ELECTROCHEMISTRY OF THE NEURON17.1.1 Baseline human visual system required to understand this...

PROCESSES INBIOLOGICAL VISION:including, ELECTROCHEMISTRY OFTHE NEURONThis material is excerpted from the full β-version of the text. The final printedversion will be more concise due to further editing and economical constraints. ATable of Contents and an index are located at the end of this paper.

James T. FultonVision Concepts

[email protected]

April 30, 2017 Copyright 2003 James T. Fulton

Performance Descriptors 17- 1

1Released April 30, 2017

2[CIE-- Commission Internationale de l’Eclairage or International Commission on Illumination;responsible for standards in this area. Most well known for the CIE Chromaticity Diagram of 1924 (2degree Standard Observer), the CIE Photopic Observer Curve of 1924 (2 degree Standard Observer) and theCIE Scotopic Observer curve of 1951 (2 degree Standard Observer) The Science of Color says they wereadopted to aid in color measurement (i.e., not for use in color research)

[xxx reconfirm all Section references to or in 17.2.2, etc. ][xxx reword references to constant quantum efficiency ]

17 Performance descriptors of Vision1

Probably more error has crept into the subject of colour vision from inexact description ofexperimental conditions and the nature of the stimuli employed than from any other cause.

Sir John Parsons, 1915

Because of the amount of color artwork in this chapter, it has been necessary to divide it into threeparts for distribution over the INTERNET.

PART 1A: INTRO, LUMINANCE & NEW CHROMATICITY DIAGRAMPART 1B: EXTENSIONS TO THE NEW CHROMATICITY DIAGRAMPART 2: TEMPORAL AND SPATIAL DESCRIPTORS OF VISION

PART 1A: INTRO. LUMINANCE & CHROMINANCEThe press of work on other parts of the manuscript may delay the final cleanup of this PART but itis too valuable to delay its release for comment. Any comments are welcome at [email protected].

17.1 Introduction

This Chapter and Chapter 16 form a pair. While the last Chapter developed equations that are applicable to anyanimal, this Chapter will concentrate on the most highly developed performance descriptors, those applicable to thehuman. The visual system is considerably more capable, more flexible and more complex than reflected in even thescientific literature. To understand the operation of the visual system has required the development of a considerablymore advanced model of the visual system than previously available. This model has defined many of the operatingmodes of the visual system for the first time. It has also indicated that considerably more sophisticatedinstrumentation is required than was used in the past.

Discussions of the shortcomings of the instrumentation and many of the current theories based on inductivereasoning and floating models used in vision research were originally included in the main body of this Chapter. This material has now been moved to Chapter 19. The material stresses the many degrees of freedom that have notbeen adequately controlled in most experiments. It also stresses the inadequacies of the theory of vision adopted bythe C.I.E. based almost entirely on the inductive approach2. This approach did not call for rigorous experiments toverify the theory.

This chapter will concentrate on the descriptors of vision that can be formulated from the electrophysiology of theactual system as presented earlier in this work. While much of this electrophysiology has developed and can beconfirmed using psychophysical experiments, it is extremely difficult to develop precise descriptors based onpsychophysics alone. This is due to the very large number of uncontrolled variables encountered in the experimentsreported in the literature. Section 17.8 of this chapter provides a discussion of this problem. It also provides aninitial experimental framework that can be used to pars the description of an experiment provided by the author of a

2 Processes in Biological Vision

3Goldsmith, T. (1990) Optimization, constraint, and history in the evolution of eyes. Quart. Rev. Biol. vol.65, no. 9, pp 281-322

4Gavrik, V. (2002) Tetrachromacy of human vision: spectral channels and primary colors SPIE Proc vol2241, pp 315-318

5Greenwood, V. (2012) Super human vison Discover Special Issue, Jul/Aug pp 29-31

published paper. More usefully, it can be used to define their future experiments and report their results moreprecisely.

The primary descriptors are; the luminance, chrominance and temporal performance descriptors. A brief discussionof a combined luminance/chrominance descriptor solid will be presented; however, this concept is shown to havelimited utility. The noise limiting and spatial performance descriptors of vision will only be discussed briefly in thisdocument. Stochastic noise plays a remarkably small role in vision. Many of the major descriptors are compatiblewith other members of the animal kingdom format-wise but require different scales.

Using the temporal descriptors with other animals is primarily a matter of incorporating the appropriate timeconstants. The first known theoretical derivation of the waveforms found in the Electroretinogram will be presentedhere. After-images, a primarily temporal effect, are based on the state of adaptation of the various chromaticphotodetection channels, the performance of the vascular system and the background illumination during the afterimage. After images will be discussed in Chapter 18.

To appreciate this Chapter, the reader must recognize the previously poorly documented fact that the humanvisual system is fundamentally tetrachromatic. As shown in Chapter 5, the fundamental photochemistry of allbiological vision is tetrachromatic. Goldsmith has also pointed out that virtually all vertebrate vision istetrachromatic3, at least as some time during the species lifetime. Chapter 11 shows how the signaling architectureof the visual system is designed to exploit this tetrachromatic capability. Less capable visual system appear to haveevolved as an adaptation to a specific habitat. In the case of humans, and other large chordates, ultravioletsensitivity has been lost as a traded-off with physical size. The tetrachromatic capability of the retina of humans iseasily demonstrated in the case of aphakic eyes. The retina in such an eye exhibits the precise tetrachromaticsensitivity function predicted by this theory. As a result of its growth in physical size, the lens of the human eyeexhibits an optical density of 3.5 in the ultraviolet spectrum between 325 and 395 nm. Because of this absorption bythe lens, the human visual system can be considered a degenerate tetrachromatic system. More specifically, it couldbe described as a ultraviolet blocked tetrachromatic system. Less specifically, it could be described as a longwavelength trichromatic system.

The use of the term tetrachromatic in this Chapter does not include the proposed variants on human vision describedby Gavrik4 or similar variants suggested in women due to a genetic mutation5. In both cases, the authors suggest thepresence of a fourth chromophore in the region between the normal M– and L– channel photoreceptors. However,the proposal is based on psychophysical testing and does not include any electro-physical or other physiological.data..

17.1.1 Baseline human visual system required to understand this chapter

17.1.1.1 Historical Background

Beginning in the very early 1900's, significant effort was expended in attempting to characterize the performance ofthe human eye. These efforts can be described in terms of three areas; the luminance response, the chrominance


response, and the temporal response of the eye. Much of the effort was concentrated in the first two areas.

Because of the complexity of the visual system and the lack of a model, debate raged in the vision community withregard to the adequacy of many workers efforts. This led to considerable social difficulty and historically interestingstatements by many leaders and groups of leaders of the day. Several of these positions were incorporated intoofficial documents because of the positions occupied by some of these leaders in the scientific societies.

By the 1950's, the leadership had changed but the official text, The Science of Color, of the Committee onColorimetry of the Optical Society of America, L. A. Jones Chairman, took a number of very defensive positions. As an example, on page 242-243, it stated under the heading

“Data independent of all theories of color vision.Theories of color vision purport to explain the phenomenon in terms of retinal structure andfunction, nerve action, and cerebral projection. Color-mixture data on which are basedcomputations of color specifications are independent of all theories.”

Unfortunately, most of their work is based on a theoretical foundation which employs linearaddition of spectral component data using the human eye as a null detector and mixing illuminantson an energy basis instead of a photon flux basis. These assumptions lead to problems withboth the r-g-b system and the x-y-z system of color description.

A major difficulty in the literature is nomenclature. Nearly all languages have a limited to very limited vocabularyassociated with the parameters of vision. The limitation is a particular problem with regard to color. This has led tomany attempts by scientists to use the same word in many different contexts, usually without specific definition, intheir papers. The result has been considerable confusion. A specific example has arisen in the literature during the1990's with regard to a 2-dimensional representation of a color space represented by hue and saturation and a 3-dimensional color space represented by either lightness (or brightness) and hue and saturation. Whereas the bulk ofthe literature defines color separately from lightness, several authors discussing a 3-dimensional representation, thathas traditionally been called a color solid, have chosen to use a contraction and also call the 3-dimensionalrepresentation a color space. In this way, they implicitly define color as a perceived sensation resulting from avisual excitation that is defined in terms of lightness, hue and saturation,. Whereas the 2-dimensional color space isusually described as containing a few thousand discriminatable colors, the authors calling the 3-dimensional colorrepresentation a color space usually describe it as containing a few million discriminatable colors.

The bottom line is that inadequate theoretical investigation, limited previously by the state of the art in the requisitetechnical disciplines, has resulted in a lack of adequate experimental design discipline. This lack of an adequateframework and adequate experimental discipline has resulted in slower than desired advances in knowledge of theprocesses in vision. The lack of semantic flexibility has also contributed to this problem. The result has beenunnecessary controversy among investigators. The problem exists today.

17.1.1.2 Baseline

The currently available descriptors of the human visual process do not form an adequate foundation for research. They are limited in two major respects. They are not based on a clear set of definitions relating to the illuminationenvironment. They are not based on a detailed understanding of the mechanisms and operation of the visual system.

