1995

No definitive theories of stereopsis, separate from discussions of fusion and depth perception, were found in the recentliterature. The more general “theories” tend to emanate from either clinical or psychophysical investigations. Most werein the psychology literature. Based on limited physiological data, the theories related to stereopsis developed in the 20th

Century were necessarily conceptual and quite general.

All these theories assumed the visual system was based on imaging sensors. They therefore assume stationarygeometries when they discuss fusion, stereopsis, etc. The assumption of a stationary geometry, along with buildingcaricatures with very large vergence angles, has impeded progress in understanding fusion and stereopsis. Progress hasalso been impeded by the lack of an understanding of how the spatial information in the scene is converted into electricalsignals within the neural system. Noting that many stereograms presented in the literature are about three inches square

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396Weinshall, D & Malik, J. (1995) Review of computational models of stereopsis In Papathomas, T. ed. EarlyVision and Beyond Cambridge, MA: MIT Press397Howard, I. & Rogers, B. (2002) Seeing in Depth. Toronto, Canada: I Porteous pg 65398Anderson, B. & Julesz, B. (1995) A theoretical analysis of illusory contour formation in stereopsis.Psychological Review vol.102, 705-743.399Sperling, G. (1970) Op. Cit.400Nelson, J. (1975) Globality and stereopscopic fusion in binocular vision J Theor Biol vol. 49, pp 1-88

and are normally viewed at twelve inches is also important. The resultant field of fifteen degrees is much larger thanthe visual system can analyze at one time. It requires many saccades to explore such a scene in roughly 1.2 degreediameter instantaneous fields (requiring about 200 milliseconds each). Thus, the visual system makes many trips aroundthe state diagram of vergence and stereopsis in analyzing such a complete scene. Making global pronouncementsconcerning the performance of the visual system in analyzing such a scene is dangerous.

Weinshall and Malik provided a very brief review of computational models of stereopsis with many references but littlecritical content396. They did provide one controversial figure they credited to Krol & van de Grind. It shows “the doublenail illusion.” Accepting their illusion as real is difficult based on their description and the author’s personal experiencein many similar situations. Howard & Rogers provide the additional caveats required to understand this “illusion397.”The bibliography of Anderson & Julesz provides a better reference list on this subject398.

Sperling provided a broad review of what he called binocular vision in 1970399. It was followed by an equally broadreview by Nelson in 1975400. The terminology and variations in terminology between these two works are striking andwill be addressed below.

While Sperling titled his important 1970 paper “a physical and a neural theory,” a more current description woulddescribe his physical theory as a computational theory based conceptually on a physical analog. He states that his neuraltheory is speculative. He does review the Keplerian view of stereopsis, features of which are adopted later by Julesz.While he employs a smaller vergence angle in his caricatures of stereopsis, he continues to suggest that his and theKeplerian theory of stereopsis recreates a three-dimensional equivalent of the external world withing the cortex.

Sperling treats fusion and vergence as equivalent mechanisms, along with accommodation, and develops highlyconceptual interactions between each of these pairs. His separate physical models are not defined at the physiologicallevel. Thus, they could be overlays on a common physiological system.

He does claim his secondary neural binocular field (NBF) provides “outflow” to control the primary NBF. Thisinterpretation is consistent with this work.

Sperling expands on Helmholtz procedure for determining the fusion capabilities of the eyes. He noted that followingfusion, the images presented to the two eyes could be increased in vergence by as much as eight degrees before fusionwas lost by the subject. Although he did not discuss the initial fusion requirements in the same paragraph, he doessuggest that initial fusion requires a vergence error of less than plus or minus one-tenth degree. This value correspondsto six minutes of arc. At another point in the discussion, a figure of one-eighth degree is given.

The Nelson paper of 1975 provides a very detailed outline of what was known then about all aspects of binocular vision.However, it is quite conceptual in nature. He defines “fusion” as meaning sensory fusion and continues. “It is importantto distinguish between sensory fusion, which bespeaks unknown cortical processes, and motor fusion, or oculomotorconvergence and divergence, which produces apparent contour displacement by trivial eyeball turning.” Whileconceptually very useful, the expressions must, may, perhaps and apparently appear quite frequently in the paper. Thepaper treats fusion and stereopsis on a full retina basis. It also assumes a stationary scene geometry. The paper doesnot define the range of vergence angles it is discussing. It therefore must address the point-to-point correlation taskassociated with the two complete binocular images and address the resultant ambiguity problem. The paper definesretinal disparity detectors and additional disparity detectors in the cortex (no further delineation) without defining theirphysiological embodiment. In an analysis on page 31, Nelson stipulates that the visual fields are stabilized withoutrealizing that the visual system becomes totally blind to fully stabilized visual fields. Nelson does define a noniushoropter but the definition is torturous. After the midpoint, the paper provides a wealth of information concerning theobserved features of stereopsis and fusion but very little definitive material on the whys and wherefores related thereto. The Summary and conclusions are useful. However, Nelson does not cross the bridge to a two-dimensional correlator.He addresses the elements of such a correlator in terms of individual processes, using terms like inhibitory and mutuallyfacilitatory.

The papers of the late 1970's through the early 1990's are all focused on Keplerian projection and develop a variety of

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401Marr, D. & Poggio, T. (1976) Cooperative computation of stereo disparity Science vol. 194, pp 283-287402Grossberg, S. & Mingolla, E. (1985) Neural dynamics of form perception: boundary completion, illusoryfigures, and neon color spreading Psychological Rev vol. 92, pp 173-211403Grossberg, S. (1987) Cortical dynamics of three-dimensional form, color and brightness perception Percept.Psychophys vol. 41, pp 87-116 & 117-123404Yuille, A. Geiger, D. Bulthoff, H. (1991) Stereo integration, mean field theory and psychophysics Network,vol. 2, pp 423-442405Anderson, B. & Nakayama, K. (1994) Toward a general theory of stereopsis: binocular matching, occludingcontours, and fusion Psychol Rev vol. 101, no. 3, pp 414-445

rationales for solving first the correspondence problem and then the false target problem associated with a stationarygeometry. The false target problem is frequently described as the “disambiguity problem.” Several invoke complexmask shapes to be implemented within the neural system. None of the papers discuss the physiology of the visual orneural system. Several papers invoke a two-stage processing algorithm. However, none of these papers quantify thespatial extent of the individual stages.

The Keplerian projection adopted in these papers invariably involves targets closely spaced relative to the interoculardistance. The result is vergence angles suggestive of targets located less than three to five inches from the eyes. Severalpapers have invoked a multidimensional memory site in their concept. A few call for coarse motion between the eyesand the scene as an additional tool in solving the false target problem. Marr & Poggio called for the use of stabilizedimage tests in future work401. They were apparently unaware of the work of Yarbus showing this approach is not asolution.

Grossberg and Mingolla were aware of the limitations on stabilized images demonstrated by Yarbus402. However, bothGrossberg & Mingolla and Grossberg403 are highly philosophical in content. They frequently reference the paradoxicalqualities of visual imaging, introduce the retinex theory of color vision, and focus on area 17 of the cerebral cortex asthe location of percept extraction related to depth perception. They are the first to offer a block diagram of the neuralsignal processing required to satisfy their computational algorithms. Their binocular percept (extraction) stage,ostensibly in area V4 of the prestriate cortex corresponds functionally with the PGN-pulvinar correlation processor ofthe midbrain proposed in this work. In a detailing of his proposed circuitry, Grossberg introduces the concept of twosyncytia. The first syncytium processes monocular information and the second processes binocular information.Grossberg does focus on a boundary contour approach rather than a bulk object approach to signal processing.

Many papers in the 1980's focused on the partial occlusion of targets as a cue in the determination of depth perception.No substantial results were offered. In 1991, Yuille, et. al. presented a highly conceptual and intuitive discussion relyingupon probabilities and statistics (the Bayesian approach) to solve both the correspondence and false target problemsrelated to depth perception404. Their conclusions are not in a concrete form that can be implemented.

In their 1994 paper, Anderson & Nakayama continued to assume a stationary geometry in discussing paths “Toward aGeneral Theory of Stereopsis405.” However, they take a refreshing look at the “false target problem” as noted in Section7.4.3.1.1. Their description of Keplerian projection (pg 416) is one of the clearest found in the literature. They introduceconsiderable new material related to the perception of occluded scenes and occluded features within scenes. Anderson& Nakayama also address the question of the relationship between binocular fusion and stereopsis. They assert that mostvision scientists “would acknowledge that the relationship between stereopsis and fusion is tenuous at best.” They dointroduce several comments on the differences between fusion theories and suppression theories as they relate tostereopsis. Their paper concludes without making any strong assertions. Alternately, they “hope that our attempts tounify the stereoscopic phenomena described herein will motivate psychophysical and physiological experiments todiscover both the merits and the shortcomings of these ideas.”

7.4.5.5 Recent “physiologically–based” theories of stereopsis by of Qian & colleagues

Qian and colleagues have, during the 1990's to date, been expanding studies begun by Hubel and colleagues of the1960's. Their studies have been focused on measuring action potentials from stage 4 neurons accessible in the striatedvisual cortex of cats.

While they use the word physiology–based to support their mathematical models, their concept and backgroundin physiological models is elementary. They do not recognize the dual signal paths involved in stereopsis; theinitial coarse and later precision stereopsis achieved in human vision (Section xxx and then Section 15.2.5 forgreater detail). The role of the foveola and the role of the perigeniculate nucleus (PGN) and pulvinar are criticalin establishing precision stereopsis (after achieving precision convergence.) Their investigations related to the

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Dynamics of Vision 7- 211striate cortex of the occipital lobe are only applicable to coarse stereopsis. Even in this role, they do notrecognize the importance of the lateral geniculate nucleus (LGN) in establishing the initial convergence of theeyes upon a specific feature in external environment, or the role of the LGN in the initial merging of the imagesfrom the two eyes. They also fail to consider the role of the saliency map of stage 4 in its ability to present acoarse stereopic perception to the stage 5 cognition engines before being updated by the precision stereopticinformation from the foveola-PGN–pulvinar signal pathway (Section 4.3.6 and Section 19.6.3 for even moredetail).

Generally, their investigations have been primarily electro– physical in character (measuring electrical signals withinthe striate cortex following the binocular projection of patterns onto the retinas of cats. They have largely ignored thephysiological role of the LGN and apparently totally ignored the role of the foveola–PGN–pulvinar signal pathwayassociated with precision convergence and precision stereopsis. When members of the Qian group use the expressionreceptive field, RF, they are normally referring to the receptive field in the external environment associated with theneurons of the striate cortex, and not the photoreceptors of the retina. In general, they have used extracellular probingof the neurons of the striate cortex and monitored the amplitude of stage 3 action potentials to insure observations wererestricted to one neuron. They have categorized both simple and complex neurons of the striate cortex. Categorizationwas based primarily on whether the neurons showed a relatively narrow bipolar response to adjacent spatially diversestimulations (simple neurons) or a broad unipolar (analog or demodulated pulse) response to multiple spatially diversestimulations (complex neurons), as illustrated in figure 1a and 1b of the 1997 Ozhawa et al. paper. While they focus ontransforming their data into Cartesian coordinates in that paper, they noted that the striate cortex of cats was not arectilinear representation of the external visual field. Their stimulation in the Ozhawa et al. paper consisted of 5° by0.5° bars. These size bars were not conducive to precise convergence and precise stereopis via thefoveola–PGN–pulvinar signal path. They are compatible with the peripheral–LGN–occipital lobe signal path. The scalesassociated with figure 3 of their paper confirms this assertion.

The patterns in figure 3 show a variety of signal intensity patterns but they are not directly relatable to either the coarsevergence or coarse stereopsis tasks. they do appear to map the individual stimulus bars or patterns of bars. They employa process called a “binocular reverse correlation procedure” similar to a monocular reverse correlation procedure firstintroduced in the 1960's to further reduce their data. Their Results section does not focus on the advantages of thiscorrelation procedure or develop clearly how coarse stereopsis signals are derived that show how stereopsis is achieved.

The Ozhawa et al. paper introduces their proposed “disparity energy model” after explaining how the name relates toa general concept for “energy models” as those that compute the sum–of–squares as an indication of the desired signaloutput (as in their example of “the integral over time of the square of a voltage waveform across a resistor is proportionalto the energy dissipated within the resistor.”). They assert this notion may be generalized to neural signals with nofurther justification.

They explore a variety of options relating to their disparity energy model and show it reasonably predicts the wide rangeof disparity tuning curves derived from their electrophysiological experiments on anaesthetized cats. However, they donot show how this model outputs a signal in either absolute spherical coordinates relative to the external visualenvironment of the eyes, or in relative coordinates related to a reference distance (of an initial feature forming the pointof attention of the brain) from the first principle point of the optics of the cats eyes.

7.4.5.5.1 Mathematical model of Qian & Anderson paper of 1997

[xxx expand intro to this subject ]Qian & Andersen (1997) focused on the Pulfrich Effect;

“The classical Pulfrich effect refers to the observation that a pendulum oscillating back and forth in the frontalparallel plane appears to move along an elliptical path in depth when a neutral density filter is placed in front ofone of the two eyes. It is known that by reducing the amount of light reaching the covered retina the filter causesa temporal delay in the neuronal transmission from that retina to the cortex. The standard explanation of thiseffect is that since the pendulum is moving the temporal delay for the covered eye corresponds to a spatialdisplacement of the pendulum which produces a disparity between the two eyes and therefore a shift in depthThis interpretation becomes problematic however when it is observed that the Pulfrich depth effect is presenteven with dynamic noise patterns since there is no coherent motion in these patterns to convert a temporal delayinto a spatial disparity It was further discovered that the effect is still present when a stroboscopic stimulus isused such that the two eyes never see an apparently moving target at the same time and therefore noconventionally defined spatial disparity exists. It has been suggested that more than one mechanism may beresponsible for these phenomena. Our mathematical analyses and computer simulations indicates that all of theabove observations can be explained in a unified way by our integrated model.”

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406Qian, N. & Li, Y. (2011) Physiologically based models of binocular depth perception, in Harris, L. & Jenkin,M. eds. Vision in 3D Environments Cambridge: Cambridge University Press, Chapter 2, pp 11-45.407Ohzawa, I. DeAngelis, G. & Freeman, R. (1997). Encoding of binocular disparity by complex cells in thecat’s visual cortex. J Neurophysiol vol 77(6), pp :2879–2909.408DeAngelis, G. Ohzawa, I. & Freeman, R. (1993) Spatiotemporal Organization of Simple-Cell ReceptiveFields in the Cat’s Striate Cortex. I. General Characteristics and Postnatal Development J Neurophys vol69(4), pp 1091-1118409DeAngelis, G. Ohzawa, I. & Freeman, R. (1993) Spatiotemporal Organization of Simple-Cell ReceptiveFields in the Cat’s Striate Cortex. II. Linearity of Temporal and Spatial Summation J Neurophys vol 69(4),pp 1118–1135

Unfortunately, their mathematical model does not address an adequate physiological model. It is suggested thatthe signal flow diagram of Section 15.2.4 more clearly describes the physiological situation. The Qian &Anderson model does not describe clearly whether the signals they collected by probing the striate cortexrepresent the stage 3 pulse signals arriving at the striate cortex or leaving the cortex.

It does not incorporate the time delay introduced into the signal path of one eye due to the filter. This time delayoriginates in the photoreceptors of stage 1 according to the P/D Equation (Section 7.2.4) and not in thesubsequent signal path. Specifically, their phase parameter difference, equation (4), although defined preciselycontains a term not accounted for in their analysis, a delay introduced into one signal path as a function of thedensity of their optical filter.

The corrected equation (4) should read: Δφ / φl – φr ± φf(D) where the sign of the last term depends on whichoptical path contains the filter of density, D. The introduction of the filter term changes the apparent straight pathof Pulfrich’s pendulum in their figure 1 into an elliptical path with a minor axis proportional to the density, D.

7.4.5.5.2 Mathematical model of Qian & Li paper of 2011

Figure 7.4.5-8 shows an extension of a figure originally by Qian & Li406 which others have modified. The extendedcaption of the Qian version is worth reviewing. The first principle points of the two eyes are labeled Ol and Or in theirfigure and the distance between these two points is given by “a” in this figure. Frame b of the modified figure definesseveral terms as they are defined in the “nomenclature” section below.

There is a significant problem with the figure as modified by unknown authors. They have added a point labeled Rto frame B. While, the differential disparity, ΔR shown is reasonable, the binocular disparity shown is not. The dottedtriangle in frame A, added by this author, is realistic for the differential disparity. However, the it is not reasonable forthe binocular disparity as drawn. The location of the triangle in frame B for the left eye must be necessarily be fartherfrom the mean disparity than that for the right eye. The location of the two small diamonds in frame B must be reversedin order to represent a realistic feature in external space.

Contrary to their assertions in the cited paper, Qian and colleagues have been working primarily on mathematicalmodels of stereopsis. Their references to the physiology of vision are primarily conceptual. They note, “In aneffort to address this shortcoming, we have constructed physiologically based algorithms for disparitycomputation according to the quantitative properties of binocular cells in the visual cortex reported by Ohzawaand coworkers407 (section 2.1).” Two earlier papers by DeAngelis et al408,409. provides details related to theOhzawa paper. They encounter the behavioral parameters related to but do not identify or differentiate betweenthe precision and coarse signal processing paths of stereopsis leading to the saliency map of stage 4. Nodescription of the actual neural circuitry involved is provided in the paper. The models described are staticmodels; the cited paper and references do not include the terms, tremor, saccades or micro-saccades associatedwith the critically important motion of the oculars in the mechanism of stereopsis. Later in section 2.1, theyintroduce a simple photoreceptor cell and its receptive field (RF). They note, “Because of the phase dependence,simple-cell responses cannot explain the fact that we can detect disparities in static stereograms and in complexdynamic stereograms. Their description of the critical features of a simple cell are not supported in this work.Their focus on the cells of the visual cortex is not supported in this work either.

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“For simplicity, we consider only the plane of regard defined by the instantaneous fixation point (F) and theoptical centers, (ol and or) of the two eyes (i.e., the points n the eyes’ optical system through which the light rayscan be assumed to pass in straight lines).

This statement includes the implicit assumption that the angle (olFor) is small, less than about one degree.Otherwise, the thick lens equivalent of the lens must be used. Then, the Vieth–Muller circle passes through thefirst primary point of each lens, located within the lens portion of the ocular (Section 7.4.1.5).

The two foveas (fl and fr) are considered as corresponding to each other and thus have zero disparity.

The condition of no disparity between the two retina is only achieved at the point of the Vieth–Muller circle atits intersection with the sagittal plane formed by the eyes. This limitation is due to the muscular mountingassociated with the oculars.

To make clear the positional relationship between other locations on the two retinas, one can imaginesuperimposing the two retinas with the foveas aligned (bottom).

This sentence applies to a non-existent “bottom” portion of the image.

The fixation point F in space projects approximately to the two corresponding foveas (fl and fr) with a near-zerodisparity.

This condition is a result of the precision steropsis mechanism fine tuning the vergence system.

The disparity of any other point in space can then be defined as φ1 – φ2, which is equal to ψ2 –ψ1.

Correct only for within the horizontal plane.

It then follows that all zero-disparity points in the plane fall on the so-called Vieth–Muller circle passing throughthe fixation point and the two optical centers, since all circumference angles corresponding to the same arc (olFor)are equal. Other points in the plane do not project to corresponding locations on the two retinas, and thus havenonzero disparities.

Figure 7.4.5-8 The geometry of binocular projection and definition of disparity ADD. (a); the geometry within the planeof regard. (b); image points along the curved retina at its intersection with the plane of regard. See text. Modified fromQian & Li, 2012.

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Each circle passing through the two optical centers defines a set of isodisparity points.

Only within the nominal 51 degrees of binocular vision for quality binocular vision. Only within a 8.7 degreecircle about the point of fixation for processing within the fovea. Only within one degree for precision(stereopsis) binocular vision (using a nominal 1.2 degree diameter foveola), where the circles are usuallyapproximated by frontoparallel planes.

When fixation distance is much larger than the interocular separation and the gaze direction is not very eccentric,the constant–disparity surfaces can be approximated by frontoparllel planes.”

This statement corresponds to the small–angle condition required to use the thin lens approximation mentionedabove. This approximation only applies to the precision binocular (stereopsis) condition.

In summary, the drawing of Qian & Li, and similar drawings by many others, only apply to the region of one degreediameter at the intersection of the sagittal plane and the Vieth–Muller circle. By adding additional points in object space,the operation of the fusion and depth perception mechanisms can be outlined.

7.4.5.6 The proposed physiological theory of stereopsis

[xxx need to discuss here or in section on LGN extracting and/or merging of disparity information leading to the meandisparity and differential disparity values. ]

[xxx need to separate peripheral, qualitative (LGN path) and precision (PGN path) binocular operation ]Based on the above analysis, a concise physiological theory of stereopsis can be proposed.

Stereopsis is primarily a mechanism associated with the precision analysis of imagery presented to thefoveola of the visual system. Stereopsis is complemented by a separate mechanism associated withthe remaining peripheral retina and providing generally qualitative estimates of depth perception.

Stereopsis defines a mechanism performed within the 2-dimensional associative correlator of theperigeniculate nucleus that mathematically merges the information from the two foveola, calculatesthe x,y & z parameters associated with each edge presented by the foveola, within the effective spatiallimits of the correlator. It then delivers a vector, in the form of an initial interp of the information tothe pulvinar. The pulvinar performs additional correlation against data in its memory and delivers aninitial percept of vision to the saliency map.

[xxx mean disparity and differential disparity ][xxx how is this tied to Panum space? ]The stereopsis mechanism calculates the mean and deviation from the mean (both in two dimensions) of edges appearingin the images presented to the foveola within the spatial limits imposed by the effective outer spatial dimensions, theglobal correlation range, of the correlator. The associative properties of the correlator allow it to examine edges withina local radius, the local correlation range, of each image from the foveola in calculating the mean and deviation fromthe mean of each edge. Finally, the correlator calculates a global mean in x,y & z associated with the scene. The values,x0, y0, specify the nominal point of fixation of the scene. Deviations from the global mean associated with the local meanof each edge define the mathematical location, xn,yn, of each edge in the original scene. Deviations from the mean z0,of the deviation associated with each edge define the location, zn, of each edge relative to the nominal point of fixation.The stereopsis mechanism transfers these parameters, which as a group constitutes an initial interp of the scene imagedon the foveola, to a local interp map. It then collects these values over a period of time and places them into a largercontext associated with the complete scene.

The value z0 is a descriptor of the disparity error associated with the scene compared with the a priori eye disparity usedto image the scene initially. The value x0,y0 describes the eccentricity error associated with the scene compared withthe a priori pointing angles used to image the scene initially.

The associative correlator is organized to accept two-dimensional information from each foveola separated into verticaland horizontal components by the tremor mechanism. The data is stored in logically definable, but not necessarilyspatially definable, independent planes before processing. The extent of these two-dimensional planes is determinedby the effective global dimensions of the correlator. For purposes of this work, this dimension is nominally 1.2 degrees

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in diameter in object space, centered on the point of fixation, and corresponds closely with the defined diameter of thefoveola of each retina. In cases where the foveola are not converged on a single point of fixation, it is the effectivediameter of the correlator, not the combined fields of view of the foveola, that defines the limits of Panum’s area. Thisdifference introduces a limitation similar to physical occlusion in object space into the signal processing of the visualsystem. Information only loaded into the effective area of the correlator from one foveola is effectively occluded.

In this physiological theory of stereopsis, the associative correlator of the PGN is the physiological embodiment of thecomputational portion of the conceptual cyclopean retina of Julesz. The set of mathematical values, xn, yn, zn for all ncomprise the “image” analogous to the image of the cyclopean retina.

7.4.6 Fusion and Depth Perception as phenomena related to stereopsis

The phenomena of fusion and high performance depth perception both rely on the underlying mechanism of stereopsis.Because of this, it requires care to differentiate between the two phenomena in many experimental activities. Thisinteraction is complicated by the use of both dichotic and dichoptic test configurations. It is still further complicated bythe frequent use of simple test stimuli, frequently consisting of only two points of light or two simple objects–lines,squares etc. As a result, much of the data in the literature requires very close study to interpret the results and the claimsby the authors involved correctly.

The use of more complex targets in fusion experiments highlights the importance of the role of the torsion muscles ofthe oculars in generating superimposable images. Lacking this capability, the eyes would not be able to combine imagesof scenes distant in angle from when the eyes were pointed straight ahead. See Section 7.4.3.6 and the broaderdiscussions of convergence in Sections 7.4.3 & 7.4.5. See also Section 15.3.2.

7.4.6.1 The phenomenon of fusion

A closer marriage of the physiology of the visual system with the psychophysical data base leads to a more specificinterpretation of the fusion phenomenon than that found in the literature. It clearly defines two different fields of viewassociated with, and two different mechanisms supporting, fusion.

This work will differentiate between fusion associated with images within the field of view of the foveola (and processedby the PGN), and fusion associated with images within the more peripheral retina (and processed within the LGN). Forthe area imaged upon the foveola, stereoptic fusion is achieved (with its veridical relationship between disparity andperceived depth of field. For the area imaged outside the foveola, a simpler fusion is achieved where depth perceptiondoes not produce a significant veridical relationship.

Ogle has provided a good description of the conditions involved in the phenomenon of fusion. “It is the contours, thedemarcations between light and less light areas, that provide the pattern of the images and the stimuli for fusion whenthey exist in both eyes410.” This may be the case both within the field of view of the foveola and in the surrounding field.

A preliminary discussion of peripheral fusion appears in Chapter 9 of Ogle.

Stereoptic fusion as a phenomenon is limited primarily to the imagery presented to the nominally 1.2 degree diameterfoveola. The spatial resolution of the visual system is so poor outside this region, fusion becomes academic in theperipheral regions of the retina. The phenomenon is encountered when the following conditions have been met:

1. The vergence system has assumed a rest position or other a priori vergence condition based on experience.

2. The area of the scene imaged on the foveola of the two eyes has been scanned by means of the tremor mechanismand a set of signals relating to each edge of each significant object in the scene has been transferred to the two-dimensional correlator of the thalamus.

3. The two-dimensional correlator and the associated signal processing of the perigeniculate nucleus have calculateda nominal global vergence error for the imaged scene relative to the a priori vergence condition.

4. The precision optical system has rotated the eyes into convergence at a location near the point of fixation. It doesthis by minimizing the average vergence disparity error calculated using the edges of all of the significant objects imagedon the foveola. This is the condition where the global vergence response most nearly equals the global vergence

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stimulus.

5. The accommodation of the two eyes has been optimized for the same target distance as suggested by the above globalvergence condition.

6. The local vergence values (errors), relative to the global vergence condition, have been calculated for each significantedge associated with an object in the scene imaged on the foveola.

7. The local vergence values for each edge of each significant object have been assimilated with other values associatedwith the object and placed in the saliency map representing the area imaged by the foveola.

8. The saliency map representing the area imaged on the foveola has been accessed by the higher cognitive centersand a multidimensional perception of the scene has been arrived at. This multidimensional perception includeschromatic, brightness, depth, transverse velocity, historical and other information (including that from other sensorychannels) concerning the scene.

Under the above conditions, the instantaneous image of the scene is commonly said to be fused.

To achieve a multidimensional representation of a larger scene, the above process is repeated in a stepwise procedureat intervals of about 200 msecs. Each foveola-size area of the full scene that is within the binocular range of the visualsystem is assembled. If the head or body is allowed to rotate, a larger visual contribution to the saliency map may bemade. After all of the individual contributions to the saliency map have been made, the higher cognitive centers canaccess the more extensive saliency map and perceive a more complete scene. Note the perceived saliency map may alsobe larger than the total visual field of view in the sense that it may contain other sensory inputs obtained independentlyof the visual system.

The question of fusion as it relates to the peripheral retina is largely academic. The higher cognitive centers only accessthe saliency map for information about the outside world. This map contains information concerning the scale anddistance of every object in its surround that the eyes have observed. Wherever the eyes have imaged an area on thefoveola, a more precise estimate of the three dimensional aspects of that scene have replaced any previous estimate basedon peripheral fusion. It is the final estimates that are accessed by the higher centers. In the absence of such access, thehigher cognitive centers are largely unaware of, and unable to identify, objects in the peripheral field of view.

Ogle has provided a discussion of fusion as a function of the specific features of a simple scene411.

7.4.6.1.1 Misconceptions and the Keplerian Projection related to fusion

Several authors have written on the “fusion compulsion412.” The use of the word compulsion suggests the question ofwill is involved. As seen in this discussion, the circuitry of the pointing system, and the overlays leading to fusion areentirely “hard wired” and deterministic. The phenomenon of fusion occurs spontaneously when appropriate imageryis presented to the visual system. The term is closely associated with the concept and phenomenon of rivalry. Rivalryinvolves the commonly observed situation where the visual system will continue to change from one perception of adichoptic scene to another because of the difference between the two images provided (Section 7.4.1.1.2). Rivalry andcompulsion are phenomena related to the two-dimensional associative cross-correlator of the PGN. Ogle has provideda set of symbols frequently used to illustrate fusion, compulsion and rivalry phenomena413.

No signal processing (other than related to the steps outlined in the state diagram of stereopsis) is required to achievecorrespondence between points in the two foveola. The combination of the global vergence value and the individuallocal vergence values, both the mean and the deviation from the mean, related to each individual object in the sceneimaged on the foveola completely describe the spatial parameters of the perceived scene.

Julesz reintroduced the Keplerian projection to discussion of stereopsis in the 1960's after a very long hiatus. It hasappeared in many technical articles since. However, the caricatures of this projection always exhibit three distinctproperties. They always lack scales. They always describe static conditions. They typically describe target vergenceangles of greater than 45 degrees. Contrary to this literature, false targets (or ghost targets) are not a significant problemin stereopsis as defined here. Stereopsis only involves a nominal instantaneous field of view of 1.2 degrees. With a

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Dynamics of Vision 7- 217nominal interocular separation of 6.4 cm and a typical minimum viewing distance of 30 cm or greater, the actualvergence angles of vision are nearly always less than 12 degrees. As a result, virtually no false targets are generatedunder realistic visual conditions.

Unless more realistically drawn, the Keplerian projection should not be used for pedagogical purposes or research. Forevaluating the actual world of stereopsis, the Keplerian projection should be limited to two converging 1.2 degree beamsintersecting at a target vergence angle of 12 degrees or less. The beams should be labeled to show they each containabout 175 distinct sub-beams associated with the individual fields of view of the photoreceptors of the foveola. Thebeams should also be labeled to show they are synchronously scanning the scene, in two-dimensions, at approximately30 Hertz with an amplitude of about 2-6 seconds of arc. It is the scanning mechanism and the small size of the individualbeams that insure that no false targets are encountered.

7.4.6.1.2 The fusion phenomenon

Fusion as a phenomenon depends upon the process of stereopsis as performed within the associative correlator of thePGN. It is constrained to the common field of view of the two foveola. Fusion is also dependent on the mechanism oftremor to generate the pair of temporal signals related to each edge in the scene. The phenomenon is therefore limitedto a small instantaneous field of view described by foveola vision within the larger shared field described by binocularvision. Through the assembly of a percept of an entire binocular scene, the phenomenon of fusion can appear to applyto a full scene. This however is a cognitive perception based on a large saliency map in memory. It is not aninstantaneous event associated with stereopsis as a mechanism. This relationship suggests that fusion as a completepercept and the related phenomenon of rivalry occur after the information from the correlator of the PGN is turned overto the pulvinar.

The phenomenon of fusion relies upon the calculation of a mean and deviation from the mean related to the two imagesprojected onto the foveola from a scene in object space. Therefore, each significant edge in object space must be imagedon both foveola. To obtain a meaningful description of a complete object, its entire perimeter must be found within theinstantaneous field of view of both foveola. Because of this last requirement, small objects can appear over a wide arearelated to the foveola. However, large objects frequently extend outside of the imaged area. The perception of depthrelated to such large objects is generally constrained to that provided by the qualitative mechanism associated with theawareness mode of vision and the LGN/occipital lobe couple.

The local deviation of the mean associated with an object in a scene is calculated with respect to the global meanvergence error of the entire scene. It is this local deviation that is linearly related to the distance of the object from theglobal mean vergence of the scene. This linear relationship is described as veridical in the literature.

7.4.6.1.3 Fusion as a routine event

It may seem obvious but a primary requirement must exist before fusion can occur. The instantaneous scene projectedonto the two foveola must contain at least two separate edges resolvable into either horizontal or vertical components. In theory, two separate edges are required that are resolvable into both horizontal and vertical components. However,vertical vergence plays a minor role in vision compared with horizontal vergence. While a single edge appearing in bothimages is adequate for vergence and accommodation, it is not adequate for fusion and the description of the relativelocations in depth of the edges. Fusion requires the calculation of a global vergence value for the scene and thecalculation of at least two local vergence values relative to that global value. Once these calculations are performed,the location of the edges (and the shape of any associated object) can be defined in three-dimensional space.

Fusion will always occur under the above conditions. No need exists to invoke a mechanism related to the will. As longas multiple edges appear in the scene imaged on the foveola, fusion will occur. It usually occurs within less than 100msecs of PGN processing. The overall time delay following stimulus encountered in the laboratory is likely to be closerto 200 msecs when various transit times and latencies are recognized.

To optimize the stereopsis process leading to fusion, the edges in object space should not be too short. If they are veryshort, the full two-dimensional capability of the cross-correlator is not used effectively. It is also true that if the sceneis very complex, such as a random dot stereogram, fusion may become difficult. Ancillary clues may be necessary toachieve an acceptable state of fusion within a finite time.

A question is frequently found in the literature concerning how large a target disparity error can be introduced beforethe phenomenon of fusion will be destroyed. The answer depends heavily on the nature of the scene being viewed. Ifit contains relatively long high contrast edges, fusion can be maintained up to the point where secondary mechanisms,such as the ability of the eye muscles to create divergent values of eye vergence, are encountered.

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7.4.6.2 Effects related to the phenomenon of fusion

7.4.6.2.1 Spatial hysteresis related to stereopsis and fusion

The fusion phenomenon exhibits an asymmetry sometimes described in terms of hysteresis. Under laboratoryconditions, two images of a 3-D scene can be presented to the eyes at a disparity considerably different than the restdisparity of the visual system. Under these conditions, the images will not be fused. The subject will encounterphysiological diplopia and perceive a “double image.” If the difference in disparity between the two images and the restdisparity of the subject is gradually reduced, a point will be reached where the correlation function of the PGN canproduce a meaningful vergence disparity error. At that point, the pointing system will be enervated to cause fusion ofthe two images. This enervation will cause the eyes to adopt a disparity as equal to that of the test images as possible.The critical disparity error prior to fusion is about XXX.

Following fusion, increasing the disparity between the two images presented to the eyes by a considerable amount ispossible before fusion is destroyed. The vergence overlay and the pointing system will attempt to vary the vergence ofthe eyes to maintain a minimum disparity vergence error. Ogle has noted that the perceived image becomes double attwo different conditions414. For horizontal lines in the scene, doubling usually occurs near +/– two degrees. For verticallines, doubling usually occurs near +/– eight degrees. These early measurements did not give the absolute disparityassociated with these values.

7.4.6.2.2 References to peripheral fusion

Ogle has noted, “Fusion has usually been thought of in terms of central vision when the acuity is highest, and in the main,fusion in the central parts of the visual field is considered more important and dominant than fusion in the periphery (pp94-100).” The discussion is enlightening. However, calibration is largely absent from the data. The only conclusionthat can be drawn is limited in its practical utility. If large enough peripheral targets are used (0.5 degree visual angle),fusion of narrow lines at the point of fixation can be disturbed by these targets at angles of 12 degrees from the line offixation in the vertical direction. The experiment is worthy of repeating under more sophisticated test conditions.

7.4.6.2.3 Temporal hysteresis and other temporal aspects of fusion

Fusion exhibits a temporal hysteresis along with its spatial hysteresis. Records has discussed this hysteresis on page 657.He notes that fusion is achieved rapidly after even a very short exposure such as from a spark source or flash bulb. Ofcourse it is not perceived until later due to the signal propagation delays inherent in the visual system. However, theprocess appears to be complete within about 30 msecs for simple targets. For complex targets, the required time is muchlonger. On the other hand, Julesz & Tyler found that if the fusion associated with a scene was disrupted and thenimmediately reestablished, the disruption could be detected for intervals as short as four msecs. The shortness of theinterval suggests that the integration time of the photoexcitation/de-excitation process may have been affected in theseexperiments.

Records has also provided some comments on visual evoked potentials as a result of fusion experiments.

7.4.3.2.4 Fusion as a function of peripheral angle

Figure 7.4.6-1 reports the general transition between fusion and diplopia as a function of eccentricity for the normal eyeusing a specifically configured stimulus. At the detailed level, the transition described by Panum’s limit is asymmetricalbetween vertical and horizontal eccentricities.

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Figure 7.4.6-1 Fusion as a function of peripheral angle inthe normal eye. No measurements were reported for lessthan one degree. From Ogle, 1950.

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7.4.6.3 Theories explaining the fusion phenomenon

7.4.6.3.1 Previous theories of image fusion

Only a few theories of fusion appear in the literature. They are generally conceptual and use only loosely defined, andfrequently generic, terms. More significantly, they fail to pass the Yarbus Test of applicability (Section 7.4.1.2.1).

The discussion in this section borrows heavily from a short section in Schor & Ciuffreda (S & C pp216-210). QuotingSchor & Ciuffreda in 1983,

“There have been four classic approaches to the binocular fusion of stimuli in the two eyes into asingle percept; the synergy (Panum, 1858), local sign (Hering, 1864), eye movement (Helmholtz,1866), and the suppression hypotheses (Verhoeff, 1935). Each is subject to serious misgivings andall four have been rendered essentially obsolete by neurophysiological data on binocular responsesof cortical neurons, which give rise to a fifth, physiological hypothesis.”

Note carefully the dates associated with these theories. None of these theories is based on a realistic physiological modelof the visual system.

Considerable speculation arose concerning how the visual system fused the images from the two eyes (binocular fusion)during the 19th Century. Four simple concepts were offered. They were almost totally lacking in experimental support.(1) The synergy hypothesis of Panum (1858) originated the suggestion that binocular fusion is due to the “binocularsynergy of single vision by corresponding circles of sensation.” The Panum concept is enshrined in the designation ofPanum’s area as the range over which fusion occurs. (2)The local sign hypothesis of Hering (1864) was first appliedto both stereopsis and binocular fusion. It assigned an address to each target location imaged on the two retinas. If thetwo addresses were within a specific tolerance, the images were seen as one. (3) Helmholtz (1866) proposed analternative to Hering (it seems they always proposed alternatives to the work of the other). He proposed an eyemovement hypothesis of fusion, where the imprecise fine movement of the eyes led to an opening of a region in whichthe two images could be considered one. (4) du Tour proposed a suppression hypothesis in the 18th Century. It focusedon the rivalry of two dissimilar targets presented in equivalent areas of the two retinas leading to rivalry. In hishypothesis, the signals from the two retinas attempted to suppress each other through manipulations within the visualcortex.

During the 20th Century, several experiments were performed to validate or refute the above hypotheses. Schor &Ciuffreda summarize the problems associated with each hypothesis. This included the material in both the popular pressand technical literature by Hubel and his team. These studies continued to point toward what were described asphysiological theories. These were generally associated with the occipital lobe of the cerebral cortex. However, nosignificant new theories developed during the entire 20th Century. This was basically due to a lack of a comprehensivemodel.

Chapter 16 of Howard & Rogers, “Linking Binocular Images,” introduces a long series of empirically derived rulesconcerning fusion rather than a single concise theory of fusion.

7.4.6.3.2 The proposed Physiological Theory of Image Fusion

The hypotheses reviewed above are all relevant to the mechanism of fusion. However, they are all first ordercharacteristics gleaned from a black-box approach. They involve observations of the external parameters associated withthe internal operation of a complex system. Each of these hypotheses offers something that will be recognized in thetheory proposed in this section with one exception. It will become obvious that the visual cortex plays no direct role inthe mechanism. The phenomenon of fusion is focused on mechanisms concentrated in the midbrain and the POS. Whilesignals may be found within the cerebral cortex that can be correlated with events associated with fusion, they are notparticipants in the mechanisms resulting in the fusion phenomenon.

It is proposed that the fusion of images occurs within the two-dimensional correlation capability found anatomicallywithin the thalamus of the midbrain. The visual cortex plays no role in this mechanism. The overall process involvesthe operation of an outer (coarse) servomechanism associated with the awareness channel of vision and an inner (fine)servomechanism associated with the analytical channel of vision (see Section 7.3.3). It also involves the operation ofa two-dimensional correlator of major importance to the operation of the visual system in the higher primates, raptores,and many other arboreal and carnivorous species. It is this correlation capability that provides the superior acuityassociated with these species. Here, the higher primates are limited to humans, Hominidae, chimpanzees, Pan, Gorilla,

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Dynamics of Vision 7- 221Gorilla, and the Orangutan, Pong. This capability is not shared fully with the other members of Anthropoidea, such asthe monkeys. It is interesting that a similar capability appears to have evolved among some higher members of Molluscathrough evolutionary convergence. The eyes of squid, Loligo, and octopus among Cephalopoda appear to haveintroduced such a correlation capability into their visual systems.

The outer loop operates as a Type 0 servo due to the limited resolution of the optical system supporting the retina in theperiphery. In this role, the outer loop provides steering instructions, based primarily on angular position information.This information is used to point both eyes conjunctively and bring the target to a position along the line of fixation.The tolerance on this operation is about 10 arc minutes. This dimension is well within the 1.18 degree diameter of thefoveola. The inner loop operates as a Type 1 servo. It relies upon the tremor generated within the POS to provide theangular velocity required to convert the spatial position of targets imaged onto each retina into electrical signalsoccurring at specific times. It is the difference in these times associated with a specific small target that are used todevelop the first order steering commands used by the inner loop. These commands are used to bring the target to withina few arc seconds of the line of fixation.

Simultaneously, with the final positioning of the target using conjunctive eye movements, the correlator providesvergence signals to move the eyes disjunctively and accommodation signals to focus the eyes on the target. Thesesignals are derived from different aspects of the two electrical signals provided by the sensory signals delivered fromeach eye. The conjunctive pointing signals are based on the average difference between the arrival times of the sensorysignals and the “zero crossing time” obtained from the tremor generator. The disjunctive signals are derived from theabsolute difference in time between the arrival times of the sensory signals. The accommodation signal is derived bymeasuring the slope of the leading edge of the signals received from the sensory channels. The goal is to maximize theseslopes.

The above actions by the two-dimensional correlator are sufficient to raise the acuity to approximately the diameter ofan individual photoreceptor. However, the equivalent spatial range of the correlator is dynamic. It can use the samememory allocation capabilities found in a modern track while scan radar. Initially, a special high amplitude tremor signal(labeled a flick in this work) is generated. This flick causes the entire correlator ( with a capacity of n times 175 cellsin diameter) to concentrate on a single small target area (possibly 10-17 elements in diameter). Once the target is broughtwithin an adequate precision of the line of fixation, the tremor signal is changed, along with the switching pattern usedto load the correlator. The change causes the correlator to correlate the signals over the lengths of longer elements (inboth the horizontal and vertical dimensions). This process increases the signal-to-noise ratio of the signals required toperform the final conjunctive, disjunctive and accommodation adjustments. The final output of the correlator providesthe ultimate acuity of the visual system (of about six arc seconds in untrained humans). Training has been known tomarginally increase this acuity. This is particularly true for complex targets exhibiting unique patterns.

Because of this mechanism of fusion, the human, and many other, visual systems exhibit multiple levels of acuity as afunction of location within the field of view and specific target configuration. Once the target has been positioned nearthe line of fixation, a separate sequence of steps occurs that can be described as a “pull-in” process. The correlationprocess optimizes the performance of the overall physiological optics to maximize the acuity of the system for that target.The result of this pull-in process leads to the ultimate condition of “lock-in” during a period of up to 200 msecs beforethe next flick or mini-saccade. [xxx merge this paragraph with previous on flicks ]

It is quite clear that the ultimate acuity of the visual system is highly dependent on at least four properties of the scene.1. the light level, 2. the specific shape of the target (a grid offers a much higher correlation coefficient than a small filledcircle), 3. the contrast of the target and, 4. the performance of the lens group. Astigmatism, and other physical andneurological disorders are also obvious deterrents to the optimum operation of the overall correlation process.

As part of the correlation process, signals are output by the correlator that define the location of every distinct targetwithin the field of the foveola. These signals are used to provide depth of field relative to the reference target nearestthe line of fixation. They are also used by the lookup tables associated with the pulvinar to define the meaning of groupsof individual target elements in conceptual space. This is the methodology for defining patterns and ultimately achievingthe function of reading.

The proposed Theory of Image Fusion states: Fusion is achieved among the higher chordates bydynamic merging of the information received from the two eyes through two-dimensional correlation.The process is inherently dependent on the tremor associated with vision in these species. Thecorrelator is physically located within the perigeniculate nucleus of the thalamus, a major element ofthe POS. The optimum operation of the correlator also creates the final pointing, convergence andaccommodation signals that are used by the physical layer, including the plant, to implement optimumacuity in three dimensions. Optimum operation is dependent on the prevailing conditions ofillumination, scene contrast and target complexity. The perception of depth for individual targets

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within the field of the foveola is directly associated with the secondary statistics (residual disparity)relating those targets to the reference target.

The theory appears to satisfy the majority of the problems associated with the four hypotheses from earlier times (S &C pp 216-218).

Signals at each location in the retina are differenced in general accordance with the local sign concept. However, thequestion of rivalry is associated with, and explained by, the higher level correlation process.

Whereas Helmholtz hypothesized small perturbations as an instability degrading the performance of the eyes, theseperturbations are in fact the raison d’etre for the unique performance of the human visual system. It is this smallperturbation (tremor) that provides the desired acuity through correlation.

The du Tour rivalry hypothesis is quite compatible with the above proposal. The correlator can issue signals in timesequence that are quite different. These signals reflect the signal-to-noise limitations of the correlation process. Undercertain circumstances, these signals can be interpreted as rivalry. Under other circumstances, they may lead to vertigo.

Inconsistent imagery provided to the two eyes can also introduce problems generally associated with rivalry. Thecorrelator cannot reach an optimum level of performance if the two images are not consistent in their structure.

7.4.6.4 The phenomenon of precision depth perception

The study of depth perception has a less formalized history than the study of fusion. Defining the depth perceptionphenomenon succinctly has been more difficult for four reasons.

1. No concerted effort has been undertaken to determine the reason for the difference between qualitative depthperception (as associated with the peripheral retina) and the precision depth perception (associated with the foveola ofthe eyes).

2. The unique role played by the photoreceptor channels connecting to the perigeniculate nucleus and generallyassociated with the foveola has not been recognized. It is the signal processing associated with this limited group ofsignaling channels that provides the precise depth perception achieved in human vision.

3. Because of the above, a robust theory of stereopsis has not emerged to build upon.

4. In addition, no natural null point, such as the fixation point along the plane perpendicular to the midpoint of theinterocular line, is available when discussing fusion. The distance from the eyes of the fixation point under restconditions varies substantially among individuals, and apparently with time, for a single individual.

Because of these factors, a considerable empirical literature concerning qualitative depth perception exists. However,a much smaller, almost anecdotal, literature exists concerning precision depth perception.

The difficulty in studying the phenomenon of depth perception is also due to two complications related to its commonantecedent mechanism with fusion, stereopsis. This contribution of parameters related to stereopsis, frequently labeleda double-duty linkage, complicates the data reduction process. The second complication relates to the simplicity ofintroducing dichoptic images to the two eyes. These images frequently introduce information related to both fusion anddepth perception. The need to separate the contributions to these two phenomena during data reduction is not alwaysunderstood by the investigator.

Ultimately, the parameter known as Panum’s limit, that describes the spatial extremes of the associative correlator ofthe PGN, impacts the depth perception phenomenon. It does so in a complicated way that is mathematically related tothe instantaneously achievable range of fusion.

7.4.6.4.1 Dichotic versus dichoptic instrumentation

The human visual system is optimized for viewing dichotic scenes, where the same information is presented to eachfoveola but from a slightly different perspective. The eye vergence associated with these scenes is usually less than 12degrees and the eyes are usually turned toward each other by the same angle relative to their far-field alignment. Theease with which dichoptic images are presented to the two foveola in the laboratory frequently leads to additionalsituations that the visual system is not designed to handle. These situations can introduce limitations into the visual

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415Coutant, B. & Westheimer, G. (1993) Population distribution of stereoscopic ability Ophthalmic Physiol Optvol 13, pp 3-7416Regan, D. (2000) Human Perception of Objects. Sunderland, Mass: Sinauer Chapter 6.417Tyler, C. (1983) Sensory processing of binocular disparity Chapter 7 in Schor, C. & Ciuffreda, K. Op. Cit,pg 237

signal processing that are difficult for the researcher to appreciate fully and account for.

Panum’s limit, when defined at the level of the associative correlator, forms a very important part of this overall limit.

7.4.6.5 Data for perceived depth

The available experimental data on depth perception is very large. Much of it is based primarily on psychophysicalexperiments where many pertinent parameters were not recorded. While still useful, such shortcomings place the datain the exploratory category with respect to its utility. Some of the most useful data involves the limits on fusion anddepth perception combined. This data appears in Section 7.4.6.3.

Coutant BE, Westheimer G. have provided some data relating to stereoscopic depth detection415. Their abstract reads:“Of 188 unselected biology students participating in one or both of two tests measuring stereoscopic depth detectionability, 183 (97.3%) were able to see a depth difference at horizontal disparities of 2.3 min arc or smaller. At least 80%could detect depth differences at 30 sec arc disparity. These findings indicate that most people are able to take advantageof the increasing utilization of stereoscopic displays.”Regan reviewed the literature on three aspects of stereo vision including (1) static stereoacuity,(2) motion in depthperception evoked by a rate of change of disparity and (3) cyclopean perception of motion within a frontoparallel plane.416.

7.4.6.5.1 Depth perception as a function of binocular disparity

Figure 7.4.6-2 is reproduced from Tyler with the addition of the nominal diameter of the foveola417. The original wasbased on data from Richards and Richards & Kaye using two different experimental techniques under dichopticconditions. The curve was drawn freehand but shows several pertinent features. The maximum perceived depth occursat a disparity only slightly below that associated with the diameter of the foveola. More important, this diameter alsodescribes the maximum correlation range of the two-dimensional correlator of the PGN. The perception of depth fallsrapidly for targets of greater binocular disparity. It is shown reaching a minimum value at a binocular disparity of aboutten degrees. Within the range of the PGN correlator, the perception of depth is directly proportional to the disparityintroduced (the perception of depth is veridical). Beyond the functional diameter of the correlator, the perception ofdepth is associated with the LGN and a variety of cues. Depth perception in this region is described as qualitative.

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Figure 7.4.6-2 Relative depth perception as a function of the binocular disparity of a target under dichoptic conditions.The dashed line shows the putative linear relationship between perceived depth and binocular disparity (veridical region).See text for details.

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418Tyler, C. (1973) Stereoscopic vision: cortical limitations and a disparity scaling effect Science vol. 181, pp276-278419Tyler, C. (1975) Spatial organization of binocular disparity sensitivity Vision Res vol. 15, pp 583-590420Schor, C. & Tyler, C. (1981) Spatio-tempral properties of Panum’s fusional area Vision Res vol. 21, pp 683-692

Figure 7.4.6-3 Region of fusion versus spatial frequency forimages centered on the point of fixation. The stimuli forthe lower frame were under each other and not as shown.From Tyler in Schor & Ciuffreda, 1983.

7.4.6.5.2 Depth perception associated with spatial frequency (interval)

The reader is reminded that the basic concept of frequency requires a periodic event (consisting of more than twooccurrences). Frequency defined as the reciprocal of the period between only two events is a technical and semanticcrutch.

Figure 7.4.6-3 is reproduced from Tyler418,419. It shows a significantly different correlation ability in the vertical andhorizontal directions. While he describes this experiment in terms of a sinusoidal line stimulus, it is only the one linethat is sinusoidal in the plane of the image. The two lines were both high contrast. They were presented straddling thepoint of fixation.

Tyler ended his experiments at a minimum frequency ofabout 0.04 cycles/degree. This is a pitch of 25 degreesper cycle and corresponds to lines at plus and minus 12.5degrees from the point of fixation. At the other extreme,his minimum period was about 0.25 degrees. Tylerfrequently speaks in terms of period or interval in hiswritings.

Noting the challenge faced by the two-dimensionalcorrelator of the PGN in Tyler’s experiments is useful.Comparing one straight and one wavy line is obviouslymore difficult than correlating two straight lines.However, the length of the lines was held constant at 15degrees in object space. Because of this, both linesappeared to be straight within the analytical channel ofvision. His data apparently applies predominantly to theawareness channel and the peripheral retina.

Schor & Tyler also studied the fusional area of vision bymoving a pair of lines closer and farther apartsinusoidally420. These and other experiments show thatfusion occurs within about 33 msec, the nominal sampleinterval of the POS of human vision. As Helmholtzshowed much earlier, fusion will occur for imagesacquired in a much shorter interval. He used a spark lightsource to demonstrate this.

7.4.6.6 Theories explaining the depthperception phenomenon

The analysis of depth perception can be separated intotwo distinct fields. The study of precision (or quantitative) depth perception associated with the analytical channels ofhuman vision, and the study of all other aspects of depth perception. This section will only address the subject ofprecision depth perception associated with the analytical channel of human vision. This channel contains the foveolaof the eyes and the associative correlator of the perigeniculate nucleus found in the thalamus of the precision opticalsystem. The PGN is closely associated with the pulvinar. The two, acting as a couple, are critical to the evaluation ofthe phenomena of fusion, depth perception and the process of reading.

7.4.6.6.1 Previous theories of precision depth perception

The study of depth perception represented by the literature has not evolved to the point of providing succinct theories

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421Ohzawa, I. DeAngelis, G. & Freeman, R. (1990) Stereoscopic depth discrimination in the visual cortex:neurons ideally suited as disparity detectors Science vol. 249, pp 1037-1041422Nakayama, K. & Shimojo, S. (1990) Da Vinci stereopsis: depth and subjective occluding contours fromunpaired image points Vision Res vol. 30, pp 1811-1825423Grossberg, S. & Raizada, R. (2000) Contrast-sensitive perceptual grouping and object-based attention in thelaminar circuits of primary visual cortex Vision Res vol. 40, pp 1413-1432

of the depth perception phenomenon. Neither the texts by Schor & Ciuffreda or Howard & Rogers directly address orreview the theoretical aspects of depth perception.

The Psychology Departments of several colleges are still relying upon a theory of depth perception by Gibson of the1950's. It is too conceptual to be considered here.

A series of articles during the 1990's has focused on vertical disparity as the potential source of depth perception. Theyhave generally been based on the “traffic analysis” form of physiology used earlier by Hubel and others. They generallydepend on psychophysical experiments on humans combined with electrophysiological experiments on cats andmonkeys. The results are conceptual theories that do not rely upon detailed physiology. They generally define uniquecircuits of the occipital lobe that act as disparity detectors. No attempt has been made to define the actual circuitry ofthe retina and midbrain that support these putative disparity detectors. Nor has the circuitry of the disparity detectorsbeen defined except to say they take differences between signals from the two retinas. These papers have employedcomputational analysis as a major tool, rather than physiological events. They have remained qualitative and have notdifferentiated between different areas of the retina or different signaling channels within the visual system.

Ohzawa, et. al. have provided the clearest description of the “archetypal disparity detector421.” They define both a simpleand complex type of disparity detector. They also state the theme of most of the theories described above: “The neuralprocess of stereoscopic depth discrimination is thought to be initiated in the visual cortex. However, the neuralmechanisms of this process are not clear.” Their first endnote lists references supporting their statement.

Nakayama & Shimojo have contributed insights based on occlusion experiments422. They note: “depth from binocularlypresented targets depends critically on the solution to the correspondence problem” highlighted by Julesz. However,they do not propose a comprehensive single theory of depth perception.

Grossberg & Raizada have provided considerable background and references related to the problem of depthperception423. However, their neural model is at a very high level and their exposition is based primarily oncomputational analysis. It does include contributions from both the LGN and V1 & V2.

Mathews et. al. have recently proposed a theory of depth perception, labeled physiological but appearing to be primarilya computational theory. It is based primarily on traffic analysis to assign a major role to disparity detectors in theoccipital lobe. They did not offer a quantitative description of depth perception nor did they define the portion of theretina or the visual system contributing to their model. Their assumption that no motion occurs within a 200 msecinterval following a major saccade cannot be supported. It is well documented that tremor contributes considerable finemotion during this interval (Sections 7.3.3.1.2 & 7.3.5.3).

Their experimental configuration did depend on a priori knowledge to achieve the proper state of vergence of the eyes.It also depended heavily upon their equation (6) which predicts a conversion of a vertical disparity to an equivalenthorizontal disparity under certain conditions. It is the assumption that a vertical disparity, “V will be ‘mistaken’ as anequivalent horizontal disparity . . . ” that is the key to their theory.

7.4.6.6.2 A proposed Physiological Theory of Precision Depth Perception

The analysis of depth perception can be separated into two distinct fields. The study of precision (or quantitative) depthperception associated with the analytical channels of human vision, and the study of all other aspects of depth perception.These other aspects are generally associated with the awareness channel and the LGN/occipital couple. They must beseparated into individual phenomena to develop appropriate theories related to them. These descriptions and theoriesof qualitative depth perception will not be pursued further in this section.

A clear description of the phenomenon of precision depth perception can be derived from the previous discussions. Thedescription can be thought of as a corollary to the theory of stereopsis in Section 7.4.6.4.

Precision depth perception is a phenomenon derived from the mechanism of stereopsis performed within the associative

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424Howard, I. & Rogers, B. (2002) Seeing in Depth, vol 2, Depth Perception Toronto, Canada: I Porteous,Chapters 18-24425Reading, R. (1983) Binocular Vision. London: Butterworths pg 121426Millodot, M. (2009) Dictionary of optometry and visual science NY: Elsevier page 298

correlator of the perigeniculate nucleus within the precision optical subsystem of human vision. Precision depthperception is the perception of depth associated with the local vergence disparity calculated by the correlator for eachsignificant edge within the purview of the correlator. Within the purview of the correlator, the perception of depth isa linear function of the local vergence disparity. This linear characteristic is labeled veridical depth perception.

The purview of the correlator is circumscribed by Panum’s limit in correlator space. This limit reduces to Panum’s limitin x,y space for z = 0. The area enclosed by this limit is known as Panum’s area. This limit can also be expressed bythe maximum value of z for the condition x = y = 0. This limit describes the maximum range of depth perception relativeto x0,y0,z0. For other values of x,y,z, a volume can be defined that is conceptually equivalent to Panum’s area. It definesthe combined range of fusion and depth perception achievable by the subject.

Precision depth perception is dependent on tremor to convert the images in spatial coordinates into temporal signals thatcan be projected to the correlator. Tremor provides separate temporal signals related to both the vertical and horizontalcomponents of the images.

7.4.7 Evaluating stereopsis through fusion and depth perception

The current pre-eminent source of information on the subjects of fusion and depth perception is the compendium byHoward & Rogers424. It devotes seven chapters to these subjects. While this work does not support the concept ofindividual disparity detectors or the involvement of spatial frequency sensing circuits in vision, the data obtainedempirically is extensive, comprehensive and valuable. Their Chapter 18 titled “Tokens for stereopsis” is a particularlyimportant starting point. As noted in that chapter, the edges of objects in the scene are important in stereopsis andtherefore fusion and depth perception. The next paragraph will express certain cautions involved in interpreting someof their data. Howard & Rogers explored a variety of special dichoptic conditions that will not be explored here. Theseinclude various occluded images (the field of view of one eye was restricted compared with the other) and camouflagedimages. Similarly the secondary phenomena of rivalry, shimmer and aura will not be discussed here.

Lit has provided a graph describing the threshold of stereopsis as a function of retinal illuminance in Trolands425. Forilluminance greater than one Troland, the threshold remains near ten arc-seconds.

When evaluating depth perception in the laboratory, Millodot has described a “pseudoscope” designed to reverse theperception of depth426. It is not clear whether this device reverses the perception of depth with respect to a mean distanceor whether it reverses the perception of depth relative to the point at infinity.

7.4.7.1 Discussion

Stereopsis is a mechanism associated with the two-dimensional associative correlator of the perigeniculate nucleus.While defining the effective spatial dimensions of this correlator using its surrogates, the foveola, is frequentlyconvenient, caution is needed here. It is the correlator that is the source of the mechanism.

A similar area of caution involves the test instrumentation used. While generating dichoptic images of a pseudo-sceneto explore the performance associated with stereopsis is frequently easier, it is the actual scene and the resulting dichoticimages that the visual system was designed to process and evaluate.

Remembering that the results may become discontinuous when either the local or global correlation ranges of thecorrelator are exceeded is important when defining either dichotic or dichoptic experiments. These common stereopticlimits can be exceeded by either the fusion or depth component of a single measurement. The result is that mostexperiments exploring either fusion or depth perception contain boundaries associated with the other phenomenon.

The expression of the common stereoptic parameters, the local and global correlation ranges of the correlator, in boththe fusion and depth perception phenomena is frequently labeled the double-duty linkage. Howard & Rogers describethe exploration of this linkage on pages 132-135. It suggests that Panum’s area is more directly related to the effectivedimensions of the correlator of the PGN than the physical dimensions of the foveola. As a result, Panum’s limitdescribes a limit on a function combining the parameters of fusion and depth perception. Because of this functionalrelationship, the linkage is more symmetrical than suggested by the references to Gettys & Harker and to Westheimer.

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Figure 7.4.7-1 A stereogram from Howard & Rogers withadded parameters. Specified to be viewed at 12 cm withthe provided viewer. Small circle shows relative size ofPGN correlator in this experiment. After alignment of theNonius lines, one set of vertical lines appears behind andthe other in front of the vertical bar. The perception ofdepth is essentially all qualitative in this figure.

A distinct experimental problem arises when using only a pair of test objects, points, lines, etc., to evaluate either fusionor depth perception. The results invariably exhibit components related to both fusion and depth perception because ofthe double-duty linkage. The basic problem is that two objects do not define a specific point of fixation from whichindependent fusion or depth measurements can be made. A minimally sophisticated test environment should includesufficient objects to cause a mean point of fixation to be calculated. From this mean, differences in x,y coordinatesrelated to fusion and in z coordinates related to depth perception can be measured.

When defining a test stimulus for exploring precision stereopsis, it is important that the dimensions of the stimulus notexceed the effective dimensions of the associative correlator. This parameter has frequently been overlooked in the past.As an example, figures 18.37 and 18.38 in Howard & Rogers cannot be viewed within the confines of the effectivedimensions of the correlator (typically a 1.2 degree diameter circle). To explore these stereograms requires arepositioning of the point of fixation and a calculation of a new mean for the point of fixation of the horopter. In theiroriginal publication, the vertical height of the stereo-pair shown in Figure 7.4.7-1 was 50 mm. At the prescribed viewingdistance of 12 cm (4.7 inches), the nominal diameter of the associative correlator is only 2.5 mm. As a result, the depthperception associated with most of the stereogram is perceived qualitatively.

The selection of 12 cm as a viewing distance in Howard & Rogers appears awkward. Mostadults cannot hope to view a scene in proper focus at such a short range. The range may havebeen chosen to reduce the size of the stereo-pairs reproduced on a typical 216 x 279 mm pages.

The need to reposition the gaze was noted in their caption.It was impossible for this naive viewer to obtain a singleinterp of the entire scene at the prescribed distance.

A distinct difference in conceptual (and mathematical)complexity arises between scenes of complex random-dot-stereograms (RDS) and simple geometric shapes. It isproposed that the two approaches lead to the sameconclusions concerning the mechanisms and phenomena ofinterest here. The same proposal applies to dichopticimages containing color differences. The results obtainedwith simple geometric shapes are easier to describe andinterpret. The performance of the correlation capability ofthe correlator is also easier to demonstrate with simplegeometrical shapes. The lack of straight edges in RDS’sdegrades the performance of the correlator.

7.4.7.2 The plasticity of fusion and depthparameters

Howard has addressed the plasticity of fusion limits froma variety of perspectives on page 272-281. Similarly,Howard & Rogers discuss the plasticity of depthperception limits on pages 132-135. The latter discussionis in the context of what they describe as “double dutylinkage.” This empirical terminology of these discussions is associated with the performance limits determined by thefinite effective spatial dimensions of the associative correlator of the PGN. The calculations in the correlator requiredto establish the mean and the deviation from the mean of edges in the scene presented to the foveola require that theseedges be represented in the field of view of the correlator. If not, the calculations cannot be performed within theprecision signal processing channels of vision. This requirement is the key to the plasticity of the limits on the fusionand depth perception phenomena.

To evaluate the plasticity of fusion and depth perception, using imagery more complex than just two sources that canbe moved to emulate motions in either the x,y or the z dimensions is necessary. The reason is that the point of fixationand the vergence of the visual system must be held constant during the experiments. Howard & Rogers noted the needto control the vergence in their discussion. By introducing targets at a distance from x0,y0,z0, understanding the plasticityin the limits of the fusion and depth perception phenomena is possible. For small distances, these targets introducesignals into the associative correlator that are at distinctly different positions within the effective maximum dimensionsof the correlator. The correlator can calculate the mean position of a single edge in object space based on therepresentation of the two edges in the correlator. The correlator is also able to calculate the difference in the positionof the two edges in the correlator. These values represent the fused two-dimensional representation of the scene plus

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427Simonet, P. & Campbell, M. (1990) Effect of illuminance on the directions of chromostereopsis andtransverse chromatic aberration observed with natural pupils Ophthal Physiol Opt vol 10, pp 271-279428Tyler, C. (1975) Spatial organization of binocular disparity sensitivity Vision Res vol. 15, pp 583-590

its depth relative to the nominal point of fixation.

As the distance of the object in object space increases relative to x0,y0,z0, one of the edges associated with the objectwill no longer be processed properly. Its image on one of the foveola will no longer fall within the maximum effectivedimensions of the correlator. At this point, the calculation of the mean and deviation from the mean for the edge incorrelator space will fail. This dimension defines Panum’s limit in correlator space. Clearly edges with a small z-dimension can have a larger x and/or y-dimension without exceeding the capabilities of the correlator. Conversely,objects with small x and/or y-dimension can have a larger z-dimension without exceeding the capabilities of thecorrelator. This situation is the underlying characteristic leading to the empirical concept of double-duty linkages.

7.4.7.2.1 Use of “double-duty” parameters in depth perception

When imagery is presented to the two foveola that contain edges well separated from each other in both x,y and in zdimensions, the limited capability of the associative correlator may be taxed. In this case, Panum’s limit, expressed interms of either the dimensions of the foveola or the dimensions of object space, may appear to shrink considerably.

7.4.7.2.2 Chromostereopsis and transverse chromatic abberations

Simonet & Campbell have provided an update on research related to chromostereopsis in 1990427. They define thephenomenon, “Chromostereopsis, also known as chromatic stereoscopy or the colour stereoscopic effect, occurs whentwo coloured adjacent objects located in the same frontal plane are perceived binocularly as separated in depth.Chromostereopis is positive if the red object is perceived in front of the blue one, the opposite perception gives negativechromostereopsis'. The magnitude of chromostereopsis is measured by the relative physical displacement betweencoloured objects which gives a perception of coplanarity. ” They note (supported by many citations), “The majority ofstudies on chromostereopsis have been conducted with a small sample of four subjects or less, or were not performedwith natural pupils but with fixed dilated pupil, or with artificial. In studies performed with natural pupils th ewavelength and the luminance of the targets, as well as the pupil diameter of the observers are not known. Theillumination of the targets and the ambient illumination reported by Kishto' present substantial variations. As Einthoven'and Kishto' disagree about the most frequent direction of chromostereopsis, there is a need for a study of thedirection of chromostereopsis under controlled experimental conditions and to investigate its dependence onilluminance.”

Simonet & Campbell provided data drawn from a cohort of 30 subjects under a wide range of conditions. The discussionis extensive but is generally in the context of a psychology laboratory where a variety of parameters are not controlledadequately and no circuit model of the visual system is employed as a framework. As an example they note, “Theambient illuminance at the level of the cornea is set respectively at 10 and 1000 lx (10 and 1000 cd/m2 respectively) forlow and high illumination levels. Ambient illumination, controlled by a rheostat, is provided by two 500 W halogenlamps, located in the temporal visual field of each eye at an eccentricity of 50 degrees in the horizontal meridian.” Nocolor temperature for the ambient illumination was given. The two extremes of their illumination range both occurwithin the mesopic range where color constancy is not preserved (Section 2.1.1.1). More significantly, they measuredtheir monochromatic light sources using broadband light meters. Their measurements should have been in watts persquare meter at the specific wavelengths used. Filters were made from available sheets of ordinary plastic. They didnote that the orientation of their two targets, whether positioned vertically or horizontally with respect to each other wasimportant in the literature. They did not take note of Maxwell’s spot (Section 17.3.1.7.2). Taking the expected positiveview, they conclude, “This study, with well-defined experimental conditions, has determined, in a relatively largesample, that the colour stereoscopic effect does not have a preferential direction associated with the level of illuminationfor levels of 10 and 1000 Ix. Our results do not support or reject any theory proposed for explaining the reversal ofchromostereopsis perceived by some subjects.”

7.4.7.3 Combined fusion and depth data in the literature ADD EXAMPLES

While not supporting a unique chapter related to fusion, Howard & Rogers dedicate chapters 21 through 23 to materialon depth perception (other than that due to parallax and cues unrelated to stereopsis).

Although using crude instrumentation by current standards, an early paper by Tyler is informative428. He explored avariety of test conditions beyond those discussed here. Figure 7.4.7-2 provides a modified composite of two of his

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Figure 7.4.7-2 Perceived depth as a function of vertical line interval. Dotted, dash-dot and dash-dot-dot lines added.Left; 15 degree high lines presented at 30 cm. Right 1.5 degree high lines presented at 3 meters. Dashed and dash-dotlines represent slopes of minus one with respect to frequency (plus one with respect to interval). Dash-dot-dot linerepresents minimum interval achieved for 30 cm presentation. Dotted line represents diameter of foveola. Long dasheson right are image of curve on left. Adapted from tyler, 1975.

figures. He used an oscilloscope on its side as a test source. It apparently provided two signal channels with onebaseline unmodulated and the other modulated in both amplitude and frequency. Using polarizers, this instrumentationgave the desired dichoptic presentation with the lines presented alternately in time. The measured brightness of thedisplay is within the photopic operating region. The sharpness of the lines generated probably contributed to the limitedthe performance of the subject in these tests. However, Tyler also provided data on several subjects that variedconsiderably in perceived minimum disparity difference. Tyler also presented off-axis data showing that the minimumdepth perception performance of one subject fell by a factor of about four for stimuli presented in the region betweenseven and ten-degree eccentricity.

The figure presents two situations. The size and orientation of the lines are shown at the upper right in each frame. Mostof the data was taken with a single sinusoid as a stimulus. However, other data was also presented in the paper. Whilethe actual eye vergence during the tests was not given, the effective target vergence upon fusion at 30 cm would be 12.3degrees. At three meters, it would be 1.2 degrees. These values would relate to the stereoptic performance of thecorrelator in the PGN. The frame on the left relates generally to the region of qualitative perception of depth. Most of the relevant signalinformation falls outside the foveola. The figure shows the perception of depth to be constrained between an area ofdiplopia, an area of no apparent depth and an area of limited spatial resolution. The minimum perceived peak-to-peakdepth perception was about one arc minute. The maximum depth perception was about 1000 arc minutes. The minimumrepresents about one part in 738 at 12.3 degrees target vergence. The maximum represents a peak perception of depth(his maximum depth limit), each side of the effective point of fixation, slightly greater than one half (500/738) the

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429Allison, R. & Howard, I. (2012) Stereoscopic motion in depth In Harris, L. & Jenkin, M. eds Vison in 3DEnvironments. NY: Cambridge Univ Press Chap 8430Shioiri, S. Kakehi, D. Tashiro, T & Yaguchi, H. (2009) Integration of monocular motion signals and theanalysis of interocular velocity differences for the perception of motion–in–depth J Vis vol 9, pp1-17

distance to the effective point of fixation (+/– 67% for the peripheral retina).

The dashed and dash-dot lines suggest that the ratio of disparity to interval remains constant with respect to bothmaximum depth perceived and minimum depth perceived.

The right frame shows that projecting the stimuli on an area only the size of the foveola increases the spatial resolutionperformance related to stereopsis significantly, although it is probably still test set limited. It also improves the minimumperception of depth to about 0.3 arc minutes (20 arc seconds). This minimum represents about one part in 240 at 1.2degrees. The maximum perception of depth is more difficult to define for this case. The images of the bars exceededthe diameter of the putative correlator within the PGN when the two images were fused since the effective targetvergence was about 1.2 degrees. Using the value at an interval of 1.2 degrees, this data gives a ratio of one part in fiveeach side of the fixation point (+/– 20% for the foveola alone). The curve at the lower right describes the monocularlimit for perceiving the sinusoidal curvature of the one stimulus. The minimum in this curve also suggests a combinedsubject and test set limit near 20 arc seconds, or about 4-6 times the spatial limit of the normal foveola for small objects.

7.4.7.4 Depth perception experiments of Allison & Howard

Allison & Howard429 have reported on a series of experiments related to changes in disparity associated with apparent“to and fro” motion using the geometry introduced in [Section 7.4.1.4]. They also noted some competitive work beingpursued by Shioiri et al. in Japan430. In their discussion, they introduced the terms change of disparity (CD) andinterocular velocity difference (IOVD) signal. As an introduction, they presented Figure 7.4.7-3

Figure 7.4.7-3 Potential motion in depth mechanisms. The “change in disparity” operates on the disparity signal (i.e.,in the cyclopean domain) to signal a changing disparity. The “difference–of–velocity detector detects a pure interocularvelocity difference between monocular motion detectors. The “dynamic disparity detector” is directly sensitive tochanging disparity in binocularly matched features. See text. From Allison & Howard, 2012.

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431Bradshaw, M. Cumming, B. (1997) The direction of retinal motion facilitates binocular stereopsis ProcRoyal Soc B vol 264(1387) pp 1421-1427

They described “three ways in which the visual system could, in theory, code changes in relative disparity. C First, the change in binocular disparity over time could be registered. We will refer to this as the change–of–disparity(CD) signal.C Second, the opposite motion of the images could be registered. We will refer to this as the interocular velocitydifference (IOVD) signal.”C “Third, the motion in depth could be coded by specialized detectors sensitive to changing disparity in the absence ofinstantaneous disparity signals.”

The physiological elements defined in the caption to their figure are only conceptual. They did not cite any materialdefining these elements (the disparity detector, the “difference–of–velocity” detector or the “dynamic disparity detector”[the quotation marks were in their caption]) in detail. No representation was made as to where in the signal chain theseconceptual elements, and the related elements in the figure, would even be found.

The flow diagrams in the figure are too simple to relate to any processing of two and three dimensional information bymechanisms involving engines distributed to different regions within the neural system.

In their experiments, all motion was related to the motion of the object space presentations. No motion of the ocularsas a result of tremor was considered.

- - - -

Allison & Howard conclude (page 179), “ Several lines of evidence favor the existence of a true IOVD mechanism basedon monocular motion signals [with citations].” [xxx expand on this from my perspective ]

- - - -.

Bradshaw & Cumming made an observation in their 1997 paper that focuses a basic situation431.

A considerable amount of recent empirical evidence suggests that binocular disparity and motion information arecombined during visual processing, although the purpose of this combination remains open to question. Herewe investigate the suggestion that retinal motion can facilitate the solution of the binocular correspondenceproblem. The correspondence problem refers to the difficulty faced by the visual system in establishing whichfeatures in the left and right eyes' images originate from the same location in physical space. Establishing thecorrect matches is prerequisite to the measurement of binocular disparity, which in turn specifies thethree-dimensional structure of the world. The number of potential matches can be large, particularly when thereis a dense distribution of image features as in, for example, a typical random dot stereogram.

From a physiological perspective, it is obvious that the lateral position differences between the two retinal images at agiven time are all of the information available to decode into true lateral and axial positions. The derivatives of thesetwo motions clearly describe the lateral and axial motions associated with these positions. The complexity of the scene,particularly the part imaged on the foveola, only defines the processing load on the appropriate stage 4 engines. Figure2 of Bradshaw & Cumming describe the sub-threhold to resolved stereo imaging situation but without defining theseparate situations related to the foveola and the periphery visual fields. They define the transition region aspykno–stereopsis.

Their protocol used a random dot pattern slightly larger than the foveola. “The stimulus comprised a 2 degree square(120 x 120 pixels) patch of random dots centered within an 8 degree square of static random dots. A new array of dotswas computed for each interval and for each trial. Observers fixated the centre of the stimulus pattern.” They employeda “standard Wheatstone stereoscope” meaning apparently a two–channel dichoptic presentation. They did not describethe tilt of their fronto-parallel planes with respect to the vertical or the subjects diopter. The overall size of their imagerytends to achieve qualitative binocular vision based on the stationary surround pattern, and then evaluate the precisionstereopsis achievable with imagery presented to the foveola related portion of the visual system. However, it is possiblethey achieved precision convergence before the imagery applied to the foveola began moving. The test pattern wasgenerated by a square wave impressed upon the raster lines at a rate of 15 cycles of depth modulation per degree of visual

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Dynamics of Vision 7- 233angle. “This frequency was chosen as it is well beyond the resolution limit of the stereo and motion systems.” However,this frequency is well below the resolution of the transduction process at the photoreceptors.