The human visual system, like that of all higher primates and virtually all mammals operates as described in theearlier chapters. It consists of:

< a multi-channel signaling system, channelized differently in different regions


C the initial part of the system employs two eyes in order to achieve a stereoscopic capability.C each eye contains photoreceptors having four different spectral responses (ultra-violet, short, medium andlong wavelengths) with the ultraviolet photoreceptors ineffectively used in humans because of the thicknessof the lens system.C each spectral set of photoreceptors operate in a output-stabilizing feedback loop of variable gain thatestablishes the color constancy characteristics of the system under photopic conditions.C the higher density of the M-channel photoreceptors in the retina leads to a higher apparent sensitivity ofthis channel prior to the onset of output-stabilization by the feedback loop.C the output of each photoreceptor cells is logarithmically converted from a current driver within its axon toa voltage source at its pedicle.C the spectral outputs of the photoreceptor sets in humans and other mamals are converted into a set of difference signals within the neural circuitry of the retina.C each eye delivers three major signaling channels (brightness, geometric, & chrominance) from the entire retina to the midbrain, particularly the thalamusC The foveola of each eye delivers un formated signals from a group of about 38,000 photoreceptorsdirectly to the perigeniciulate nucleus of the thalamus without any signal encoding.C Two-way signaling paths project to and from the occipital lobe to support auxiliary signal processing.C The thalamus is responsible for both information extraction from the signals provided and signalswitching between portions of the cerebral cortex. This switching involves at least six definable signalingchannels.C The signals delivered to the saliency map of the parietal lobe, for cognition by the frontal lobe, are inabstract form that can not currently be decoded by man.C Within the cerebral cortex, signals are passed back and forth using a star-mesh interconnectionarchitecture.

< A precision optical servo system (POS). Part of this system was previously known as the auxiliary optical system.C This system is used to control the version (pointing) and (con)vergence of the two eyes.C This system integrates sensory signals from the awareness, analytical and alarm modes under the directionof the thalamic reticular nucleus of the thalamus.C This system integrates signals from the vestibular and skeletal nervous systems.C This system prepares both volition and alarm mode commands for transmission to the musculo-skeletaland glandular systems.

< Analytical and awareness operating modes that accept the signals from the brightness channel and differentialsignals from the chrominance signals received via independent subchannels. It processes these signals orthogonallyresulting in the two-dimensional perceptual chromaticity diagram and the three-dimensional color space defined inthis work.

C The resulting perceptual chromaticity diagram and three-dimensional color space are compatible with, andmore precisely define, the Munsell color space.

< An analytical operating mode, with operations centered on the perigeniculate nucleus, and the pulvinar of thethalamus (with support from the POS and the cerebellum) that is responsible for pattern extraction and perceptionleading to cognition.

C This pattern perception capability is the key to the analysis of fine detail and the reading capability ofhumans.

17.1.1.2.1 Regions of the radiometric and illumination environment

Section 2.1.1 discussed the radiation environment of the visual system in general terms, particularly its ability tooperate over a dynamic range of at least 15 orders of magnitude. The available estimates of the transition pointsbetween the distinctly different operating environments has not been quantified to a significant extent. This appearsto be due to the considerable number of parameters and mechanisms involved. There is a problem in differentiating


between the historical, and largely clinical, descriptions of the visual operating regions and the more detailed andresearch oriented regions. It is difficult to define the transition between these regions precisely because eachtransition involves more than one hallmark. This work will adopt a framework similar to that used in the study ofthe medical syndrome of achromatopsia (with the suffix, -psia). This syndrome includes a more specific disease ofachromatopia (with a suffix, -pia) Unfortunately, the analogy will need to be reversed to match the historicalterminology. The clinically defined regions are the hyperopic, photopic, mesopic and scotopic regions.

The definition of the mesopic region is particularly difficult to define precisely because it abuts two other regions ofmajor interest and it involves many observable changes in mechanisms and conditions. These include the physicallyobservable changes in the iris subsystem, the perceptual changes in the color fidelity of the system (including theloss of color rendition entirely), the clinically observable changes in the threshold sensitivity of the system as afunction of wavelength, and the electrophysiological changes in signal characteristics within the system.

For purposes of this work, the mesopic region will be defined as the radiometric region encompassing all of theabove changes (as encountered in the clinical setting). The more narrowly (and precisely) defined mesotopic regionwill be defined as involving only that portion of the radiometric region involving electrophysiologically identifiablechanges in the visual system (See Section 17.2.1.2.2). As an example, the operation of the physiological iris isincluded in the mesopic region but not in the mesotopic region. Unfortunately, these definitions do not definedistinctly separate regions, only distinct mechanisms and thresholds. The illumination levels found in Section 2.1.1and Figure 2.4.3-1 provide only a rough estimate of the transition points between the mesopic and mesotopicregions and the neighboring regions.

17.1.1.2.2 The baseline schematic of the visual system

The only detailed baseline of vision available is the Top Level Schematic of the visual process presented in this workand repeated in the following sections (Section 17.1.1.4).

17.1.1.2.3 The baseline for operations leading to perception and cognition

Very little work has been done in the interpretation of the spatial signal processing of the visual system beyond theexperiments related to bipartite edges and concentric fields. Lacking a comprehensive model, these experimentshave been limited to the exploratory regime. Going beyond these simple configurations into actual patterns hasgenerally resulted in the documentation of interesting special situations but little scientific formalism. This chapterand Chapter 19 will provide many new insights into the interpretation, perception and cognition of external imageswithin the human field of view, with particular emphasis on the foveola.

17.1.1.2.4 Past difficulties in performing experiments

With the availability of the model used in this work, the difficulty of separating the functional capability of thehuman, and animal, eye into discrete and orthogonal characteristics related to luminance, chrominance and temporalcharacteristics can be appreciated. The visual system is based fundamentally on a simple change detector. Itappears that this change detector has been exploited to the maximum in the chordate eye. As exploited, it includes:

+ a single highly elliptical optical system that does not have an axis intersecting the fovea,

+ multiple independent input channels (exhibiting considerable chromatic overlap in their spectral sensitivities),

+ a dispersion and interdigitation of chromatically sensitive photoreceptors over the retina with almost completelyunknown parameters,


+ each input channel is supported by an asymmetric, state-variable based, adaptation amplifier,

+ logarithmic conversion of all photoreceptor cell output signals prior to further signal manipulation,

+ sum and difference amplifiers processing the state variable signals into multiple parallel and orthogonal signalingchannels,

+ multiple signal projection channels with different characteristics,

+ a luminance signal projection channel containing species specific combinations of pre-emphasis andthresholding features,

+ multiple independent asymmetric chrominance/polarization signal projection channels,

+ signal recovery and interpretation circuits in the brain that have been mapped topographically, and to a lesserextent topologically, but have not been analyzed from a signal handling and interpretation perspective.

The presence of so many adjectives, particularly “asymmetric” and “state-variable” in reference to individualmechanisms, in the above paragraph leads to great difficulty. It becomes absolutely mandatory in describing a visualsystem that great care be taken in specifying the conditions under which an experiment is conducted. Lacking thislevel of precision, any individual work is subject to criticism and the correlation of multiple experiments becomesdifficult. It also becomes obvious that using broadband radiation as a test input is usually a sign of poor testprocedure design.

The asymmetries of the visual signal processing circuits account for many of the difficulties in repeating manyexperiments. A change in a parameter must be explicitly reproduced in any corroborating experiment. This meansthe change must begin from the same initial level, probably to better than +/-10%, and proceed in the same direction.

The state-variable aspect of many parameters requires that the initial and any corroborating experiments must beprepared to discuss the condition of the system for a period of at least three time constants longer than the relevanttime constants. This interval is usually over 30 minutes.

The above conditions imposed by the asymmetries and state-variables account for the few repeatable experiments, toeven +/-20%, in the literature other than those related to a fully dark adapted eye. Generally, to achieve even +/-20%, the irradiation must refer to the retina, or the external aperture and a fixed artificial iris. This latter situation isthe foundation for the use of Trolands as a unit of measure. The Troland does not apply to the actual illumination onthe retina. The Troland is defined for the on-axis (thin lens) model of the eye. It does not account for the greatvariation in effective pupil size of the eye for the off-axis condition (Section 17.1.1.2.4).

The logarithmic processing of all signals emanating from the photoreceptor cells makes it absolutely necessary tospecify whether the changes in irradiance being applied to the eye are of the large signal, typically greater than 2:1,or small signal type. For a symmetrical change about an average value, the 2:1 factor is represented by a modulationof about +/- 33% of the mean.

In human, no substantial literature exists describing any pre-emphasis type signal processing within the eye. Thepredominant performance limitations at low levels are related to noise thresholds. At low flux levels, quantumprocesses are inherently noisy. There is a standard deviation associated with the mean intrinsic flux. At higher fluxlevels, the discrimination capability of the eye is controlled by the noise performance of the signal recovery circuits


6Kelly, D. (1979) Motion and Vision. I. Stabilized images of stationary gratings. J. Opt. Soc. Am. vol. 69,pp 1266-1273

at the termination of the signal projection circuits in the brain. Both minimum perceptible luminance and minimumchrominance changes are based on the signal to noise ratio at the output of the terminal neuron of the signalprojection system.

In the chrominance channels of human, there is an additional complication due to the form of encoding used in theprojection system. The hue and saturation in each channel are not independent. Furthermore, a single noisecomponent impacts them both. As the saturation of a chromatic input is reduced, it becomes more difficult todiscriminate in either (or both) hue and saturation.

To aid in the development of the various performance descriptors of vision, approximately eight distinct definitionsof the basic term color will be employed. Because of the paucity of synonyms in colloquial English for color, usewill be made of precisely defined two-word expressions closely aligned to the situation being discussed.