The typical statement was made, “All three subjects had normal or corrected-to-normal vision.” How their stereopsiscapability was determined is not stated. Figure 7.4.7-4 shows an example of their results.

“A two-interval forced choice procedure was used. In one interval (chosen at random on each trial) the disparityof the square wave (i.e. its peak-to-peak amplitude: d1– d2) was set at zero and in the other it was set to one ofa range of non-zero values. The disparities were chosen so that responses spanned the range from chance (50%)to perfect performance (100%).”

In experiment 1, the thresholds for depth segregation were compared with a control condition in which all of thedots moved in the same direction (dashed line and open bars in figure 4). In the correlated condition, thresholdswere significantly lower than the control (p50.05 for all three observers), indicating that stereo matching isspecific for the direction of motion.

Experiment 2 investigated whether there is a similar advantage for correlated disparity and motion if thesquare-wave was de¢ned by differences in speed rather than by differences in direction. The results (figure c)show that this is not the case, differences in speed alone do not affect performance appreciably.

“When near threshold, the stimulus with non-zero disparity would appear as a slightly thickened plane.”

Bradshaw & Cumming subsequently determine, “Together, these experiments provide clear psychophysical evidencethat different directions of motion, but not different speeds, are processed separately in stereopsis.” And, “The resultsreported here show clearly that different directions of retinal motion, but not different speeds, affect the ability ofobservers to resolve two spatially overlaid planes, defined by binocular disparity, into two surfaces separated in depth.”These statements are consistent with the physiology that suggests lateral and axial disparity are computed before speedsare determined.

Figure 7.4.7-4 Example psychometric functions for dot patterns are shown for one observer from experiment 1 (a) andexperiment 2 (c). Each symbol represents the mean of at least 80 trials and the error bars indicate s.e. based on thebinomial distribution. Correlated disparity-motion is represented by the open circles, uncorrelated disparity-motion bythe closed circles and the translation (control condition) by the open squares and dashed fit. From Bradshaw &Cumming, 1997.

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432Tong,C. & . Ng, V. (2010)http://www.polyu.edu.hk/so/images/research/file/Cecilia%20Tong-Poster%20of%20Depth%20Perception%20(amended).pdf 433Zeki, S. & Moutoussis, K. (1997) Temporal hierarchy of the visual perceptive systems in the Mondrian worldxxx pp 1415-1419434Vidyasagar, T. (1998) Gating of neuronal responses in macaque primary visual cortex by an attentionspotlight Neuroreport vol. 9, no. 9, pp 1947-952

[xxx discuss Cummings & Parker method of differentiating between CD and IOVD signals, pg 165 in Allison &Howard]

7.4.7.5 Dynamics of stereopsis and role of non-declaratory (implicit) memory

It is not commonly known, but measuring a subjects horopter is highly dependent on his quiescent state of visualperformance432. If a subjects performance is measured a natural and then measured again within a short period whileemploying corrective glasses, his performance usually deteriorates drastically. The numbers are startling;

Depth perception (sec of arc)Subject Case 1 Case 2 Case 3Unaided +8.8 -2.93 +12Aided -73.49 -67.61 +24

They noted, “Correcting the refractive errors of athletes is a common management in order to maximize their visualperformance. It is generally suggested that uncorrected refractive errors would adversely affected the depth perception,which is one of the most important visual performance in sports playing. These cases, however, demonstrated the athleteswith well- adapted monovision can show a marked deterioration of depth perception immediately after refractivecorrection.”

This author encountered this problem while putting on glasses he only wore intermittently during a badmintongame. His depth perception deteriorated greatly.

Changes of the above magnitude in stereopsis performance are indicative of the considerable amount of neuralcomputation and rewriting of the scaling parameters associated with stage 4/6 non-declaratory memory (within thecerebellum) involved in stereopsis. See Sections 17.1.1.3 and xxx in Chapter 17 of “The Neuron and Neural system”for more discussion of non-declaratory memory. See Section 4.6.3 in Chapter 4 of that work showing the role of thecerebellum, and potentially the striatum/pallium couple, in the stage 4 to stage 6 reflex arc associated with stereopsis.See Sections 8.5.3 & 8.6.3 in “Hearing: A 21st Century Paradigm” for additional material associated with non-declaratorymemory. [xxx reproduced 8.6.2 of early version into 17.1.1. look also at the figure showing reflex arcs via the cerebellum]

7.4.8 Overall temporal response & latencies

Considerable literature exists concerning the latencies found in the visual system. However, the parameters are describedusing a variety of definitions and criteria. Zeki & Moutoussis have provided an overview with many references433. Theyhave also highlighted the significance of “the retino-tecto-cortical branch, the latter bypassing V1 and reaching V5 atlatencies of about 35 ms, to which it delivers signals from fast-moving objects (>10° s -1).” Vidyasagar has provided avariety of latencies. He generally relates the latency for a signal arriving at the primate visual cortex of from 50 to 100ms434. The minimum appears to be 50 ms for a signal not intercepted for further processing within the midbrain. Hedefines the cells exhibiting this latency as AR cells (attention related). He describes the cells exhibiting the longerlatencies as AS cells (attention specific). In this work, the signals arriving at the AS cells have undergone processingwithin an engine of the thalamus before relay to the primate visual cortex. In the last paragraph of his paper, he presentsa concept that is analogous to the POS of this work.

7.4.8.1 Definition and tabulation of latencies

Latency has lacked a precise definition throughout the vision literature. It is frequently used quite differently inelectrophysiology and psychophysics. In electrophysiology, it is usually used as a generic term for the time between

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Dynamics of Vision 7- 235the initiation of an impulse stimulus and the beginning, the leading edge, of the electrical response at a later point in thevisual system. In psychophysics, it is frequently used to describe the time between a stimulus and the conclusion of asaccade designed to bring the line of fixation to the location of the stimulus. The latter description obviously includesboth a latency (period before any measurable output) and a response time.

In electrophysiology usage, ambiguity is frequently found concerning what feature on the rising edge of the responseshould be used as an indication of the beginning of the response. Since most of the responses are described initially bya first order differential equation, the logical feature is where the response departs from the quiescent level. Althoughthis point is frequently obscured by test set noise, it can be readily determined. Projecting a first line through themidpoints of the quiescent level and then a second line back along the rising waveform to its intersection with the firstline will define the start of the signal waveform. This feature provides a latency that is independent of the slope of theresponse and leaves the description of the response as a separate parameter. For a ganglion cell, the time delay beforethe response reaches a threshold value is then assigned to the ganglion cell and not to the prior signal path.

In the psychophysical case, the situation is a bit more difficult because the instrumentation frequently does not allowmeasurement of the subsequent fine motions following the saccades. In these measurements an arbitrary velocitythreshold is frequently imposed to define the completion, and frequently the start, of the saccades. The above definitionhas little relevance to a microsaccade that never reaches the conventional velocity threshold. It is also possible that themicrosaccade may be the result of a second order mechanism. This makes the start of the saccade, as a function ofposition, less defined. Either a lower velocity threshold is required or a zero crossing definition may be preferred.

The literature has accumulated many measured latencies but it has not evolved a framework for correlating these manyvalues. By reviewing this material, such a consistent framework can clearly be assembled. Such a frameworkconcerning the motions of the eyes, and the related motions of the skeletal system that will not be addressed here, canbe formed if at least four operating modes of the visual system are recognized. These modes can be described asinvolving;

+ an awareness mode. In the absence of any visual threat to the animal, this mode involves all of the visual field exceptthe foveola of each eye.

+ an analytical mode. This mode involves only the object space imaged on the foveola.

+ a volition mode. This mode involves a spontaneous decision by the cortex to change the line of fixation. The resultingcommand is independent of the field of view of the eyes.

+ an alarm mode. This mode involves a change in the line of fixation in response to changes in the scene peripheral tothe part imaged on the foveola. The change in the line of fixation may exceed the original field of view if inputs fromother sensory channels are involved.

Figure 7.4.8-1 presents a flow diagram of the visual system based on these modes. The complete diagram is complex.The individual mode diagrams at the bottom simplify tracking the signals. Note that the total latency, or the totalresponse time through the initial saccades, is determined largely by the length of the signal paths involved. The signalpaths involving the optic nerve and the oculomotor signal paths from the superior colliculus do not change with mode.However, the other paths do change. This figure can be compared with a similar one by Reichle focused on eyemovements during the reading process. His focus on the thalamus, superior colliculus, oculomotor plant and theintraparietal and frontal eye fields (labeled 5, 6, 7, 8 & BS) is very similar to the focus of this figure.

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Figure 7.4.8-1 Nodes and transit times affecting the latencies and response times of the visual system. Upper frame;full flow diagram. Blue boxes represent areas concerned with interpretation and initial perception of fine detail. Brownboxes represent elements of the awareness mode of vision. Green boxes represent higher cognitive centers. Lowerframe; individual flow diagrams by mode. Tan boxes represent the LGN. Blue boxes represent the Pretectum(perigeniculate nucleus and pulvinar). See text for discussion.

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Figure 7.4.8-2 presents a tabulation of the transport times involved in the various legs of this diagram and the processingtime at each node. It presents the best available data describing the time required for the human visual system to respondto a stimulus while in each of these operating modes. For convenience, the various potential delays have been listed onthe left of the figure. The right of the figure is divided into three parallel sections of two columns each followed by acomment column. Each pair of columns is arranged to show absolute time delays on the left and cumulative delays onthe right. The comment column is necessarily brief and is only used to describe key parameters. The followingdiscussion is more definitive and presents comments on an individual row and column basis using the labels on the leftand at the top of the table. The left of the figure follows the general division of the visual system into the stagesdiscussed elsewhere in this work. It begins with signal detection (stage 1) and is followed by retinal signal processing(stage 2), signal projection (stage 3) and the initial signal processing within the brain (stage 4). These stages arefollowed by higher level information analysis within the brain (stage 5). This stage is then followed by a less definedstage 6 involving the generation of a group of instruction signals to be sent to the thalamus. Implementation of theseinstructions follows.

The first column to the right of the location descriptors is labeled the ROUTINE PATH. This path is meant to encompassthe performance of the signaling environment of the eye during its routine operation. This path has been defined in twosegments. These segments have been presented in one column for artistic convenience. The upper segment describesthe Awareness mode of operation. It can be used to describe the time spans associated with the absorption of informationconcerning object space within the total field of view of the subject. It concludes with the delivery of the sensedinformation to the cortex at the level labeled 5-2 on the left. This level is labeled Area (multiple) to suggest that itinvolves many information processing engines in the dispersed cognitive areas of the frontal lobe. Because of thisdispersal of information within the frontal lobe, level 5-1 provides only an average absolute time of transmission overthe multiple association fibers operating in parallel. The cumulative time can only be calculated to the point of deliveryof the information to the appropriate engines of the frontal lobe. The lower segment of this column describes theVolition mode of operation. In this mode, the mind has decided to change the line of fixation (independent of anyexternal stimulus) to examine some element of the field of view in detail. No time can be assigned to the decisionprocess. The implementation time begins with the travel of the command over the association fibers leading to the initialmotor instruction generation area in area 7A of the parietal lobe.

The second column is labeled the Alarm mode. This mode is initiated by the Lateral Geniculate Nuclei in response toa change or changes in object space peripheral to the foveola. Before this initiation, the signal path is the same as forthe Awareness mode. The subsequent response is complicated by the nature of the change(s) and may be under thecommand of the control point (TRN) to be discussed in detail in Section 15.2.2. For a single change in object space,the initial response is transmitted to the cerebellum where a reflex response is generated and passed back to the superiorcolliculus for implementation. Beyond this point, the responses are essentially identical to those of the Volition mode.

Some evidence exists that the neurons called W-cells in cats are associated with this alarm function. While they aredescribed as connecting the retina to the superior colliculus, this claim appears based mostly on behavior experimentswith induced lesions. If they do not actually pass through the LGN, they are probably the neural paths defining areasof the retina in terms of azimuth and elevation coordinates. These signals would allow the superior colliculus to drivethe POS without requiring trigonometric calculations.

If multiple changes are sensed in object space within a finite interval, the TRN senses this complication and reroutes thealarm response along an alternate path providing additional analytical capability before creation of a response decision.In the figure, this alternate path is shown being passed to area 7 and area 7A of the parietal lobe. The data may travelfurther into the frontal lobe on its way from area 7 to area 7A. As a result, two distinct and parallel subpaths are shownalong the alarm path to the superior colliculus. It is likely that the TRN participates in the choice of which signal isimplemented by the superior colliculus. From this point on, the response follows the same timeline as the Volitionmode.

The existence of an alternate, and slower, alarm-processing mode is well known. It is important whenthe system is faced with multiple threats. It explains precisely why “swat teams” and other militaristicactions are timed to present the subject with multiple threats at the same instant.

The third column describes the Analysis mode of vision. This is arguably the most important mode of vision and isfound in its most sophisticated state primarily in the higher members of Chordata. The signal path is essentiallyindependent of the other modes in that the signal detection function only involves the photoreceptors of the foveola andthe PGN/pulvinar couple. Much of the retinal signal processing is bypassed in the signaling path of this mode. Inaddition, the LGN and the so-called primary visual cortex of Area 17 are also bypassed.

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To achieve the very high speed analytical capability required to evaluate a complex threat or a nutritional opportunity,it is important that the system can analyze a small complex scene quickly. To accomplish this function, the signals fromthe foveola are projected directly to the PGN (alias pretectum) and pulvinar where they are processed for both scanninginformation and contextual information. The contextual information is passed directly to Area 7 of the cortex via thePulvinar pathway for immediate analysis by the information extraction engine located there. If appropriate, thisinformation is then passed to the frontal lobe for analysis by additional engines. This activity may result in commandsbeing passed back to the premotor command generator at Area 7A. There is no requirement that this time criticalinformation be processed through the “primary visual cortex.”

Meanwhile, the extracted scanning information is passed back through the superior colliculus, via a parallel path, to theother elements of the oculomotor subsystem to aid the continuation of the scanning process. The signal path from thephotoreceptors of the foveola directly to the PGN and then to the superior colliculus and the oculomotor subsystem formsa servomechanism designated the Precision Optical System, POS. This servomechanism includes the elementspreviously included in the auxiliary optical system. The purpose of the auxiliary optical system was previouslyunknown. The POS is a very high performance servomechanism exhibiting the minimum possible time delay.

The two sets of commands received by the superior colliculus are merged, possibly under the guidance of the TRN,before following the same signal path to the oculomotor subsystem as in the Volition mode. The Analytic modecommands passed directly from the PGN to the superior colliculus are limited to microsaccades and flicks. Thecommands from Area 7A can call for larger amplitude saccades, especially when merged with commands from theVolition and or Alarm modes.

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Figure 7.4.8-2 Flow chart of latencies in the human visual system. See text.

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7.4.8.2 Comments by line

In the table, the transport delays associated with phasic signals (employing action potentials) appear under two differentdesignations. When outside the brain, it is labeled signal projection and is associated with the optic nerve. When insidethe brain, it is labeled association projection because it is carried over association fibers.

Although the line is blurred, for purposes of discussion, the signal processing within the brain that is not related tocognition is labeled signal processing. This includes the reflex responses associated with the Cerebellum and thatassociated with areas 17 through 22 in the posterior cortex. That associated with cognition is assumed to occur in theparietal and frontal lobes of the cortex and is labeled information analysis.

As can be seen from the table, some cumulative numbers are available for some modes of processing although individualvalues for segments of a given path may not be available from the literature.

Line 1. The time delay in the signal detection stage is dominated by the delay associated with the P/D process withinthe Outer Segment of the photoreceptors. This delay is sensitive to the temperature and the photon flux rate. Forhumans, the temperature is essentially constant. The variation as a function of photon flux has not been reported underrigorous test conditions. The best data appears in Figure 16.3.6-2 and dates from the 1930's. Based on this data, thedelay varies from three milliseconds in the photopic region to 10 ms or more at very low light levels.

Line 2. The signal processing within the retina is carried on in the analog domain and the transport velocity of the signalsis quite high. The minimum delay is as shown. For additional processing through the lateral paths, the delay may bemarginally longer.

Line 3-1. Reyem’s loop. This variable path distance for phasic signals between the ganglion cells and the lamina cribosaintroduces a variable time delay into the awareness path. This delay is proportional to the location of the source ofillumination on the retina. This can introduce an additional path length of up to 10 mm or 0.44 ms relative to the fixeddelay associated with the analytical path.

Line 3-2. The signal projection over the optic nerve from the lamina cribosa to the midbrain employs the phasic domainand is relatively slow. The nominal signal is for a path length of 75 mm.

Line 4-1. The time delays associated with signal processing in the LGN and the PGN are assumed to be small andapproximately equal because of the size of the structures involved. The TRN operates as a major switching point here,directing the signals to different elements of the brain based on a previously defined set of rules (that may be changeablethrough training).

Line 4-2. The pulvinar pathway is assumed to have a length of 50 mm in humans for purposes of discussion.

Line 4-3. The geniculocalcerine pathway has a variable length due to Meyer’s loops. The minimum pathway lengthis taken to be 50 mm in humans for purposes of discussion.

Line 4-4. The time delay associated with the cerebellum is only an estimate. Little data was found concerning thisparameter.

Line 4-5. The visual signal processing in the cortex is concentrated in the posterior lobe. In transferring signals fromarea 17 to area 7, it is not clear how much signal propagation is by analog means and how much is by phasic means.The transport delays associated with these modes are quite different. It is also unclear how much time is used in signalprocessing within areas 17 through 22. Specific values are becoming available from fMRI studies.

Line 5. The time delays associated with information processing within the frontal lobes can only be given as estimatessince the processing is so dispersed and the variety of techniques for stimulating the system varies so widely.

Line 5-1. This line provides an average delay for association fiber projection of 2.0 ms for purposes of discussion. Thecumulative values shown on this line are the best available based on the variety of data available in the literature.

Line 5-2. This line is meant to hold an average processing time for all of the engines of the frontal and parietal lobesassociated with a given experiment.

Line 5-3. This line provides an average delay for association fiber projection of 2.0 ms for purposes of discussion. Thecumulative values shown on this line are the best available based on the variety of data available in the literature.

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435Underwood, G. (1998) Op. Cit. pp 177-179436Wolfe, J. Alvarez, G. & Horowitz, T. (2000) Attention is fast but volition is slow Nature vol. 406, pg 691437Becker W. & Fuchs, A. (1969) Op. Cit.438Mulligan, J. (2002) Sensory processing delays measured with the eye-movement correlogram. Ann. N.Y.Acad. Sci. vol. 956, pp 476-478

Line 6-1. The values shown are small reflecting the size of the visual processing engines in Area 7.

Line 7-1. The TRN operates as the decision maker and gatekeeper, determining what signals are to be implemented bythe superior colliculus

Line 7-2. The superior colliculus directs signals to the oculomotor portion of the POS.

Line 7-3. The oculomotor portion of the POS implements the prescribed saccade

Line 8. The command signals to the oculomotor muscles encounter a constant time delay

Line 9-1 The only delay shown on this line is the absolute delay associated with the electrical performance of theoculomotor muscle fiber. The delay associated with the mechanical performance of the fibers depends on their designfunction. This value has been lumped into Line 9-2.

Line 9-2 The total time required to accomplish a specific saccade varies with the starting eccentricity of the eye and thetarget eccentricity. In the first approximation, this time is proportional to the change in eccentricity angle.

The cumulative values shown in Line 9-2 provide important information about the overall performance of the visualprocess. They highlight the large difference between the time to recognize a threat imaged on the foveola and one notimaged there. For a threat not imaged on the foveola, its evaluation time is highly dependent on whether the threat issingle valued or multivalued.

7.4.8.3 Correlation with the literature

When attempting to correlate the times shown in the above figure with those found in the literature, it requiresconsiderable effort to understand precisely the experimental procedure used by various investigators and thecorresponding specific path in the above table. Kennedy has provided some data of this type435. Jones has also provideddata that can be interpreted in this framework (pp 300-306 in S&C).

Wolfe, et. al. have provided some simple experimental results recently comparing searches involving volition and“anarchic searches436.” The reader is cautioned they use the term rate in place of interval. A rate is an expression withtime (or another independent variable) in the denominator, such as frames/ms. They show that the selection of objectsin a simple scene is much slower if volition is involved rather than a simple anarchic search (presumably under thecontrol of the TRN and POS).

7.4.8.3.1 Volition mode experiments

Becker & Fuchs give excellent data on a variety of volition mode eye movements437. The primary variant was whetherthe eyes could fixate on a visible object or not. They generally found that a volition mode movement made without avisual reference reached a lower velocity and therefore took longer than its counterpart with visual cues. Themeasurements in the dark followed a period where the subject attempted to memorize the location of the desired pre-and post saccade locations. After the light was extinguished (for at least three seconds) the duration of the volition modesaccade was increased by 10 to 35 ms and the maximum velocity was 46 to 108°/sec slower for a desired movement of40°. Their values were shown to be statistically significant for some of their subjects but not for others. Some subjectswere not able to produce a saccade close to the desired 40° without visual cues. Because the dark and illuminated fieldresults were so different, Becker & Fuchs also examined the transition state by varying the dark time between thememorization step and the actual dark saccades. They found a shoulder near 1100 ms that defined the transition betweenthe two modes of operation. They then explored the ability to prevent or interrupt a saccade by changing theenvironment.

Mulligan has recently provided data on the delay in volition tracking movements as a function of the contrast of aGaussian target spot438. A typical delay of about 100 msec was found before any movement.

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439Zeeki, Y. & Peli, E. (1979) Latency of peripheral saccades. J. Opt. Soc. Am. vol. 69, no. 9, pp 1274-1279440Findlay, J. (1980) The visual stimulus for saccadic eye movements in human observers. Perception, vol. 9,pp 7-21441Carpenter, R. & Williams, M. (1995) Neural computation of log likelihood in control of saccadic eyemovements. Nature, vol. 377, pp 59-62

7.4.8.3.2 Alarm mode experiments (including conflict resolution)

In some of the final discussions in Becker & Fuchs, the experiments fall into a more complex mode than the simplevolition mode. While useful as an overview, their terminology appears to stretch their assumed baseline. Extractingmore data from their paper may be possible but its precision may suffer from their lack of a sufficiently sophisticatedmodel when they were preparing the text. They described this “package hypothesis” and further experiments to exploreit in detail on their pages 1253-55.

Zeevi & Peli have presented data on the saccadic latency following the movement of a test stimulus within the central10° field of view of the subject439. Their tests involved a change in location of 4° but the starting and ending locationswere unusual. They also defined a reaction time corresponding to the time between the movement of the test stimulusand the first antisaccade. Their results highlight the inhibitory process involved in the “dual target” task suggested bythe alternate alarm path between lines 4-4 and 7-1. The initiation of a saccade by the superior colliculus is clearlyinhibited until the decision has been made about which target upon which to concentrate.

Findlay investigated the dual alarm phenomenon in some detail440. Under the simplest scenario, he said (citing Levy-Schoen) an additional nominal 30-40 ms was required to resolve what saccade was to be implemented. This scenarioinvolved two alarms placed symmetrically relative to the prior fixation point. This decision process involves either anunrecognized area of the midbrain or area 7. Findlay’s own experiments used an 8° eccentricity stimulus and a secondstimulus at an eccentricity that varied from 4° to 6° to 8° and occasionally 12° and 16°. A variation is size between thetwo stimuli was also introduced. Findlay introduced the concept of a saliency map in object space to report his results.Findlay performed experiments to define the saliency due to sudden appearances of stationary lights and thenexperiments to determine saliency as a function of movement of extra-foveola lights. He rapidly noted that both thevelocity and the direction of the stimulus were important. He was also careful to note that he employed apparent motionas opposed to real motion by rippling the illuminated lines on the face of the monitor. The apparent velocities were 6,12 and 18 degrees/sec. The monitor imposed a variety of limitations on the quality of the simulation. These limitationwere related to both the apparent motion of the moving stimulus and the apparent brightness of the fixed stimulus.

Although the title of Findlay’s paper focused on saccadic motion, the results provide significant information about thesensitivity of the eye as a function of eccentricity to both brightness and velocity changes. He also reviews the evidencefor a gating of the data from the “deeper cells” of the superior colliculus by the upper cells (page 18). This gating mightbe controlled by the TRN. He then discusses the fact that cells have been found among the ganglion cells that providea transient output that may be related to saccade generation. In this work, these cells are a result of spatial diversitybefore subtraction in the signal processing stage. It should be noted that this mechanism is distinctly different in thecentral 2° of the retina than in the extra-fovea area. This spatial diversity encoding provides a method for the visualsystem to differentiate between a flashing source of illumination and a moving source of illumination. His work wasinconclusive with respect to biases favoring one direction of saccadic motion over another and in sensitivity to thedirection associated with motion in object space. A tendency for saccades to favor a rightward direction in reading isprobably not shared with readers of Hebrew and other languages using a right-to-left or top-to-bottom presentation.

The fact that the subject’s performance improves so rapidly with training in the Zeevi & Peli study is interesting. Itsuggests that the shortest times given by them for the cumulative values applicable to line 9-2(D) of 200 ms +/– SD 30ms corresponds to the direct variant of the alarm path. It also suggests that their unusual test protocol causes the subjectto initially follow the alternative path that employs additional analysis. This path results in an initial value for line 9-2(D)that ranged from 610 +/- 14 ms to 310 +/- 39 ms among three subjects before converging toward the 200 ms value withtraining. With only three subjects, they were unable to provide a statistically relevant average observer but diddemonstrate both the variability and the training aspects of the times involved with Line 9-2(D). Zeevi & Peli made theassumption that the visual system is symmetrical with respect to temporal and nasal saccades.

Carpenter & Williams have presented data on the latency of alarm mode signals from 15° eccentricity (either left or right)in object space441. Their thesis assumed an entirely stochastic process after their discussion dismisses synaptic delaysand conduction velocities as not providing viable answers. They also assume the visual system is random noise limitedunder presumably photopic conditions. They used an unusual graph with a probit vertical scale and a logarithmic scalerepresenting “reciprocal latency.” Each figure shows two distinct families of loci that bear further study to determine

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442Hanes, D. & Carpenter, R. (1999) Contermanding saccades in humans. Vision Res. vol. 39, pp 2777-2791443Hanes, D. Patterson II, W. & Schall, J. (1998) Role of frontal eye fields in countermanding saccades: . . . J.Neurophysiol. vol. 79, pp 817-834 and references

relevancy. One family extends beyond the boundaries of the graph.

7.4.8.3.3 Interrupted alarm mode and other experiments

Hanes & Carpenter provide excellent data, and a bibliography of recent work, on a strategy of interrupting a normalalarm path response in humans442. They employed a 14 by 23 arc-minute size yellow LED against a “color-matchedbackground” at a uniform luminance of 4.5 cd/m2. The goal was to learn how late in a normal alarm path response, thesubject could inhibit his initial saccade. They defined this interval as the stop-signal reaction time (SSRT). A similarset of papers has been presented by Hanes, et. al working with the rhesus monkey443. Lacking a functional model in theirpresentations, the work of both groups must be considered exploratory. Although the analyses are exemplary inpresentation, they do not appear to allow a combination of determinate and stochastic processes in the explanation ofthe SSRT and other cumulative time intervals.

These authors did not address the alternate signal paths through the visual system employed by signals from differentlocations in the retina developed in this work. Lacking this level of discrimination, determining the precise paths(analytical, awareness or volition) involved in their experiments is difficult based on their text alone.

Using the model of this work to describe the signal paths taken by signals resulting from their stimuli, their protocolcan be seen to involve more variables than they controlled. When correlated with the Flow and Latency Profile presentedabove, their experiments emphasize the critical importance of the TRN (or other unrecognized element of the midbrain)in the overall operation of the visual system. The TRN is responsible for controlling the flow of responses through thealternate loops of the cerebellum, and to the parietal areas of the cortex. It is also critically involved in the final selectionof which responses received from these elements are carried out. Further correlation would suggest their experimentinvolved two alarm path responses plus a complex relationship between the two. They used the reappearance of theinitial fixation spot as a signal to stop their saccade to the second spot. However, the use of an audio tone to requestinhibition may have been more appropriate. In the case instrumented, the stop signal effectively introduced a two-targetsituation (with one target stimulating the faster, foveola related, signal path) upon which an additional decision had tobe made.

Hanes & Carpenter controlled the light level and contrast of their test environment and recognized a small but significantdifference in the temporal and nasal saccade implementation times. They determined the difference in saccade time withdirection was trivial in their experiments. At high contrast, the average delay for the control experiments, across severalthousand tests, was 227+/-0.4 ms for a target presented at 9° eccentricity. The reduced contrast tests introduced anadditional delay of 32 +/-0.4 ms.

As for their SSRT experiments, they found “the latency required to inhibit the production of a saccades followingpresentation of a stop signal is similar across subjects, on average 137 ms, and is approximately 40 ms longer than inrhesus monkeys.” This value is specific to their signaling protocol. They discussed their protocol in relation to otherson their page 2790. Below that discussion, they discuss their future plans involving varying many parameters. Certainconclusions can be drawn based on this model and a reading of their published description. The 137 ms value isassociated with the difference in time between an initial stimulus traversing the dual alarm mode signal path and asubsequent signal traveling the analytical mode path. Based on the small statistical variation in this value, discussedbelow, it would suggest that 137 +/- 11 ms can be assigned to a specific path in the latency profile. It appears to matchthe cumulative value for the analytical path from the photoreceptors of the foveola to the PGN/pulvinar decision point(Line 7-1 in the Latency Profile). It also appears that the 40 ms difference for the rhesus monkey is due primarily to theshorter signal projection distances involved in this smaller animal.

Their variation in performance with contrast appears to agree with the threshold level of the ganglion cells in the R-channel of this work.

The discussion of their results in terms of a race model can be described with greater relevancy in terms of a delay loopmodel. In that model, the TRN acts as a gatekeeper for signals passed to the superior colliculus for implementation bythe oculomotor subsystem. In this interpretation, their figure 4 is replaced by a graph with an ordinate defining thepercent path length (normalized) between the TRN as a signal distributor and the TRN as a decision maker. The abscissaremains a plot of time. Neural signals travel at either of two principal speeds, a high speed over signal projection (actionpotential) circuits and a low speed over analog (tonic) circuits. The total time delay for a signal to travel out from the

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444Hanes, D. Patterson II, W. & Schall, J. (1998) Op. Cit.445Robinson, D. (1972) Eye movements evoked by collicular stimulation in the alert monkey. Vision Res. vol.12, pp 1795-1808

TRN and back primarily depends on the physical length of the signal projection circuits plus the equivalent length ofthe signal processing circuits. The length of the signal processing circuits within a given engine may change throughlogic controlled switching. Under this analog, the progress of each signal along its prescribed path can be plotted asa percentage as a function of time. Note, the slope of the normalized curves does not represent a velocity since thecurves are normalized.

In the time delay analog, the first signal to reach the TRN will theoretically control the decision process. In practice,either the signals take a statistically variable time to travel through some of the signal processing engines or the TRNtakes a statistically significant time to make a decision. As a result, a finite statistical range may be associated with theprocess. Hanes & Carpenter define this range in stop-signal reaction time in their table 2. This range averaged +/-11ms at high contrast and +/- 6.5 ms at low contrast.

Using the model of this work and a modified Hanes & Carpenter protocol should provide additional information aboutthe operation of the visual system. This combination would not require a broadly based Monte Carlo simulation. Itwould significantly enhance our knowledge of the various signaling paths leaving the LGN and TRN.

7.4.8.3.4 Participation of the frontal eye fields of the cerebrum

The arrival of the MRI and the fMRI has introduced an additional non-invasive research capability of great value. These techniques have illuminated the precise location and size of the frontal eye field (FEF). The large area of this fieldfocuses attention on the approach of Hanes, et. al444 whom have probed this area in search of individual neurons thatshow activity prior to the onset of a saccade. Based on the area of this field, it is estimated to contain over 100,000individual neurons. It is likely that a great many of these neurons participate in a complex analog signal manipulationprocess. This process is best described using boolean algebra. Only a few neurons will be involved in the generationof action potentials to be sent over association fibers to other engines leading to the POS. However, this number maystill be in the hundreds to thousands. The method of encoding the action potentials to represent the vector informationrequired by the POS is still not known. It is possible that a group of parallel association fibers must be activatedsimultaneously to transmit the desired vector. The path these activation signals follow is also poorly understood. Itappears to go via area 7A (and possibly via the TRN) to the superior colliculus for further signal processing beforegeneration of the final commands by the Oculomotor Nuclei. Prior to the development of the above techniques,Robinson commented on a measured discrepancy between the shortest latency between stimulation of the FEF andstimulation of the superior colliculus445. They noted that the shortest reported latency from the FEF was 15 ms whilethe shortest reported latency from the superior colliculus was 20 ms. Again, lacking a detailed model of the signal pathoptions, knowledge of the size of the subjects involved, and a careful comparison of the stimulation techniques used,reconciling this difference is difficult. In the Robinson paper, figure 3 speaks of the mesencephalon instead of thesuperior colliculus thereby showing the potential variation in experimental results based on the precise location involved.This is an area of current and fertile research. Further discussion of these matters will be found in Chapter 15.

7.4.9 The lens and aperture control subsystems: accommodation

The lens and the aperture control system are elements of two separate closed loop subsystems. Portions of each systemare found within the ocular globe and portions are found in the midbrain. These elements are interconnected by nervesprojecting distally from the superior colliculus to the interior of the eye (See Section 2.3.4). The circuits also appearto contain an analog computational function associated with the PGN/pulvinar couple. The details of how the neuralsignals are decoded and converted to an analog signal capable of controlling the appropriate muscles is beyond the scopeof this discussion. It is addressed more completely in (Section 15.3.3.2.2). The neural signaling techniques are probablythe same as for any other muscle system and similar to those discussed in Chapter 14. Performance errors associatedwith this system are discussed in Section 18.8.3.

The vergence control system is also a closed loop servomechanism. It is a more complicated loop physiologically. Theinitial information is extracted from the data of the two eyes in the layers of the LGN. This information is fed to thethalamus where correction signals are generated via the superior colliculus. The foveola signals obtained by each eyefollowing the initial vergence are probably used by the PGN/pulvinar couple to perform a second level of vergence. Iftrue, the overall vergence control system is a two level system of considerable expanse in terms of the individualelements of the visual system.

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446Westheimer, G. & Blair, S. (1973) The parasympathetic pathways to internal eye muscles. Invest.Ophthalmol. Vis. Sci. vol. 12, pp 193-197447Kuwabara, T. & Cogan, D. (1977) The eye In Weiss, L. & Greep, R. Histology, 4th ed. Chapter 32448Stark, L. (1988) Presbyopia in light of accommodation. Am. Jour. Optom. Physiol Optics, vol. 65, no. 5, pp407-416449Blaker, J. (1980) Toward an adaptive model of the eye. J. Opt. Soc. Am. vol. 70, n0. 2, pp 220-223450Jennings, J. & Charman, W. (1978) Optical image quality in the peripheral retina. Am. J. Optom. Physiol.Optics vol. 55, no. 8, pp 582-590

Figure 7.4.9-1 Image of the lens and pupil taken from theposition of the retina LARGE FILE. See text.

Westheimer & Blair have provided a block diagram of the signal paths associated with these three elements of thePrecision Optical System446. Because of its complexity, the vergence control subsystem will be discussed in Section7.4.3 & 7.4.9 following the broader discussion of the pointing system. [xxx does this belong here?]

Few images of the plant associated with the lens and aperture subsystems are found in the literature. Figure 7.4.9-1 fromKuwabara & Cogan in Weiss is particularly useful447. Taken from the position of the retina, but with no specifics relativeto location of the optical axis or foveola, it clearly shows the gross size of the lens, and both the nominal maximumdiameter (note change in shading) and current diameter of the iris. It also shows the radial arrangement of structure (parsplicata) of the ciliary body probably related to the equalizing structure maintaining the tension on the lens. Beyond thisstructure is the more uniform ciliary body (pars plana).

7.4.9.1 The lens control system

The lens control system involves a broad collection of elements based on different technologies and mechanisms. Thissection will attempt to place these elements in perspective and note the unique performance limitations imposed by someof them.

7.4.9.1.1 Background

As usual, the discussion of the lens control system is addressed independently and from different perspectives in varioussegments of the vision community.

The papers of L. Stark448 and Blaker449 are important in understanding the operation of the lens control system. Starkprovides a review of earlier attempts at developing a model of the physical plant. Blaker provides some actual data onthe operation of the plant. It was collected by Fincham in 1937. One useful piece of information was found in Jennings& Charman450. Coleman has presented a paper analyzing the lens system in terms of a hydraulic model involvingpressures between the various humors and the lens. It is described as the “catenary” approach based on the shape of onesurface of the lens. As usual, no complete model, either static or dynamic, is provided.

Grosvenor & Flom have edited a significant compendium on the subject of refractive anomalies (with a concentrationon the physiology of myopia). Schor, writing in theirbook (pp 310-317), introduces the subject of a closedloop servomechanism controlling accommodation, based

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451Schor, C. (1979) The relationship between fusional vergence eye movements and fixation disparity VisionRes vol. 19, pp 1359-1367452Schor, C. (1991) Effects on the resting states of accommodation and convergence in Grosvenor T. & Flom,M. Ed. Refractive Anomalies. Boston, MA: Butterworth-Heinemann, Chapter 18453Wallman, J. (1990) Introduction in (Ciba Symposium 155) Myopia and the Control of Eye Growth. NY: JohnWiley & Sons454Wallman, J. (1991) Retinal factors in myopia and emmetropization: clues from research on chicks inGrosvenor, T. & Flom, M. Refractive Anomalies. Boston, MA: Butterworth–Heinemann Chapter 15455Jiang, B-C. (1997) Integration of a sensory component into the accommodation model reveals differencesbetween emmetropia and late-onset myopia. Invest Ophthal Vis Sci vol. 38, no. 8, pp 1511-1516456Glasser, A. (2001) On modeling the causes of presbyopia. Vision Res. vol. 41, pp 3083-3087 (Note the lastparagraph probably required by the reviewers).457Weale, R. (2000) Why we need reading-glasses before a zimmer-frame. Vision Res. vol. 40, pp 2233-2240458Koretz, J. Cook, C. & Kaufman, P. (2002) Aging of the human lens: changes in lens shape uponaccommodation and with accommodative loss. J. Opt. Soc. Am. A, vol. 19, no. 1, pp 144-151459Koretz, J. & Handelman, G. (1986) The lens paradox and image formation in accommodating human eyes.Topics in Aging Research in Europe, vol. 6, pp 57-64 A similar discussion in Scientific American, vol. 259, pp92-97460Koretz, J. Cook, C. & Kaufman, P. (2002) Op. Cit. pg 150.461Coleman, D. (1970) Unified model for accommodative mechanism. Am. J. Opthalmol. vol. 69, no. 6, pp1063-1079462Koretz, J. & Handelman, G. (1986) How the human eye focuses. Sci. Am. vol. 259, July pp 92-97

on his earlier work in vergence451, but does not pursue it in detail452.

Two brief discussions including block diagrams have appeared recently. The same material of Wallman appears in twoseparate publications453 ,454. The simple and largely conceptual figures in that material suffer from a number of structuralproblems (note the question mark along one of the signal paths in the servomechanism diagram) and do not address thesignal processing associated with the servomechanism at all. The Boolean logic associated with the diagram does notappear to relate to any realizable servomechanism. Jiang has also contributed a largely conceptual floating model455.He introduces two non-linear elements into the basic conceptual servomechanism of the accommodation subsystemwithout providing any substantive justification or references for the concepts. This work has found no justification fora nonlinear operator in real visual systems describing a symmetrical dead space related to the amplitude of the sensorysignals. The stage 3 circuits do include a unidirectional threshold level. However, this level is very low and correspondsto the lowest level of scotopic performance. It is generally not relevant in discussions of accommodation. Heincorporates a nonlinear gain element (gain is proportional to the average signal input level) that he associates with thesensory part of the system His words suggest that this operator is actually intrinsic to the input signal. In real visualsystems, the adaptation process exhibits a characteristic that is the exact inverse of the suggested operator. As a result,the product of these operators is a null condition throughout the photopic range of vision. The product does becomesignificant in the mesotopic range, but the net result is the opposite of that described by Jiang. Jiang proceeds to developclosed loop equations that ignore the “plant” shown within his servoloop and any time delay associated with signaltransmission within the loop. The relevance of the resulting equations are at least questionable.

Recently, a spirited (might I say vituperative) discussion has appeared by Glasser456. He takes considerable exceptionto the theory presented by Weale457 (without either having the benefit of a physical model of the subject). His discussionhighlights the ongoing approach of the vision community to rely upon experiment and intuition and avoiding physicalmodels based on engineering principles.

A parallel school is engaged in analysis of the lens servomechanism from a more physical and materials-basedapproach458. They have even begun using elementary ray tracing to confirm that their analyses are compatible with theactual operation of the eye.

The fact that very few references are shared between the papers of the groups defined above isinteresting. They generally do not reference each other. This shows a lack of thoroughness inaggregating ideas to create a more comprehensive and consistent model. As a positive example, aparadox appeared recently in the Koretz school459. A paradox is similar in concept to a magic trick.It is not understood by one party because of an inadequate model. This paradox was rapidly resolvedby more attention to the detail boundary conditions of the situation460. For a good example ofaggregating ideas coherently, see Coleman461.

Before proceeding, reviewing the art in the papers of Coleman referenced above and of Koretz462 is useful. They develop

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463Coleman, D. (1986) On the hydraulic suspension theory of accommodation. Trans. Am. Ophthalmol. Soc.vol. 84, pp 846-868464Fisher, R. (1969) The significance of the shape of the lens and capsular energy changes in accommodation.J. Physiol. vol. 201, pp 1-19 & 21-47465Dubbelman, M. & Van der Heijde, G. (2001) The shape of the aging human lens: curvature, equivalentrefractive indes and the lens paradox. Vision Res. vol. 41, pp 1867-1877466Smith, W. (2000) Modern Optical Engineering. NY: McGraw-Hill, pg 138467Fisher, S. & Ciuffreda, K. (1988) Accommodation and apparent distance Perception vol. 17, pp 609-621

many subtle features of the physical plant associated with the lens servomechanism. A more recent Coleman paper isalso useful463.

Additional work is required using ray-tracing (or by introducing more optical design experience into the field). Nearlyall of the recent papers are struggling to show the surfaces of the physiological optics are either spherical or paraboloid.Occasionally, it is claimed they are hyperboloid. It is proposed that a full ray-trace, even with the precision of theavailable numbers would show that the cornea is of necessity ellipsoidal in shape. Otherwise, the wide angle coverageof the eye could not be obtained. Some authors have justified their choice based on a 2nd order conic section. All of theabove forms can be described as 2nd order conic sections. Fisher’s very careful analyses of the materials of the lensesand humors used the term ellipsoid to describe the anterior surface of the cornea (page 36)464.

Dubbelman & Van der Heijde provide information on the great latitude in many parameters of physiological optics465.The scatter diagrams are very broad. They raise the question whether a best fit first order line through the data ismeaningful. Maybe additional cross correlation diagrams are needed to discover underlying relationships between pairsof data points. This team could also use the help of an experienced optical design engineer.

The requirement on the accommodation servomechanism is to achieve a focus at a given range within the depth of focusof the optical system itself. This value is about ±1/8 diopter for a three-mm aperture466. For a one mm pupil diameter(typical of photopic conditions), the servomechanism needs only meet a ± 1/4 to ± 3/8 diopter requirement.

Little data appears in the literature on the performance of the lens control system (see Section 7.4.9.1.3). Fisher &Ciuffreda have provided coarse data on the static response of the lens system to changes in the accommodativestimulus467. They note that the role of the lens control system in distance perception remains controversial. Nosignificant data on the role of the lens control system in depth perception was found in the literature.

7.4.9.1.2 The overall servomechanism of accommodation

The overall servomechanism of accommodation proposed in this work is shown in Figure 7.4.9-2. The diagram beginsat the lower right with the creation of the physiological optical system. The brackets behind the integral sign indicatethe processes involved in the growth of the eye are essentially unidirectional. As the cornea and lens begin to createoptical refraction with respect to light, the ocular globe begins to expand and move the retina away from the optics. Post-partum, these processes proceed at independent rates up through the teen years. The scaled difference between theserates can result in an ammetropic condition under anatomical conditions (the ciliary muscle completely relaxed andhaving not affect of refraction). This gross refraction error (relative to an image at infinity) can be affected slightly bythe tonus of the ciliary muscle. The result is the net anatomical refraction condition. Optimally, this condition imagesa source at infinity perfectly on the retina. To achieve ideal focus at closer distances, the lens must provide a net changein refractive power that is called accommodation. This change is achieved by the physical distortion of the lens by theciliary muscle under in-vivo conditions. The resulting accommodated refraction is designed to match perfectly thechange in refraction needed to image a source at an arbitrary finite distance from the eye. If it fails to do this, anaccommodation error is associated with the image projected on the retina at the plane representing the entrance to thephotoreceptor cells.

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Figure 7.4.9-2 Block diagram of the accommodation servomechanism. Note the plurality of plus signs in the figure.The servomechanism is unidirectional. If the gross anatomical refraction error is significantly positive, the system cannot compensate for it. As a result, the subject is hypometropic and is said to suffer from myopia. The stage 1, 2 & 3circuits are not shown explicitly in this figure but they are important to the dynamic operation of the subsystem. See text.

The error in accommodation sensed at the retina is processed within the two-dimensional correlator of the perigeniculatenucleus which is charged with ascertaining the quality of the edge response within each signal channel due to the tremorof the oculomotor pointing subsystem. An auxiliary calculation is also performed in the lateral geniculate nuclei toprovide a coarse accommodation signal derived from the vergence servomechanism. These two signals are showncombined into a net analog accommodation correction signal although these signals are transmitted independently to thesignal conditioner within the Edinger-Westphal complex associated with the superior colliculus. This signal processingengine appears to accept a variety of other signals in order to process the appropriate instruction to control the ciliarymuscle. These include an accommodation signal obtained from the saliency map suggesting the correct accommodationsignal value based on prior examination of the stimulus. It may also accept a bias signal used to establish the quiescentaccommodation level (sometime called the dark focus condition) in the absence of any other signal. Changes in the

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468Owens, R. & Wolf-Kelly, K. (1987) Near work, visual fatigue, and variation of oculomotor tonus InvestOphthalmol Vis Sci vol. 28, pp 743-749469Glasser, A. & Campbell, M. (1999) On the potential causes of presbyopia. Vision Res. vol. 39, pp 1267-1272

quiescent focal accommodation are known to occur with activity level468. This change may be due to a calculation basedon time-integration within the signal processing engine using unknown sensory inputs, or it may be due to the enginecontinuously referring to the accommodation level updated frequently and stored in the saliency map.

The signal processing engine may also accept a copy of the perturbation signal used to cause tremor in the oculomotorsubsystem. This would be used to cancel any artifacts of tremor in the net signal sent to the ciliary muscle. The Edinger-Westphal complex processes these signals in the analog domain and then converts the information into action potentialsfor transmission to the ciliary muscle.

The so-called ciliary ganglion, found along the signal path between the brain and the ciliary muscle is used to introduceemergency control signals associated with the Alarm Mode of the visual system. These emergency signals are normallyinsignificant. The low-pass electrical characteristic of the ciliary muscle integrates the action potential pulse stream fromthe ciliary ganglion and generates a physical response proportional to the original analog signal from the Edinger-Westphal complex. This physical response distorts the lens, thereby introducing the degree of accommodation requiredand closing the accommodation servomechanism loop.

It is important to note that the accommodation servomechanism is essentially a unidirectional servomechanism. Onlya single ciliary muscle is present in each eye. This muscle works with the elasticity of the lens and its support structureas an antagonist. This unitary character is suggested by the number of plus signs shown at the summing junctions withinthe diagram. A disease (myopia, or hypometropia) arises when the net anatomical refraction (resulting from the growthprocess) is significantly positive. The unidirectional accommodation servomechanism is unable to compensate for sucha condition.

The stage 1, 2 & 3 circuits are not shown explicitly in the figure. They are described more completely in Sections 7.3,7.4.2 & 7.4.3 and in the chapters related to their specific roles. The performance of these circuits are important to theshort term dynamic performance of the accommodation servomechanism. Little research has been reported concerningthe short term performance of the accommodation servomechanism.

The sophisticated lens support system is discussed in Section 7.4.9.1.3. Other aspects of the servomechanism will bealso addressed in the following sections.

7.4.9.1.3 The performance of the overall accommodation servomechanism

Figure 7.4.9-3 presents a nomograph describing limits imposed by the nature of the above schematic. The nomographstarts at lower left giving the distance from the subject of a stimulus. By projecting horizontally and then vertically tothe horizontal axis, from the characteristic representative of the subject, the required accommodation relative to thecollimated condition is found. The two bounding curves represent the anatomical refractive error of the subject. A log-normal distribution representing the degree of ametropia found in the general population is shown at the lower right.This distribution shows a slightly sharper edge on the hypermetrope side and properly describes the slightly higherfrequency of 4D hypometropes compared to 4D hypermetropes. It suggests plus and minus four diopters are reasonablevalues to describe the limits of ametropia found in the general population other papers have used six diopters as acriterion. Notice that a four diopter hypermetrope (myope) requires a negative degree of accommodation for stimuli atdistances greater than 25 cm. By projecting the value on the horizontal axis up until it reaches the fold line and thenhorizontally to the vertical axis, the available correction is determined for the stimulus originally postulated. As notedabove the accommodation mechanism cannot provide negative accommodation. This area of operation has been shaded.

Normally, it is found that the human visual system operates with a small amount of accommodation associated with thetonus of the ciliary muscle. This tonus may be supported by a neural signal of a nominal value as discussed in Sectionxxx. The quiescent focal condition due to this level of tonus is indicated by one diopter on the upper left scale. For theemmetrope, this level represents a normal quiescent accommodation to a stimulus distance of 100 cm, whether there isa stimulus present at that distance or not. For the four diopter myope, the quiescent accommodation distance isnominally 20 cm.

The limits of the nominal human eye as a function of aging is shown by the figures along the fold line469. Young eyesnormally provide accommodation up to at least 14 diopters. As the subject ages, the maximum accommodationdecreases, a condition known as presbyopia. By 50 years, the nominal emmetrope can only accommodate over a range

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250 Processes in Animal Visionof zero to two diopters. The subject can no longer read newspaper size text held within arms length but he can stillaccommodate to long distances. By the time he is 60 years of age, the lower part of the fold line will also be lost. Hewill need spectacles to accommodate to long distances as well. As another example, a two diopter hypermetrope willbegin requiring spectacles for reading at about 30 years and also require spectacles to aid accommodation at longdistances at age 48.

This nomograph, along with the data of later sections, clearly supports the definition of “young eyes”.Young eyes for physiological research purposes should be restricted to fully matured emmetropes notover 25 years of age. If necessary, hypermetropes within the same age boundaries can be included.Hypometropes will introduce asymmetrical results into many test protocols.

It is interesting to note the ability of a hypermetrope to properly image scenes presented to his eye that involveconverging light rays (a situation not found in nature). Within their degree of hypermetropia, young eyes can actuallybring such a scene (such as generated by a set of misadjusted binoculars) into correct focus.

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Figure 7.4.9-3 A nomograph describing the performance of the accommodation subsystem.

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470Abbot, M. Schmid, K. & Strang, N. (1998) Op. Cit. pg 18471Radhakrishnan, H. Pardhan, S. et. al. (2004) Unequal reduction in visual acuity with positive and negativedefocusing lenses in myopes Optom Vis Sci Vol. 81(1) pp 14-17472Radhakrishnan, H. Pardhan, S. et. al. (2003)Effect of positive and negative defocus on contrast sensitivityin myopes and non-myopes. Ophthal Physiol Optics Vol. xxx pp xxx473Gwiazda, J. Thorn, F. Bauer, J. & Held, R. (1993) Myopic children show insufficient accommodativeresponse to blur Invest Ophthal Vis Sci vol. 34, no. 3, pp 690-694

Figure 7.4.9-4 Accommodation performance of the “young”emmetrope eye as a function of stimulus intensity. Modifiedfrom Owens, 1991. The emmetrope cannot correct forstimulus distances beyond infinity (converging lightbundles).

The above nomograph can be extended to also represent the situation when the scene contrast is low. For the idealemmetrope without any age limitation, the curve is precisely as shown by Owens (pg 324 in Grosvenor & Flom) andreproduced here as Figure 7.4.9-4. For other eyes, the quiescent focal condition must be determined and a similar setof lines drawn. As Owens has noted (pages 326-340), previous clinical investigations have been contradictoryconcerning the quiescent focal condition (also called the dark focus condition).

7.4.9.1.3.1 Static performance errors inaccommodation (clinical)

[xxx this section will move to Section 18.2.4 ]Abbott, et. al. have shown that the first order staticperformance of the closed loop accommodationsubsystem is quite good, particularly at high degrees ofaccommodation470. Errors with a mean of less than 0.1D +/– 0.1 D were reported for absolute accommodationdemand greater than 1.0 D. The errors wereconsiderably higher in the range of 0.0 to 1.0accommodation demand. This is the region where thespring force associated with the lens mounting system isminimal and any neural bias is small.

Radhakrishnan, et. al. recently presented data on thesecond order asymmetry of the accommodationservomechanism based on precise acuitymeasurements471 and precise contrast measurements 472.Their data applies to the second order anomaliesassociated with subjects fully corrected for sphericalrefractive error. The title of their paper does not indicatethe fact their subjects were corrected. The cause of theseanomalies were not discussed in detail but theysuggested they may be related to the data andmechanisms discussed the papers of He, et. al.referenced below.

A small negative change in accommodation may beavailable by allowing the bipolar output signal of the PGN to subtract from a small static bias applied continually to theciliary muscle as part of a quiescent accommodation signal. This capability can be inferred from some of the literaturebut it is difficult to confirm. Radhakrishinran, et. al. reported a residual accommodation after cycloplegia was about 0.2Din both hypometropes (myopes) and hypermetropes. Their abstract did not define the reference point for their differentialmeasurements. The literature shows that averaging groups to obtain a quiescent focal accommodation condition isfraught with difficulty. The mean values obtained are associated with a very wide standard deviation. Other literaturesuggests the quiescent focal accommodation is time and activity dependent.

Gwiazda, et. al. have provided unexpected support for the presence of a two dimensional correlator within theperigeniculate nucleus and the effect of reduced low frequency response of the overall visual system at low spatialfrequencies473. They note the unexpected improvement in the operation of the accommodation subsystem when smallerletters are used as a test source. They also surface once again a terminology problem. First, the visual system does notoperate based on a phenomenon described in the literature as blur. The system employs edge detection of scene elementsaided by the application of tremor to the oculomotor system. The edges are detected using standard electronic techniquesthat include the measurement of the slope of the edge expressed in volts. The slope in measured indirectly by subtracting

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474He, J. Burns, S. & Marcos, S. (2000) Monochromatic aberrations in the accommodated human eye VisionRes vol. 40, pp 41-48475O’Leary, D. & Allen, P. (2001) Facility of accommodation in myopia Ophthal Physiol Opt vo. 21 no. 5 pp352-355476Stark, L. (1988) Op. Cit.477Wyatt, H. (1988) Some aspects of the mechanics of accommodation Vision Res vol. 28, no. 1, pp 75-86

the instantaneous value of the correlator output at two points in time separated by one half the period of the tremor signal.The magnitude of this measurement (the strength of the stimulus in the prior figure) is an estimate of the product of theintrinsic sharpness of the image, and the quality of the focus and modulation transfer function of the physiological opticalsystem. Second, the signal to noise performance of the accommodation signal generated as above can be considerablyimproved if there are more edges in the stimulus scene and a correlation process is used to optimize the resulting signal.The quality of the achieved accommodation is proportional to the number (and length) of sharp edges ( both vertical andhorizontal) occurring within the 1.6 degree diameter foveola and supported by the perigeniculate 2-dimensionalcorrelator See Section 15.6.3).

The data of Gwiazda, et. al. and of Jiang both show that the accommodation subsystem operates as a high quality type2 (rate controlled) first order servomechanism. High quality in this case refers to adequate loop gain to insure effectiveclosure of the servoloop under most conditions. To improve the quality of operation at low absolute dioptric values(imaging sources near infinity) would require implementation of an absolute error signal relative to the stimulus intensity.Such a capability is not available in the visual system.

He, et. al. have presented data on the errors in accommodation related to aberrations in the physiological opticalsystem474. These are generally small second-order errors when compared to the developmentally related errors.However, they do highlight the movement of the lens along the optical axis and perpendicular to the axis duringaccommodation. The latter errors introduce asymmetries that may account for the second order errors found to be moredominant in myopes.

7.4.9.1.3.2 Dynamic performance errors in accommodation (clinical)

[xxx this section will move to Section 18.2.4 ]Only a few papers were found discussing the dynamic performance of the accommodation subsystem. The paper byO’Leary & Allen only lists six references dating from 1982475. Their instrumentation was minimal and they reportedsettling times following changes of 2.0 D using a flipper bar containing only one –2.0 D lens, or changes of 4.0 D usinga flipper bar containing +2.0 and – 2.0 lenses, on a continuing basis. The resulting cycle times peaked in the 12-18 cycleper minute range for the 2.0 D changes at long range. At the shorter ranges, the cycle times showed a broader peak inthe 6-18 cycle per minute range. These values appear to be compatible with the more detailed physiological experimentsdiscussed below.

7.4.9.1.4 The physical plant of the lens control servomechanism

The physical plant portion of the servomechanism of lens control has been studied in detail by L. Stark476. The situationis more complex than suggested by the block diagram of [Figure 18.2.4-3] because of the unique physical arrangementof the ciliary muscle and associated structure. This arrangement was explored in detail by Helmholtz in the 19th Century.His model has an awkward name because of its precision. It has become known as the “dual indirect, Active Theoryof Accommodation.” It is dual because both the lens and its capsule appear to play active roles. It is indirect becausethe ciliary muscle does not act directly on the lens/capsule. It operates through a complex trusswork (trabecularmeshwork within the community) designed to insure equal forces around the perimeter of the lens/capsule. Finally,accommodation is achieved through an active mechanism. Positive accommodation requires contraction of the ciliarymuscle. This configuration is interesting in that it can avoid astigmatism due to lens distortion if desired. Alternately,it could be used to introduce astigmatism. The ciliary muscle is a unified muscle as opposed to a sphincter muscle. Itis served by multiple nerve endings. If programmed separately, various portions of the muscle could be used to introducea desired astigmatism. Conversely, if the nerves are not all functioning normally, an astigmatism can be introduced thatis not related to distortion in the geometry of the retina or sclera.

Stark has provided a static biomechanical model of the lens control plant based on the above truss configuration firstexplored by Helmholtz. Wyatt has provided some valuable data concerning the movements of the lens capsule477.However, he was not satisfied with his model of the accommodation mechanism plant, within the region labeled O, P& S. His discussion of the accommodation plant elements in this area of the eye will not be reported here. Figure 7.4.9-

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478Beers, A. & van der Heidje, G. (1994) In-vivo Determination of the biomechanical properties of thecomponent elements of the accommodation mechanism Vision Res vol. 34, no. 21, pp 2897-2905

5 presents a more explicit bio-mechanical model based on Beers & Heidje478. The outer shell of the ocular is shownusing solid lines. The interior details related to the retina, lens and iris are shown using thin dashed lines. The vitreoushumor in contact with the retina and the anterior humor between the cornea and the lens are not shown. If present, apressure difference between these two media could be significant in the dynamics of the accommodation system. Mostof the literature discounts this difference because of the apparent porosity of the structure surrounding the lens capsule.The lens is suspended from a floating link between the accommodation muscle, the ligament connecting to the capsuleof the lens and a ligament connecting to point O.

The paucity of data on the accommodation mechanism is illustrated by the age of the references in Stark. Wyatt providesthe broadest collection of data relative to accommodation, but does not include the data of Stark published the same year.Stark, Wyatt and Beers & Heidje use significantly different models to analyze this structure. Stark assumes the ocularis a rigid structure while the others do not. Wyatt takes two internal structures, the pars plana and the pars plicata of theciliary body to be functionally rigid while the others do not. Beers & Heidje treat the lens as a spring and dampingelement while the others treat it as only a spring. Stark does not address the axial motion of the lens while the othersdo (to various degrees). While both Wyatt and Beers & Heidje use concepts drawn from the discipline of statics, neitheraddresses all dimensions of the appropriated free-body model. They both focus on the radial motions of the point P whilerecognizing axial motions are also present. Future researchers must study the points made by each of these authorscarefully before developing more appropriate unified models.

Most investigators have discounted the angular geometry associated with this mechanical mechanism. This isunfortunate since the lens will clearly move axially as the ciliary muscle contracts unless it is constrained. Figure 2 inWyatt expressly describes the axial motion. Both the radial and axial motions are transcendental because of thegeometry. Fortunately, the relevant angle does not change significantly in human vision.

The above authors have not addressed the optical equations appropriate to this situation. The fundamental lens equationis shown at upper right in the figure to illustrate a concept. This is also known as the thin lens equation. The distances,f1 and f2 are measured form the centerline of a thin lens. Neither the cornea or the lens are thin lenses. For thick lenses,separate principle planes are defined at the entrance aperture and the exit aperture of the lens. The distances must bemeasured from the appropriate principle planes of the lens. The principle planes are shown generically for both thecornea and lens. These planes are addressed more thoroughly in Section 2.4.1.2.1. When two separate lenses form alens group, a different equation applies. Such a group exhibits its own set of principle planes, P1 and P2, as shown inthe figure. The equally important equation for a lens group consisting of two thin lenses is shown below the fundamentalequation. This equation shows that the Effective Focal Length, EFL, of the group varies with the spacing between theadjacent principle planes, d. In most man-made optical systems, the focus is adjusted exclusively by varying the distanced. Only in physiology is the power of the second lens also varied. The result is a more compact design. However, asthe equation shows, both the distance, d, and the focal length of the second lens, Fl, are important in the overall equation.The angles involved in the geometry of the accommodation plant appear to be chosen to recognize the relative effectsof the change in position and the change in optical power of the lens in response to contraction of the accommodationmuscle. Wyatt gives values for these angles as appropriate to his free-body-diagram.

Early man-made variable focal length optical systems (“zoom” systems) did not include automatic focus mechanisms.The correct focus was achieved by calibrating the lenses and providing a cam-operated mechanism to control theseparation of the lenses and their position relative to the focal plane. The physiological system provides a focus sensorthat controls the accommodation muscle in a unidirectional servomechanism (as opposed to the push-pull or bidirectionalsystems used to rotate the eyes). The relative motion of the second lens relative to the focal plane and the power of thatlens are adjusted simultaneously by the linkage shown by the heavy dashed lines.

The Beers & Heidje model illustrated here is based on the same interpretation of the physiological structure asHelmholtz. The details were provided by those investigators. “The component elements are: the ciliary muscle, the axialand peripheral zonules, the choroid and the lens. . . . The ciliary muscle is a unified muscle with a single physiologicalaction. . . . It has a single origin, the scleral spur, and a single insertion namely the ciliary body epithelium andsuperficial stroma between the ciliary processes, where the span fibrils of the zonules are attached. The elasticantagonists of the muscle are the choroid and the peripheral zonules.” They also stated the action clearly. “During near-to-far (NF) accommodation, when the ciliary muscle relaxes, the elastic force of the antagonists pulls at the axial zonulesand lens capsule, thus flattening the lens. During far-to-near (FN) accommodation ciliary muscle contraction takes upthe elastic tension in the antagonists, thus relaxing the axial zonules and allowing the lens capsule to mold the lens intoa more convex shape.”

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Figure 7.4.9-5 Static biomechanical model of the lens servomechanism and relevant equations. Note the foveola is noton the optical axis and the line of fixation is not parallel to the optical axis. The plant serving the accommodationfunction is shown between the anchor point, points O, P and S, and the capsule containing the lens. See text. Muscleand ligament arrangement based on Beers & Heidje, 1994.

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479Fisher, R. (1969) Op. Cit.480Koretz J. & Handelman, G. (1986) Op. Cit.481Brown, N. (1974) The change in lens curvature with age. Exp. Eye. Res. vol. 19, pp 175-183482Koretz, J. & Handelman, G. (1988) How the human eye focuses. Scientific Am. July , pp 92-99

Stark presents the predicted performance of two conceptual theories that are both based on the Helmholtz model. TheHess-Gullstrand lenticular theory assumes the muscles of the eye remain capable throughout most of life but the lensbecomes less compliant. The Duane-Fincham extra-lenticular theory is based on the results of pharmacologyintervention. It assumes the capability of the ciliary muscle degrades with age. Stark recognizes the correctness of theresults claimed by Duane-Fincham but shows they are not representative of the actual in-vivo operation of the plant. Theresults predicted by the Hess-Gullstrand approach provide better answers. Accommodation is degraded by changes inthe lens/capsule. The change is probably due to the continued increase in volumetric size of the lens although a changein viscosity cannot be ruled out. The debate concerning whether presbyopia is due to lens hardening or muscle aginghas been solved. Successful surgical intervention now provides a new, more compliant, lens and relies upon the muscleto operate normally regardless of the age of the subject.

The complexity of the accommodation servomechanism is high and careful choice of words is needed in any discussion.In some cases, considerable discussion is needed to explain simple assertions. As an example, Stark makes the statementthat “The Hess-Gullstrand theory is a nonlinear theory.” This may be a poor choice of words concerning hisinterpretation of his figure 6. He is discussing presbyopia, the loss of accommodation with aging. With age, several ofthe parameters associated with accommodation may change. Over the available operating range, the system operateslinearly. Only over an extended operating range does the response show nonlinearity. Technically, the model hepresents and the performance the Hess-Gullstrand theory projects are both linear for small signals from a control theoryperspective. Wyatt also notes the linear character of his model over its operating range. The values shown for the totalforce in the different structural elements of the Stark and Wyatt models are based on the literature of the time. Theyappear large to the uninitiated. Fisher uses values of one to two grams versus Stark’s 30-40 grams. Stark discussesseveral “ground points” associated with this model. They help explain the character of the performance presented below.

When discussing the loss in performance due to presbyopia, Stark chose to interpret the Hess-Gullstrand Theory usinga “piece-wise linear” approach. He describes the major active portion of the response as the manifest zone and the areaof falloff, as a function of aging, as the latent zone. Here again, using latent appears to be a poor choice of words. Heis speaking of a loss in performance unrelated to any time delay. The true latency in this process will be developed inthe section on transient performance. He does not address the transition region. Unfortunately, Beers & Van der Heijdealso employ a piecewise linear approach and assume the source impedance of the ciliary muscle is negligible. Thecriticism concerning using a piecewise linearization must also be extended to the paper of Fisher, particularly regardinghis figure 3479.

Based on the assumptions they used, Beers & Van der Heijde have analyzed their data in terms of a simple exponentialcurve. However, the data in their figure 3 clearly do not follow an exponential curve. Their time constant in figure 5are actually averages of a continually changing underlying time constants. This is shown in Figure 7.4.9-6.

Coleman has critically reviewed the above Helmholtz model concerning several shortcomings. By adding in a hydrauliccomponent, he proposes to eliminate some of these shortcomings. Koretz has introduced another interesting factor480.She supports the view of Farnsworth that the zonules connecting to the lens change their relative position with age. Asa result, the zonules lose much of their mechanical advantage relative to the shape of the lens.

A major problem in discussing the lens servomechanism is the great amount of scatter in the data when multiple subjectsare involved. Brown has provided an excellent example of this481.

7.4.9.1.5 The physical parameters of the materials of the servomechanism

Koretz & Handelman have provided some excellent electron micrographs of the mounting of the lens to the zonule. Theyalso provided excellent caricatures of the physical plant, in both perspective and cross section482.

Fisher has provided extensive measurements and analyses concerning the physical characteristics of the lens. However,the experimental techniques are now dated and he made several linearizing assumptions. His energy storage calculations also lead to a solution of the paradox developed in the above papers. His papers providea series of trend lines versus age. They also provide the characteristics of several materials found in the eyes. Glasserand Campbell have recently made a range of similar measurement, using current (1999) computer-augmented

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483Glasser, A. & Campbell, M. (1999) Biometric, optical and physical changes in the isolated human crystallinelens with age in relation to presbyopia. . vol. 39, pp 1991-2015484Adams, A. Wong, L. Wong, L.& Gould, B. (1988) Visual acuity changes with age: some new perspectives.Am. J. Optom. Physiol. Optics vol. 65, no 5, pp 403-406485Ciuffreda, K. & Kenyon, R. (1983) Accommodative vergence and accommodation in normals, amblyopes,and strabismics In Schor, C. & Ciuffreda, K. eds. Vergence Eye Movements: Basic and Clinical Aspects.Boston, Butterworhs, pp 101-173

equipment483. They included an extensive source list. Although their sample size was small (19 pairs of eyes) theymeasured many parameters as a function of age.

7.4.9.1.6 The neural circuitry of the lens servomechanism

The specific nature of the neural circuits supporting accommodation has not been reported in detail. It appears the signalis extracted from the data presented to the PGN/pulvinar couple by the foveola of the eyes. The operation of the systemclearly varies with the contrast in the fine detail of the image484. This would suggest the performance is controlled bythe sharpness of the edges in the scene presented to the retina, as converted into an electrical signal by the action oftremor. A key question is whether the derived signal is an average of the values for several points in the scene or not.If it is, this implies the signal is extracted by the two-dimensional correlator of the PGN. Simple experiments coulddetermine the relationship between quality of accommodation and the spatial extent of the fine detail within a scene.

Many suggestions appear in the literature that the lens control system involves a memory element in its computationalunit. As a result, measurements of the time delay associated with a change in distance to the scene are highly dependenton whether the subject anticipating the change to a previously fixated point or whether the change is completely random.This is consistent with the casual experiments of this author. The characteristics of this memory element will bediscussed further in the next section. It appears that the system can call on recent data in the short term saliency map(see Section 15.2.1). With this data, a volition command can be generated containing two, or three components. It canreturn the line of fixation to a given scene, and adjust both the required vergence and required accommodation stateduring the saccade.

The analog operation of the ciliary muscle is a strong indication that the neural signals controlling it consist of a quasi-continuous stream of action potentials. It can be expected that these signals will have a frequency that increases inproportion to how much accommodation is required. Whether this relationship is a simple linear one or whether it ismore complex is unknown. It may include nonlinear compensation to account for the geometry of the physical plant andpossibly the nonlinearity of the stress/strain relationships associated with the ciliary muscle and the lens. These signalsoriginate in a nucleus near those that prepare the drive signals for the oculomotor system. The signals pass through anucleus known as the ciliary ganglion near the eyeball before entering it.

It should be noted that the lens accommodation is not a symmetrical closed loop servomechanism. Instead, it operatesfrom a position of basal accommodation in the absence of a signal to the contrary. Such a system is sensitive to errorsin calibration. These errors can be compared to a windage error in pointing a rifle. Since the lens accommodationsystem involves analog signal computation and signal preparation, it is subject to offset errors similar to those found incolor blindness. There are clinical symptoms that suggest that such errors are encountered in practice. A numericallysmall group of subjects, primarily myopes, have consistently reported seeing scenes in better focus immediately afteropening their eyes than one half to one second later. These “flashes of clear vision” are repeatable. They say theyattempt to focus on infinity before opening their eyes. For a myope, this is equivalent to going to their basalaccommodation level. However, there is a problem. This experiment is suggestive of a significant computational ortransmission error involving a DC offset in the analog signal before it is converted to a stream of action potentials.Defining both the refractive and the neural components of the basal accommodation level is necessary. The basalrefractive accommodation level is that assumed by the physiological optics of the eye. It is the level reached with theeyes closed and relaxed. Upon opening the eyes, the neural system evaluates the distance to the scene and provides anincorrect signal that is the basal neurological accommodation error. The total basal accommodation level is now in errorby an amount that is time dependent. It remains at the basal refractive error level for approximately 200 ms and thentransitions to the total error level in another 100-200 ms depending on the light and contrast level of the stimulus.

7.4.9.1.7 Steady state operation of the lens servomechanism

Cieffreda & Kenyon have provided a graph of the accommodation response to the introduction of an artificialaccommodation error (their figure 5.1)485. The figure is similar at the detail level to the graph presented in the nextparagraph.

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486Blaker, J. (1980) Toward an adaptive model of the human eye J. Opt Soc Am vol. 70, no. 2, pp 220-223487Saladin, J. & Glasser, L. (1975) Presbyopia: New evidence from impedance cyclography supporting the Hess-Gullstrand Theory. Vision Res. vol. 15, pp 537-541

Figure 7.4.9-6 Accommodation efficiency based on data of Fincham in Blaker, 1980.

Blaker has provided data on the change in radius of the anterior surface of the lens of two 20-year-old males in responseto a forced accommodation plant486. However, he does not record the change in the radius of the posterior surface. Byassuming the posterior surface remains unchanged, the performance of these two eyes can be interpreted as shown inFigure 7.4.9-6. The figure shows the achieved accommodation level in response to a commanded accommodation. Thecurve tilts up at the left. That curvature is an indication of a residual accommodation level in the absence of anycommand. This is called the basal level of metropia in this work. Using Blaker’s data, this residual was about 1 D inthe two hypermetropic individuals. The one individual, #1, could achieve a linear change in response to a command outto about 10-10.5 D before his performance began to degrade. If this individual were typical based on Blaker’s model,this would occur at a near point of 11.76 cm (4.6 inches). The second individual, #2, did not perform as well. Hissystem exhibited a shoulder near 7 D. The break points in the maximum accommodation of individuals move to the lefton this graph with age. Jennings and Charman indicate one 32-year-old female, #3, had an accommodation range of 6.5D. No details were given as to the criterion for this measurement. This figure begins to show the progression inaccommodation performance with biological (not necessarily chronological) age. There is no way to calibrate theabsolute efficiency on this type of curve. Stark does observe that the firing rates among the ciliary neurons appear tocontinue to fire at a rate required to achieve a specific accommodation level even after the individual is no longer ableto achieve this level. This would suggest the signal extraction circuits are still working properly but the plant associatedwith the lens is unable to respond. This continual high signaling rate may account for some of the pain associated witheye strain.

Saladin & Glasser have provided a few more data points that can be plotted on the above figure487.

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488Glasser, A. (2001) Op. Cit.489Weale, R. (2000) why we need reading-glasses before a zimmer-frame. Vision Res. vol. 40, pp 2233-2240490Phillips, S. et. al. (1972) Analysis of accommodative response times using histogram information. Am. J.Optom. Arch. vol. 49, no. 5, pp 389-401491Smith, W. (2000) Modern Optical Engineering NY: McGraw-Hill, pg 137

Figure 7.4.9-7 Accommodation range of the human eyeversus age. Glasser used the term amplitude instead ofrange. From Glasser, 2001.

Glasser has recently provided more data that helps fill in the voids in the static database488. Figure 7.4.9-7 reproduceshis figure 2. The solid line and data points appear compatible with the above figure. However, they do no provide aclear way to establish a precise comparison based on the protocols used. A similar compilation of data has been providedby Weale489. The reduction in the accommodation range falling to about 1 D at 60 years is consistent with this authorsexperience.

7.4.9.1.8 Transient operation of the lensservomechanism

A variety of studies have been made of the transientoperation of the lens servomechanism at a gross level.The instrumentation is demanding. Phillips, et. al.provided considerable early data and compared it to manyother studies490. Unfortunately the data is reduced tohistograms rather than to the parameters of transientresponse curves. They appear to use the term latency todescribe the time to peak response following a change inthe required accommodation level. This approach lumpsmany discrete time intervals (including the true latency)before the physical plant begins to respond. Often, theyhave averaged the time to peak response for differentchanges in accommodation. It appears they have notexamined the variation in response time require torespond to a given size accommodation change as afunction of the position along the accommodationfunction. Care is suggested in analyzing the data provided and referenced.

Smith has provided a curve showing the time to accommodate to a 1.3 diopter change versus age491. The value variesfrom 0.6 seconds at 20 years linearly to 1.6 seconds at 60 years. A change of this nature would suggest, but not specifiy,a change in the time constant of the lens plant rather than a change in the strength of the ciliary muscle.

The discussion in the paper by Phillips, et. al. does not suggest a familiarity with the laws of optics. The shape of thecornea is certainly not spherical. It is most likely not parabolic. Achieving the desired wide field of view requires theoptics to be ellipsoidal. However, the geometrical differences between the above three shapes are measured in very smallfractions of a millimeter.

Phillips, et. al. do observe a significant difference in time to achieve a change in accommodation in response to a randomchange in required accommodation than in response to an expected change. This clearly suggests an ability of the subjectto call on information in his short term saliency map in order to perform on repetitive tasks. It is also likely thiscapability is widely used, especially in reading (See above and Chapter 18 on reading). The gross data in Table I ofPhillips, et. al. report times to peak response. The means are on the order of 370 ms for non-repetitive tasks and 200 msfor repetitive tasks (three or four subjects per test). Little difference is shown between tasks involving near-to-far andfar-to near accommodation. While this is quite possible with the physical plant shown above, it would be unexpected.His remarks may apply to small signal conditions (small changes in accommodation) where it would be expected.