This Chapter will present the performance descriptors of the eye using a format consistent with the historicalliterature. It will discuss the luminous, chrominance, temporal, and spatial descriptors of the visual systemseparately. This is the only rational way to avoid serious intanglements. However, the interdependence of many ofthese parameters cannot be avoided. With these individual groups of descriptors presented, it is then possible todiscuss more complex phenomena resulting from interactions between or second order effects of the processes usedto support vision.

A fundamental separation will be maintained between the characteristics of perceived color, represented by hue andsaturation, and the characteristics of perceived brightness. Justification for this choice is based on the nearlycomplete independence of the signaling paths related to these perceived characteristics in the visual system. As aresult of this decision, color will be discussed in the context of a 2-dimensional color space that is planar andrectilinear. Brightness will be discussed in terms of a 1-dimensional intensity space that is linear. Later, a 3-dimensional sensation space will be developed that is fundamentally different from any 3-dimensional space in thecurrent literature related to vision. It will be shown how this space relates to, and includes, similar 3- dimensionalrepresentations of the perception of vision. This new space will be formally called a sensation space and informallycalled a color solid. When combined with other visual and non-visual sensory data, it will be referred to as asaliency space.

The discussion will make it perfectly clear that it is not appropriate to speak of the sensation space of vision in termsof a spherical coordinate system or to speak of specific differential volumes within this space as representing a“color.” The more appropriate volume is a cylinder that will describe a perceived sensation represented by abrightness and a color. This notation is conceptually compatible with the more comprehensive vector notation usedin the cortex. It is also compatible with the potentially infinite extent of the luminous intensity of the scene andsimultaneously with the finite extent of the 2-dimensional color space.

It will become clear that the same signaling channel is involved in the perception of both the temporal and spatialfrequency aspects of a scene. In addition, the impact of tremor is significant in this complex arena when highprecision is sought. In agreement with this work, Kelly has shown that the performance of the system in spatialfrequency space can be defined as the same as the performance in temporal space times a conversion constant withunits of angular velocity6. This conversion can be accomplished by introducing an external motion or by relyingupon the normal tremor of the eyes.

17.1.1.2.4 Separation of the CIE functions from the threshold functions of this work


7Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation J. Opt Soc Amvol. 43, no. 6, pp 485– , fig 3

Because of the many conceptual problems with the definition of the CIE luminous efficiency functions, V(λ), thiswork will define a separate pair of luminance and chrominance threshold functions, T(λ, F) and C(λ,F) respectively. These descriptors are defined as functions of both wavelength and stimulus intensity when using a 7053 nm blackbody source as shown. At this color temperature, the photon flux density is nominally uniform with respect towavelength across the visual spectrum at a specific intensity, F. Specified in their individual test protocols are boththe spectral width of the sampling mechanism and the angular diameter of the stimulus. The spectral width shall benot greater than 10 nm. The stimulus diameters are specified as two degrees for a quasi photopic descriptor, Twithout an accent mark, and ten degrees for a quasi scotopic descriptor, T’. Other subscripted versions of thesedescriptors can be calculated for other conditions. Of particular interest would be a 0.6 degree field for defining thedifference in chromaticity threshold with spatial field due to the finite diameter of the foveola (See Figure 17.3.2-8,color shift with field size). Over a considerable range of stimulus, known as the photopic region, the two degreeluminosity threshold function will be relatively constant as a function of stimulus intensity. By spectrallysmoothing the luminance threshold function within this range, a numerical equivalent to the CIE photopic luminousefficiency function, V(λ), can be obtained. Achieving an equivalent to the CIE scotopic luminous efficiencyfunction is also possible. However, the luminance threshold function changes significantly as a function of stimulusintensity in the mesopic region. This variation is confirmed in the data of Hurvich & Jameson7.

The shape of C(λ,F) is considerably different from T(λ, F) as will be shown below.

17.1.1.3 Goal

The development of meaningful descriptors of the overall performance of a visual system is difficult because of thephysical complexity associated with the situation described above. It is made more difficult by the inability of thehuman to discriminate clearly and distinctly between changes in luminance and chrominance. This Chapter isdesigned to present a set of descriptors that are as clearly defined as possible. Human frailty being what it is, it maybe necessary for the reader to rely on the discussion accompanying a given descriptor as well as the explicitannotations. The following paragraphs can not be made to stand completely independently because of the abovediscussion. They are therefore presented in an arbitrary order, are primarily based on work in previous Chapters butmay sometimes rely on references that are forward looking.

The individual spectral absorption characteristics of the four chromophores of vision have been presented in earlierChapters. They will not be repeated here.

The fact that the luminance and chrominance signaling channels of vision are orthogonal to each other have thwartedthe development of a meaningful “three dimensional color space.” Section 17.4 will address this subject.

The effects of aging on the visual system are primarily in two areas. The hardening of the lens which makes themuscles associated with accommodation less effective with age is the most obvious. The increased attenuation in theshort wavelength portion of the spectrum due to increased Rayleigh scattering in the physiological optics is thesecond area. The accommodation problem will not be explored in this Chapter. Comments on the increasescattering will be addressed briefly.

17.1.1.4 Perspective

The sequence in which the above mechanisms are invoked in the visual system can be seen with the aid of the TopLevel Schematic shown in Figure 17.1.1-2 as applied to human. The primary modifications to the global Top Level


Figure 17.1.1-2 Top level schematic of the visual system of Chordata. See text for details.

Schematic are few. The secondary (nictating) eyelid marked (E) is omitted. The lens marked (B) shows a highlyasymmetric absorption spectrum that greatly attenuates the ultraviolet light reaching the photoreceptor cells labeled(UV). While this filtering leaves the photoreceptors (and probably one of the chrominance signaling paths), non-functional with regard to signaling, they remain functional at the circuit level. This circuit level functionality can bedemonstrated in aphakic eyes (eyes with the lens malformed or removed through surgery).

All of the other elements in the figure are important to the functioning of the visual system in human. In this figure,the first lateral processing matrix is primarily associated with forming the chrominance channels of human vision. The second lateral processing matrix is associated with forming any spatial processing channels, appearancechannels, within the retina of human vision. It appears that this function is rudimentary in humans.

17.1.1.4.1 Closed loop feedback in the motor-neural circuits of vision

There are three main closed loop feedback circuits in the human visual system ( HVS). The first is that associatedwith the analysis and perception of fine detail by the circuits related to the foveola. This figure shows the distinctdifference in signaling paths associated with the foveola, the very central portion of the fovea, and the remainder ofthe retina. The signals from the photoreceptors of the foveola are believed to connect directly to the Pretectum, aportion of or closely related to the Superior Colliculus. These signals are used in the exquisite analytical function ofthe brain that is associated with the foveola. They are believed to control the small saccadic movements of the eyevia the eye muscles ((C) that are first seen in the work of Yarbus. This control of the position of the eye based onthe data collected by the foveola of the retina is the most important example of closed loop feedback in the visualprocess. It is a major function of the so-called Auxiliary Optical System (OSA).The signals originating from outsidethe foveola are transmitted to the magnocellular portion of the brain.

The second most important example of closed loop feedback involves control of the aperture/iris (A) of the eye. How the signals from the retina are extracted and sent to the Superior Colliculus for this purpose is unknown.

The third and equally important closed loop operation is that of the eyelid (D). It appears to be under neural control


but not to rely heavily on simple signals from the retina. This loop is controlled by a more complex signalprocessing block within the cortex. The eyelid appears to be controlled as a result of a complex computationinvolving both simple brightness information, perceived threat to the animal and housekeeping functions related tothe maintenance of the surface of the cornea. The command to close the eyelid is also closely coordinated with thecommands to redirect the point of fixation of the eye. Through this coordination, the short term memory of thevisual system is not corrupted by information collected by the retina during the large saccadic motions.

17.1.1.4.2 Other feedback within the signal processing circuits of vision

It should be noted that the diagram does not show any closed loop (external) feedback among the signaling circuitsof the retina or the projection neurons connecting to the cortex of the brain. The analyses presented in this workhave not uncovered any external feedback within the vision system outside of the cortex. The term external is usedto differentiate feedback involving a distinct signal path antidromic to the normal signal paths from the internal, andorthodromic, negative feedback found within individual signal processing and signal projection neurons. Suchfeedback is normally associated with an impedance in the poditic signal lead of an Activa within a neuron. Thisinternal and orthodromic feedback is key to the operation of all signal inverting neurons and all encoding neurons ofthe projection system.

A similar orthodromic feedback mechanism is also associated with the support of the signal processing system bythe vascular system of the eye. There are two main contributions, one global and one photoreceptor specific. First,the vascular bed of the retina provides a common impedance associated with the collector supply terminals of all ofthe photoreceptors in a specific region of the retina. This common impedance tends to stabilize the operating pointof all of the photoreceptors in that region. A more photoreceptor cell specific impedance is also associated with thevascular system. This impedance effectively controls the gain characteristic of the adaptation amplifier within thephotoreceptor cell. It is critical to the adaptation of the eye to various conditions of irradiation.

17.1.1.4.3 Application of various mechanisms

The mechanisms outlined above do not all operate in synchronism. Nor do they operate in sequence. There isconsiderable overlap in their operation. Some of these idiosyncracies of the visual system in human can beillustrated by Figure 17.1.1-3. The horizontal scale is logarithmic and has been given in a variety of units asindicated in Chapter 2. The vertical scale is linear and represents the brightness attribute of vision. The curveddotted line represents the instantaneous transfer function between the illuminance of the scene and the perceivedbrightness of that scene. This curve can slide horizontally as a function of the adaptation process. This process isdesigned to keep the dynamic range of the brightness channel matched to the dynamic range of the informationcontent associated with the scene.