It is clear from the simplest behavioral experiments that the performance of the accommodation mechanism is closelytied to the performance of the oculomotor system. For random tasks, accommodation cannot be performed with precisionuntil the line of fixation has settled on the object of interest. Beers & Van der Heijde found it took about 200 msecbefore the lens accommodation plant began to respond. It then took from 100 to 500 msec for the plant to respond(depending on the change required). This would suggest the total response consists of several time intervals. First, thesubject must perceive the need to reestablish the line of sight, the vergence and possibly the accommodation (or at leastsome of these depending on the test configuration). Fortunately, the computational engine required to make these

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492Ciuffreda, K. & Kruger, P. (1988) Dynamics of human voluntary accommodation. Am. J. Optom. Physiol.Optics. Vol. 65, no. 5, pp 365-370493Beers, A. & Van der Heijde, G. (1994) In vivo Determination of the Biomechanical Properties of theComponent elements of the Accommodation Mechanism Vision Res vol 34(21), pp 2897-2905

Figure 7.4.9-8 Dynamic biomechanical model of theaccommodation plant, with the angle, θ, added. It remainsnearly constant with accommodation. Original shows themodel superimposed on the anatomy of the outer eye. FromBeers & Heijde, 1994.

decisions is found in the POS of the midbrain. This allows this initial perception to be performed within a period ofabout 50-100 ms. This interval would be shared between the correlation time (correlator cycle time of 50 ms) and thetravel time for the signals from the retina to reach the PGN/pulvinar couple (transmission delay of 1.0 ms). The grosscommands must then be generated in the superior colliculus. These are then processed further in the various nuclei ofthe pointing and focus circuits. The commands leave the midbrain following an interval of about 350 ms. Thetransmission time between midbrain and muscle innervating neuron (omitting any delay at the ciliary ganglion nucleus),is only about 1.0 ms. The response of the muscles generally varies according to the size of the change required. Thisresponse is well documented regarding the saccades. However, it is not as well known with respect to the focusmechanism. Careful study of the raw data supporting figure 7 of Phillips, et. al. could give good data on this time as afunction of required accommodation change (from various starting accommodation levels). The longer latenciessuggested by Phillips, et. al. as a function of age are most likely associated with the response time of the physical plantand not a true temporal latency before the lens begins to deform. The data of Beers & Van der Heijde provide specificdelay times as a function of required change in accommodation.

A careful review of the records of Phillips, et. al. could provide more data concerning the type of transient responseexhibited by the accommodation system. Is it impulse driven as with the oculomotor system or is it continuously driven?Ciuffreda & Krueger have provided detailed data showing that the lens servosystem is essentially a first order system492.It exhibits a simple exponential transient characteristic regardless of amplitude.

Beers & Van der Heijde provided a better schematic of the accommodation plant and better data recently but theiranalysis was too brief493. Their interest was only in the change in shape of the lens under a set of linearized forces.Figure 7.4.9-8 reproduces their figure 2a.

To simplify their analysis, they ignored one of the twoorthogonal components of the forces applied at an angleto the lens perimeter. The angle associated with the forceis 25 degrees and varies less than +/– 2 degrees during

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494Wyatt, H. (1988) Some aspects of the mechanics of accommodation Vision Res vol. 28, pp 77-86

accommodation according to Wyatt494. These values suggest the sine and cosine of 25 degrees play significant roles inthe accommodation mechanism. Their radial force applied to the lens should be multiplied by the cosine of 25 degreeswhereas the axial force (with respect to the axis of the eye) applied to the lens perimeter should be given as the appliedforce times the sine of 25 degrees. Since the angle remains nearly constant, there is an axial motion associated with thelens that is equal to the radial motion at the perimeter of the lens times the tangent of 25 degrees. This axial motion isrequired to maintain the Petzval surface in congruence with the entrance aperture surface of the photoreceptors of theretina. Without this axial motion, the system will go out of focus with any change in the lens power.

While not generally recognized in the vision literature, the combination of the cornea and lens represents a“zoom” type optical system. It is designed, like any zoom system , to achieve optimum focus over a range ofoperating distances by performing two actions. It first changes the power of one of the elements. It thencompensates for the resultant change in focal position relative to the centroid of the optical assembly, by changingthe spacing between the optical elements. Both actions are necessary to maintain proper focus at the retina.

Figure 7.4.9-9 presents an expanded schematic of the arrangement in Section 7.4.9.1.2 using more convenientsymbology. The expansion in A only addresses the overall forces applied to the periphery of the lens. It incorporatesthe elements of both the Stark and the Beers & Van der Heijde models but provides a more appropriate model of themuscle. The springlike elements are shown as coils rather the zigzag symbols for continuity. The muscle is replacedby an active source in parallel with a mass and a dashpot. These elements are connected to the remainder of the networkby a spring, km. The muscle delivers a force to the system through this spring. With the symbols used, thisconfiguration can be considered an electrical analog of the actual physiological circuit. In that case, the force isrepresented by a voltage. If the muscle is held tonic, a constant voltage is applied to the network. As noted in both Starkand Beers & Van der Heijde, only one half the lens is represented here. The center of the lens is considered a virtualground for purposes of the analysis on the assumption it does not move radially. In B, the “axial zonular spring, kza,of Beers & Heidje is resolved into two components by the “resolver.” The resolver is merely the geometry associatedwith the axial zonular spring and the lens capsule. At a nearly constant angle of 25 degrees, the radial component ofthe force applied to the capsule via the axial zonular spring is given by the total spring force multiplied by the cosineof 25 degrees. The axial component of the force applied to the capsule via the axial zonular spring is given by the totalspring force multiplied by the sine of 25 degrees.

Look first at frame A. Without any force due to the ciliary muscle, the position of the edge of the lens is determined bythe tensions generated among the three tension elements, kc, kzp & kza, and the tension of the lens, kL. This positiondetermines the unaccommodated optical power of the lens (lacking pharmacological intervention).

The left portion of frame C shows the forces involved in both distorting and moving the lens. When a force is applied,the perimeter of the lens moves in response to the force applied through the tensile elements, km. The net force is dividedbetween overcoming the tensions associated with kzp & kc and the force available to move the lens perimeter. The morestructurally rigid km and kc are, the less force required to distort them. However, they are essential as a restoring forceand must exhibit a useful spring constant. On the other hand, if the element kza is not rigid, the muscle will be unableto apply significant force to the periphery of the lens. The distortion of the lens by a change in the radius of its perimeter(the radial position) does not result in a large change in the location of the center of mass. The term, mL, can generallybe ignored when computing accommodation.

The right portion of frame C shows the forces involved in moving the lens axially. The motion is small and slow. Asabove the mass of the lens plays a small role in this motion. The main point is that the axial motion is significant if theangle, θ, is to remain nearly fixed. The primary opposition to this motion is believed to be the resistance, bv, and thespringiness, kv, associated with the viscosity of the humors surrounding the lens.

Conformation of the axial motion of the lens in the process of accommodation has not been widely discussed inthe literature. However, the author recently underwent post-pupil lens replacement in his right eye. Post-pupillens replacement means the biological lens was removed from its capsule and replaced by an acrylic substitute.Thus, the precise geometrical configuration of the musculatura is maintained but the lens element has beenreplaced. This had an unanticipated result. On the second day after the replacement procedure, and using myglasses from before the surgery, I observed an unusual event. Immediately after removing my glasses with myleft eye closed, I observed a change in the quality of my distant vision over a period of a few seconds. It appearsthe fixed acrylic lens was being moved axially by the ciliary muscle in an attempt by the focus servomechanismto optimize my vision through the right eye. I discussed this with my ophthalmologist and he confirmed therewere reports in the literature of patients exhibiting accommodation of as much as two diopters following post-pupil lens replacement.

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Figure 7.4.9-9 Schematic of the plant of the lens servomechanism. A; full diagram that portrays both the actualphysiology using an electrical analog of that physiology. The “resolver” is undefined in this view. C; the electricalanalog resolved into its radial and axial components. The electrical analog uses the current = force & voltage = radialdisplacement relationships. See text for discussion. B; data in upper right frame from Beers & Van der Heijde, 1994.

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495Hung, G. (2001) Models of Oculomotor Control. London: World Scientific pg 35

Beers & Van der Heijde proposed that the response of the lens accommodation system followed an exponential function.However, frame B of the figure disputes this fact. Two pure exponentials have been overlaid on one of their frames ofdata. It can be seen that the initial rise is much too fast to be represented by an exponential. This is the situation in most,if not all, of their data frames. Some frames at only a one diopter change are difficult to analyze. In their data, therelaxation of the lens system was always faster than the change to a higher level of accommodation (except possibly forthe one diopter change).

The force applied by the muscle must be defined, as a function of the innervation, if this network is going to becompletely understood. Similarly, the characteristics of the tensile force kL need to be understood. Muscles do notnormally exhibit a constant tensile strength as a function of innervation (or extension). Similarly, the tensile strengthof a gel enclosed by a thin walled membrane does not conform to Young’s Law for solids, defining a linear tensile strainin response to a linear tensile stress. The relationship is more complicated. These two nonlinearities, the musclesforce/innervation relationship and the strain/stress relationship of the lens, account for the non-exponential relationshipsshown in the data of Beers & Van der Heijde. They also lead to an explanation of the awkward time constantrelationship shown in their paper. The time of response is not given by a single time constant as suggested by Beers &Van der Heijde. Their equations employ several simplifications that may obscure the actual values. Furthermore, theresponse of the network depends on the precise state of accommodation of the eye in each test run.

By introducing more realistic values in this analysis, more realistic time constants can be defined based on the lowerportion of the figure. This calls for a more realistic forcing function, a more reasonable tensile performance for the lens,and the recognition of other circuit elements related to the ciliary muscle.

Fisher has provided some early data on the stress/strain relationship for the human lens. However, he was well awareof the delicacy of the measurement and the difficulty of analyzing it precisely. His analyses did rely upon a piecewiselinear assumption. As a result, he has provided initial values for the energy stored in the lens as a function of distortionlevel.

A better understanding of the operation of the lens accommodation system could be obtained by measuring the timerequired to make a one diopter change (or smaller), in each direction, from positions differing by one diopter throughoutthe adaptation range. The resulting functions could be integrated to more clearly define the time required to makemultiple diopter changes. The resulting responses would be much closer to an exponential form. Assuming the noisecomponent in the recording is not excessive, more meaningful time constants could be read from this data.

7.4.9.2 Short term accommodation errors

Hung, crediting Ong & Ciuffreda, gives the nominal accommodation system error as 0.3 to 0.5 D495.

7.4.9.3 Presbyopia due to refraction errors is a normal consequence of aging

The analysis of this section has provided a clear graphical explanation of presbyopia and its impact on humans beyondthe age of 10. Before that age, the individual elements of the physiological optics are subject to such a variety of growthrates that little can be said about their ultimate visual performance. Figure 7.4.9-10 illustrates the situation. The grayband in the figure represents the range from zero to plus 4 diopters. This is the normal range required for focusing from25 cm (10 inches) to infinity and includes the range of most human activity. The properly functioning accommodationsystem has more than sufficient range to cover this zone. However, the accommodation system is not symmetrical. Thesystem goes from a fully relaxed condition to a condition of accommodation some 10 diopters more positive.

Two problems arise in the visual process. First, if the relaxed accommodation level (called the basal accommodationlevel here) of an individual is already positive, the eye cannot accommodate to zero diopters. This is the condition shownby the solid triangle. The bottom of the triangle intersects the basal accommodation scale on the right of the figure. Sucha person is considered near sighted, refractively myopic, and will normally require glasses of at least minus one dioptersto achieve proper distant vision. For a serious myope, a basal accommodation level of plus five is not unusual. Anyonewith a basal accommodation level exceeding plus four will require glasses at all ranges throughout his lifetime. Mostsubjects with a basal accommodation level that is negative do not have a need for glasses during their early years. Theaccommodation level of such individuals will almost always include the shaded zone as shown by the dashed triangle.However, if he should have a basal accommodation level more negative than minus five, he may require glasses forreading, and other close work, beginning at an early age.

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496Bremner, F. (1999) Disorders of pupillary function in Acheson, J. & Riordan-Eva, P. Fundamentals ofClinical Ophthalmology: Neuro-ophthalmology. pp 183-190497Phillips, et. al. (1972) Op. Cit.498Myers, G. & Stark, L. (1993) Level dependent signal flow in the light pupil reflex Biol Cybern vol. 68, pp229-246 (three papers)

Figure 7.4.9-10 Presbyopia as a normal process of aging.The gray band shows the normal range of accommodationneeded to properly image from 25 cm to infinity. This rangeincludes the zero line. See Text.

In this discussion, the basal accommodation level is anoperational level found when the eye is relaxed by thesubject. It is not the level of relaxation achievable bypharmacological means.

Most people exhibit an accommodation range of at leastten diopters at age ten. This range decreasesmonotonically with age as shown, for bothhypermetropes and hypometropes (myopes). The resultsare the same but occur at different times as shown. Forthe myopic subject, he will require glasses for far visionfrom an early age. He will begin to suffer a loss ofaccommodation and require glasses at short rangebeginning somewhere around 45 years of age. Thispoint will depend on both his basal accommodation leveland his initial accommodation range at age 10. Thehypermetrope cannot achieve as high a level of absolutepeak accommodation as the typical myope, because ofthe offset introduced by his basal accommodation level.Therefore, the hypermetrope will lose his ability to focusat short range earlier than the myope. This frequentlyhappens around 40 years of age. These people are theones that need “reading glasses,” particularly for menus in dark restaurants, etc. As his accommodation capabilitycontinues to decline, he will begin to have difficulty seeing at a distance. This occurs when his accommodation rangebecomes numerically less than his basal accommodation level. This latter phenomenon appears to equate to the “distancehyperopia” of Donders. At an age of 45-50, the typical hypermetrope will need positive lenses for seeing both near anddistant objects. Bifocals become the order of the day for hypermetropes more than 50 years of age.

7.4.9.4 The aperture control system

7.4.9.4.1 The iris control system

Bremner has described the detailed neural circuits controlling the iris and some examples of their operation, describingboth the parasympathetic and sympathetic pathways496.

Phillips, et. al. provide a brief discussion of the change in iris aperture during their accommodation experiments497.However, they did not provide sufficient detail about the light levels involved as a function of required accommodationto show that such a change is correlated with accommodation in the absence a change in light level. Myers & Stark haveprovided considerable recent material on the operation of the aperture control system498. Surprisingly, they did notinvestigate the asymmetrical operation of the iris, between increases in light levels versus reductions in light level, indetail. Their model in figure 2 appears to only apply to increases in light level. Their models related to increases in lightlevel “have been made parsimonious to simulate the main experimental findings reported here. . . .” They specificallysay their models are not meant to be homologous with the physiology of the visual system. They did, however, recognizethe logarithmic transformation occurring in the photoreceptor cells.

Careful analysis of their data reveals the operation of several distinct mechanisms. Their test protocol involved relativelylong pulses of illumination. The leading edge of the characteristic shows the variation in delay and in initial slopecharacteristic of the Photoexcitation/De-excitation process discussed in Section 7.2. The droop in the signal during theinterval following peak response appears characteristic of the adaptation process. The time constant appears very similarto that expected in that process, about six seconds, and reported in Section 2.4.3.1. Saturation in the adaptation process

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Dynamics of Vision 7- 265is quite evident in the response to a maximum stimulus of 10,000 foot-Lamberts. Following the end of the stimulus, thetrailing edge of the transient exhibits a combined time constant of about five seconds. This value appears to be acomposite of the time constants of the adaptation process and the plant associated with the iris. The decay time constantof the P/D process is too short to contribute. It is less than 12.5 msec.

Based on the above analyses, a model quite different from that suggested by Myers & Stark appears more appropriate.It separates the small signal mathematical model in the s-plane into three distinct portions. The first portion relates tothe P/D process, the second to the adaptation process and the third to the plant associated with the iris. To develop themodel further for the large signal case requires introduction of the logarithmic transform (also found in the Myers &Stark model) occurring at the pedicle of the photoreceptor cells. This model suggests the neurological portion of themechanism is the same as that associated with the photoreceptors of the eye and developed in Sections 7.2 & 12.5. Theremainder of the model is associated with the servomechanism plant associated with the iris. Note that in this model,the intrinsic delay is also divided into three portions. A portion is associated with the phototransduction process (stage1), a portion is associated with the servomechanism (stage 5), and a portion is associated with the transport delay withinthe signal projection process (stage 3). The minimum total delay encountered by Myers and Stark, about 180 ms, isprobably accounted for by the sum of the neural transport delay and the delay associated with the plant. The variabledelay of up to an additional 70 ms can be attributed to the P/D process.

Although Myers & Stark show inputs into their model from the vergence and accommodation subsystems in concept,they did not discuss these inputs in detail. References to earlier papers are provided. Based on this work, the influenceof these two subsystems (if substantive) is primarily through their earlier influence on the stored values within the lookuptables of the superior colliculus. The resting pupil area, and the related a priori command value to the iris plant are alsostored in the superior colliculus. These proposals are consistent with the position of Myers & Stark that the control ofthe iris rests within the midbrain. The control of the iris is “via the third nerve to the ciliary ganglion and then to the irismuscle.”

The model proposed here exhibits a variable term in the phototransduction process that provides a deterministic solutionto the overall response that does not require the conceptual “adaptive bucket brigade” mechanism introduced by Myers& Stark.

The comment of Myers & Stark concerning the operating range of the iris control system agrees with other sources(Section 2.4.3.1). They found that below one foot-lambert stimulation, the pupil was fully open (typically 6.4 mmdiameter in their case). One foot-lambert corresponds to the bottom of the photopic range of vison for most subjects(within a factor of two). At 10,000 foot-lamberts, the iris became fully open (typically 3 mm diameter) after less thantwo seconds. Their subject appears to have a narrower than normal range of iris operation.

The third paper of Myers & Stark both summarizes the work of others and explores oscillations related to the iris.

7.4.9.4.2 The shutter control system

The 1st and 2nd shutters are simple curtains operating primarily in a two-state mode, either opened or closed. Humanscan modulate this situation to a slight degree by transmitting a rapid sequence of open and close commands. However,this mode of operation is fatiguing. The process appears to be designed to be binary in character. What is describedhere as the 1st shutter is relatively, but far from completely, opaque. Its purpose is to block high frequency spatialinformation from reaching the retina. The information handling portion of the visual system is not sensitive to lowfrequency changes below about three hertz. Therefore, completely blocking illuminance changes occurring in thetemporal region from zero to three Hz is not necessary.

The 2nd shutter operates in the same manner as the 1st. However, it is normally not an opaque structure. It is usually anearly transparent structure used in two different modes. It is frequently used by terrestrial animals and birds as aprotective device against abrasion by the environment. In semi-aquatic animals, it is normally used as a compensatinglens. This compensating lens allows proper operation of the optical portion of the eye in media of significantly differentindexes of refraction. It is not used in humans.

The neurons controlling these shutters are not associated with the optical fiber bundle of the eye but travel along thetemples in humans.

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499Rashbass, C. & Westheimer, G. (1961) Disjunctive eye movements J Physiol vol. 159, pp 149-170 & 361-364500Brodkey, J. & Stark, L. (1967) Accommodative convergence: an adaptive nonlinear control system IEEETrans Systems, Sci Cybernet vol. SSC-3, pp 121-133501Zuber, B. & Stark, L. (1968) Dynamic characteristics of the fusional vergence eye-movement system IEEETrans Systems Sci Cybernet vol. SSC-4, pp 72-79502Myers & Stark, L. (1993) Op. Cit.503Westheimer, G.& Mitchell, D. (1956) Arch Ophthalmol vol. 55, pp848-856 504Jones, R. & Kerr, K. (1971) Motor responses to conflicting asymmetrical vergence stimulus information AmJ Optom vol. 48, no. 12, pg 993

7.4.10 Interplay of version, vergence and accommodation subsystems

Because of the relative simplicity of the experimental procedures, many investigators have documented the relationshipsbetween the various functional overlays on the pointing and accommodation subsystems499,500, 501,502.

The relationships most often reported include;

Function Independent of Dependent on

Vergence accommodation, accommodationVergence version versionDepth Perception accommodation, accommodationAccommodation vergence, vergenceAccommodation depth perception, depth perception

Clearly, these reported relationships or lack thereof are inconsistent. However, many of the test protocols used earlierwere limiting. This is illustrated by experiments associated with the “Independent” column of the table. Westheimer& Mitchell have documented this situation for the vergence response503. Noting that vergence data acquired with thehaploscope is under conditions of fixed accommodation is also important. While Rashbass & Westheimer point out thatdisparity vergence is continuously controlled, their model is inadequate. At a finer level of detail, the vergence systemstill relies upon stage 3 projection neurons. These circuits are pulse circuits with a minimum refractory interval (SeeChapter 14).

It is only through the participation of the memory elements of the superior colliculus that estimates of the most probablevalues of the individual functions are provided based on changes in the “Dependent” variable. These estimates areclearly based on experience.

7.4.10.1 Cross-coupling of functional overlays– servomechanisms EMPTY

7.4.10.2 Relationship between vergence and version

Jones & Kerr have made measurements related to the response of the visual system to an alarm mode signal as a functionof time in milliseconds504. They note that the version response is usually completed before the vergence response. Thiswould be expected based on the model. While the stimulus causes a rapid version response, and an initial vergenceresponse based on a priori value, the final vergence value requires a few additional tens of milliseconds to establish anoptimum value of vergence.

Jones & Kerr quote Rashbass & Westheimer as having “shown that conjugate and disjunctive eye movements are entirelyindependent; each can accept and respond to stimulation irrespective of whether the other is responding, is beingstimulated, is within a reaction time, or is fatigued.”

Rashbass & Westheimer have also shown that version responses are much faster than vergence responses. This wouldbe expected if the vergence subsystem was expected to optimize its performance following a version response wherethe vergence subsystem was provided an a priori value from memory. The vergence system must await completion ofat least the first saccade before going into optimization mode. They also showed that the vergence system suffers fromsignificant fatigue effects (pg 347), even at a forced frequency of only one Hertz.

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505Fry, G. (1983) in Schor, C. & Ciuffreda, K. Op. Cit. pg 407506Records, R. ed. (1979) Physiology of the Human Eye and Visual System NY: Harper & Row, pp 605-608507Stark, L. (1983) Normal and abnormal vergence, In Schor, C. & Ciuffreda, K. Op. Cit. pg 11508Scott, A. (1979) Ocular motility, Chapter 21 in Records, R. Physiology of the Human Eye and Visual System.NY: Harper & Row pp 605-607509Hung, G. (1998) Dynamic model of saccade-vergence interactions Med Sci Res vol 26, pp 9-14

7.4.10.3 Change in accommodation with vergence

Fry has studied the change in accommodation in the presence of only changes in vergence. His results illustrate the smallchanges in accommodation encountered for changes of vergence of up to +/– 2.5 degrees around the nominal vergencevalue for a scene505.

7.4.10.4 The ratio of accommodative convergence to accommodation

One of the simplest laboratory experiments related to the functional overlays to the pointing system is the introductionof a change in accommodation. Records details the procedures involved in detail506.

Stark has noted a failure in accommodation to respond to vergence changes is due to a deficit in controller signalgeneration in the central nervous system507. It is proposed that the deficit is most likely in the operation of the lookuptable in the superior colliculus.

7.4.10.5 The ratio AC/A

The ratio of accommodative convergence to \accommodation is frequently used diagnostically in the clinical setting.Scott has provided a good exposition on this subject including the relevant dimensions (with standard deviations)508.He notes that the ratio is calculated using “prism diopters” in the numerator and regular diopters in the denominator.Hence, the ratio is not truly dimension-less as usually assumed. Unfortunately, he does not differentiate between thesetwo terms in his discussion. It is left to the reader to understand the difference. The reader is also cautioned that hisstatement that the difference between distance between the nodal points and the distance between the centers of rotationis negligible only applies in the clinical situation. The difference becomes significant in research. He does refer to theimportance of this factor on page 607.

7.4.10.6 Recent research in virtual and augmented reality

With the rise in interest and the resultant increase in laboratory investigations related to virtual and augmented realityfor both games and industrial processing, the subject of mental fatigue has arisen and traced to the conflicts in the visualmodality between the natural (learned) relationship between accommodation and vergence. In the process of optimallyfocusing on a scene, a two step process is employed. Initially the signals from the two eyes are compared in time todetermine an initial estimate of the vergence angle required to optimize stereo vision (Section xxx). This first ordervergence estimate is used to extract an accommodation signal. The accommodation signal is used to focus the two eyesat the approximate distance to the target of interest. With the quality of the images projected onto each retina, a secondcorrected estimate of the vergence angle is made and implemented via the oculomotor system. At the same time, asecond accommodation estimate is made and implemented. In virtual and in some cases augmented vision, the imagepresented to the visual modality involves a virtual image. This virtual image does not necessarily present the sameconditions for both the vergence and accommodation parameters simultaneously. As a result, the previously learnedvalues in the lookup table may not be optimal. This creates a “version-accommodation conflict” within the visualmodality. The visual modality will then attempt a third round (or more) of optimization. This causes a degree of fatigueand/or vertigo within the subject being evaluated.

7.4.11 Other models of version, vergence and accommodation in the literature

A wide range of independent models and schematics of the version, vergence, and accommodation subsystems haveappeared in the literature. Even a putative fusion subsystem has appeared in the literature. These have generally beenfloating models that did not relate to, and interconnect with, other major elements of the visual system. Based on thiswork, these models have suffered from three primary problems. First, they have not addressed how the spatialinformation presented to the retina is converted into a temporal signal. This failing leaves most of these models asinteresting but largely irrelevant models. Second, they have generally not recognized the temporal frequency aspectsof the photoexcitation/de-excitation mechanism Figure 35 in Hung (2001) and attributed to Hung (1998) is a goodexample of this situation509. The model assumes a perfect square pulse is applied to the neurological sections of both

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510Hung, G. (2001) Models of Oculomotor Control. London: World Scientific511Semmlow, J. & Hung, G. (1983) The near response: theories of control Chapter 6 in Schor, C. & Ciuffreda,K. Op. Cit.512Zuber, B. & Stark, L. (1968) Dynamic characteristics of the fusional vergence eye-movement system IEEETrans Syst Sci Cyber vol SSC-4, no. 1, pp 72-79513Krishnan, V. & Stark, L. (1977) A heuristic model for the human vergence eye movement system IEEE TransBiomed Eng Vol. BME-24, no. 1, pp 44-48514Schor, C. (1979) The relationship between fusional vergence eye movements and fixation disparity VisionRes vol. 19, pp 1359-1367515Patel, S. Ogmen, H. White, J. & Jiang, B. (1997) Neural network model of short-term horizontal disparityvergence dynamics Vision Res vol. 37, no. 10, pp 1383-1399516Hung, G. & Ciuffreda, K. (1999) Adaptation model of nearwork-induced transient myopia Ophthal Physiol.Opt vol. 19,pp 151-158517Hung, G. Ciuffreda, K. & Rosenfield, M. Proximal contribution to a linear static model of accommodationand vergence Ophthal Physiol Opt vol. 16, pp 34-41

the disjunctive and conjunctive servomechanisms. These models have then tried to account for these aspects in a morecomplicated model associated with the neurological circuits and physical plant associated with these subsystems. Manyof these models include adaptive switching of discrete filter elements in an attempt to account for the inherently adaptive,but continuous, nature of the P/D process. Third, they have attempted to provide a hard-wired representation of theinterplay between the version, vergence and accommodation subsystems and their excitation by the alarm and volitionmodes of operation. Often, the models have attempted to define and describe discrete disparity detector circuits (insteadof the actual correlation device suggested by and definable at the detailed level by physiology). They have also failedto include a priori inputs from memory in their overall operation. These attempts, which have been primarily at theconceptual level, lead future investigators along a deviant path.

Hung has provided a recent introductory text that includes a variety of floating models of the type described above510. Earlier, Semmlow & Hung summarized a variety of models in Schor & Ciuffreda511. Their discussion centered on thetriad of version, vergence and accommodation. Others in historical order include a paper by Zuber & Stark focused onfusional vergence512, a subsequent heuristic model by Krishna & Stark focused on vergence513, Schor514 and a largelyconceptual paper by Patel, et. al. focused on potential neural networks and subdivided into seven discrete stages(including discrete disparity detector circuits)515.

The basic model developed in Section 7.3 and the overlays developed in Section 7.4 provide a more realistic descriptionof the overall models appropriate to version, vergence, accommodation and amplitude control of the light stimulus. Akey element of the model is the presence of the superior colliculus (and cerebellum when required) inside theservomechanism loops. The colliculus provides a complete set of a priori or “most likely” values for the version,vergence, accommodation and amplitude control subsystems. These are used in the absence of more explicit values fromthe alarm and volition modes of vision. Of similar importance is the general computational capability of the pulvinar,probably shared with the superior colliculus. This capability can provide a wide range of output signals. These completesets of output signals may be provided in the presence of incomplete sets of input signals. To do this, the system reliesupon previous training and the values and the instruction-to-command transforms stored in the superior colliculus.

The general computational capabilities provided by the pulvinar and superior colliculus (computation plus memory)essentially replace the discrete cross-strapping circuits proposed in Hung & Ciuffreda516, Hung, Ciuffreda &Rosenfield517, and Krishnan & Stark (figure 3) and others.

7.5 Higher level functional aspects of the dynamics of the eyes

As noted in the introduction to section 7.3, significant differences exist in the performance of thevisual systems of each species within the higher primates and the monkeys. These differences makethe use of surrogates in the exploratory and precision performance laboratories less than ideal. Often,and particularly regarding the higher level functions of vision discussed in this section, the use ofsurrogates is completely inappropriate. No known animal can approach the performance of the humanin the areas to be discussed in this section 7.5.

A large empirical literature exists on the operation of the human visual system in perusing a scene and in reading text.However, it invariably ends with the supposition that the eyes remain stationary in a gaze between saccades exploringthe scene presented to them. This is a major fallacy in the science of vision. The eye is highly active during the gazeat a scale that cannot be observed without special instrumentation. During each gaze, the eye makes a series (up to aseveral hundred) of individual small motions (microsaccades and flicks) that support the processing of large amounts

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518Findlay, J. (1980) The visual stimulus for saccadic eye movements in human observers. Perception, vol. 9,pp 7-21519Underwood, G. (1998) Eye Guidance in Reading and Scene Perception. NY: Elsevier. pp 286-291

of information within the retina. The information is then transmitted along the individual nerve fibers connecting the23,000 photoreceptors of the foveola of the retina to the brain. While the rest of the retina is operating in the Awarenessmode, the portion of the visual system associated with the foveola is operating in the analytical mode. This section willdiscuss the operation of the visual system from this perspective.

There are two easily differentiated areas of visual system operation. That associated with the viewing of objects in theirrelationship to a scene is one. That associated with the viewing of semantic symbols in reading (where the symbols carryno relationship to the surrounding scene) is another. This differentiation is so important, it divides the field of perceptionstudies into two distinct classes. Findlay observed this considerable gap between the two types of study in 1980 and saidfew attempts had been made to bridge it518. This differentiation is still important. The two sides of it will be addressedbelow in separate sections. Henderson & Hollingworth noted a hiatus in the study of eye-movements during the 1980-90's. The renewal of interest is almost certainly associated with the advances in technology related to accuratelyrecording eye movement. They also report some of the first experiments designed to bridge the gap between theperception of scenes and text and discuss the relationship between the saliency maps of object space and cortical space519.

The major role played by memory in the perception and interpretation of ones environment has not been adequatelyaddressed when studying the functional aspects of vision. It appears that the visual system avoids analyzing most of theelements of every scene presented to it by bringing forth the previously memorized information about that scene. Thisis illustrated by the ability of a person to walk into a room and almost instantly notice that one small change has occurred.The ability to walk into a room through different doors with the same result supports the importance of memory. Itstrongly suggests that a vectorized saliency map of the room is stored in long term memory. Such a vectorized mapwould be independent of orientation and, to a large extent, scale. It is automatically independent of light level becausethe visual system normalizes light level prior to the analysis function.

Similarly, the major role of training in the function of perception has not been quantified. There appear to be a seriesof default routines used in the visual process based primarily on training (in conjunction with memory). This seems truein both reading, where one routine has been traditionally described as a “dumb default,” and the perception of scenes.

7.5.1 Background

In the following material, it is crucial that a consistent set of definitions for different size saccades is relied upon. Figure7.5.1-1 reviews the terminology to be used here. All references cited in the literature will be converted to thisnomenclature. Most of the literature related to the fundamental dynamics of the eyes has concentrated on the large andsmall saccades. Investigations related to reading and scene analysis have generally concentrated on the realm of theMinisaccades. The area of the flicks and microsaccades have only been explored by a few investigators, primarily inRussia (Yarbus and Shakhnovich), and England (Ditchburn), although Riggs in the USA should not be excluded frommention.

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Figure 7.5.1-1 Definition of saccades by size. Although shown in polar coordinates ( and on a logarithmic scale forconvenience), all indications point toward their description in terms of rectilinear components relative to the surface ofthe spherical retina. The circles are at 2 minutes of arc, 1.2° and 6°. The term tremor is used synonymously with theterm microscaddes and occupies the area of the inner circle. Not shown is tremor with a nominal excursion less than30 arc seconds peak-to-peak.

7.5.1.1 The continuing philosophical debate

The role of microsaccades (and tremor) in vision has been debated for a very long time, with the detractors (and somesupporters) generally assuming the eye operates as an imager as opposed to its fundamental character as a scanner. The

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520Ditchburn, R. (1980) The function of small saccades. Vision Res. vol. 20, pp 271-272521Kowler, E. & Steinman, R. (1980) Small saccades serve no useful purpose. Vision Res. vol. 20, pp 273-276522Fisher, D. Monty, R. & Senders, J. (1981) Op. Cit. pg 229523Fisher, D. Monty, R. & Senders, J. (1981) Op. Cit. pg 202

most recent published colloquy on the subject was between Ditchburn520 and Kowler & Steinman521. In this colloquy,both sides discuss small saccades in terms of their possible role in stabilizing the image on the retina. Both papers arestrong on philosophical arguments and empirical observations but very short on theory and numbers. Ditchburn carefullysubdivides and defines the saccadic movements of less than six minutes of arc to frame his arguments. He defines tremoras involving movements of less than one minute of arc. He also says: “The primary visual signal is probably proportionalto dL/dt where L is the retinal illuminance.” He also notes that “Very precise fixation would produce the loss of visionthat occurs when the retinal image is stabilized.”

The opposition offered by Kowler & Steinman obviously involves trying to prove a negative. They recognize thephenomenon exists and they close with the statement: “We believe that this (existence) creates an evolutionary puzzle.Why should human beings, and only human beings, exhibit a penchant for making such small high velocity eyemovements if they serve no useful purpose? We do not know.” [emphasis added] They argue that:

+ Microsaccades can be suppressed without training.

+ Smooth eye movements, not microsaccades are optimal for maintaining clear vision.

+ Microsaccades are not needed for visual information processing.

+ The functional significance of microsaccades remains a mystery.

As both sides stipulated, the visual system is blind in the absence of motion.

Unfortunately, Kowler & Steinman did not define their term microsaccades. Their discussion is in terms of informationprocessing. It refers to counting groups of objects that are individually larger than the resolution threshold of the eyeand confined to a circle of 30 arc minutes. They speak of minisaccades, and natural body movement, as providing allof the motion required to overcome any latent blindness of the eye caused by a stabilized image. However, they did notaddress the staring mode of vision where presumably little normal eye motion exists. What they do not address at allis the subject of reading, the one capability that is not shared with other chordates and that requires the analysis offeatures much smaller than the objects they were counting. It is the capability of the human to perceive and interpretminute differences in symbols imaged near his/her threshold of resolution that differentiates the human from all otheranimals. It is this capability that allows us to communicate on paper without carrying around large tablets of charactersin 72 point type.

Kowler & Steinman did not address or demonstrate that the visual system is capable of reading in the absence of tremoror that reading was possible during a continuous saccade.

7.5.1.1.1 An alternate view adopted in this work

Ditchburn couches his argument for tremor, as recognized by Kowler & Steinman, as introducing a fine motion thatcontributes to the change in illumination required by the eye. Kowler & Steinman rebut, in the context of tremor as amechanism required for image stabilization, the proposition that tremor is not needed for this function and would actuallydegrade the performance of the imaging capability of the visual system. They argue that such tremor would actuallydegrade the excellent performance of what they describe as the slow eye movement performance of the system. Theyare clearly arguing apples and oranges here. It must be said that Ditchburn still did not appreciate the functional roleof tremor in 1981. Then, he added a paragraph to a discussion that began: “In passing, we may note that frequencycomponents of eye movement below about 10 Hz operate to maintain vision while the higher frequency components(particularly above the critical flicker frequency) effectively blurs the retinal image and impairs vision522.” He continues:“Thus a damping system that nearly eliminates the high frequency components . . . is advantageous to the visual system.. . .” This passing remark may have been introduced to avoid conflict with Stark & Ellis writing in the same text. Theysaid, “In any case, their amplitude makes them an unsatisfactory candidate for any visual function523.” These are thetypes of statements that have significantly impeded our understanding of the reading process. The list of unresolvedproblems on page 235 of that text is instructive.

This work views the subject of saccades in a specific context. The photoreceptors act as change detectors andlimitations are placed on the signaling channels by the performance characteristics of the adaptation amplifiers associated

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524Engbert, R. & Mergenthaler, K. (2006) Microsaccades are triggered by low retinal image slip PNAS vol 103,pp 7192-7197525Fisher, D. Monty, R. & Senders, J. (1981) Op. Cit. pg 257-268

with each individual photoreceptor. Within this context, the servomechanisms controlling the movement of the eyes canbe interpreted from an entirely different perspective. The presence of a foveola in many advanced chordates alsointroduces a critical feature. The result is recognition that the performance of the servomechanisms can be divided intotwo distinct categories responsible for two major functions. The first is to provide an effective alarm function, inassociation with providing a general situational awareness, to protect the animal. The second is to provide the analyticalcapability associated with the foveola that supports the needs of the great hunters for precision vision and the needs ofhumans to communicate through reading and writing.

7.5.1.1.2 Dispersion in the empirical literature

By vectorizing the information involved in the visual process, the system can avoid any reliance on the scale of theimagery presented to it. However, this flexibility has made it difficult to interpret the perceptual performance of thevisual system in the laboratory. Because of the flexibility in scale allowed by the system, investigators have employeda large variety of test configurations and image samples. This has inhibited development of a clear model of theperceptual process. It would be very useful if the community could settle on a set of standard test samples or test samplestyles for further exploration. It is extremely important that investigators quantify precisely the scale at which materialis presented to a subject for interpretation. A reading test using 18 point type may involve distinctly different internalparameters than a similar test using eight point type at the same distance.