The maximum value of the brightness attribute within the signal processing circuits (the bipolar and lateral cells) isapproximately +130 mV relative to the nominal –154 mV membrane potential of the neuron at cutoff. Thus, thismaximum voltage corresponds to approximately -20 mV. relative to the inter-neural matrix. This level correspondsto saturation in the output signal of the photoreceptor cells (corresponding again to about –20 mV. relative to theINM). The four principle regions of visual operation are shown above the figure and are defined in the followingglossary.


8Hurvich, L. (1997) Essays concerning color constancy. Chap 7 In Readings on Color; vol. 2: The Scienceof Color, Byrne, A. & Hilbert, D. ed. Cambridge, MA: The MIT Press. pp 177-198

Figure 17.1.1-3 An overall descriptor of the illuminationrange of the eye. Luminance values as measured with aconventional photometer. Color temperature of source(integrated sky) was not documented..

The central rectangle of this figure illustrates theremarkably wide stable region of operation for thehuman visual system (HVS). It covers nearly 5orders of magnitude of illumination. Within thisregion, all of the signal processing circuitry operatesin a “constant amplitude” regime, insuring stabilityin all of the luminance and chrominance channels. This constancy of amplitude accounts for theremarkable stability in the perception of both colorand luminance contrasts over this region. Thisregion of stable operation is due primarily to theadaptation amplifiers of the photoreceptor cellsaugmented by the operation of the aperture control,the iris. It should be noted that the dynamic rangeassociated with the iris is only a factor of 16:1 in thenominal eye. The dynamic range of the adaptationamplifier is a much greater, 3500:1.

Above and below the region described by the rectangle, the eye continues to perform in a more limited mode. In thenext higher illumination region, the hypertopic region, the performance is degraded by the saturation initially in theM-channel due to the adaptation amplifier gain falling to a constant value of one. This causes saturation in the M-channel input to the luminance and chrominance channels, probably due to cutoff in the distribution amplifier of thephotoreceptor cells. The result is an initial perceived shift in scene color toward the yellow, related to the Qchrominance channel, followed by a shift toward the magenta as the P chrominance channel is also affected by thesaturation. As illumination levels, and hence signal levels, increase further, a region of considerable perceived painis encountered. In this region all of the distribution amplifiers of the photoreceptor cells, at least in the fovea, go intocutoff.

At illumination levels below the photopic region, there are two distinct regions of operation, the well known scotopicregion and the lesser appreciated mesotopic region. The mesotopic region is characterized by two phenomena. Theadaptation amplifiers are now operating at full amplification and the iris is open to maximum. The underlyingsquare law characteristic of the photodetection process in the L-channel now introduces a more rapid loss of signallevel in this channel relative to the other photodetection channels. This loss also exhibits two specific phenomena. First, the overall spectral absorption characteristic perceived by the system is gradually degraded to that associatedwith scotopic vision. Second, the characteristic report of the scene changing to a bluish green caste just before lossof all color perception is common. As the response of the L-channel becomes insignificant relative to the other twochannels, the region of scotopic vision is reached. In this region, the signal to noise ratio in the chrominancechannels has become so low that there is no reliable perception of color even though there may be significantperception of shape information via the luminance channel. As the illumination continues to fall, even the signal tonoise ratio in the channel labeled “luminance” becomes so low that perception of shape is also lost although somerudimentary detection of differences in brightness may be perceived. This is the area where detection of signals bythe brain frequently leads to inaccurate perceptions of dangers.

Hurvich noted the above phenomena with respect to the mesotopic and scotopic regions but did not appreciate theimpact of the adaptation amplifiers in limiting the rate of rise of the signal associated with the L-channel within thephotopic region8. His analysis was in terms of Opponent (Hering) Theory.


9Burns, S. & Elsner, A. (1985) Color matching at high illuminances: the color-match-area effect andphotopigment bleaching J Opt Soc Am A vol 2(5), pp 698-70410Burns. S. & Elsner. A. (1993) Color matching at high illuminances: photopigment optical density andpupil entry J Opt Soc Am A vol 10(2 ), pp 221-230

At illumination levels above the photopic region, the hypertopic region is encountered. It is defined primarily by thefact that color constancy is not maintained in this region due to saturation in the signal at the output of the sensoryneurons. Burns & Elsner have provided the clearest demarcation between the photopic and hypertopic regions9,10. Figure 1 of the first paper shows the distinct loss in color fidelity beginning at 10,000 Trolands for any test field sizefrom one to eight degrees.


11Distl, R. (2000) Measure what you see. Photonics Spectra, May, pp. 176-18012Jones, L. (1937) Colorimetry: Preliminary draft of a report on nomenclature and definitions J. Opt. Soc.Am. vol. 27, pp 207-213

17.1.2 Terminology

17.1.2.1 Photometric units are archaic in research

The visual science community has traditionally used photometric units. Unfortunately, these units were designedoriginally for application engineering purposes in society. They are grossly inadequate for research purposes. More specifically, the commercial instrumentation available does not emulate an actual visual system. They arefrequently photoconductive based and record energy, not photon flux. They do not report in units of photon fluxdensity and still would not recognize the unique parameters related to the luminance channel if they did. Distl11 hasdocumented the deviation between the typical photometer and the C.I.E. (1924) luminous efficiency function. Thedeviations are large in both the blue and the red. At the current time, the instruments are not available with auxiliaryfilters to match the spectral absorption of the individual chromophoric absorbers. With the slightest degree ofchromatic adaptation of a test subject, the instrumentation becomes grossly inappropriate for research.

A similar situation exists with respect to illumination sources. The use of various low temperature quasi-blackbodysources for research purposes is quaint and archaic. As noted earlier, even the C.I.E has failed to define a source forthe defined Illuminant C. Illuminant C is very deficient in the short wavelength spectrum. Any illuminant with ablack body temperature of less than 7053° Kelvin is deficient in the short wavelength spectrum and should not beused for research without careful notation of that fact.

The practice of recording the intensity of a source using a photometer and then passing the light through a filter,(defined at best by a catalog number) before being applied to the retina of a subject leaves the researcher with themonumental task of determining what the effect of that irradiance was on the performance of the eye of that subject.

Although seldom noted, use of a sodium glass envelope for a light source also restricts the short wavelengthradiation from that source. Only quartz envelope sources should be used in research involving the short wavelengthregion of vision.

In summary, serious research requires more serious attention to the source of radiation applied to a visual system andthe intensity recording instrumentation. A source with a very controlled blackbody temperature, not merely arecording of the current through a filament, is required. The spectral adequacy of the source should be confirmedthrough calibration. Similarly, any filters used should be calibrated. The intensity recording instrumentation shouldbe photoemissive in character in order to record photon flux and should employ filters matched to the actualchromophores of vision. By using a three channel device with appropriate signal summation, an instrument can beobtained that closely matches the performance of the human eye under any state of adaptation.

The community has long suffered problems of maintaining technical specificity in the presence of semanticconvenience. The suffixes of terms are frequently changed to make sentences appear more grammatically correct. Itis important that precise terms be used in research. Jones has provided the most lucid discussion of the agreed termsto be used in photometry12. Although dated, it is still largely relevant.

The international standards community is progressing. In 1979, they defined a new Candela that is independent ofthe CIE luminous efficiency function. See Section 17.1.3 or the Glossary. However, the NBS program in opticalradiometry continues to be based on energy detection, not photon detection. However, their detector of choice isnow a “high quality silicon photodiode.” These are photoelectric (quantum) detectors that exhibit an output current


13Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 100-105

proportional to the input wattage. However, the current output is a function of wavelength. It decreases at shorterwavelength because there are fewer photons in one watt. These photodiodes are quantum detectors just like the eye.

17.1.2.1.1 Limitation on the Troland, an archaic unit of photometry

During the 1960's, the Troland was defined as the equivalent of the earlier term Photon in honor of Dr. L. T. Trolandwho had been an early experimenter in the field of photometry. The term is used to define the irradiance, inphotometric units, at the pupil of the eye prior to any absorption by the tissue of the eye. Although it is frequentlyused to describe the retinal illuminance, this is misleading. The actual irradiance of the retina is a function of thespectral absorption and scattering of the tissue prior to the photoreceptors and the focal length of the eye. It is also afunction of the F/# of the optical system of the eye. The focal length is a function of field angle relative to theoptical axis. The effective pupil size is also highly dependent on field angle. The actual irradiance is therefore astrong function of retinal position. Wyszecki & Stiles13 discuss this situation in some detail and recommend use ofthe expression “Troland value” as opposed to “retinal illuminance” to describe the illumination at the pupil. Theactual retinal illuminance is considerably less than 10% of the Troland value. Just the difference in the index ofrefraction between air and the vitreal fluid introduces a factor of 1.76:1 between the pupil irradiance and the retinalirradiance. Following contemporary practice, Wyszecki & Stiles differentiated between photopic and scotopicTroland values, reflecting the different luminosity functions of the eye in these two regimes. They did not recognizethe fact that the luminous efficiency function varies continuously throughout the mesotopic region. As a result,either Troland misrepresents the excitation applied to the eye in the mesotopic region.