The development of stylistic rules in writing, and more specifically printing, has highlighted the importance of the spacebetween words, the length of words and similar features in our perception of textual material. Unless required by thenature of the experiment, standardizing the spacing and length of word groups when performing experiments to discoverhow visual perception is achieved would be useful. Using words of variable length introduces additional statisticalvariables that are poorly documented into eye movement experiments.

Englebert & Mergenthaler have recently provided a discussion of fine retinal motions524. Their definition ofmicrosaccades corresponds to the minisaccades defined in the above figure.

7.5.1.2 The available laboratory equipment

Leigh & Zee have provided a list of the methods available for tracking eye movements in their Appendix B. Theequipment available has always been complicated and of limited precision. Sheena & Borah have provided a discussionof the merits of the different available equipments525. At the current time, one of the most widely used is an infraredpupil tracker. The AmTech ET3/4 provides a precision of 0.1 degrees or six minutes of arc at a sample rate of 400/500Hz. This sensitivity is not adequate for recording microsaccades at the few seconds of arc level required to analyze themost sophisticated motions of visual interpretation such as reading.

7.5.2 Aspects of examining a scene

Two major modes of examination are employed in viewing a bucolic scene, the awareness mode and the analytical mode.If the scene contains elements that might create a threat to the subject, the alarm mode becomes critical to the subject’sinterpretation of the scene. For the bucolic scene, the subject initially creates an awareness of the entire scene and a(probably) prioritized list of high information content regions of the scene. In the scene perception community, a termfor the non-quantized level of information content has been labeled “informativeness.” The eye(s) then proceeds to scanthe scene in a series of generally small saccades, pausing to gaze at each area of high interest according to itsinformativeness. These pauses are quite long compared with the time spent performing saccades. What functions thevisual system is performing during this interval is not well understood. If the bucolic scene is interrupted by a sudden change in the scene, characterized by a local change in illumination (thatcan be and frequently is due to motion in the scene),The above saccade-examination scenario, associated with a bucolic scene, can be abruptly interrupted by an alarm signalgenerated in the LGN. The alarm signal can be generated by any sudden change in the scene characterized by a localchange in illumination (that can be and frequently is due to motion in the scene). This signal causes two probablysimultaneous actions, an immediate saccade to bring the line of fixation of the eyes to the point of the dynamic elementof the scene, and a reorganization and re-prioritization of the saccade-examination sequence. Such a change in a localelement of the scene is frequently labeled a “wiggle” in the scene perception community.

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526Underwood, G. (1998) Eye Guidance in Reading and Scene Perception. NY: Elsevier.527Kowler, E. & Steinman, R. (1980) Small saccades serve no useful purpose. Vision Res. vol. 20, pp 273-276528Henderson, J.& Hollingworth, A. (1998) Does consistent scene context faciitate object perception? J. Exp.Psychology: General, vol. 127, pp 398-415529Henderson, J. Weeks, P. & Hollingworth, A. (1999) The effects of semantic consistency on eye movementsduring complex scene viewing. J. Exp. Psych. vol 25, pp 210-228

A variant on the bucolic scene involves a uniform degree of motion for the entire imaged scene. Such motion causesthe visual system to attempt to remove the apparent motion of the image on the retinas by introducing a pursuit signalinto the oculomotor commands generated by the POS. As indicated above, this action involves a Type 0servomechanism tracking a moving object. In the absence of any cognitive input, such a system could track a movingimage with a fixed displacement error. It is well within the cognitive powers of the brain to introduce a bias into the POSto compensate for this error (commonly called Kentucky windage in hunting and the military). Although this action hasmany interesting parameters and its effect can blossom into a variety of ancillary phenomena such as vertigo, it will notbe discussed here.

7.5.2.1 Aspects of examining a bucolic scene

The recent text edited by Underwood provides a good jumping off point for the following discussion of the perceptionof a scene526. However, it can only be considered an introduction. The index to this text does not include the wordtremor and the word microsaccades appears on only one page. On page 34, microsaccades are discussed briefly withonly a hint of their possible importance. Inhoff & Radach (citing Kowler & Steinman527) say: “they could indicate fineattentional adjustments or reflect an intrinsic tendency to move the eyes after some delay has passed. So far, noconsistent functional explanation has emerged . . . to relate them to perceptual or cognitive processes.” The conclusionis drawn that limit criteria can be used to eliminate microsaccades from further experimentation, analysis and discussion.This position has unfortunately been perpetuated in the perceptual portion of the vision community for more than 20years.

Henderson & Hollingworth have provided a good overview of eye movements during scene viewing in Chapter 12 ofUnderwood. However it should be noted that their color plates 1a & 1b and 2a & 2b are not of the same scene (note thechanged positions of the stoves). For convenience, most laboratory investigations have employed artificial scenes,frequently presented by a television monitor. See Table I of Henderson & Hollingworth for a summary of theseinvestigations. This technique usually excludes a large saccade from the investigation except possibly during the setupinterval. It also limits both the vertical and horizontal resolution of the image to a value far above the tremor level ofthe visual system. Because of this last limitation, the use of a cathode ray tube or LCD monitor cannot be used inexploring the limits of the visual system related to fine detail (whether it involves images or text).

Figure 7.5.2-1 shows a typical presentation and the resultant saccades from Henderson, et. al528. The length of eachsaccade was typically less than 6° and the average was given as 2.4°. These saccades will be defined as small accordingto the nomenclature of this work. The subject was given 15 seconds to view this figure. The duration of each saccadewas not presented in Henderson, et. al. although the average fixation (gaze?) was given as 327 ms. Their figure 2presents the proportion as a function of latency for gazes, and for a variety of test materials. No information wasprovided concerning the microsaccades and flicks occurring within these gazes. As a result, a time line for the activitiesof the eye during the allotted 15 second time interval contains large voids as noted in the auxiliary figure provided belowthe original figure. The solid bars show the height and duration of a typical small saccade. Between these bars, noactivity is recorded for the eye(s), yet each interval represents sufficient time for more than one hundred flicks andmicrosaccades. The question is, what is the visual system doing this 96% of its operating cycle?

It is a major premise of this work that the system is performing a detailed analysis of the portion of the image fallingwithin its foveola during this interval. The analysis employs both microsaccades and flicks. These activities cannot beobserved with the conventional eye trackers optimized for observing wide angle saccades because of their noise thresholdand frequently their quantization levels.

In their color plate 2 and 2B, Henderson, et. al. provide an estimate of the time the gaze remains on a given element ofthe scene. This time appears to correlate to local scene complexity except for something in the original drawing thatcannot be defined from the figure. Henderson introduced the concept of a saliency map (in object space) in 1992 toaccount for these areas of increased attentiveness. It assigns a weighting to the coordinates of each point of potential(or observed) interest.

Henderson, Weeks & Hollingworth defined a set of experiments that appear to surface an additional alarm condition ata very high level of cortical performance529. These experiments focus on uncovering semantically illogical elements

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530Brewer, A. Press, W. Logothetis, N. & Wandell, B. (2002) Visual areas in macaque cortex measured usingfunctional magnetic resonance imaging J Neurosci vol 22(23), pp 10416–10426

within an otherwise bucolic scene. The visual system appears to focus attention on these objects to a greater degree thanmight be expected.

Recently Brewer et al. have provided material similar to that of Hendersen and associates with more emphasis onintegration with object recognition530. The work is discussed in more detail in Section19.10.4.1.4.

7.5.2.1.1 The familiarity default procedure in examining a scene

A cursory reading of the chapters in Underwood related to the perception of a scene leads to the conclusion that thereis a familiarity based dumb default processing routine similar to that found in reading. The length of time spentanalyzing a familiar scene is significantly shorter than that for a new scene of similar complexity. Also, the subjectfocuses on changed elements of a familiar scene more rapidly than expected by chance. These observations suggest atwo step process. First, following the initial review of a new scene by the visual system, it prepares a vectorized saliencyspreadsheet (map) of the scene based on areas of high information content. Second, it prepares an initial schedule ofsaccades with which to analyze the scene. They also suggest that the saliency map is stored as a permanent vector recordof that scene. When the same scene is reviewed again, it appears that the system again computes a vectorized saliencymap that can be compared with the copy stored in memory. The system rapidly determines the difference between thetwo maps and arranges the second schedule of saccades to focus on the areas of change before performing a completescene analysis.

The vectorization of the saliency spreadsheet is important. Besides reducing the storage capacityrequirement, it makes the stored memory independent of scale and orientation. The subject can beshown the same scene photographed from a significantly different angle and it will still be recognizedas familiar.

In the above scenario, the visual system interprets a scene in two steps. It initially prepares a vectorized saliency mapthat can be compared with those stored in long term memory. If an appropriate match is obtained, the difference betweenthe new and old maps is prepared and the schedule of saccades is prepared that places a priority on the difference. Thisroutine shortens the overall analyses considerably and can be likened to the “dumb default” of reading. In the absenceof a match, the system prepares a saliency map and a more extended schedule of saccades designed to analyze the entirescene at an appropriate level of detail. The saliency map is stored and the schedule is started in due course. This canbe considered the normal analytical procedure.

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Figure 7.5.2-1 Viewing pattern for a complex line drawing. Green dots represent discrete fixations within a 10° x 14.5°field of view in ordinal order beginning at the center of the field. Green lines represent individual saccades. The verticalresolution of the image was quantized to one minute of arc by the monitor. Top frame from Henderson, et. al. 1999.

7.5.2.2 Aspects of examining scenes of finer structure Empty

[xxx this area should include the classic faces of Yarbus and include the limitations of the foveola & PGN/pulvinar when

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531Underwood, G. (1998) Op. Cit. pp 313-336532Findlay, J. (1980) The visual stimulus for saccadic eye movements in human observers. Perception, vol. 9,pp 7-21

Figure 7.5.2-2 A time sequence for viewing a scene on amonitor. See text. From De Graf, 1998.

examining specific scenes. ]

7.5.2.3 Aspects of examining a scene containing a local transient event

If an element of a scene should change rapidly and substantially in illumination, the visual system will be alerted to sucha change by the LGN. This will cause a major re-prioritizing of the operations of the eyes. A new saccade will beintroduced into the operating schedule to examine the appropriate area of the image immediately. This phenomenon hasbeen studied in some detail without an underlying explanation for its occurrence. Figure 7.5.2-2 is the typical result ofone of these investigations reproduced from De Graef writing in Underwood531. The initial experimental sequence wassimilar to the previous protocol involving a bucolic scene. However, after a given interval, an element or elements ofthe scene are caused to vary in intensity.

The protocol used for this scene is described as:

+ The subject fixates on a cross on a blank monitorscreen for at least 200 ms.

+ The image is changed to a scene presented for eightseconds that always contained an object in place of thecross.

+ After 160 ms, an object in the scene began moving upand down through four minutes of arc, performing twocycles within 120 ms. Four minutes of arc is near thecommonly accepted resolution limit of five minutes ofarc corresponding to the height of the E on a StellenChart at 20/20.

The wiggle is intended to elicit a saccade from the primeobject to the wiggled object.

De Graef provided an additional degree of complexity tothe experiments to analyze the results more effectively.He provided prime objects of two distinct types, thosethat fit semantically within the context of the larger sceneand those that were obviously out of contextual place.

The statistical results of De Graef are not of interest here.Describing the above sequence of events, in terms of theawareness, analysis and alarm modes of visual operationis useful. While this description does not affect theempirical results obtained by De Greaf, it does provide afoundation for the discussion of the results and possiblysuggest alternate follow-on experiments.

7.5.2.3.1 The simultaneous dual alarmscenario

Findlay has examined the introduction of two signals into the visual scene simultaneously and studied the resultantpropensity of the system to align the line of fixation to one or the other of the two events532. Considering the time lineof such activity to determine if it suggests the course of the signals moving through the visual system is instructive.Certain time lines may suggest activity limited to the POS, to the POS in conjunction with the cerebellum or to the POSin conjunction with either area 7 or the posterior areas of the cerebrum.

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533Koch, C. & Ullman, S. (1985) Shifts in selective visual attention: toward the underlying circuitry HumanNeurobiol. vol. 4, pp 219-227

7.5.2.4 Strategies Employed in Scene Perception and Interpretation

Koch & Ullman have explored the options used by the visual system to explore a scene533. They introduce severalconcepts regarding visual attention and build on the earlier work of Treisman relative to the saliency map. Theyexamine the potentials of both a serial and a parallel computing machine at the heart of the visual process. They discussselective visual attention and the conspicuity of a scene element. Two rules are presented based on the assumption ofa three-stage mechanism.

When viewing a natural scene, the awareness channel employs a primitive set of learned rules that relate to the totalscene. These rules are largely independent of the size and orientation of the scene relative to the observer. The rules aidin the determination of the major objects within the scene and the instruction of the analytical channel to image, perceiveand interpret each of these objects in turn. The strategy is roughly as follows.

1. The awareness channel decomposes the scene into a list of probable objects with their associated coordinateswithin the scene. 2. It prepares an initial sequence of saccades required to perceive the details related to each of these objects.This sequence is used by the analytical channel of vision. 3. It performs each saccade in the above list in turn to present the image of each object to the foveola. 4. The image of the object is held on the foveola for a finite interval during which it appears the eye is fixated.

• The eye is not actually fixated, it would be better to say the eye gazes at the object. 5. The Precision Optical System causes the image to be scanned rapidly through a series of microsaccades(tremor) that generates a signal within the analysis channel associated with the foveola.

• These microsaccades are not visible to the typical clinician or researcher. 6. The PGN/pulvinar pair of the midbrain extracts the perceivable features of the signal and projects theresulting vectorized signal to area 7 of the cortex. 7. The vectorized analytical signals received at area 7 are interpreted and an initial file is created relating thatobject to the overall scene. This interpretation is a reiterative two-step process.

• The tentative outside contour of each object is determined. • The texture of the object inside the tentative contour is determined. • IF the texture is not uniform, or of a recognizable pattern, the object is determined to contain

additional internal objects and the above process is repeated at a finer level of detail. • The initial file for that object defined above is expanded to include the details derived by the scanning,

perception and interpretation steps. • The initial file is integrated with the saliency map within the cortex of the individual.

• It is at this point that the cortex examines the file for any conflicts with the expected context of the overall scene.

Steps 3 through 7 are repeated until all of the objects on the original saccades sequence list have been perceived andinterpreted. Following the above series of steps, the mind of the subject has a fully interpreted understanding of the scene presented.It can then take any cognitive actions it desires.

7.5.3 Oculomotor aspects of reading

Because of the global involvement of the visual system in reading, the overall process will be described at the detail levelin Section 17.8 and at a more functional level in Chapter 19. Only the dynamic mechanical aspects associated withreading will be discussed here.

It is a premise of this work that reading specifically involves the phenomenon of tremor and its resolution into horizontaland vertical microsaccades and flicks. It will be shown in the following section that most research on reading has notprogressed beyond the stage of measuring the duration of the “fixation intervals” composing the gaze interval allotted

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Figure 7.5.3-1 The characters of text imaged on the foveola (black bar) and the fovea (Gray) as a function of scale. Theblack area actually consists of individual dots representing the individual photoreceptors of the retina as will be shownin a later figure.

to each significant word of text. A great deal of literature exists at this level. However, very little, if any, literature existsat the level describing the motions of the eyes within these periods of nominal fixation. Following the backgrounddiscussion, the thesis of this work regarding the phenomenon and mechanism of reading will be presented.

It is obvious that the human is adept at reading almost regardless of the scale of the symbolic characters relative to theresolution limit of the eyes. However, an argument can be made that above a certain scale, the characters may be viewedas an element of a bucolic scene and not strictly symbolic notation. Nevertheless, recognizing this independence of scalecan be important when discussing the details of the reading process.

Recognizing the difficulty of using a television or computer monitor in the evaluation of the reading phenomenon at itsmost fundamental level is important. The displayed imagery must not be limited by the monitor used. The refresh rateand phosphor decay characteristic of the monitor can have a significant impact on the quality of the investigation andthe conclusions drawn. To explore the reading phenomenon in detail even requires the careful choice of type font forthe imagery. The serifs used at the corners of letters are there to improve character recognition. They are not there tomake the text look pretty. They affect the net contrast of small features of individual characters when the characters areprojected on the retina at a scale near the resolution limit of the eye. High integrity investigations should either employhigh quality printed material in hard copy or projected form or employ carefully selected monitor equipment. The screenof the monitor should be demagnified sufficiently to eliminate any interference with the tests due to the parameters ofthe monitor. The selection of the type face used in the experiments should be declared and justified in the design of theexperiments.

Although scale does not play a major role in casual reading, it does play a significant role in how effectively we readand on research into reading. Figure 7.5.3-1 illustrates the number of characters that can be placed on the nominalfoveola at one time as a function of the scale of the characters. At the scale of 20/20 vision, approximately fifteencharacters (three five-character groups separated by one-character spaces) can occupy the diameter of the foveola at onetime. At 20/40, only about eight characters can occupy this diameter. At 20/80, less than five characters can be imaged.20/80, or characters that are 20 minutes of arc high at 15 inches, corresponds to 6.28 point type. This is a small size notusually found in books except possibly for footnotes. 9.4 point type corresponds to 20/120 or characters that are 30minutes of arc high--a typical document size for reading.

This figure shows that the typical subject only images about three characters at a time on his/her foveola when readingnine point type at 15 inches. He may image as many as sixteen characters across the width of the fovea. Casual reviewof text at these sizes suggests that the typical subject cannot perceive eight characters in a single fixation and requiresa second saccade to determine the precise meaning of an eight-character word. An example is deciding whether a suffixrelates to a case or a tense in the absence of other cues. Based on these numbers, the size of the type used and the fontof that type plays a significant role in the experiments usually carried out and reported in the literature. In addition, apreliminary conclusion would be that the space between letters plays a significant role in the planning of subsequentsaccades, even if this space occurs outside of the foveola but within the fovea. It appears such a space plays a larger rolein planning subsequent saccades than does the length of the subsequent words. Looking at smaller type suggests theimportance of having the individual characters separated by more space to perceive them individually.

7.5.3.1 Background from the recent literature

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534Becker,W. Deubel, H. & Mergner, T. (1999) Current Oculomotor Research. NY: Plenum

Chapters 3 through 12 of Underwood provide a broad overview of the field of perception during reading as of 1998.As indicated earlier, the words tremor and microsaccades do not appear in any of these chapters. The focus is on words,word string length and semantic usage in and out of context. Kennedy in Chapter 7 does explore the influence ofparafoveal words on foveal inspection time. The precise definition of the foveola, fovea and parafovea are key to a clearunderstanding of the reading function. Such a definition was not provided in Kennedy. He describes his testconfiguration as using a “high resolution (8x16) monopitch font in negative polarity (i.e., white characters on a blackbackground) on a Manitron display driven at a refresh rate of 100 Hz.” At a viewing distance of 525 mm, threecharacters of this font subtended approximately 1° of visual angle (20 minutes of arc per character). This scale is farabove the resolution limit of the normal 20/20 eye where the height of the E is defined as subtending five minutes of arcin object space. Note that a refresh rate of 100 Hz, if not essentially filtered out by the decay time of the phosphor ofthe display, may introduce a significant conflict with the natural small scale tremor of the eye.

Becker, et. al. have also provided empirical material on the reading mechanism as of 1999534. Both Underwood andBecker, et. al. concentrate on eye movement as the key to our understanding of reading. This work takes an entirelydifferent view. It treats observable eye movement as merely a mechanism for imaging individual scene features, symbolsand character groups onto the foveola where the actual process of perception is initiated. This perception involves eyemovement at a level not normally observed by the clinician or academician.

Based on the conceptualization developed in this work, the following definition is offerred. Readingcan be defined as the act of assembling a sequence of perceptions acquired through thesequential analysis of individual symbols or character groups and interpreting these perceptionsaccording to a set of syntactical rules. In this definition, symbols include hieroglyphics and otherglyphs. The initial interpretation of each symbol or symbol group by the POS results in the generationof an individual “interp.” When a series of interps are combined, the resulting interpretation will becalled a percept.

Within this work, the foveola and the fovea are defined based on the morphological characteristics of the retina. Thefoveola is defined as 1.18° in diameter, the fovea is defined as 6.26° in diameter in object space and the parafovea isdefined as beyond 6.26° from the fixation point. Therefore the fovea of Kennedy conforms closely to the foveola of thiswork and his parafovea will be assumed to equal the fovea of this work.

Kennedy also states “In reading, each word is inspected by an initial fixation at a particular position resulting from an‘entry saccade’ of a given size, launched from a particular location in another word.” The conditions, variations andsignificance of this entry saccade are discussed in some detail on page 152-153. The relationship of such saccades onthe empirical model of Rayner, Reichle and Pollatsek in Chapter 11 is also reviewed. The referral to a “location inanother word” is about as close to the discussion of characters in a word achieved in the overall Underwood text. Morematerial is presented on regressive saccades, from one word back to a previously examined word, than is given to theexamination of the characters within a word.

Kennedy discusses the term prompt, with the word gaze in parenthesis following it, as the sum of all fixations beforethe first excursion outside its boundary (page 157). In the Abstract to the chapter, he says the time to process one of twopossible foveal “prompt” words was examined using measure of gaze and fixation duration.

Figure 7.5.3-2 presents a modified, semi-standard figure from Liversedge, Paterson & Pickering in Underwood. Itshould not be inferred that most of each time interval shown relates to the latency before the next saccade. Thesesaccades may be a part of a planned saccade sequence.

In Chapter 19, the PEEP procedure is defined (Programmed element evaluation in Perception) as the serialsequence of saccades and fixations employed by the stage 4 engines and the oculomotor servo mechanisms priorto extracting information from the signals thereby generated. Such a PEEP procedure is use at all levels of visualmodality object recognition, including reading, face recognition, etc.

This sequence need not involve a significant latency between the end of analysis within one gaze, and the beginning ofa saccade to the next gaze location. Thus, a more specific set of subdivisions of the term latency is probably called forhere. The times do define the maximum length of time required for the visual system to analyze the structure of thesymbols within the foveola adequately. Adequately here means sufficient time to ascertain their semantic content(probably via a lookup table). The above authors did not address the size of the type (subtense of the height of thecharacters) used in their experiments but they did say the tracking data was quantized every millisecond.

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535Deubel, H. & Bridgeman, B. (1995) Perceptual consequences of ocular lens overshoot during saccadic eyemovements. Vision Res. vol. 35, 529-538 & 2897-902.536Becker, et. al. (1999) Op Cit. pg. 341

Figure 7.5.3-2 Hypothetical eye movement record showingthe time in milliseconds spent in a gaze between saccades.The text being read is shown above the line. The zig in theline is indicative of a regressive saccade.

Inhoff & Radach, writing in Chapter 2 of Underwood,reported on eye movements when viewing long strings ofprinted characters. Their data provides good informationon the precise nature of the small saccades related to eyemovement during reading. However, they did notprovide information at the microsaccade level or on thenature of the saccades used to perceive word meaning inthe context of reading. Their text introduces manypotential experimental variables (flexibility of the eyeballleading to transient movements of the lens group–corneaand/or lens) but does not provide a foundation forovercoming or controlling them. Their figure 1shows many minisaccades at the 0.1-0.2 character width level betweensaccades of one and seven character widths. However, the noise level of their equipment was not specified or shownand they may have excluded microsaccades from their analyses. Their discussion includes presentation of an interestingdichotomy (citing Deubel & Bridgman535). First, they say the eye is an imager and that small “post saccadic movementswill smear the retinal image.” Second, they note that the post saccadic motions are relatively small and principled, andthe reader may be able to extract useful information during that movement period [emphasis added].

Radach & McConkie prepared Chapter 4 in Underwood. It discusses the determination of fixation positions in wordsduring reading. One of their conclusions is that, “In all cases (where there are spaces between the character groups), eyemovement control during reading appears to be word-based.” This control appears to involve two distinct mechanisms,a selection mechanism and a performance mechanism. It is proposed that the selection mechanism determines how oneword rather than another is selected as the target of a saccade, and the performance mechanism determines where theeyes actually land given the above selection. The discussion centers on the general likelihood that the saccade is aimedat the center of the selected word. In the data presented, the imagery was presented (a German translation of the initialtext in Gulliver’s Travels) in page format with five to seven double-spaced lines of up to 72 ASCII characters each ona 15 inch VGA monitor. At 80 cm viewing distance, each letter corresponded to approximately 0.25° of visual angle(15 minutes of arc or three times the 20/20 character definition).

A conclusion of the above authors is that “where the eyes go with respect to selected saccade target words, is the resultof low-level visuo-oculomotor control factors, almost completely unaffected by higher cognitive processes.” This isprobably true for relatively familiar words not calling for regressive saccades or multiple saccades within one word. Theabove authors go on to caveat their statement. One of their caveats is “in the case of regressive inter-word saccades, thesaccade parameters we have looked at suggest a control mode different from the low-level default routines.” The intra-word characteristics of the reading process were not discussed in their chapter. Here again, the word inter-word appearsin the index to Underwood but the expression intra-word does not. Heller & Radach made note of two important facts536.They noted the work of Dunn-Rankin in 1978 that showed that the initial fixation point on words was not at their centerbut at positions left of center. They also noted the work of Rayner & Pollatsek in 1981 that showed that the finaldecision concerning the direction and magnitude of the next saccade was made during a given fixation interval.

Rayner, Reichle & Pollatsek presented Chapter 11 in Underwood. They discuss the effect of limiting the length of timeavailable within a gaze to analyze the text characters. They show that if a given gaze (the traditional fixation intervalby name, even if it involves tremor) is interrupted before 50-70 ms have elapsed, the reading process itself is interruptedand comprehension suffers or is lost. They also suggest that a preview of a word, while it is imaged in the area outsidethe foveola, has a positive impact on reducing the time required to interpret it when it is moved into the foveola.

The above authors review several conceptual models of the eye movement control system required to implement reading.A process model by Morrison is summarized. This model is still conceptual but includes the concept of some preanalysisof a word before it enters the foveola or before it is brought to the point of fixation within the foveola. A logic isprovided that controls the length of the gaze and/or the series of interim fixations associated with each word. The modelexplains two aspects of the eye movement phenomenon in the reading process: (1) the fact that there are fixations thatare much shorter than the nominal 175-200 ms saccade latency in simple oculomotor tasks and (2) the occurrence ofunusual landing positions, such as between words. A competing model by O’Regan, that they describe as a strategy-tactics model, is also summarized along with a critic of its features.

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Dynamics of Vision 7- 281Finally, the authors summarize their proposed E-Z Reader Model. They describe it as similar to Morrison’s processmodel except more refined through the use of two additional facets. First, it decouples the signal to shift attention fromthe signal to program a saccade. Second, it is better specified in that it has been implemented as a computer simulationprogram. They refer to the fifth generation of this program as the program under current discussion. They describe thesimulation with a schematic representing five basic processes:

1. A familiarity check on a word.2. Completion of lexical access.3. An early, labile stage of saccadic programming, which can be cancelled by subsequent saccadic programming.4. A later, non-labile, stage of saccadic programming.5. The actual saccadic eye movement.

They define the first two steps as products of a single cognitive process. This process occurs during a preview whilethe word is still in the fovea (not the foveola) and occurs before the movement of the word to the center of the foveola.They develop the fact that completion of the familiarity check depends on two additional factors. These factors slowthe rate of processing as the eccentricity of the word, relative to the point of fixation becomes larger. This factor wasadded to recognize the rapid falloff of the resolution (acuity?) of the eye with eccentricity.

They also discuss the operational distinction between an interword and an intraword saccade. They suggest the basiceye movement strategy conforms to the “dumb” default strategy: That strategy is to plan to fixate each word from morethan one viewing location unless the word’s familiarity indicates that a refixation is unnecessary. The dual fixationstrategy could obviously be useful in words that frequently have unusual or multiple suffixes (syllables).

The dumb default strategy emphasizes the importance of having a large vocabulary in the field encompassing the textbeing read. It also suggests that the average reading rate is dependent on the frequency of occurrence of words foundin the vocabulary.

Some authors have argued that no “magic moment” of word identification exists; that identification (of individual wordsor a total thought) only comes with a growing amount of data collected on a continuous basis. This may be a questionof semantics between authors since the motion of the eyes is clearly not continuous with time.

7.5.3.1.1 The familiarity default procedure in reading

The above “dumb default” strategy suggests a major change in the operating mode of the POS during reading. Whena word is recognized cognitively (the magic moment?), the POS initiates a saccade and the line of fixation is moved tothe next fixation point. This suggests that the visual system incorporates a feature similar to the “auto complete” featureof an INTERNET browser. The browser compares the initial key strokes of an entry with its short term memory andsuggests the appropriate completion of the typed entry. If the suggestion is wrong, the typist is free to enter analternative. An equivalent scenario can be defined for the visual system. After analyzing only a few symbols, initiallyin the fovea area surrounding the foveola, the system may believe with high probability that it knows what the entiresymbol group means. In that case, it will instruct the POS to proceed to the next symbol group. If the subsequent symbolgroup is recognized but it does not fit logically into a recognized syntax with the first group, the POS may be instructedto perform a regression saccade. This will allow a further review of the previous symbol group to see if an alternatesuffix, or other difference from the assumed meaning, exists. This procedure is illustrated in Figure 7.5.3-3. The systemattempts to interpret a short sentence. It can methodically perceive and interpret each character group as in A.Alternately, it can adopt a more aggressive approach and make a guess based on the likelihood that the character group“dres” is part of the longer word “dressed.” This results in the sequence shown in B and some time is saved as one gaze(fixation) is eliminated from the initial saccades sequence. If however, the assumption was made that “dres” was partof the word “dresses,” the same procedure can be followed until the second or third character group in “yesterday” isreached. At this point in the interpretation, a context conflict is recognized through comparison of the initial conceptfile with the saliency map of the individual. As a result, a regression saccade is called for back to the word that wasactually “dressed” and not “dresses.”

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537Becker, W. Deubel, H. & Mergner, T. (1999) Current Oculomotor Research. NY: Plenum Publishers, pg320-325.

Figure 7.5.3-3 The procedure of perceiving and interpretinga sentence showing three alternatives.

Considering the time line of the above activity, to decideif it suggests the course of the signals moving through thevisual system, is instructive. Certain time lines maysuggest activity limited to the POS, to the POS inconjunction with the cerebellum or to the POS inconjunction with either area 7 or the posterior areas ofthe cerebrum. Figure 7.5.3-4, from Becker, et. al.addresses this subject directly537. A statistically shorterlatency can be associated with the regressive saccadethan with the progressive scan. Apparently, when thesystem notes an inconsistency in the proposed syntax, itcancels the analysis of that character group and calls fora regressive saccade to reestablish a viable baseline.These experiments were carried out with considerablestatistical precision and the original source should bereviewed before proceeding.

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538Glezer, V. (1965) The receptive fields of the retina Vision Res vol 5, pp 497-525539Masson, G. & Perrinet, L. (2012) The behavioral receptive field underlying motion integration for primatetracking eye movements Neurosci Biobehav Rev vol 36, pp 1-25

Figure 7.5.3-4 Distribution of fixation duration for twosubjects in a standard reading experiment. Top, cumulativedistribution. Middle, fixation duration following syntaxfailure at fixation after a “dumb default.” Bottom,distribution of fixations before normal progression to nextfixation. See text.

7.5.3.1.2 The question of identification ofcharacter groups outside the foveola

Although relying on limited precision in their definitionof the foveola, fovea and parafovea, a school of thoughthas developed that the eye can perform two criticalfunctions. It can identify, to some degree, charactergroups while they are in the parafovea. This initialidentification can affect the subsequent identificationactivity (including the saccadic sequence). Murrayaddresses this possibility in Chapter 8 of Underwoodwhile still avoiding a geometrically specific definition ofthe areas of the retina. He stresses the continuous natureof the retina, based on the apparent continuous loss inacuity with angle from the line of fixation.

7.5.4 Statistics of recentering in vision

Glezer has expanded the earlier work of Cornsweetinvestigating the tendency of the human visual system torecenter on a target feature of interest following a gradualdecentering of the point of fixation538. A small, three arcminute source at 100 nit on a dark background was usedas a target. Figure 7.5.4-1 shows his results for sevensubjects. No description of the time course of thedecentering was provided. Neither was there anydiscussion of the phenomenon when examining morecomplex scenes.

7.5.5 Empirical data on eye movements

There is a vast archive of empirical data on eyemovements taken without the benefit of any theoreticalmodel of the neural system involved. Specific aspects ofthis data are incorporated into the discussion of the performance of the visual modality in Sections 17.6 to 17.9 of thiswork.

7.5.5.1 Data from Masson & Perrinet

Masson & Perrinet provided considerable data in a 2012 review on eye movements with the receptive field as aparameter539. [xxx The paper has not been obtained or filed in my archive. It is available on line for viewing only ] Thewas abstract of the paper notes, “Short-latency ocular following are reflexive, tracking eye movements that are observedin human and non-human primates in response to a sudden and brief translation of the image. Initial, open-loop part ofthe eye acceleration reflects many of the properties attributed to low-level motion processing. We review a very largeset of behavioral data demonstrating several key properties of motion detection and integration stages and theirdynamics.”

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540Ong, D. (1985) Vitamin A-binding proteins. Nutrition Reviews vol. 43, no. 8, Aug. pp.

7.6 Mechanical dynamics of the PC/RPEinterface

Figure 7.6.1-1 illustrates the photoreceptor cell/RPEinterface, from both the morphological and functionalperspective. It consolidates many features and issuesdiscussed earlier. Some of these features appear in afigure by Ong540. The static morphology includes boththe topology and topography. The dynamic functionalaspects focus on the topology, disk life cycle, andsignaling. The figure is quite complex, but it tells manystories.

7.6.1 Description of the interface

The Figure segregates the material into three namedcolumns and eight distinct rows. Four backgroundregions are defined. From left to right, they are; (a) theinterneural matrix (INM), (b) the inter-photoreceptormatrix (IPM), (c) the unnamed material shown betweenthe RPE cells and Bruch’s Membrane, and (d) theVascular Matrix supported by the choroid artery. Theseregions are separated from each other by distinctstructures that prevent diffusion, and usually preventelectrical conduction, between regions.

On the left, the barrier structure consists of the Inner Segments of the photoreceptor cells and the material between thecells, usually defined as Muller type glial Cells. This combination is frequently labeled the external or outer limiting“membrane” based on early work at low magnification. Boycott & Dowling generally define a separate and distinctouter limiting membrane proximal from the Inner Segment-Muller cell combination. On the right, Bruch’s Membraneprovides a barrier between the Vascular Matrix and the region extending to the RPE cells. This region is in turn isolatedfrom the Inter-photoreceptor matrix by the RPE cells and any material between these cells acting as a barrier. Theliterature usually describes the RPE cells as so tightly packed that no separate material is needed between them to providethis isolation. A confetti pattern has been used to define all three of the named matrices. The unnamed material is shownas a black region fading to white at the barrier. The IPM is the material surrounding the Outer Segments in the centralcolumn of the drawing.

---[xxx next three paragraphs need editing]

The photoreceptor cells are drawn to emphasize the difference between the Inner Segments and the Outer Segments.Each Inner Segment exhibits a cup-shaped feature in which the protein material, opsin is initially formed by exocytosis.The specific shape of the extrusion cup breaks and forms the protein into individual disks. This breaking and formingis suggested by the line emanating from the black dots in rows one and two. The resulting disks of opsin form theframework of the Outer Segment.

The Outer Segment is a dynamic structure external to the photoreceptor cell. Following formation of the individualdisks, the disks are coated with chromophoric material from the IPM as shown in row two. The process of continualextrusion forces the disk stack to move continuously toward the right. The rate of movement is about one disk per hourin humans. A similar rate is found in all warm blooded chordates.

The Inner Segments are shown without regard to the cell nuclei, which may be enclosed by the Inner Segments or maybe found remotely and closer to the pedicles of the cells. Two primary functions of the Inner Segments are shownexplicitly. The first is the extrusion cup on the right of each Inner Segment. Many mitochondria and ribosomes arefound to the left of the extrusion cup. They are believed to produce the protein material passed through the cell wall intothe extrusion cup. The process is one of exocytosis. This material is shown initially as a black dot that is formed intoa ribbon. This ribbon is fractured and formed into disks of protein by the extrusion cup. The material of these disks is

Figure 7.5.5-1 Development of the oculomotor reflex (inpercent probability of occurrence) as a function ofdisplacement of the fixation point (in arc minutes). Shadedarea-standard deviation. Interrupted line is the frequency ofthe development of flicks from Cornsweet, 1956. FromGlezer, 1965.

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541Wolken, J. (1966) Vision: biophysics and biochemistry of the retinal photoreceptors, Springfield IL: CharlesC. Thomas pp. 71-74

known as Opsin. Second, an electrical path is shown from the dendrites (generally nine in number and shown by theheavy black lines) surrounding the Outer Segments to the pedicles found within the INM (but not shown explicitly).These dendrites enter the Inner Segments from the IPM near the extrusion cup in an area known as the calyx, or collar(shown along the top edge of the Inner Segments of row four and five).

The RPE cells are shown containing four different types of chromophoric granules. The granules containing thechromophores of vision are stored as palmitates. In color photography based on reflected light, these granules appearin their complementary color since they are highly absorbent. The complement to a narrow band absorber is a wide bandtransmitter. Using conventional color photography, the S-channel chromophores appear yellow, the L-channel materialsappear cyan, and the M-channel material appears magenta. The UV-channel material does not absorb any radiation whenilluminated by conventional light. It appears transparent when imaged onto conventional color film designed to recordimages as seen by normal human vision. Wolken appears to have captured three of these granule types (UV-, S-, & M-)in a single photomicrograph from a swamp turtle.541 He also presents spectrums for three of the granules from a chicken.Unfortunately, his laboratory methods were harsh and his terminology is now a bit archaic. His choice of color namesmay be due partially to the wide spectral width of his spectrometer. He labels the S-channel absorber as yellow byreflected light. The spectrum associated with the UV-channel absorber is only partially recorded and is labeled greenalthough it shows little absorption at any wavelength longer than 500 nm. It appears transparent in his figure. Thespectrum of the M-channel absorber is labeled red but is more appropriately labeled magenta as it appears in his figure.No record of a L-channel absorber, which would record as aqua, appears in his figure. A full color version of Figure7.6.1-1 is available on the author’s Web Site. In the color version, the disks of Row 2 are transparent and sensitive inthe Ultraviolet. The disks of Row 3 are cyan and sensitive to red. The disks of Row 4 are magenta and sensitive togreen. Finally, the disks of Row 5 are yellow and sensitive to blue.