Although not defined explicitly in the definition of the Troland, the value of the parameter is a function of thespectral intensity, or color temperature, of the source. For the basic definition, based on the Candela, the assumedcolor temperature is only 2042 Kelvin (confirmed in W & S (1982, pg 253) by the Conference Generale des Poids etMesures (CGPM) in 1967). A large correction factor must be introduced for other color temperatures (2.464:1 forD65) based on energy rather than flux. The correction factors calculated by Wyszecki & Stiles ignore any variationin luminous efficiency associated with the mesotopic region.

The Troland value is only equal to the product of the luminance of the source times the aperture (real or artificial) ofthe eye along the optical axis of the eye. Even for the point of fixation, a minor correction is required (althoughgenerally ignored) in this value. When discussing off-axis conditions, both the effective pupil size and the thick-lensmodel of the eye must be used in Troland related investigations.

17.1.2.1.2 Available commercial photometers lack precision

Commercial photometers have traditionally been simple radiometers modified to include a fixed filter. Thecombination of the filter and the spectral response of the photodetector were matched to provide an overall spectralresponse matching as close as practical the smoothed C.I.E. luminous efficiency function. Sometimes thephotodetectors were photoconductive (energy sensitive) units. Sometimes they were photoelectric units. In recenttimes, dual range units have become available that also provide a filter combination matching the smoothed C.I.E.scotopic luminous efficiency function. Such units suffer from the archaic nature of the C.I.E. standards and can onlyemulate the performance of the eye that is not chromatically adapted and is not operating in the mesopic or lowerphotopic regions. To emulate the visual system in these regions, a more sophisticated instrument would be required. This instrument would sense the individual spectral ranges of each photoreceptor channel, introduce a squareingmechanism in the long wavelength channel and sum the resultant signals logarithmically in accordance with theluminance equation.


14Sziklai, G. (1951) A tristimulus photometer J. Opt. Soc. Am. vol. 41, no. 5, pp 321-32315Crone, R. (1999) A History of color. Boston, MA: Kluwer Academic Publishers, pg. 24716Fehrman, K. & Fehrman, C. (2000) Color; the secret influence. Upper Saddle River, NJ: Prentice-Hall,pp. 1-217Goldsmith, T. (1994) Ultraviolet receptors and color vision: Evolutionary implications and a dissonance ofparadigms. Vision Res. vol. 34, no. 11, pp 1479-1487

An early design of a typical multichannel photometer was described by Sziklai14. He accepts the imaginary aspectsof the CIE tristimulus functions and compensates for the artificial hump in the x-bar channel. He was apparentlyunaware of the square-law nature of the L–channel. Thus, his design is more properly labeled a tristimulusphotometer for the photopic region only. Thornton has more recently defined a similar photopic regime only multi-band photometer.

17.1.2.1.3 Precision requires photon-flux based radiometric units

Although photometric units have been used throughout the exploratory phase of vision research, the precisionrequired in future precision research demands the use of more precise spectroradiometric units. This will bedemonstrated throughout the remainder of this chapter. The photometric system of units is only adequate for thedesign of general lighting and photographic systems. The majority of the instruments sold as photometers are singlechannel devices that measure an integrated response over a given spectral region weighted to match the CIEphotopic luminosity function by a transmissive filter. In some cases, the filter can be changed to emulate a scotopicluminosity function. However, the luminosity function varies continuously in the transition from the photopic toscotopic region. Most of these units employ energy sensitive rather than photon-flux sensitive detectors. Theseweight the spectral content of the sensed image improperly and are not capable of emulating the HVS. Moreseriously, these units are not able to emulate the adaptation characteristics of the visual system or the logarithmicsignal summation mechanism employed in vision. These are serious handicaps when performing research.

By using a modern spectroradiometer with computer interface, the researcher can enter the actual spectral absorptionof the individual chromophores and logarithmically calculate the actual luminosity function of the visual system forany illumination level.

17.1.2.2 The precise definition of “color”

Defining color with precision has been a problem for centuries15. Fehrman & Fehrman even go so far as to definecolor as an illusion16. However, as any magician will tell you, something is an illusion only to those that do notunderstand the trick. Relying on logic and their assertion that color is an illusion, Fehrman & Fehrman continue anddefine color as an intangible, “a vast interactive process.” This section will show that color is not an illusion, is notintangible and is not interactive with the sensor. It is a rigorously defined phenomena. If as they state, the colorexperience only exists within the observer’s brain, it would be impossible for a television system to create thecommon A-scope and C-scope presentations. These presentations are created at the studio using non-color cathoderay tubes, to monitor the quality of the “color” sensed by the electronic circuitry. It would also be a waste of timefor the (currently very large) robotics community to attempt to create robotic eyes.

It is also necessary to address some recent comments by Goldsmith17. He attempts to separate the perception ofcolor by certain animals from the wavelength dependent behaviors of other animals. Naturally, being homocentric,he initially limits the perception of color to humans. He then broadens this capability to other primates and thenbroadens it further to include his life long subjects, bees. This distinction is not supported here. It can be shown thatthe same differential chromatic signals are transmitted to the brains of any number of animals crossing all phylogeniclines. Whether one wishes to say one animal appreciates the color of an object more than another is probably


permissible. However, all animals use these signals to make wavelength dependent behavioral decisions. Ipersonally do not eat Rhubarb because of the color. I know it is virtually identical to celery. So what! Whether thisis behavioral or intellectual will be left to the reader.

A specific solution to the definition of color and individual colors will be presented in Section 17.3.4.

17.1.2.2.1 Expanding the definition of colorimetry

Colorimetry has been defined by Wyszecki & Stiles (p. 117) as “The branch of color science concerned in the firstinstance, with specifying numerically the color of a physically defined visual stimulus.” They then continued byappending to the definition a series of conditions allowing the human eye to be used as a null detector in colorimetryexperiments. In essence, the conditions required an illumination level in the photopic regime (in order to insurecolor constancy) and a numerical framework that uses continuous functions. To complete the framework, Wyszecki& Stiles invoke what is generally described as the trichromatic generalization:

“Over a wide range of conditions of observation, many color stimuli can be matched in color completely byadditive mixtures of three fixed primary stimuli whose radiant powers have been suitably adjusted. Othercolor stimuli have to be mixed with one of the primary stimuli before a complete color match with a mixtureof the other two primary stimuli can be obtained.”

Within the above framework, many simple concepts, such as Grassman’s Laws have been adopted without detailedjustification. However, the above context does not allow for any variation in the performance of the visual systemwith retinal position, or under non-photopic conditions, or under transient conditions. Under these conditions, abroader framework is required.

To provide a broader framework, it is useful to define that part of colorimetry defined within the laws of linearity as object-space colorimetry. Within this framework, the visual system is used as a null detector in steady-statelaboratory measurements. Flicker experiments and experiments using a rotating wheel are not included in the fieldof object-space colorimetry. Most commercially available instrumentation is limited to this operating regime. Thebroader framework encompassing all visual conditions can then be defined as perceptual colorimetry. The intensitynonlinearity, spatial irregularity, and transient performance of the visual system are accommodated within thisregime. Most commercial instrumentation designed for photometry and colorimetry is inadequate in this extendedcolorimetric framework.

17.1.2.3 Metameres, initial conceptual definitions

A major problem in previous discussions of color has been the problem of metamerism. Many sources in objectspace with different spectral distributions can appear chromatically identical to the human eye. These scenes arecalled metameres.

Wyszecki & Stiles introduce metameres in their chapter 3 at primarily a conceptual level. The material quicklydegenerates into requiring an “imaginary color stimulus” because of their underlying trichromatic generalization (pg117). They provide two definitions of metamers on page 184;

Metamere color stimuli are color stimuli with the same tristimulus values but different spectral radian powerdistributions.

An equivalent definition states that metameric color stimuli are color stimuli that have different spectral


18Thornton, W. (1992) Toward a more accurate and extensible colorimetry. Part 1. Introduction Color ResAppl vol 17(2), pp 79-12219Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. John Wiley & Sons pp 183-221

radiant power distribution but match in color for a given observer.

These definitions require the control of many parameters that are not described further here. These parameters arediscussed more fully in Section 17.3.4.3.1. Two additional definitions are important in discussing metameres, that of metameres of course and also of color.

Color– (a. k. a. perceived color) that aspect of visual perception by which an observer may distinguish differencesbetween two structure-free fields of view of the same size and shape, such as may be caused by differences in thespectral composition of the radiant energy concerned in the observations (W & S, p. 487).

The above can be considered the formal definition of color. It is based on perception. An alternate definition isfrequently useful that describes the color of a structure-free field of view in object space that generates the aboveperception. This definition of color is frequently described as psychophysical color.

Psychophysical color– that aspect of a structure-free field of view in object space specified by the tristimulus valuesof the radiant power (color stimulus) entering the eye.

Both of the above definitions of color play a role in current colorimetry. However, it will be shown below that it isonly the definition based on perception that is precise. Many pairs of psychophysical metameres do not in factappear to be metameres to the human eye. The differences are frequently significant.

Metameres have traditionally been defined in the psychophysical context and is the only context discussed in thecolorimetry chapter of Wyszecki & Stiles. However, the fact that two different structure-free fields of view withdifferent tristimulus values frequently appear to be perceptual metameres is troubling18. As a result, this workdifferentiates between the two definitions of Wyszecki & Stiles that they considered equivalent.