Row 1 has been drawn in simplified form to illustrate how the disks are formed into a stack that is pushed away fromthe Inner Segment. The disks are formed at the rate of about one per hour in warm-blooded animals. When the stackin a fully mature human eye reaches about 2000 disks, the outer most disks reach the region of the RPE cells. The RPEcells also form a cup like structure around each disk stack. The RPE cell uses this structure to phagocytize the diskswithin the cup. The broken disks within the cup in rows four through seven are to symbolize this process. A stack ofdisks as shown in Row 1 is not photosensitive and the situation as described can be considered pathological.

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Figure 7.6.1-1 Illustrative cross section of the PC/RPE interface. See Text.

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288 Processes in Animal VisionRow 2 shows the activation of the photo-receptive structure. A primary purpose of the RPE cells is to create thechromophoric material, store it in chromatic granules until needed and then release these chromophores into the IPM.Once released into the IPM, they diffuse to the region of the extrusion cup of each Inner Segment. There are indicationsthat these cups have passages between the zone of exocytosis and the extrusion die. These passages allow the chromaticmaterials, the Rhodonines, to enter the cup from the IPM and coat the protein substrates before they complete theextrusion process. Once the disks are coated with a liquid crystalline chromophore, they are photosensitive.

The coated disk stack of Row 3, and also Row 4 & 5, is shown surrounded by another material, the bio-energetic fuelthat provides electrical energy for all neural cells. The presence of this material has frequently been confused with aputative extension of the Inner Segment cell wall surrounding the Outer Segment. However, in high resolution imagery,no sign of a bilayer cell wall surrounding the Outer Segment is found in this region. The bio-energetic material candiffuse into the region between disks and into the grooves along the disks where the microtubules associated with thedendritic structure are found. However, these diffusion paths are very limited in their capacity to diffuse bio-energeticmaterial.

Looking at Row 2 and 3 simultaneously, note that both (all Inner Segments) exhibit exocytosis but the process is onlyshown explicitly for a few cells. Note also that there is no one-to-one correlation between the RPE cells and the InnerSegments. When a disk stack reaches the region of the RPE cells, the RPE cells form a cup around the stack, or part ofa stack, in order to carry out phagocytosis. The entire coated disk is phagocytized. The chromophoric material isabsorbed and probably recycled within the RPE. The protein material is absorbed and probably returned to the VascularMatrix for recycling within the animals body. Four different types of chromophoric granules are shown within the RPEcells, even for humans. Although the ultraviolet spectral capability of the human eye may be only residual, it is clearlypresent as discussed earlier regarding aphakics. No correlation is known between the type of chromophore in a givenRPE cell and the absorption spectrum of a specific Inner Segment. Most RPE cells contain a variety of chromophoricgranules.

The signal path between the coated disks of the Outer Segment and the pedicles of the cells have been shown explicitlyin Rows 4 and 5. What has not been shown explicitly is the location of the distribution amplifier within each InnerSegment. These Activa may be arranged so their podites contact the IPM or the INM. Furthermore, some of them maybe located outside the Inner Segment per se. They may be located in a hillock at the junction of the Inner Segment andthe Axon. Here, the podite terminal would be on the surface of the initial segment (of the axon) as it is frequently inbipolar cells.

Rows six and seven illustrate the condition of a tear in the retina. Such a tear frequently causes a shearing of a largegroup of Outer Segments. In the case shown in row seven, the tear results in a displacement of the alignment of theOuter Segments. If the tear is physically repaired by a physician before excessive time has passed, the disk stacks willcontinue to grow normally and the physical damaged material will be swept into the cups of the RPE cells. A dangeralways exists that a tear will destroy the protective environment of the IPM and allow oxygen and/or other oxidizers toenter the IPM space. This can damage the chromophores coating the disks and cause further disease.

Row eight shows an important special case. This case illustrates the formation of a new disk stack by an immaturephotoreceptor cell. This is the only way that a conically shaped disk stack can exist within a normal retina. Until acomplete disk stack reaches the RPE, the conditions within the IS extrusion cup are not nominal and undersized disksmay be formed. After the disks reach the RPE, the pressure within the IS extrusion cup is raised to the point that fulldiameter disks are formed routinely. Once these full size disks have traveled to the RPE, the disk stack maintains aconstant diameter after that. It is such an immature photoreceptor cell that is sometimes labeled a “cone” although thisdesignation would have no relevance to the absorption spectrum of the particular photoreceptor.

7.6.2 Summary of the dynamics

Rows 1 through 5 are seen to involve a variety of active processes that must occur if vision is to be achieved on acontinuing basis:

+ The protein substrates must be formed by the photoreceptor cell on a continuing basis, approximately one disk perhour.

+ The RPE must extract Vitamin A from the vascular matrix, convert it into one of four chromophores, the Rhodonine,and release these materials into the IPM on a continuing basis.

+The RPE must extract bio-energetic material, primarily that associated with the glutamate cycle, from the vascularmatrix and release it into the IPM on a continuing basis.

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Dynamics of Vision 7- 289+ Both the Rhodonines and the bio-energetic materials must diffuse through the IPM to their target locations on acontinuous basis.

+ The reactant products of the bio-energetic processes must diffuse away from the reaction location and be disposed ofon a continuous basis.

+ The disks, upon reaching the vicinity of the RPE, must be disposed of properly. The chromophoric material can berecycled within the RPE. The protein material must be transported to the vascular matrix where it may be recycled backto the photoreceptor cells or used for other purposes in the body.

Failure of any of the above actions to occur will result in a pathological condition, if not blindness. Rows 6 & 7 describea common event in vision, the shearing of the retina at a plane through the Outer Segments. This condition, describedas a retinal tear, has an interesting pathological course. The immediate symptom is a localized de-focus in the visualimage. If not repaired promptly, the IPM is subject to mixing with the vitreous humor and/or the INM. This cansignificantly disrupt the diffusion processes described above. It does not significantly affect exocytosis and extrusionof the protein substrates. If the tear is repaired promptly, the long term prognosis is interesting. The integrity of the IPMis restored. Diffusion of the bio-energetics and chromophores is restored. The formation of new functional disks re-starts. The disk stacks continue to proceed toward the RPE and the death of the oldest disks. After approximately sevendays, all signs of physical damage to the retina are removed. Whereas Row 6 shows a broken stack, Row 7 shows adisrupted stack. Because of the close packing of Outer Segments, such a disruption is limited in extent. The surroundingdisk stacks confine the disrupted stack in-vivo and phagocytosis occurs in due time. It is only in-vitro that a drasticdisruption of a disk stack is likely.

Row 8 shows an interesting special case. A short conical shaped Outer Segment is shown. It has not reached the regionof the RPE. Such a situation may be a sign of an immature growth process or a pathological abnormality. If it is animmature situation, the Outer Segment will continue to grow, achieve a more constant diameter and eventually reachthe RPE. Upon reaching the RPE, the disks will enter the region of phagocytosis. After about seven days in humans,such a Outer Segment will no longer exhibit a conical shape. If the reason for the conical shape is pathological orgenetic, the effect on the operation of that overall photoreceptor cell is currently unreported.

7.6.3 The visual cycle of the Rhodonines

As discussed in an earlier chapter, this Section illustrates the normal closed cycle use of the Rhodonines. They areformed within the RPE cells from Vitamin A received from the vascular matrix and stored in the chromophore granulesas esters until needed. When needed, they diffuse to the extrusion region of the Inner Segments of the photoreceptorswhere they are deposited as a liquid crystalline coating in their final chemical form on the protein substrates. They arephysically transported back to the RPE cells by the growth of new disks pushing the disk stacks into the cup of the RPEcells where phagocytosis takes place. Following phagocytosis, the Rhodonines are returned to the chromophore granulesready for reuse. This cycle takes about seven days in the human. Additional Vitamin A is only required as a makeupmaterial when the Rhodonines are degraded beyond recovery. Such degradation is apparently significant and newVitamin A is required continuously.

7.7 The hydraulic, metabolic features associated with the electrostenolytic system

The bulk of Section 7.7 has been moved to Section 8.6.

7.7.5 Tracking respiration related to the neural system

Early work on understanding the operation of the neural system was based largely on tracking the flow of a few nuclearspecies contained in molecules able to cross the blood brain barrier. The work was focused on the use of labeleddeoxyglucose. More recent work has expanded these studies using PET and MRI techniques. These latter techniqueswill be discussed in Section 7.7.6.

7.7.5.1 Use of the radionucleotide, [14C]deoxyglucose

Kennedy, et. al. explored a method of using [14C] deoxyglucose, abbreviated to [14C]DG, as a tracer to follow the

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542Kennedy, C. Des Rosiers, M. Reivich, M. Sharp, F. Jehle, J. & Sokoloff, L. (1975) Mapping of functionalneural pathways by autoradiographic survey of local metabolic rate with [14C]Deoxyglucose. Science, vol. 187,pp 850-853543Sokoloff, L. Reivich, M. Kennedy, C. et. al. (1977) The [14C]Deoxyglucose method for the measurementof local cerebral glucose utilization. J. Neurochem. vol. 28, pp 897-916

conversion of glucose into glucose-6-phosphate in neural tissue542. Sokoloff, et. al. have provided a mathematicaldemonstration of the efficacy, and a method of calibration of, the proposed method543. Their work discussed a numberof conditions related to the effective use of the technique. However, the conditions appear acceptable within thelaboratory environment.

The method accurately represents the cumulative conversion of glucose into glucose-6-phosphate, a part of the stage 1process described above. The process involves the integration of a rate sensitive mechanism. Calibration is mosteffective over a period of tens of minutes after injection of a charge of the radionucleotide into the blood stream of ananimal. The technique is useful because the radionucleotide is initially processed just like glucose into a hexo-6-phosphate by the hexokinase enzyme. However, it becomes trapped within the most active tissue for a short period sinceit is not enzymatically processed beyond the 6-phosphate stage. Thus the animals had to be sacrificed in a timely mannerand the neural tissue frozen immediately to prevent the rate sensitive information from being obscured. Radiographictechniques are then used to determine the location of the accumulation of the radionucleotides and the relative amountof the material at each location. Unfortunately, the method only applies to the initial portion of stage 1 of the processof powering the neural system. It does not allow the process to be traced through the additional steps associated withstage 2, 3 or 3.5. As a result, the technique is unable to differentiate between glucose-6-phosphate that is ultimately usedto power the electrolytic portion of the neuron from any material used for respiration and possibly the physical formationof new synapses.

Even with this shortcoming, the nucleotide has been extremely useful. It allows recording the differential respirationof thin layers of cerebral material in animals following light stimulation of the retina. These results will be summarizedin Section 15.2.8. Film exposures involved in the process have usually been measured in days.

As Sokoloff, et. al. point out, with the development of computerized emission-based tomography, the technique offerspotential for in-vivo experiments on humans as well as other animals.

7.7.5.2 Potential use of the radionucleotide, [14C]L-Dopa

Based on this work, it appears that another useful radionucleotide would be [14C]L-Dopa. This material is a mono-carboxylic amino acid with a dihydroxyphenyl ring. It is known to pass through the blood-brain barrier and has beenshown to participate in the electrostenolytic process in place of glutamic acid. Therefore, this material offers thepotential for tracing the flow of glutamic acid directly to the site of electrostenolytic power generation on an individualneuron and confirming the electrostenolytic reaction of glutamic acid to form GABA and carbon dioxide. Bothexploratory activities similar to those of Kennedy, et. al. and an analysis similar to that of Sokoloff would be needed todetermine the utility of this radionucleotide.

If the location of the radionucleotide could be specified on L-Dopa (that it was not associated with the carboxyl radicalnear the amino group), tracing the conversion of L-Dopa to a residue similar to GABA might be possible.

By tracing the L-Dopa to various local areas on an individual neuron and confirming the production of the L-Doparesidue, clear evidence for the role of glutamate in the powering of the neurons would be available. The tracing wouldrepresent the lower right most reaction in [Figure 7.7.2-3].

7.7.6 Physiological uncoupling between cerebral blood flow and metabolic oxygen consumption

The advent of PET, MRI and fMRI procedures has introduced a new era in imaging of the brain, and other parts of thebody. These studies have demonstrated the critical role that glutamate plays in the operation of the neural system throughits relative abundance in neural tissue. They have also uncovered the highly unexpected fact that the relativeconsumption of oxygen by the brain does not rise in proportion to the relative consumption of glycogen during neuralactivity. While glycogen consumption may rise by 40-50%, the rise in oxygen consumption rises by 5% or less. Thisfinding highlights the fact the neurons of the brain do not rely upon oxidative metabolism during their short termoperation. Oxygen’s primary role is in restoring the reactants used in the electrostenolytic process over a longer interval.

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544Fox, P. & Raichle, M. (1986) focal physiological uncoupling of cerebral blood flow and oxidativemetabolism during somatosensory stimulation in human subjects. Proc Natl Acad Sci USA vol. 83, pp 1140-1144545Fujita, H. Hiroto, K. Reutens, D. & Gjedde, A. (1999) Oxygen consumption of cerebral cortex fails toincrease during continued vibrotactile stimulation J. Cereb Blood Flow Metab vol. 19(3) pp 266-271546MVafee, M. Meyer, E. Marrett, S. Paus, T. Evans, A & Gjedde, A. (1999) Frequency-dependent changes incerebral metabolic rate of oxygen during activation of human visual cortex. J Cereb Blood Flow Metab vol19(3) pp 272-277547Buxton, R. (2002) Introduction to Functional Magnetic Resonance Imaging. Cambridge: CambridgeUniversity Press

7.7.6.1 Background

Until 1986, the conventional wisdom was that the brain operated on an oxidative metabolism related directly to oxygenin its operation. In that year, Fox & Raichle demonstrated a significant decoupling between the rate of cerebral bloodflow (CBF) and the cerebral metabolic rate of oxygen consumption (CMRO2)544. They hypothesized that the CBF wascontrolled by a mechanism independent of the cerebral metabolic rate of oxygen. Subsequent studies confirmed thisstartling decoupling545. Both Fujita and Vafee546 have provided some transient data on oxygen consumption both duringand following neural activation. Confirmation of these results has led to a variety of explanations attempting torationalize this coupling relationship between the CBF and CMRO2. To date, these studies have not recognized the roleof glutamate in providing power to the neurons independent of the rate of oxidative metabolism.

Until the advent of PET and MRI techniques, nearly all studies of brain activity were based on global calculations,frequently influenced by the restrictions introduced by the blood-brain-barrier. Since then, the studies have been muchmore local in nature. They are currently limited largely by the resolution of the PET and MRI techniques. Thisresolution is described in terms of the voxel ( the volumetric pixel).

The complexity of measuring the CBF and CMRO2 should not be underestimated. As will be shown below, indirectmeans are used followed by complex calculations. The investigators should be given great credit for achieving theprecision illustrated in their data.

Buxton has provided a readable, but complex description of the methods required to determine the CBF and CMRO2547.

His presentation is limited to the conventional wisdom concerning neural system operation. The following sections willdeviate from his presentation in order to provide a broader context. This context will explain the decoupling foundexperimentally and suggest additional experimental activity.

7.7.6.2 Framework

The PET and MRI techniques rely upon the interactions of various constituents of organic tissue with crossed magneticand radio frequency fields. These constituents incorporate a molecule that exhibits distinctive magnetic characteristicsthat can be recognized easily. The techniques used, and the associated mathematical processing, have advanced rapidlysince the early 1990's. As with sonography in medicine, PET and MRI currently employ most of the techniques foundin modern radar and sonar equipments. This level of sophistication makes it difficult to describe all of the optimizationtechniques used in PET and MRI. Buxton has provided an introduction to many of these specialized techniques as well.The signal sensed by the simplest equipments is in what is generally called the spatial frequency domain. The moreadvanced machines sense signals in the spatial frequency domain under transient temporal conditions. Converting thesesignals into a spatial position domain is necessary prior to interpretation. This requires the use of the two-dimensionalFourier Transform. This in turn requires considerable computational capability only available with the largest availablecomputers. To conserve on computational power, or computational time until an answer is available, the FourierTransform process is frequently truncated. This results in the Gibbs phenomenon familiar to all electrical circuitdesigners. Edges are emphasized in the imagery in spite of the underlying data.

Because of the four-dimensional nature of the most desirable signals, presentation of the resulting data is frequently aproblem. The most common presentations present the desired transient data overlaid on a static presentation to providevisual reference to the voxels of interest. Frequently, the overlay is in a contrasting color for clarity.

7.7.6.2.1 Nomenclature

The nomenclature used in PET and MRI revolves around the notion of the voxel, the volumetric pixel of organic tissue.

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548Edelman, R. Hesselink, J. & Zlatkin, M. (1996) Clinical Magnetic Resonance Imaging, 2nd Ed. vol. 1.London: W. B. Saunders. Chapter 1

Figure 7.7.6-1 Simplified diagram of image contrast as afunction of TR & TE. From Edelman, et. al. 1996.

It is the metabolism of the tissue enclosed within an individual voxel that is of interest. To study this subject, the flowof nutrients into and out of the voxel must be quantified. The complexity of the tissue involved within an arbitrary voxelmakes this process quite difficult. Some volume of the voxel is occupied by blood vessels transporting bulk blood.Some volume is occupied by the capillary bed providing blood components to the neural tissue. Finally, some volumeis occupied by neural and other types of cellular material.

The general approach involves two steps. The first step is to describe the cellular blood flow, CBF, into and out of thevoxel. The second step is to describe the specific components of interest in the blood both entering and leaving thevoxel. To date, the additional specific components have been primarily related to the flow of glycogen and oxygen intoand out of the voxel. As a result, the two most prominent measurements have been of the cerebral metabolic rate ofglycogen introduction, CMRGlc, and the cerebral metabolic rate of oxygen consumption, CMRO2. Both of these aretypically expressed on a local basis. This analysis will show that two other components are critical to the understandingof the local metabolism of the brain.The first is the cerebral metabolic rate of glutamate consumption, CMRGlu. Glutamic acid (or glutamate) is the fuelmost directly involved in neural operation. The second is the cerebral metabolic rate of GABA consumption,CMRGABA. This is the primary waste produce of neural operation. These two materials participate in anelectrostenolytic process on the surface of every conduit associated with every neuron.

7.7.6.2.2 Parameters involved in the Fourier transforms

Although not of great importance here, being aware of certain parameters used in optimizing MRI images is useful. Thewhite matter (primarily myelinated stage 3 neurons), the grey matter (primarily unmyelinated stage 2 neurons and thenecessary capillary beds) and the bulk cerebral fluids (frequently described as the cerebral spinal fluids, CSF) exhibitdifferent time constants when relaxing after excitation by a radio frequency, RF, field. The nominal values for thesefactors are given in TABLE 7.7.6-1.

TABLE 7.7.6-1TYPICAL MAGNETIC PARAMETERS FOR COMPONENTS OF THE BRAIN

Material M0 (arb. units) T1 (ms) T2 (ms)

Gray matter 85 950 95White matter 80 700 80CSF 100 2500 250

M0 is defined as the equilibrium magnetization of thematerial. T1 is defined as the longitudinal relaxationtime associated with the dominant magnetic specieswithin the material. T2 is defined as the transverserelaxation time associated with the dominant magneticspecies.

Also important are certain factors associated with theMRI apparatus and the transform calculations. One isthe time between repetitions of the scanning operation,TR. The second is the echo time, TE. The relationshipbetween these factors is presented in Edelman, et. al548.They are basically used in optimizing the power of themachine and in “weighting” the Fourier Transformcalculations described above. The result is highercontrast in the reconstructed images for the features ofinterest. These weightings are frequently related to thefollowing Figure 7.7.6-1.

7.7.6.2.3 Metabolic Mechanisms and

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549Lehninger, A. (1972) Op. Cit

Nomenclature

Workers in the field of developing PET and MRI techniques have used a simplistic view of the metabolic processes ofthe body. The initial assumption that complete oxidation of glycogen was to be expected within the brain does notrecognize the multitude of serial steps involved in metabolism, or the multitude of alternate paths supporting thatmetabolism. A more complete illumination of the steps in metabolism and the results of this work highlighting the roleof glutamate in neural operation leads to a different interpretation of metabolism in the neural system.

The overall concept of the utilization of food and oxygen in the support of life is generally defined as respiration.Metabolism is an important phase of respiration centered at the operations at the cellular level. Our understanding ofmetabolism, although remarkable, remains at a primitive level. The complexity is recognized inthe nomenclature ofLehninger549. His chapter 14 begins with a discussion of “Intermediate metabolism.” By this term, he means metabolismas the sum total of an immense variety of intermediate steps and residues. He does not mean some intermediate stageof metabolism.

Metabolism has historically been defined as the sum total of the enzymatic reactions occurring in the cell. These havebeen divided into four categories.

1. Extract chemical energy from the environment (food or sunlight).

2. Convert exogenous nutrients into building blocks of macromolecular components of cells.

3. Assemble the macromolecules into proteins, nucleic acids, lipids and other components.

4. Form and degrade those biomolecules required in specialized functions of cells.

The last category is very important in the neural system. One of those degradation processes is used to power eachindividual neuron. It is the process of electrostenolysis occurring on the surface of every neuron and involving theconversion of glutamic acid into GABA.

Within metabolism, the processes can also be broken down into functional categories. The two most common are:

1. Catabolism– An enzymatic degradation, largely by oxidative reactions of relatively large molecules. Process releasesfree energy as ATP.

2. Anabolism– An enzymatic synthesis of larger molecular components of cells from similar precursors. Requires energyin the form of ATP.

A third form of metabolism will be discussed below.

Fermentation is a major function within metabolism. It takes on a number of forms that are generally associated withcatabolism. However, it includes both aerobic and anaerobic variants. In general, fermentation involves oxidation-reduction reactions that do not involve oxygen. No net oxidation of the fuel and residue of these reactions occurs. Thesereactions involve primarily rearrangement accompanied by the release of hydrogen, water or carbon dioxide. Theyfrequently involve amination. The changes in energy level of the constituents are frequently small.

Glycolysis is a major activity within the fermentation function. It involves a myriad of individual steps that are difficultto annotate in a single figure. Glycolysis involves two major chemical sequences terminating in the generation ofpyruvate or lactate (depending on the personal interests of the investigator). Lactate is particularly important in muscularactivity because of its creation in an anaerobic environment and its ability to pass easily through cell walls. The interesthere is focused more on pyruvate. Glycolysis can be explained if the processes involved are divided into three types.

1. Degradation of glucose to lactate (the carbon pathway).

2. Introduction of phosphate group (the phosphate pathway).

3. Oxidation-reduction (the electron pathway).

The participation chemical energy, ATP, NAD, etc., supporting the conversions associated with the steps in the above

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550Harper, H. (1975) Review of Physiological Chemistry, 15th Ed. Los Altos, CA: Lange Medical Publ. pg 378

pathways must also be considered in a complete analysis.

Following glycolysis, the chemistry of metabolism broadens immeasurably in complexity. The framework for thisbroadening was first defined by Krebs. He proposed the citric acid cycle as the basic element of the framework. Thiscycle begins with the creation of citric acid from pyruvate via an incredibly complex enzymatic molecule known to thisday as “coenzyme A.” The cycle includes a variety of side loops, shunts and other poorly defined processes. One ofparticular interest here is the glutamate shunt discussed below. The general nature of the process of metabolism centeredon the citric acid cycle of Krebs, also known as the Tri-Carboxylic-Acid (TCA) cycle, and glutamate is illustrated inFigure 7.7.6-2. The number of carbon atoms in each molecule is given in parentheses. Noting that the cycle involvesmultiple decarboxylations along the right hand side is important. The reconstitution of the six carbon citrate from thefour carbon succinates and oxaloacetate is more complex than generally addressed in discussions of the cycle.

The steps leading to the formation of pyruvate occur within individual cells. The tri-carboxylic-acid cycle occurs withinthe mitochondria. The glutamate-to-GABA transformation occurs on the surface of the membranes of the neuron as partof the electrostenolytic mechanism.

The glutamate shunt begins with an amination of α-ketoglutarate. The resulting α-amino-glutarate is more commonlyknown as glutamate. The second step in this shunt is unique in that it does not involve an enzyme in the molecular sense.It involves the decarboxylation of the glutamate on a special area of a cell membrane acting as a substrate. Whether thisprocess requires the presence of pyridoxal phosphate as a coenzyme is unknown. However, lack of this materialgenerally inhibits neural activity (and presumably other reactions associated with glycolysis or the TCA cycle) withinthe brain.

The two walls of the bilayer membrane forming the wall are asymmetrical at the molecular level. As a result, themembrane acts as an electrical diode. The electrostenolytic decarboxylation process occurring on this membranegenerates a free electron on one side of the membrane. This electrostenolytic process is the power source for eachelectrical conduit within a neuron. It is the physical analog of the putative ion-pump proposed by Hodgkin & Huxley(1952).

Glutamate participates in a wide variety of enzymatic reactions within the organism. These reactions and the glutamateshunt are well documented550. Its support in powering the neurons has not been previously reported. According toHarper, the shunt is particularly important in the gray matter of the brain. The glutamate shunt includes a sub-loop ofinterest. The sub-loop involves the removal of ammonia from GABA by a pyridoxal-dependent enzyme. This ammoniacan participate in a transamination of α-ketoglutarate to glutamate. This sub-loop is shown by the dashed line in thefigure.

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551Frahm, J. Kruger, G. et. al. (1996) Dynamic uncoupling and recoupling of perfusion and oxidativemetabolism during focal brain activation in man Magn Resonance Med vol. 35, pp 143-148552Magistretti, P. & Pellerin, L. (1999) Astrocytes couple synaptic activity to glucose utilization in the brainNew Physiol Sci vol. 14, pp 177-182

Figure 7.7.6-2 The Citric Acid Cycle focused on the glutamate shunt. The shunt involves a decarboxylation but noinvolvement of oxygen. The decarboxylation is part of the electrostenolytic process powering the neurons. This processgenerates a free electron. The reported close coupling between the amination of α-ketoglutarate and the transaminationof GABA is shown by the dashed line.

Estimates appear in the literature suggesting as much as 80% of the glucose delivered to the brain is used in neuronalactivity. The high utilization of glutamate within a neuron suggests the processes of glycolysis and glutamate formationmay tax the capability of a single cell. Both Frahm, et. al551. and Magistreeti & Pellerin552 have suggested that a majorrole for astrocytes within the brain (and their familial neuroglia, Schwann cells in the peripheral neural system) is to aidthe neurons by providing additional lactate. The solubility of lactate in intercellular space would allow easy movementof lactate from the astrocytes to the neurons. Although the views of these authors are conventional, their conclusionsare compatible with the Activa and neuron of this work. Particularly in stage 3 projection neurons, there is a need forglutamate at locations quite distant from the soma of the neuron itself.

Figure 7.7.6-3 provides a more detailed description of the events related to the glutamate shunt variant of the tri-carboxylic-acid cycle. It is divided into four major sections. The shaded area on the left describes the chemical activityon the surface of a neuron upon excitation. The basic event is the (reversible) conversion of a small part of a pool ofglutamate into GABA with the release of an electron into the plasma of the neuron and the release of CO2. The stepsrelated to the tri-carboxylic-acid (TCA or Krebs) cycle required to remove the GABA and restore the glutamate supplyare enclosed in the large dashed box. These steps normally occur within the mitochondria of the cell. The extraction

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Figure 7.7.6-3 Trail of events supporting the electrostenolytic process in neurons. The two boxes at lower right supportthe BOLD Effect in fMRI experiments. The dashed subloop shows how ammonia can be removed from GABA and usedimmediately in the amination process forming glutamate.

of glucose from the bloodstream and the formation of pyruvate are shown at upper right. These steps normally occurwithin the larger volume of the cell. The extraction of oxygen from the bloodstream is shown at the lower right.

Synaptic excitation of any neuron results in a change in the potential of at least one of the signaling related plasmaswithin the neuron. If the activity leads to a reduction of the negative potential in any of the plasmas, the electrostenolyticpower source for that plasma will attempt to restore the nominal potential by injecting additional electrons into theplasma. This process converts glutamate to GABA. If the potential has risen, the electrostenolytic process has thetheoretical capability of extracting electrons from the plasma and causing GABA to be converted back to glutamate (asdiscussed below).

The TCA box contains two distinctly different paths. The top row describes the replacement of glutamate through theextraction of glucose from the bloodstream. This is the path usually considered when discussing BOLD signalgeneration in the fMRI technique. However, it should be noted that a second path exists as shown in the second row.This path reconstitutes the glutamate from GABA without using any new material derived from glucose. Here, no BOLDsignal, related to direct extraction of glucose from the blood stream and its conversion into glutamate, is found.

Note that the extraction of glucose from the bloodstream and its conversion into glutamate does not involve oxidationinvolving oxygen. It merely involves a series of oxidative-reductions (which actually releases oxygen in the form ofCO2).

The glutamate to GABA reaction releases CO2. The replacement of the glutamate in the pool necessarily involves thereplacement of the lost CO2. However, the top path in the figure shows that the glutamate can be replaced using glucosefrom the bloodstream without any involvement of oxygen from the bloodstream. In this case, no CMRO2 signalassociated with the BOLD signal is seen.

Alternately, the glutamate can be regenerated without the participation of new glucose using the middle and lower pathsof the figure. This method does require the acquisition of oxygen from some source. The lower row of the figure showsthe potential source of oxygen via the bloodstream. The process involves the reconstitution of the reactant used in thetransamination mechanism shown. This path has not been documented. However, it involves the removal of oxygenfrom hemoglobin within the capillary bed supporting the neuron.

7.7.6.3 Energy calculations related to metabolism

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Dynamics of Vision 7- 297The normal tendency in PET and MRI studies is to expect the complete metabolism of glucose. This involves theconsumption of considerable oxygen in the creation of 38 units of ATP, an energy carrier.

Glucose + 6O2 —> 6CO2 + 6H2O (+38 ATP)

Each unit of ATP in the above calculations contain 7500 calories.

The various phases of metabolism involved in supporting neuronal activity are quite different situations. They do notinvolve the complete reduction of glucose. The goal of glycolysis is the production of pyruvate or lactate (a more easilystored form) that can be used within the tri-carboxylic-acid cycle (TCA).

Glucose —> 2 Lactate

Similarly, each cycle of the Krebs TCA cycle consumes no oxygen.

CH3COOH + H20 —>2CO2 + 8H

These reactions only involve small changes in energy compared with that involved in complete oxidation.

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TABLE OF CONTENTS--4/30/17

7 Dynamics of Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1 Characteristics & Dynamics of Retinoids in the body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

7.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1.1.1 Overall Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

7.1.1.1.1 Scenario requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.1.1.1.2 Reinterpretation of Data Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.1.1.1.3 The BIG QUESTION–What is the shape of retinol in various

environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37.1.1.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

7.1.1.2.1 Enzymatic activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57.1.1.2.2 Naming enzymatic Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67.1.1.2.3 Transport Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67.1.1.2.4 Specifics related to TTR and its relationship to RBP . . . . . . . . . . . . . 97.1.1.2.5 The CRBP’s of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97.1.1.2.6 Structural Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7.1.1.3 Properties of the fundamental chromogens . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107.1.1.4 State of the ART in crystallography versus molecular modeling . . . . . . . . . . . . 10

7.1.1.4.1 Critical role of disorder and delocalization in chromophore transport ADD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7.1.1.4.2 Lack of chromophore planarity plays a critical role incrystallographyADD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.1.1.4.3 Application of molecular modeling and visualization versuscrystallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7.1.1.4.4 Unique 3rd order protein structures described via crystallography . 127.1.2 Transport Scenario for the retinoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7.1.2.1 Transport of the visual modality retinoids within the body . . . . . . . . . . . . . . . 177.1.2.1.1 Summary premises of retinoid transport within the vascular system

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177.1.2.1.2 Ingestion or manufacture of Vitamin A . . . . . . . . . . . . . . . . . . . . . . 187.1.2.1.3 Visual retinoid transport within the vascular system EDIT . . . . . . . 24

7.1.2.2 Transport of the retinoids within the retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.1.2.2.1 Transfer of the retinines from the SRBP + TTR to the RPE cells . . 377.1.2.2.2 Clearance of the residues of SRBP & TTR from the RPE cell area

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.1.2.3 Potential buildup of drusen resulting in macular degeneration . . . . . . . . . . . . . 387.1.2.4 Transport of Rhodonine within the RPE/IPM space of the retina . . . . . . . . . . . 43

7.1.2.4.1 Nature of the RBP’s in the RPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.1.2.4.2 Criticality of IRBP based on genetic mutation testing . . . . . . . . . . . 467.1.2.4.3 Nature of IRBP in the IPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477.1.2.4.4 Proportion of IRBP in the IPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487.1.2.4.5 Sources of IRBP in the IPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.1.2.5 Background: SRBP +TTR complex in non-visual applications . . . . . . . . . . . . . 497.1.2.6 Important extraneous material related to retinoic acid . . . . . . . . . . . . . . . . . . . . 51

7.1.3 A precise redefinition of the aspects of the Visual Cycle involving retinoids GOOD/EDIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1.3.1 Gross retinoid transport in vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527.1.3.2 The overall visual cycle related to homeostasis . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.2 Dynamics of radiation-chemistry and the photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.2.1 Radiation Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.2.2 Excitation of a Liquid Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.2.3 De-excitation of a Liquid Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.2.4 Dynamics of excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7.2.4.1 The dynamics of photon absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.2.4.2 The dynamics of excitation/de-excitation (small signal case) . . . . . . . . . . . . . 64

7.2.4.2.1 Excitation/de-excitation with transport delay, the P/D Equation . . . 677.2.4.2.2 The Hodgkin Solution to the P/D Equation for s •F•t = 1.00 . . . . . 697.2.4.2.3 Other attempts to obtain a P/D Equation . . . . . . . . . . . . . . . . . . . . . 70

7.2.4.3 The dynamics of excitation/de-excitation (large signal case) . . . . . . . . . . . . . . 71

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Dynamics of Vision 7- 2997.2.5 The dynamics of transduction to a current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7.2.5.1 Details of the two-exciton process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.2.6 Analysis of the excitation equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7.2.6.1 Parametric analysis of the P/D equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.2.6.1.1 Effect of temperature and incident flux on the delay in the response

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.2.6.1.2 Determination of the effective absorption cross section of a photoreceptor

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2.6.1.3 Determination of the effective time constant . . . . . . . . . . . . . . . . . . 797.2.6.1.4 Effect of the experimental configuration on the time constant . . . . . 80

7.2.6.2 Comparison with the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.2.6.2.1 Detailed comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.2.7 Noise measurements of Baylor et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.3 Dynamics of the physiological optics of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.3.1.1 The literature of the physiological optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.3.1.2 Overview of the dynamics of the physiological optics . . . . . . . . . . . . . . . . . . . 867.3.1.3 Subsystems of physiological optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.3.1.4 Block diagrams of the physiological optical system . . . . . . . . . . . . . . . . . . . . . 89

7.3.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.3.2.1 Classification of the rotational motion of the eyes . . . . . . . . . . . . . . . . . . . . . . 95

7.3.2.1.1 Classification of eye movement syndromes or complexes . . . . . . . . 977.3.2.1.2 Classification of clinically observed eye movements–saccades . . . . 987.3.2.1.3 Classification of clinically unobserved eye movements–flicks and tremor

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.3.2.2 Classification of the temporal characteristics of the motion of the eyes . . . . . . 997.3.2.3 Defining the operating modes within the physiological optics subsystem . . . . . 99

7.3.2.3.1 Framework for discussions of pointing and the triad . . . . . . . . . . . . 997.3.2.3.2 Defining precedence within the physiological optics subsystem . . 101

7.3.2.4 The Law of Equal Innervation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.3.2.5 Defining the motor unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.3.2.5.1 A functional description of the oculomotor muscle . . . . . . . . . . . . 1027.3.2.5.2 Defining the fatigue factor in the oculomotor response . . . . . . . . . 103

7.3.2.6 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.3.3 The physiology of the pointing subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.3.3.1 Basic operating scenarios of different species . . . . . . . . . . . . . . . . . . . . . . . . . 1077.3.3.1.1 Static mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077.3.3.1.2 Tremor mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.3.3.1.3 Modified tremor mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.3.3.2 Fixation motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.3.3.2.1 Continuous Tremor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.3.3.2.2 Slow Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.3.3.2.3 “Flicking movements” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.3.3.3 Saccadic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.3.3.3.1 Small saccadic mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.3.3.3.2 Large saccadic mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.3.3.3.3 Pursuit Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.3.3.3.4 Blanking of visual channels during large saccades . . . . . . . . . . . . 110

7.3.3.4 Operating modes of the visual system associated with the physiological optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.3.3.4.1 The coarse, type 0, (& autonomous) awareness mode . . . . . . . . . . 1117.3.3.4.2 The coarse, type 0, (& semi-autonomous) alarm mode . . . . . . . . . 1117.3.3.4.3 The fine, type 1, (& autonomous) analytical mode . . . . . . . . . . . . 1117.3.3.4.4 The (sympathetic and instruction oriented) volition mode . . . . . . . 1117.3.3.4.5 Accommodation, a fixed reference controlled servomechanism . . 1127.3.3.4.6 The critical role of memory in POS operation . . . . . . . . . . . . . . . . 112

7.3.3.5 The pointing system in humans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.3.3.5.1 The general scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.3.3.5.2 Alternate models of the oculomotor portion of the POS . . . . . . . . 1137.3.3.5.3 Data related to physiological tremor . . . . . . . . . . . . . . . . . . . . . . . 1137.3.3.5.4 Effect of stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.3.3.5.5 Inertial aspects of pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

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300 Processes in Animal Vision7.3.4 Modeling the dynamics of the pointing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.3.4.1 Developing the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187.3.4.1.1 The Cook & Stark model as a point of departure . . . . . . . . . . . . . . 1197.3.4.1.2 The expanded oculomotor plant model . . . . . . . . . . . . . . . . . . . . . 1217.3.4.1.3 The performance characteristics of the subsystem . . . . . . . . . . . . . 125

7.3.4.2 Expansion of the Top Level Schematic of Vision . . . . . . . . . . . . . . . . . . . . . . 1267.3.5 Measured open and closed loop performance of the oculomotor system . . . . . . . . . . . . . 126

7.3.5.1 The low frequency, wide angle(>6.2° diam.), case . . . . . . . . . . . . . . . . . . . . . 1267.3.5.2 The mid frequency, mid angle (1.2°<Q<6.2° diam.), case . . . . . . . . . . . . . . . 1287.3.5.3 The high frequency, narrow angle (<1.2° diam.), case . . . . . . . . . . . . . . . . . . 1287.3.5.4 The pointing of the eyes under quiescent conditions . . . . . . . . . . . . . . . . . . . . 131