Metameres– (a. k. a. perceptual metameres) color stimuli that have different spectral radiant power distributions butare perceived as identical for a given observer.

Psychophysical metameres– color stimuli that have the same tristimulus values but different spectral radiant powerdistributions.

Wyszecki & Stiles explored the subject of psychophysical metameres in great detail (38 pages)19. Whereas the datathey summarized is useful, the mathematical analyses are less useful. They attempted to explain the phenomenausing the CIE concepts of color space and tristimulus values (based on linearity and additive color). The result is adefinition of metameric color stimuli unrelated to biological vision. This definition required that two metameresmust exhibit equality in three equations, one related to the tristimulus value r-bar, one related to g-bar and one for b-bar. Thornton has shown that colors defined in this way are not in fact perceptual metameres (Section 17.2.8).

Adopting the actual model of biological color vision, the situation is simpler and more precise. Instead of using thetristimulus values of an imaginary “Standard Observer,” the actual absorption characteristic of each chromophore ofbiological vision is used. Omitting any discussion of the O-channel in human vision, three equations are required todemonstrate a complete metameric match between two color stimuli. However, they are not the three equationsfound in psychophysical colorimetry. Equation One equates the P-channel values for the two metameres. EquationTwo equates the Q-channel value for the two metameres. Equation Three equates the R-channel values for the two


metameres. These equations allow for a much larger set of metameres and a much more precise match than does thetristimulus formulation. This range of matches can be subdivided into three distinct classes, the first requiring aprecise match in each of the P, Q & R values of the color stimuli, the second requiring a complete match of twoensembles of P, Q & R values and the third requiring a chromatic match of only the individual P and Q values.

While precise metameric matches can be calculated, it is not possible to confirm the uniqueness of such precisematches perceptually at this time. As far as is known, the brain only asserts a complete match based on thesomewhat more tolerant ensemble values of P, Q & R. Figure 17.1.2-1 shows the experimental environmentassociated with chromatic and complete metameric matches. The simpler chromatic match shown in frame (A),typically uses the light reflected by two color samples from a single source of illumination. Because of the interplayof the radiation spectra of the source and the reflectance spectra of the samples, such chromatic matches are afunction of the source characteristics. Besides the spectral distribution of the samples in chromatic matches, thematch also depends on the average reflectance of the samples used. As a result, the chromatic match equating the Pand the Q values may not result in equal R values. Experiments are currently under way to resolve the differences inaverage reflectance between the currently distributed Munsell Color Atlas and the recently developed comparableJapanese atlas. Frame (B) shows the test configuration for achieving a complete metameric match. By using twoseparate illumination sources of variable intensity, a match may be obtained that equates the individual P, Q & R values. When obtained, the match is based on the radiant spectral characteristics of the sources and theaverage reflectance of the samples as well as the reflectance spectra of the samples.

The functions shown in the lower set of frames suggest the parameters that can vary and that must be controlled inthese two types of experiments. If two sources are employed, both their intensities and radiant spectra must becontrolled or known. The reflectance of the two samples can be significantly different. Scattered light must beminimized for accurate comparisons. The absorption spectra of the actual photoreceptors must be used, and notsome arbitrarily transformed set of spectra. While the resulting signal levels at the axons of the spectrally diversephotoreceptors may be of interest, it is the signals resulting from signal processing within the neural section of the

Figure 17.1.2-1 Test configuration for metameric matching. A; configuration for making chromatic matches using asingle common light source. B; configuration for making complete matches using independent light sources. Lowerrow; set of relevant performance parameters. See text.


retina that are critical to the metameric experiment. It is these signals that are evaluated by the brain in determininga match.

Several second order caveats apply to performing successful metameric matches. Because of the change in thespectral sensitivity of the visual system with intensity of the color stimuli, the experiments should be carried outwithin the photopic regime, and more precisely the regime of color constancy. To avoid inaccurate results, it is alsonecessary to carefully define the test protocol used. The most successful tests require a bipartite field with the matchdetermined by concentrating the point of fixation of vision on the midpoint of the bisecting line of the bipartite field. To avoid introducing ambiguities due to Maxwell’s Spot (Section 17.3.1.7.2), it is advisable that the bipartite fieldhave a diameter of less than 1.2 degrees, or much larger than three degrees. Large fields of ten degrees arecommonly used. The area surrounding the test samples will affect the state of adaptation, and therefore the colorconstancy, of the eyes of the evaluator. This area is best made a neutral color not significantly different inilluminance from that of the samples. The details related to matching experiments are described in greater detail inSection 17.1.9.1 and more fully discussed in Section 17.3.1.3.1.

The task of integrating the spectral distribution of a broadband source to establish a P– or Q– value requiresdetermining what the appropriate wavelengths delimiting the range of integration are. This subject needs additionalstudy as of 2016.

17.1.2.4 The “expanded exponential sinusoid” SCREWED UP ART

The fact that the simple exponential curve does not represent either of the two commonly studied branches of thedark adaptation characteristic has been recognized for a long time. The reason is simple. The underlying processesare not described by an exponential equation and the expression of these underlying processes is not through a linearrelationship. The underlying process is a higher order physical one describable by a nominally second order(sometimes third) differential equation. The solution of such an equation can take three forms depending on thedamping factor in the equation. The most common form is the product of an exponential term and a sinusoidal term. It is frequently labeled an exponential sinusoid. This solution specifies the voltage on the collector of an amplifiercircuit in the absence of coupling to other amplifiers via the vascular supply. The variation in this voltagesignificantly impacts the gain of this amplifier. This variation is normally expressed in the form of:

“The Expanded Exponential Sinusoid” Eq. 17.1.1-a

For appropriate values, such an expression still looks similar to an exponential sinusoid but clearly is not. It appearsstretched in amplitude because of both the exponent and the difference in the denominator.. Therefore, it will belabeled a “expanded exponential sinusoid” for semantic convenience.

If the coupling between amplifiers via the vascular system is assumed, the solution takes a different form that allowsthe amplitude of the sinusoid term to vary independently of the amplitude of the expnential. This solution can bewritten as:

“Alternate Expanded Expon.Sinusoid” Eq. 17.1.1-b

[ ]y

e A xx n=− ⋅ + ⋅

1

1 1( sin( )ω


In this form, the waveform may or may not exhibit a shoulder depending on the magnitude of the couplingrepresented by A. In the case of a distinct shoulder, the termination of the plateau is frequently labeled the α-breakor, because of reliance on the duplex theory, the rod-cone transition. This putative relationship is illusory.

In a second solution of the above second order differential equation, the sine function disappears and the expressionfound in the dark adaptation characteristic is of the form:

“Extended Exponential” Eq. 17.1.1-c

[ ]y

e xx n=− ⋅ + ⋅

1

1 1( ω

This solution also looks similar to an exponential but clearly is not. For appropriate values, it appears to be changingmore slowly than expected with time. Therefore, it is labeled an “extended exponential” for semantic convenience. It does not exhibit a shoulder. Wachtmeister uses the term “kohlrausch kink” to describe the abrupt change in slopeassociated with this waveform.

17.1.2.5 Nomenclature associated with the composite ERG and LERG

The ERG and LERG are discussed widely in the literature. Interpreting this information requires a carefuldetermination of whether the data was acquired in response to a change in illumination characterized as a long pulserelative to the time constants of the eye or in response to a short pulse, mathematically an impulse. For theintermediated condition, pulses of 0.1 seconds to five seconds, the interpretation becomes considerably morecomplex.

The literature contains an impressive list of labels for various features associated with the ERG waveform that reflectthe observational history of the ERG. The original names date from Jolly (1908) and were assigned in time sequenceto markers for responses due to unknown mechanisms. It is now possible to associate most of the names with theunderlying source of the features. However, it is necessary to reject any chemical bias and adopt the fundamentalelectrolytic nature of the neuron system to do this. The ERG is basically a global summation of the individualvoltage waveforms from;

+ the photoreceptor cells, both Class C and D waveforms,

+ from a combination of the lateral and bipolar cells of the signal manipulation stage, Class E waveforms, and

+ under appropriate conditions voltage waveforms from the ganglion cells of the signal projection stage, Class Fwaveforms.

Because the summation may contain signals from the lateral cells, it has an inherent variability based on the spectralcontent of the illumination used in the experiments. When present, the signals from the ganglion cells introduce avariability based on the amplitude of the test signals as they exist within the signal manipulation stage. To obtainrepeatable results between laboratories, it is absolutely necessary to specify the spectral characteristics of anyillumination (both test, background and preadaptation) explicitly and to define the adaptation state of the subjectcompletely. If Class F waveforms are present, the amplitude of the illumination must also be carefullydocumented–especially with regard to signal changes relative to any background. Under these conditions, theobservational based labels become unique characteristics of the source waveforms.


20Heckenlively, J. & Arden, G. (1991) Principles and practice of clinical electrophysiology of vision. St.Louis, MO: Mosby Year Book

A group of authors writing in Heckenlively & Arden20 have provided the most comprehensive, consistent and up-to-date discussion of these ERG features, using about half of the letters of the alphabet in the process. Theirperspective is primarily from the medical clinic. Because of this focus, they do not address the a-wave and b-wavein detail. To save space below, these authors will be addressed by name followed by the expression “in H & A–pgxx.” A tabulation of all of these features (waves) appears in Section 11.1.3. As pointed out on H & A–pg 91, someof these waves are only observable with direct current electroretinography (dc-ERG) or electro-oculaography (EOG),both external forms of retinography. The a-wave and b-wave are frequently not resolvable in clinical ERGapparatus. They require more intensive instrumentation or the use of LERG techniques to resolve them because ofthe signal levels and impedances involved. The basic ERG sums the individual signals from millions of individualdetectors, through the use of Ganzfeld illumination, in order to achieve adequate signal levels for recordingpurposes. Frequently, this summing is not adequate and additional data reduction procedures are necessary. Muchof the literature includes waveforms resulting from the averaging of a large number of individual experiments toeliminate random noise and asynchronous signals from the final result. One of the remarkable features of the retinais the uniformity of its signaling channel topology and topography. Without this uniformity, it would be impossibleto perform the amount of averaging found in most ERG figures.

Granit provided an early attempt to describe some of these features using his potential waves, PI, PII, and PIII. Theywere named based on their sequence of disappearance under anesthesia. His instrumentation was pre-transistor andless capable than used today. Page 7 of Heckenlively & Arden provides a description of Granit’s waveformsprepared by Riggs and a conversion between Granit’s notation and some of the more modern notation. The oldnomenclature will not be discussed here.

The various features of the ERG are usually discussed based on a recording where a positive voltage on the cornearelative to a second return electrode is drawn as up. The location of the return electrode is frequently a matter ofdiscussion. As shown earlier in this work, this is because of the fact that the ERG is essentially recording thecurrents in various “ground loops” of a complex and relatively poorly designed (from this particular perspective)electronic system. The voltage recorded is due primarily to these currents passing through impedances associatedwith ground bridges between various ground planes. See Section 11.1.1.3. Thus, the recorded signals are a functionof where the signal and return leads are positioned relative to this multiple ground plane visual system. This fact isexplicitly illustrated in figure 9-2 by Griff in Heckenlively & Arden. He shows three waveforms recorded by threeprobes in response to the same event. The signals are quite different and even have inverted features relative to eachother. The caption to his figure 9-4 illustrates the problem further. He pointed out that the transretinal potential wasinverted and superimposed on the transepithelial recording, and then states that it was coincidental that bothrecordings had equal amplitude. In the context of this work, they should have the same amplitude if they were dueto the same event, the probes were both located quite near to the source of that event and the test equipment was notimpacting the measurements.

There is reason to believe that some of the data recorded by the ERG may emanate from the initial circuits of thecortex, particularly when the earlobe is used as a signal return or as a ground lead.

The literature of the LERG and its variants is briefer and considerably more recent. As probability might suggest,the experimenters in electrophysiology involving probes have frequently chosen the opposite polarity for theirgraphic presentations compared to the ERG community. For consistency in this section, the a-wave will be taken asnegative going regardless of the potentials sensed by a given probe configuration. (See Section 17.6.2)

Until quite recently, with development of the suction pipette technique, virtually all ERG and


LERG measurements represented voltages. This has now changed. Excellent current data (morefundamental) is becoming available.

Because most of these waveform definitions are based on one of two approaches; external observation followed byprobing and/or external observation followed by pharmaceutical experiments, it is natural for different authors toattempt to subdivide individual waveforms into component waveforms based on the their proclivities and approach. Lacking a specific and generally accepted top level schematic of the visual system, this generally leads to anassortment of putative origins for these waveforms. This appears to be a particular problem with the b-wave. It hasbeen subdivided into an early and late b-wave, putatively defined in terms of the ever convenient rods and cones. Ithas also been subdivided into both AC and DC waves. In general, a simpler cause of these two waveforms measuredby the same probe under different, and sometimes simultaneous conditions, is the different response of chromaticallydistinct photoreceptor types to different levels of excitation. This will cause a different delay and slope in each oftheir Class D waveforms. Their summary waveform will satisfy the observed phenomena. These waveforms arefrequently discussed in some texts as components of the early receptor potential. However, the early receptorpotential is related to the Class C waveforms emanating from the dendrites of the photoreceptors located in the OuterSegments.

17.1.2.6 Concepts relating to optics

For research purposes, the physiological optical system is much more complex than the commonly used Gaussianapproach to optics can support. The optics is fundamentally an elliptical (non-spherical) thick (not thin) lens systememploying gradient (not fixed) index materials in a variable (not fixed) focal length system with a highly curved (notflat) Petzval surface. The retina is shaped to match this Petzval surface. However, the point of fixation, commonlytaken as determining the visual axis along with the center of the pupil, is not coincident with the optical axis of thissystem. These facts have not usually been recognized by the publications from the more practically aligned schoolsof optometry. The difference significantly impacts discussions of the actual spatial performance of the combinedphysiological optics and the retina.

17.1.2.6.1 Spatial characteristics of the physiological optics and retina

Although the common wisdom is that the variation in size and lattice geometry of the retina causes the variation inspatial resolution of the eye, this is not supported by the documentation or theory. The lattice spacing varies by littlemore than a factor of two while the spatial resolution varies by significantly more than a factor of ten with fieldangle. The variation is due primarily to the physiological optics. The performance of the optics is describedfundamentally by the photon flux density profile at the Petzval surface. Although actually a density profile, theprojection of this profile on the Petzval surface is known as the Airy disk (and the disk exhibits concentric ringsaround it in high quality optical systems). The profile and disk are both two dimensional and the two elliptical axesof these features grow rapidly with field angle. The profile is generally not symmetrical. Therefore, the spatialresolution associated with these profiles is determined by the complete two dimensional Fourier transform, not justthe Fourier cosine transform or the Laplace transform. Although difficult to determine, Daugman (discussed below)provides an excellent data set of the spatial resolution of the physiological system in the human eye. Only in specialcases is the one dimensional Fourier transform adequate to describe a test configuration in visual optics.

To discuss the spatial resolution of the retina, it is important to know more than just the lattice spacing andphotoreceptor size. It is necessary to make estimates about the lattice constants of each individual chromatic type ofphotoreceptor and/or how the signals from these photoreceptors are used in perception. Currently, there is virtuallyno precise data about the lattice constants of the various chromatic photosensing channels. Based on behavioraldata, it appears that the luminance channel is used to evaluate the spatial resolution capability of the system. Thechrominance channels can be used for such evaluations only after careful coaching of the subject in what appears to


Figure 17.1.2-2 Concept of optimizing the performanceof an imaging system using a variable iris with a badlyaberrated lens system.. At f/8, the lens-retina systemoperates at maximum performance (spatial frequency) butrequires a lot of light. At lower light levels, an f/3 isrequired but performance is still lost because of theaberrations of the elliptical optical system.

be an un-natural situation. If the luminance channel is used, the dominant signaling component in this channel is theM-channel.

17.1.2.6.2 Computing the limiting optical performance of the visual system

Figure 17.1.2-2 illustrates the true purpose of the iris in the human eye. Without it, the system could not beoptimized as effectively over a broad range of illumination. With it, the system operates at reduced aberrationduring high luminance by using a higher f /# (smaller pupil). As the available light level decreases, the pupil opens. The resulting f /3 lens provides more light to the retina but the quality of the image actually decreases due to theaberrations associated with an elliptical lens system optimized for a very wide field of view. This is contrary to theoperation of a modern well corrected but narrower angle lens-film system wherein a lower f /# actually gives higherresolution imagery. The graphical technique combines the scene contrast and luminance parameters with the spatialfrequency performance of the lens system in the upper but falling curves and combines the threshold noise of thecortex referred to the retina and spatial resolution of the retina on the lower rising curves. The Aerial ImageModulation (A.I.M.) point defines the operating point of the system under a given set of conditions.

17.1.2.7 Concepts involving resolution andbandwidth

The concepts of spatial and temporal resolution, andspatial and temporal bandwidth have been treated veryawkwardly over the years in the vision literature. There have been many reasons. First, thepsychophysical community have necessarily beenperforming end to end experiments without significantknowledge of the actual detailed mechanismsemployed within the visual system. In many cases, theDuplex Theory, the Univariance Principle and theassumption of Linearity in the system have led them todesign experiments that can now be shown to beinappropriate. Second, the mathematics required indescribing these concepts properly and completely isbeyond the scope of algebra and simple calculus.

Third, the difference between the available channel bandwidth and the bandwidth of the signal occupying thatchannel has not always been appreciated. Fourth, in the absence of an adequate top level schematic of the visualsystem, it is impossible to design an adequately controlled experiment to describe these aspects of the systemprecisely.

A particular problem has been the description of the temporal bandwidth of a signal produced using two different(poorly specified) colors to excite the visual system. The assumption has been made universally that the visualsystem is in some sense linear and that the perceived responses are representative of the temporal or spatialbandwidth of the system. Unfortunately, the system is neither linear nor additive. This fact is demonstrated by thewide range of results obtained by different investigators using similar experimental protocols.

The relationship between the spatial resolution of the physiological optics and the temporal bandwidth of the neuralsignals is a complex one. It involves very subtle and complex signal encoding that is well beyond the scope ofsimple illuminated bar charts, mondrians and checkerboards.


An additional problem involves the fundamentally different operating mode of the signaling system with respect tothe foveola versus the remainder of the retina. The majority of the retina is used in a staring mode for purposes ofalarm against danger. It is fundamentally a change detector with a wide field of view. The foveola, on the otherhand, operates in an imaging mode through the introduction of a tremor developed by a specialized servo system. This part of the system is fundamentally an interrogator of a small portion of the scene.