7.3.6 Measured Performance of the augmented oculomotor system . . . . . . . . . . . . . . . . . . . . . 1317.3.6.1 The interrelationship of saccades, ocular drift and eye position . . . . . . . . . . . 1317.3.6.2 The optokinetic and vestibular-ocular mechanisms . . . . . . . . . . . . . . . . . . . . . 1317.3.6.3 Oculomotor signals from the controller of the POS system . . . . . . . . . . . . . . . 132

7.3.6.3.2 Bandwidth of the neural path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.3.6.4 Histological features of the oculomotor system (will move to Chap. 10) . . . . 133

7.3.6.4.1 Histology of the muscles of the plant . . . . . . . . . . . . . . . . . . . . . . . 1337.3.6.4.2 Histology of the controller circuits . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.3.7 Definition and measurement of tremor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.3.7.1 Potential modes of signal acquisition . . . . . . . . . . . . . . . . . . . . . . . . 1337.3.7.2 Methods of measuring tremor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.4 Operational overlays on the Precision Optical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397.4.1 Framework for evaluating the operational overlays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.4.1.1 Monocular, binocular and stereoscopic domains of vision . . . . . . . . . . . . . . . 1437.4.1.1.1 Global, local, fine & coarse in discussing functional overlays . . . . 1457.4.1.1.2 Fusion & rivalry differ in foveola and peripheral vision . . . . . . . . 149

7.4.1.2 General physiology and operating modes associated with binocular vision andstereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1507.4.1.2.1 Major features of the Functional diagram and schematic related to version

and vergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.4.1.2.2 Key features of the Precision Optical System . . . . . . . . . . . . . . . . 1527.4.1.2.3 Signal paths associated with version and vergence . . . . . . . . . . . . 152

7.4.1.3 Forms, cues and protocols of depth perception . . . . . . . . . . . . . . . . . . . . . . . . 1537.4.1.4 Overview of theories of binocular and stereo-optic vision in the literature . . . 154

7.4.1.4.1 Recent papers on stereo vision from psychology laboratories . . . . 1557.4.1.4.2 The Yarbus Test as a critical hurdle for theories of fusion and stereoptic

vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.4.1.5 Alternate interpretations of the horopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.4.1.5.1 The horopter as a physiological characteristic EXPAND . . . . . . . 1647.4.1.5.2 The horopter as a test instrument . . . . . . . . . . . . . . . . . . . . . . . . . . 1657.4.1.5.3 Representations of horopter data . . . . . . . . . . . . . . . . . . . . . . . . . . 1677.4.1.5.4 Parameters important in horopter protocols . . . . . . . . . . . . . . . . . . 1697.4.1.5.5 A more realistic horopter for discussions of stereopsis EMPTY . . 170

7.4.1.6 Description of Panum’s area, depth perception and the fusional horopter . . . 1707.4.1.6.1 Panum’s area relates to the X & Y axes of object space . . . . . . . . 1707.4.1.6.2 Depth perception involves the Z-axis . . . . . . . . . . . . . . . . . . . . . . . 1717.4.1.6.3 The maximum range of fusion and depth perception . . . . . . . . . . . 1717.4.1.6.4 The fusion horopter involves the X,Y & Z or q, f, r axes . . . . . . . . 172

7.4.2 The version control subsystem: pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1727.4.2.1 The type 0 version control servomechanism (related to awareness) . . . . . . . . 1737.4.2.2 The type 1 version control servomechanism (related to analysis) . . . . . . . . . . 1737.4.2.3 Smooth pursuit versus salutatory motions EDIT . . . . . . . . . . . . . . . . . . . . . . . 1737.4.2.4 Data related to smooth and salutatory pursuit . . . . . . . . . . . . . . . . . . . . . . . . . 173

7.4.3 The vergence control subsystem: coarse convergence via the LGN . . . . . . . . . . . . . . . . . 1747.4.3.1 Review of vergence models in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . 175

7.4.3.1.1 Models of the physiology of the vergence control system . . . . . . . 1777.4.3.1.2 The practical solution to the correspondence problem . . . . . . . . . . 179

7.4.3.2 Comprehensive model of the horizontal vergence system . . . . . . . . . . . . . . . . 1807.4.3.2.1 The perception of 3D by the neural system . . . . . . . . . . . . . . . . . . 182

7.4.3.3 Detailed model of the horizontal vergence system . . . . . . . . . . . . . . . . . . . . . 1837.4.3.3.1 A mathematical model of amplitudes in the sensing portion of the

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Dynamics of Vision 7- 301vergence system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

7.4.3.3.2 A mathematical model of delays in the vergence system . . . . . . . . 1857.4.3.3.3 A mathematical model of the plant portion of the vergence system

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.4.3.3.4 Discussion of the overall mathematical model of the vergence system

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.4.3.4 The vergence data available in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . 187

7.4.3.4.1 Transient response of the vergence system . . . . . . . . . . . . . . . . . . 1897.4.3.4.2 Vergence deviation as a function of stimulus location . . . . . . . . . . 189

7.4.3.5 State diagram for the vergence subsystem RESERVED . . . . . . . . . . . . . . . . . 1897.4.3.6 The role of torsion in vergence and version . . . . . . . . . . . . . . . . . . . . . . . . . . 189

7.4.4 Filling in of a color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1907.4.4.1 The figure-ground concept of psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1907.4.4.2 Filling in for the blind spot and capillaries on the retina . . . . . . . . . . . . . . . . . 1917.4.4.3 Processing luminance versus chrominance values at a perimeter . . . . . . . . . . 1917.4.4.4 A uniform field is dependent on the luminance/chrominance at its perimeter . 191

7.4.5 Mechanism of precision convergence & Stereopsis via PGN-pulvinar . . . . . . . . . . . . . . 1937.4.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.4.5.1.1 Precision versus qualitative depth perception . . . . . . . . . . . . . . . . 1947.4.5.1.2 Block and state diagrams for the process of stereopsis . . . . . . . . . 197

7.4.5.2 Background specific to stereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2027.4.5.2.1 Stereopsis as distinct from binocular vision . . . . . . . . . . . . . . . . . . 2037.4.5.2.2 The PGN as a general purpose 2-D associative correlator . . . . . . . 2037.4.5.2.3 The general operation of the PGN as an associative correlator . . . 2047.4.5.2.4 The detailed operation of the PGN as an associative correlator . . . 2047.4.5.2.5 Putative use of spatial frequency filters and Fourier transform calculations

in vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2057.4.5.3 The mechanism of stereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.4.5.3.1 The geometry associated with stereopsis . . . . . . . . . . . . . . . . . . . . 2067.4.5.3.3 The local correlation range supporting stereopsis and fusion . . . . . 2087.4.5.3.4 The potential variation in tremor amplitude . . . . . . . . . . . . . . . . . . 2087.4.5.3.5 Forms of stereoscopes and autostereograms . . . . . . . . . . . . . . . . . . 208

7.4.5.4 Theories of Stereopsis prior to 1995 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2087.4.5.5 Recent “physiologically–based” theories of stereopsis by of Qian & colleagues

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2107.4.5.5.1 Mathematical model of Qian & Anderson paper of 1997 . . . . . . . . 2117.4.5.5.2 Mathematical model of Qian & Li paper of 2011 . . . . . . . . . . . . . 212

7.4.5.6 The proposed physiological theory of stereopsis . . . . . . . . . . . . . . . . . . . . . . . 2147.4.6 Fusion and Depth Perception as phenomena related to stereopsis . . . . . . . . . . . . . . . . . . 215

7.4.6.1 The phenomenon of fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2157.4.6.1.1 Misconceptions and the Keplerian Projection related to fusion . . . 2167.4.6.1.2 The fusion phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2177.4.6.1.3 Fusion as a routine event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

7.4.6.2 Effects related to the phenomenon of fusion . . . . . . . . . . . . . . . . . . . . . . . . . . 2187.4.6.2.1 Spatial hysteresis related to stereopsis and fusion . . . . . . . . . . . . . 2187.4.6.2.2 References to peripheral fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 2187.4.6.2.3 Temporal hysteresis and other temporal aspects of fusion . . . . . . . 2187.4.3.2.4 Fusion as a function of peripheral angle . . . . . . . . . . . . . . . . . . . . . 218

7.4.6.3 Theories explaining the fusion phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . 2207.4.6.3.1 Previous theories of image fusion . . . . . . . . . . . . . . . . . . . . . . . . . 2207.4.6.3.2 The proposed Physiological Theory of Image Fusion . . . . . . . . . . 220

7.4.6.4 The phenomenon of precision depth perception . . . . . . . . . . . . . . . . . . . . . . . 2227.4.6.4.1 Dichotic versus dichoptic instrumentation . . . . . . . . . . . . . . . . . . . 222

7.4.6.5 Data for perceived depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2237.4.6.5.1 Depth perception as a function of binocular disparity . . . . . . . . . . 2237.4.6.5.2 Depth perception associated with spatial frequency (interval) . . . . 225

7.4.6.6 Theories explaining the depth perception phenomenon . . . . . . . . . . . . . . . . . . 2257.4.6.6.1 Previous theories of precision depth perception . . . . . . . . . . . . . . . 2257.4.6.6.2 A proposed Physiological Theory of Precision Depth Perception . 226

7.4.7 Evaluating stereopsis through fusion and depth perception . . . . . . . . . . . . . . . . . . . . . . . 2277.4.7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2277.4.7.2 The plasticity of fusion and depth parameters . . . . . . . . . . . . . . . . . . . . . . . . . 228

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302 Processes in Animal Vision7.4.7.2.1 Use of “double-duty” parameters in depth perception . . . . . . . . . . 2297.4.7.2.2 Chromostereopsis and transverse chromatic abberations . . . . . . . . 229

7.4.7.3 Combined fusion and depth data in the literature ADD EXAMPLES . . . . . . . 2297.4.7.4 Depth perception experiments of Allison & Howard . . . . . . . . . . . . . . . . . . . 2317.4.7.5 Dynamics of stereopsis and role of non-declaratory (implicit) memory . . . . . 234

7.4.8 Overall temporal response & latencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2347.4.8.1 Definition and tabulation of latencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2347.4.8.2 Comments by line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2407.4.8.3 Correlation with the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

7.4.8.3.1 Volition mode experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2417.4.8.3.2 Alarm mode experiments (including conflict resolution) . . . . . . . . 2427.4.8.3.3 Interrupted alarm mode and other experiments . . . . . . . . . . . . . . . 2437.4.8.3.4 Participation of the frontal eye fields of the cerebrum . . . . . . . . . . 244

7.4.9 The lens and aperture control subsystems: accommodation . . . . . . . . . . . . . . . . . . . . . . . 2447.4.9.1 The lens control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

7.4.9.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2457.4.9.1.2 The overall servomechanism of accommodation . . . . . . . . . . . . . . 2477.4.9.1.3 The performance of the overall accommodation servomechanism . 2497.4.9.1.3.1 Static performance errors in accommodation (clinical) . . . . . . . . 2527.4.9.1.3.2 Dynamic performance errors in accommodation (clinical) . . . . . 2537.4.9.1.4 The physical plant of the lens control servomechanism . . . . . . . . . 2537.4.9.1.5 The physical parameters of the materials of the servomechanism . 2567.4.9.1.6 The neural circuitry of the lens servomechanism . . . . . . . . . . . . . . 2577.4.9.1.7 Steady state operation of the lens servomechanism . . . . . . . . . . . . 2577.4.9.1.8 Transient operation of the lens servomechanism . . . . . . . . . . . . . . 259

7.4.9.2 Short term accommodation errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2637.4.9.3 Presbyopia due to refraction errors is a normal consequence of aging . . . . . . 2637.4.9.4 The aperture control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

7.4.9.4.1 The iris control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2647.4.9.4.2 The shutter control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

7.4.10 Interplay of version, vergence and accommodation subsystems . . . . . . . . . . . . . . . . . . . 2667.4.10.1 Cross-coupling of functional overlays– servomechanisms EMPTY . . . . . . . 2667.4.10.2 Relationship between vergence and version . . . . . . . . . . . . . . . . . . . . . . . . . 2667.4.10.3 Change in accommodation with vergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 2677.4.10.4 The ratio of accommodative convergence to accommodation . . . . . . . . . . . . 2677.4.10.5 The ratio AC/A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2677.4.10.6 Recent research in virtual and augmented reality . . . . . . . . . . . . . . . . . . . . . 267

7.4.11 Other models of version, vergence and accommodation in the literature . . . . . . . . . . . . 2677.5 Higher level functional aspects of the dynamics of the eyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

7.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2697.5.1.1 The continuing philosophical debate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

7.5.1.1.1 An alternate view adopted in this work . . . . . . . . . . . . . . . . . . . . . 2717.5.1.1.2 Dispersion in the empirical literature . . . . . . . . . . . . . . . . . . . . . . . 272

7.5.1.2 The available laboratory equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2727.5.2 Aspects of examining a scene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

7.5.2.1 Aspects of examining a bucolic scene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2737.5.2.1.1 The familiarity default procedure in examining a scene . . . . . . . . . 274

7.5.2.2 Aspects of examining scenes of finer structure Empty . . . . . . . . . . . . . . . . . . 2757.5.2.3 Aspects of examining a scene containing a local transient event . . . . . . . . . . 276

7.5.2.3.1 The simultaneous dual alarm scenario . . . . . . . . . . . . . . . . . . . . . . 2767.5.2.4 Strategies Employed in Scene Perception and Interpretation . . . . . . . . . . . . . 277

7.5.3 Oculomotor aspects of reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2777.5.3.1 Background from the recent literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

7.5.3.1.1 The familiarity default procedure in reading . . . . . . . . . . . . . . . . . 2817.5.3.1.2 The question of identification of character groups outside the foveola

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2837.5.4 Statistics of recentering in vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2837.5.5 Empirical data on eye movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

7.5.5.1 Data from Masson & Perrinet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2837.6 Mechanical dynamics of the PC/RPE interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

7.6.1 Description of the interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2857.6.2 Summary of the dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

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Dynamics of Vision 7- 3037.6.3 The visual cycle of the Rhodonines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

7.7 The hydraulic, metabolic features associated with the electrostenolytic system . . . . . . . . . . . . . . . . 289

The bulk of Section 7.7 has been moved to Section 8.6.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

7.7.5 Tracking respiration related to the neural system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2897.7.5.1 Use of the radionucleotide, [14C]deoxyglucose . . . . . . . . . . . . . . . . . . . . . . . 2897.7.5.2 Potential use of the radionucleotide, [14C]L-Dopa . . . . . . . . . . . . . . . . . . . . . . 290

7.7.6 Physiological uncoupling between cerebral blood flow and metabolic oxygen consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290

7.7.6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917.7.6.2 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

7.7.6.2.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917.7.6.2.2 Parameters involved in the Fourier transforms . . . . . . . . . . . . . . . . 2927.7.6.2.3 Metabolic Mechanisms and Nomenclature . . . . . . . . . . . . . . . . . . 293

7.7.6.3 Energy calculations related to metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

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304 Processes in Animal Vision

List of Figures

Figure 7.1.1-1 Goodman’s cartoon model of alternate loadings of the SRBP-TTR complex . . . . . . . . . . . . . . . . . . 3Figure 7.1.1-2 View of an a helix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 7.1.2-1 The currently identified retinoid binding proteins, RBP’s ADD . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 7.1.2-2 Breakdown of triglycerides by pancreatic lipase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 7.1.2-3 The general metabolism of Vitamin A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 7.1.2-4 The general flow of Retinoids within the animal body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 7.1.2-5 Model of the structure of the hexameric complex (RBP)2-TTR containing retinol . . . . . . . . . . . . . 26Figure 7.1.2-6 Ribbon representation of the plasma holo-RBP (RBP4) molecule . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 7.1.2-7 Ribbon representation of 3D holo-RBP in Blomhoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Figure 7.1.2-8 Peptide sequence of human RBP from Rask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 7.1.2-9 Schematic outline of the various fragments and peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 7.1.2-10 Primary structure sequence alignment of the RBPs of six vertebrate species . . . . . . . . . . . . . . . . 35Figure 7.1.2-11 Proposed flow of chromogens (-phores) between the bloodstream and the disks . . . . . . . . . . . . . 37Figure 7.1.2-13 Conceptual schematic of potential disease conditions (drusin buildup) associated with the vascular/RPE

interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 7.1.2-14 Proposed transport of the retinoids within the RPE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 7.1.2-15 Overall scheme for retinoid transformation for both chromophore formation and operation . . . . 45Figure 7.1.3-1 Gross caricature of retinoid transport in vision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 7.1.3-2 Details of the flow of retinoids supporting the outer segments via the RPE ADD . . . . . . . . . . . . . 56Figure 7.1.3-3 A schematic of the homeostatic and transduction visual cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 7.1.3-4 Block diagram of proposed homeostasis visual cycle in the chordate eye . . . . . . . . . . . . . . . . . . . . 60Figure 7.2.1-1 The morphology and electrophysiology of the photoreceptor cell from Section 10.8.5.3. . . . . . . . 62Figure 7.2.4-1 Basic flow diagram, equivalent electronic circuit and applicable equations. . . . . . . . . . . . . . . . . . 66Figure 7.2.4-2 Theoretical responses to an impulse as predicted by the photoexcitation/de-excitation equation . . 68Figure 7.2.4-4 The idealized quantum efficiency of a photoreceptor cell as a function of irradiance . . . . . . . . . . . 72Figure 7.2.5-1 The circuit diagram of the combined P/D and transduction process. . . . . . . . . . . . . . . . . . . . . . . 76Figure 7.2.6-1 Collage of delay data versus flux level and temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 7.2.6-2 Fundamental current paths in a photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 7.2.6-3 A comparison of the theoretical and measure OS currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 7.2.6-4 CR The dynamic characteristic of the current collected from the OS. . . . . . . . . . . . . . . . . . . . . . . 84Figure 7.3.1-1 Top level block diagram of the visual system of Chordata, particularly of man . . . . . . . . . . . . . . . 90Figure 7.3.1-2 Simplified top level schematic of Chordata focused on vertical oculomotor functions. . . . . . . . . . 91Figure 7.3.1-3 The dual nature of the pointing system seen from above . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 7.3.1-4 The luminance, chrominance and appearance channels of the eye of normal and aphakic humans.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 7.3.2-1 A conceptual framework for discussing saccade amplitudes and temporal frequencies . . . . . . . . . 96Figure 7.3.2-2 A conceptual framework for saccade angular rates and amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . 97Figure 7.3.2-3 Mirror stereoscope used in disparity vergence experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 7.3.4-1 An initial block diagram of the oculomotor plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Figure 7.3.4-2 A caricature of the static push-pull operation of the ocular muscles. . . . . . . . . . . . . . . . . . . . . . . 120Figure 7.3.4-3 An expanded model of the oculomotor subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 7.3.4-4 The oculomotor servo plant with driving neurons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 7.3.4-5 The displacement and velocity profile of large-angle human optokinetics . . . . . . . . . . . . . . . . . . 125Figure 7.3.4-6 RECOPY Action potential firing rate required to maintain an angular position . . . . . . . . . . . . . . 126Figure 7.3.5-1 Saccadic duration (A) and maximum velocity (B) of human eye movement . . . . . . . . . . . . . . . . 127Figure 7.3.5-2 Spatial orientation of fine movements (<3°) of the two eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 7.3.5-3 RESCAN Record of eye movements during steady fixation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 7.3.5-4 Waveforms of tremor resolved into vertical and horizontal components . . . . . . . . . . . . . . . . . . . 130Figure 7.3.5-5 Bandpass recording of tremor in the human. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 7.3.7-1 Potential scanning modes associated with the analytical mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Figure 7.3.7-2 Caricature of photoreceptors scanning an edge near the visual acuity limit . . . . . . . . . . . . . . . . . 135Figure 7.3.7-3 Candidate tremor waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Figure 7.3.7-4 Amplitude spectrum calculated with Matlab’s FFT function from AOSLO . . . . . . . . . . . . . . . . . 138Figure 7.4.1-1 Geometry of horizontal disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Figure 7.4.1-2 Figure from Blakemore with dashed arcs of best focus added . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Figure 7.4.1-3 The visual fields of monocular, binocular and stereoptic vision . . . . . . . . . . . . . . . . . . . . . . . . . . 144Figure 7.4.1-4 A summary of the on-axis parameters of vision in object space . . . . . . . . . . . . . . . . . . . . . . . . . . 145

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Dynamics of Vision 7- 305Figure 7.4.1-5 Plan view from above of the right ocular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure 7.4.1-6 A simplified pointing schematic based on the revised Functional Diagram of human vision, ca 2002

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure 7.4.1-7 A Re-classification of cues found in depth perception from Howard . . . . . . . . . . . . . . . . . . . . . . 154Figure 7.4.1-8 The just–discriminable depth threshold (detectable difference in depth . . . . . . . . . . . . . . . . . . . . 158Figure 7.4.1-9 An overview of 3D Information Extraction from two schools of thought . . . . . . . . . . . . . . . . . . . 159Figure 7.4.1-10 Basic stimulus arrangement of Allison & Howard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Figure 7.4.1-11 A horizontal horopter showing effect of accommodation and rotation of the eyes . . . . . . . . . . . 165Figure 7.4.1-12 A simple horopter test set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Figure 7.4.1-13 A typical empirical horopter frequently used in pedagogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Figure 7.4.1-14 Theoretical framework for displaying empirical horopter data . . . . . . . . . . . . . . . . . . . . . . . . . . 168Figure 7.4.1-15 Caricature of an empirical horopter based on stereoacuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Figure 7.4.1-16 The optimal horopter for stereopsis discussions ADD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Figure 7.4.3-1 Caricature of depth perception at a bowling alley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Figure 7.4.3-2 A caricature introducing tremor to explain the mechanism providing stereopsis . . . . . . . . . . . . . . 179Figure 7.4.3-3 Caricature of vergence control problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Figure 7.4.3-4 Block diagram of the complete horizontal vergence system of human vision . . . . . . . . . . . . . . . . 183Figure 7.4.3-5 Averaged disparity vergence responses obtained for 2-degree convergent disparity pulses . . . . . 187Figure 7.4.5-1 Stereoacuity as a function of horizontal offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196Figure 7.4.5-2 Stereopsis as a function of field angle within the foveola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197Figure 7.4.5-3 Top level block diagram optimized for stereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Figure 7.4.5-4 A more detailed schematic of the top level block diagram focused on precision stereopsis . . . . . 199Figure 7.4.5-5 State diagram for the stereopsis mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Figure 7.4.5-6 The associative correlator of the PGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204Figure 7.4.5-7 The geometry of the stereopsis mechanism in object space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Figure 7.4.5-8 The geometry of binocular projection and definition of disparity ADD . . . . . . . . . . . . . . . . . . . . 213Figure 7.4.6-1 Fusion as a function of peripheral angle in the normal eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218Figure 7.4.6-2 Relative depth perception as a function of the binocular disparity of a target under dichoptic conditions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224Figure 7.4.6-3 Region of fusion versus spatial frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Figure 7.4.7-1 A stereogram from Howard & Rogers with added parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Figure 7.4.7-2 Perceived depth as a function of vertical line interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230Figure 7.4.7-3 Potential motion in depth mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Figure 7.4.7-4 Example psychometric functions for dot patterns are shown for one observer . . . . . . . . . . . . . . . 233Figure 7.4.8-1 Nodes and transit times affecting the latencies and response times . . . . . . . . . . . . . . . . . . . . . . . 236Figure 7.4.8-2 Flow chart of latencies in the human visual system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Figure 7.4.9-1 Image of the lens and pupil taken from the position of the retina LARGE FILE . . . . . . . . . . . . . . 245Figure 7.4.9-2 Block diagram of the accommodation servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248Figure 7.4.9-3 A nomograph describing the performance of the accommodation subsystem . . . . . . . . . . . . . . . . 251Figure 7.4.9-4 Accommodation performance of the “young” emmetrope eye . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Figure 7.4.9-5 Static biomechanical model of the lens servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255Figure 7.4.9-6 Accommodation efficiency based on data of Fincham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258Figure 7.4.9-7 Accommodation range of the human eye versus age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Figure 7.4.9-8 Dynamic biomechanical model of the accommodation plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260Figure 7.4.9-9 Schematic of the plant of the lens servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Figure 7.4.9-10 Presbyopia as a normal process of aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Figure 7.5.1-1 Definition of saccades by size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270Figure 7.5.2-1 Viewing pattern for a complex line drawing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Figure 7.5.3-1 The characters of text imaged on the foveola (black bar) and the fovea . . . . . . . . . . . . . . . . . . . . 278Figure 7.5.3-2 Hypothetical eye movement record showing the time in milliseconds . . . . . . . . . . . . . . . . . . . . 280Figure 7.5.3-3 The procedure of perceiving and interpreting a sentence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281Figure 7.5.3-4 Distribution of fixation duration for two subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283Figure 7.6.1-1 Illustrative cross section of the PC/RPE interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287Figure 7.7.6-2 The Citric Acid Cycle focused on the glutamate shunt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Figure 7.7.6-3 Trail of events supporting the electrostenolytic process in neurons. The two boxes at lower right support

the BOLD Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

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306 Processes in Animal Vision

(Active) SUBJECT INDEX (using advanced indexing option)

2-exciton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 4, 10-12, 29, 137, 155-161, 163, 164, 182, 183, 194, 212, 2313-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165, 203, 208, 21895% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74action potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102, 103, 118, 122, 126, 135-137, 243, 249Activa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 57, 61, 64, 72, 74, 75, 78, 83, 84, 288, 295adaptation . . . 1, 52, 57, 61, 63, 71, 72, 74, 75, 83-85, 87, 88, 116, 136, 163, 174, 181, 182, 184-188, 202, 246, 263-

265, 268, 271adaptation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 61, 72, 74, 83, 84, 116, 163, 184, 186, 188alarm mode . . . . . . . . . . . . . . . . . 92, 105, 111, 112, 127, 145, 172, 173, 180, 208, 235, 237, 242, 243, 249, 266, 272ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294, 296analytical mode . . . . . . . 85, 88, 92, 111, 112, 134, 145, 148, 172-174, 180, 189, 194, 199, 204, 235, 243, 269, 272anatomical computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203area 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237, 238, 240-242, 276, 277, 282area 7a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95, 237, 238, 244associative correlator . . . . . . . . . . . . . . . . . 105, 148, 171, 173, 179, 202-204, 214, 215, 217, 222, 223, 225, 227-229associative memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204astigmatism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221, 253attention . . . . . . . . . . . . . . . 3, 84, 96, 97, 100, 103, 140, 158, 175, 177, 211, 226, 234, 241, 244, 246, 273, 277, 281awareness mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 88, 111, 144, 172-174, 194, 204, 217, 235-237, 269, 272band gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 76Bayesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 156, 210Bayesian trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4BBB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 24bifurcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197bilayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288, 294bilayer membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294bit-serial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103bleaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52, 64, 71, 73, 75, 85blood brain barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289blood-brain barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290BOLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296broadband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204, 229calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 101, 218, 257, 290canonical forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2cerebellum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111, 151-153, 234, 237, 240, 243, 268, 276, 282cerebrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95, 106, 175, 244, 276, 282chromostereopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229cis- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 32, 47, 52, 53, 57citric acid cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294, 295colliculus . . . . 87, 92, 95, 100, 102, 103, 105, 111, 112, 132, 133, 151-153, 172, 180, 197, 202, 203, 235, 237, 238,

241-244, 248, 260, 265-268commissure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115, 118, 184, 186, 257complex neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87, 160, 203, 206, 210, 212, 234, 242, 257, 268computational . . . . 87, 99, 104, 108, 112, 113, 119, 139, 144, 156, 160, 181, 184-186, 191, 203, 206, 209, 210, 215,

226, 244, 257, 259, 268, 291computational anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87confirmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 291correlogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241critical flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108, 271cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 47, 63, 65, 66, 69, 71, 78, 79, 117, 256, 287cyclopean . . . . . . . . . . . . . 88, 92, 93, 99, 144, 146, 148, 161, 168, 172, 177, 179, 193, 203, 205, 206, 215, 223, 231dark adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71, 72, 75, 85data base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 5, 203, 215database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 12, 32, 61, 89, 96, 111, 131, 199, 203, 259declaratory memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182, 234

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Dynamics of Vision 7- 307deoxyglucose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289depth perception . . 88, 93, 100, 104, 106, 139, 145, 146, 148-151, 153, 154, 161, 164, 167, 169-172, 177, 178, 182,

193, 194, 197, 198, 203, 205, 208, 210, 212, 214, 215, 222-231, 234, 247, 266diencephalon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198dihedral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 10, 32, 33diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184, 294diol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 17, 38disparity . 87, 100-107, 139-141, 144-146, 148, 154, 156-161, 165, 166, 169, 171, 175-177, 180-187, 189, 194-197,

199, 203, 205, 209-215, 217, 218, 222-227, 229-233, 246, 266, 268drusen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 32, 38, 39, 42dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73, 74Edinger-Westphal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248, 249efferent copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132electrostenolytic process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123, 290, 292, 294-296EOG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 292ERG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48, 80evoked potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 23, 35, 51, 52, 119exocytosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285, 288, 289expanded . . . . . . . . . . . . . . . . . . . . . . . . 7, 39, 40, 55, 78, 97, 121, 146, 158, 182, 184, 186, 206, 261, 277, 283, 289exposine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72external feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 95, 99, 102, 115, 177figure-ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156, 182, 190flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108, 271fMRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133, 149-151, 240, 244, 290, 296Fourier transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187, 205, 206, 291, 292free energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293frequency of occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281fuscin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18fusion frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96, 134GABA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290, 292-296Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104, 139-144, 163, 164, 177, 193, 241genetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Gestalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156, 190glutamate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288, 290-296glutamate shunt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294, 295glycolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293-295, 297g-protein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81half-amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Helmholtz Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168Hodgkin solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68, 69horopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105, 141, 143, 144, 146, 155, 156, 163-172, 178, 189, 209, 228, 234hydrogen bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 30-32, 36hydronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64, 75, 78hydronium liquid crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64, 75hyperacuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155, 156, 163illusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190interp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105, 199, 202, 205, 214, 228, 279intrafusal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157ion-pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294knockout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47, 48lactate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293, 295, 297larynx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190latency . . . . . . . . . 68, 98, 114, 125, 149, 150, 186, 187, 234, 235, 242-244, 256, 259, 260, 273, 279, 280, 282, 283lateral geniculate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 149, 160, 182, 189, 190, 204, 211, 237, 248lgn/occipital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111, 150-152, 172, 180, 217, 226light adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Limulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70, 80, 87

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308 Processes in Animal Visionlocomotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108long term memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112, 153, 269, 274lookup table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 199, 202, 206, 267, 279machine vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157, 194macular degeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 32, 38-42masking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Maxwell’s Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229mean disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157, 160, 183, 212, 214mesencephalon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244mesotopic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74, 246microtubule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75microvilli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4midbrain . 85, 86, 94, 95, 100, 104, 111, 132, 133, 149, 179, 184, 193, 199, 202, 207, 210, 220, 226, 234, 240, 242-

244, 260, 265, 277modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232, 253morphogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14motif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110, 244, 289-293, 297multi-dimensional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136myelinated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118, 292narrow band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134, 193, 286neurite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52, 57neurites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57neuroglia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295night blindness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22nodal points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104, 140, 142, 165, 170, 267noise . . . 64, 70, 71, 83, 85, 99, 108, 114, 117, 129, 130, 135, 136, 138, 148, 150, 156, 160, 170, 174, 178, 186, 187,

204, 205, 211, 221, 222, 235, 242, 253, 263, 273, 280non-declaratory memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182, 234OCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41, 137Orangutan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 221orbital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35, 130orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 35P/D equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67-71, 78-80, 82-84, 160, 181, 182, 212pain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258parametric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74, 78parietal lobe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152, 161, 197, 237pedestal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182PEEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279percept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105, 152, 156, 190, 199, 202, 205, 210, 214, 217, 220, 279perceptual space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106perigeniculate . . 85, 87, 92, 94, 103, 105, 133, 139, 148, 149, 160, 163, 182, 184, 190, 202-204, 206, 210, 214, 215,

221, 222, 225, 227, 236, 248, 252, 253perigeniculate nucleus . . . 85, 87, 92, 94, 103, 105, 133, 139, 148, 149, 163, 182, 184, 190, 202-204, 206, 210, 214,

215, 221, 222, 225, 227, 236, 248, 252PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289-291, 293, 297pgn/pulvinar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105, 111, 150-152, 237, 243, 244, 257, 260, 275, 277phase velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132phylogenic tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89piezoelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123, 124plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228podites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288point of regard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146POS . . 86-88, 90, 99, 100, 102, 103, 105, 106, 110-113, 117-119, 121, 127, 128, 131, 132, 136, 144, 148, 152, 165,

173-175, 180-182, 185, 199, 200, 202, 205, 208, 220, 221, 225, 234, 237, 238, 241, 244, 260, 273,276, 279, 281, 282

post-holo-SRBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 8, 38, 41, 54Pretectal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91, 107Pretectum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87, 105, 160, 183, 184, 236, 238pre-holo-SRBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 8, 55probabilistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64propagation velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118, 133

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Dynamics of Vision 7- 309protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88, 112, 138, 162, 174, 232, 242-244, 264, 276Pulfrich Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160, 198, 211pulvinar . 85, 87, 105, 110-112, 133, 146, 150-153, 161, 163, 173, 179, 180, 183, 193, 194, 197-199, 202, 203, 205,

206, 208, 210, 214, 217, 221, 225, 236-238, 240, 243, 244, 257, 260, 268, 275, 277Pulvinar pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133, 238, 240pyruvate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293, 294, 296, 297quantum-mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55, 64reading . . . . . 1, 11, 42, 85, 88, 128, 139, 149, 152, 179, 180, 193, 194, 197, 199, 200, 203, 206, 221, 225, 227, 235,

242, 243, 246, 250, 259, 263, 264, 268, 269, 271-274, 277-281, 283recruitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133reflex arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 8, 12, 28, 35, 44, 290, 293resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 17, 274, 291, 292, 295retinine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 3, 6, 16-18, 28, 30-38, 49retinitis pigmentosa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39ringing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188saliency map . . . . 102, 105-107, 110-112, 140, 152, 153, 155, 161, 172, 173, 179, 180, 193, 197-199, 202, 206, 208,

211, 212, 214, 216, 217, 242, 248, 249, 257, 259, 269, 273, 274, 277, 281scotoma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233servo loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 182servomechanism . . . . 87, 88, 92, 99, 100, 102, 105, 107, 108, 111-113, 118-120, 123, 131, 132, 137, 138, 148, 172-

177, 180-182, 185-188, 220, 238, 244-249, 252-257, 259, 261, 262, 265, 268, 273signal-to-noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64, 114, 136, 170, 187, 204, 205, 221, 222signal-to-noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114, 136, 204, 205, 221simple neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211sleep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133sphincter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253square law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77SRBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4, 7-9, 14, 17, 21-25, 28, 31, 33, 36-42, 44, 49-51, 53-57, 60stage 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72, 198stage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41, 74, 158, 160, 181, 186, 193, 212, 237, 248, 249, 265, 290stage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152, 160, 170, 183, 185, 186, 237, 290, 292stage 3 . . . . . . . . . . . . . . . . 88, 112, 135-137, 177, 180, 183, 185, 186, 197, 211, 212, 237, 246, 265, 266, 292, 295stage 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 146, 158, 160, 161, 172, 183, 190, 191, 193, 210-212, 232, 234, 237, 279stage 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161, 191, 197, 198, 211, 237, 265stage 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234, 237stellate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185stereopsis . 85, 88, 91, 100, 103, 106, 111, 112, 139, 140, 142-146, 148-150, 153, 154, 156, 157, 161-166, 168-172,

175, 177-179, 183, 193-195, 197-212, 214-218, 220, 222, 226-229, 231-234Stiles-Crawford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 9, 43, 48, 95, 113, 133, 156, 257, 263striatum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234superior colliculus . 87, 92, 95, 100, 102, 103, 105, 111, 112, 132, 133, 151-153, 172, 180, 197, 202, 203, 235, 237,

238, 241-244, 248, 260, 265-268synapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123, 124syncytium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210thalamic reticular nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 105, 111, 149, 152, 161, 173, 198, 205, 206thalamus . . . . . 85, 87, 94, 104, 110, 139, 140, 148, 152, 160, 193, 198, 204, 206, 215, 220, 221, 225, 234, 235, 237,

244threshold . . . . . . . . . . . . . . . . . . . 77, 134, 157, 158, 181, 182, 190, 194, 195, 197, 227, 233, 235, 243, 246, 271, 273tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41, 137, 290topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203, 285topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61, 285torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33, 189, 215transduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 18, 36, 52, 57, 59, 60, 63, 75-78, 80, 81, 233transistor action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12, 116, 189, 190, 233, 280, 283trans- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 7-10, 18, 32, 47, 51-53tremor . . . . 85, 87-89, 95, 96, 99, 104-111, 113-115, 117, 119, 121-123, 129-139, 142, 155-157, 163, 173, 177, 179,

180, 182, 184, 189, 191, 199, 202, 206-208, 212, 214, 215, 217, 221, 222, 226, 227, 232, 248,249, 252, 253, 257, 270, 271, 273, 277, 279, 280

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310 Processes in Animal Visiontri-carboxylic-acid cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294, 295, 297TTR . . . . . . . . . . . . . . . . . . . . . . . . . 2, 3, 7-9, 14, 17, 18, 21-26, 28, 30, 31, 33, 35-42, 44, 49-51, 53, 54, 56, 57, 60type 0 servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87, 123, 131, 173, 273type 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111, 119, 173, 221type 1 servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173type 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119, 186, 253type I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42, 87, 187type III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42type IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42V2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226VEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Verhoeff’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 41, 42vestibular system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95, 131, 132Vieth-Muller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 103, 106, 140-143, 160, 164, 165, 167, 168, 170, 183visual acuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88, 135, 252, 257visual cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85, 94, 150, 210, 212, 220, 226, 234, 237, 238, 291vitamin A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 16vitamin A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 16, 24vitamin A3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10volition mode . . . . . . . . . . . . 92, 94, 102, 105, 111, 112, 127, 131, 137, 172, 175, 180, 202, 235, 237, 238, 241, 242white matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Wikipedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 13, 18xxx . . 4, 25, 49, 52, 55, 74, 79, 101, 104, 110, 130, 132, 137-139, 157, 160, 161, 164, 170, 174, 189, 197, 210, 218,

234, 249, 252, 267X-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 10-12, 26, 32, 33[xxx . . 24, 25, 32, 35, 37, 38, 53, 74, 85, 109, 110, 128, 137, 162, 172-174, 204, 211, 214, 221, 232, 234, 245, 252,

253, 275, 283, 285