17.1.2.7.1 Temporal bandwidth of the signal generated by the P/D process

The literature has not generally recognized that the signal generated by the photoexcitation/de-excitation processexhibits a variable upper frequency pole in its temporal frequency spectrum. The frequency of this pole is a functionof the irradiance absorbed by the chromophores associated with each specific photoreceptor cell. Therefore, thetemporal bandwidth of a composite luminance signal resulting from a broad band radiation source may exhibitseparate maximum frequencies for each chromatic component. This can cause minor variations in the signalamplitude as a function of temporal frequency. However, this would only be recognized in highly structured andcarefully designed laboratory experiments. The description of the signal observed in the chrominance channel ismore dramatic and is discussed below.

17.1.2.7.2 Temporal bandwidth of the generator waveform

The temporal bandwidth of the generator waveform recorded at the pedicel of the photoreceptor cells can be quitecomplex due to several factors. First, the adaptation amplifier introduces a low frequency pole at about 0.1 Hz. When combined with the high frequency poles of the P/D process, the result is a bandpass characteristic. If thesignal current passed to the pedicel is high, the logarithmic conversion to a voltage occurring at the pedicel is a non-linear process resulting in changes to the spectrum of the signal. If the signal current from the P/D process is verylarge, it may also cause saturation in the adaptation amplifier. This also introduces a non-linear process that candistort the spectrum further. The nature of the changes in the signal spectrum are complex functions of manyparameters. These last two conditions are of limited interest in this work and will not be explored further.

17.1.2.7.3 Temporal bandwidth of signal resulting from signal summation

If two broadband signals that are in phase but of different bandwidth are added together, the resulting signalenvelope in amplitude versus frequency space will be additive also. The result is a spectrum that is the sum of thetwo spectrums at each frequency along the frequency axis. Such summation will not result in any nulls in thespectrum that were not in both of the initial spectrums.

17.1.2.7.4 Temporal bandwidth of signal due to signal differencing

The minimum and maximum frequencies associated with a signal resulting from the difference between two signalsdoes not vary from the lowest minimum frequency and the highest maximum frequency of the pair unless non-linearities are introduced into the processing.

There are two distinctly different methods of signal differencing in vision. The first occurs in the image plane of theoptics and is due to the coherent nature of light itself or of the patterns created in the light. The second occurs in thesignal manipulation stage of the retina and is purely electrical in character. These methods can introduce nulls intothe resulting temporal frequency spectrum.

Many experiments have been performed demonstrating notches in the spatial frequency response of the eye due tointerference effects. These are classic physics demonstrations applicable to any optical system employing


electromagnetic radiation. Similarly, experiments have been performed using harmonic waves in spatial coordinatesto create null patterns in the image formed on the Petzval surface of the optics. These demonstrations do not relatedirectly to the performance of the visual system. They relate to the unique conditions under which the radiation ispresented to the eye. The fact that the resultant electronic signals in the temporal frequency domain exhibit thesesame effects is incidental.

Within the chrominance and appearance channels of human vision (and the polarization channels of other animals),signal differencing occurs. In the human, most of this differencing occurs in the chrominance channels receivingsignals from the output of the photoreceptor cells. It is the nature of differencing that if the two signals are of equalamplitude, the net response will be zero, a null condition. If the two signals are the result of a single signal ofvariable spectral wavelength being applied to both of the channels being differenced, it is possible, although unlikelyin vision, to measure a spectral response with any number of nulls in it. Normally there is one null spectralfrequency associated with each chrominance channel. Under dark adapted conditions, or in response to equal fluxillumination in object space, these nulls occur at 494 nm in the P-channel and at 572 nm in the Q-channel. Thepresence of these nulls is critical to the operational architecture of the visual system. A simultaneous null in both ofthese channels results in the perception of an achromatic or white scene. In the presence of non-equal-fluxillumination, the adaptation amplifiers of the two photodetection channels will change gain. Because of this changein gain, the spectral wavelength of the null(s) in object space will change. This is the mechanism that causes the eyeto compensate for unusual lighting conditions after a period of time and still perceive a white table cloth whenilluminated by a distinctly colored light.

The above discussion relates to the spectral content of the signal and not the channel through which it travels. In nocase is the resultant signal spectrum to be considered a description of the visual channel temporal bandwidth. Thiswork has not encountered any situation that suggests that the temporal bandwidth of the channel employed in signaldetection or signal manipulation is a limiting factor in the visual process. Within the signal projection stage, thereare clear limitations on the signalling channel which will be discussed later.

17.1.2.7.5 Temporal bandwidth of the spatial signal from the foveola

Because of the limited spatial resolution of the physiological optics outside the fovea, operation of the eye in thisdomain relies primarily on temporal changes in illumination to signal an alarm. The alarm causes the line of fixationof the eye to be brought to coincide with the line of sight to the change. It is only in the area of the foveola that thespatial performance of the optics is converted into a temporal signal for careful analysis in the cortex. This is doneby introducing a tremor into the line of fixation. As a result, the fine spatial detail in the scene is converted into finetemporal detail in the signaling channel. Speaking in the frequency domain, this is done by multiplying the spatialresolution in cycles/angular degree, by the velocity of the tremor in angular degrees/second, to obtain the spectralresolution in cycles/second. The calculation is easier if the tremor is of constant velocity. However, this isimpossible over any extended interval. The tremor can emulate this condition however if the muscles introduce animpulse into the rotational state of the ocular globe. There is little data on the angular characteristics of tremor. It isdifficult to measure. However, it is defined by a wideband signal with a fundamental frequency near 30 Hz andextending to 90 or 150 Hz. If the harmonics and phase of the angular rotation are appropriate, the tremor would berepresented by a sawtooth waveform approximating a constant angular rotation for over 80% of its period. Thiswaveform would result in a nearly linear transform of spatial resolution of the image into temporal resolution in thesignaling channel(s). Note that this process results in the spatial information being encoded in sidebands of a carrierfrequency, equal to the nominal tremor frequency of 30 Hz, within the signal frequency spectrum. There aresuggestions in the data base that the tremor consists of two orthogonal components supporting encoding that exhibitsa nominally vertical and horizontal component. If present, these components could be easily orthogonally decodedin the Auxiliary Optical System (AOS) of the neural system.

The presence of orthogonal encoding of the spatial data around a carrier frequency of 30 Hz strongly suggests that


21Robinson, A. Morrison, J. Muehrcke, P. Kimerling, A. & Guptill, S. (1978) Elements of Cartography, 6th

ed. NY: John Wiley & Sons

the decoding of this information occurs separately from any chromatic information since this same temporalfrequency regime is used for chrominance signal encoding. The conclusion can be drawn that interrogation of finescene detail, by the closed loop servo mechanism that includes the foveola and AOS, is accomplished using only thedirect signal pathwasy leading from the foveola to the Pretectum. This is accomplished irregardless of the chromaticsensitivity of individual photoreceptors in the fovea.

17.1.2.7.6 Temporal bandwidth of the channel supporting signaling

Electrophysiological experiments generally support a maximum temporal frequency of action potentials within thesignal projection stage of 100 Hz or possibly up to 150 Hz. This value is found in both the luminance andchrominance channels. This maximum channel bandwidth appears adequate to support the signal encoding used inboth the luminance and chrominance channels. Within the signal manipulation stage, the upper limit of the channelbandwidth is very difficult to measure. However, the nature of the electrical circuit elements present and thearchitecture of the circuits would suggest it is at least 100 Hz. wide. Risetime measurements of the generatorpotentials, Class D, as they pass through the signal manipulation stage could provide new and precise information inthis regard. The available replicas of the Class D waveform found within the retina suggest that no degradation dueto channel bandwidth has occurred.

The low pass limit of the signal manipulation stage is controlled by the adaptation amplifier in its operation toremove the wide average illumination range of the incident radiation. The half amplitude low frequency pole is at0.1 Hz.

The signal projection stage of vision does introduce limitations on and distortions to the signals passed from theretina. These limitations and distortions are of minimal importance in normal vision, especially in society prior tothe 20th Century. During the 20th Century, everything from the Kinetoscope to the switched laser has contributed toeffects that are distorted when passed through the signal projection stage. The results range from the trivial (after-effects), to the practical (movies and television) to the mysterious (magic).

17.1.2.8 Cartography requires conformality

Lacking significant theoretical input, the vision community has adopted various coordinate systems based more onconceptual analyses than any formal rigor. As found in cartography, the proper display of data requires compliancewith certain rules. These rules insure that the graphical presentation of the data can be used to draw meaningfulconclusions. The rules are grouped under the mathematical title of conformality.

A map maker usually encounters two conflicting choices21. When given a set of datapoints, he must choose whetherto make distances proportional to the actual case or to make the shapes of objects correspond to the actual case. Heseldom has the option of achieving both. Conformality relates to the level to which these two criteria are met. Itinvolves two conditions, the orthogonality of the presentation and the equiangularity of the presentation.

Conceptual attempts to describe color perceptions in terms of an equilateral triangle has formed an awkward legacyin vision. The tendency has been to define degrees of color in this space using scales perpendicular to each of thethree sides. Such scales are clearly not orthogonal. Attempts to project this triangular space onto an orthogonalcoordinate system (such as the C.I.E. XYZ color space) result in a new coordinate space wherein the angles relatedto features in the old space are greatly distorted. This is caused by the lack of proportionality between the unitvectors associated with the axes of the new space compared to the old space. This is illustrated by:


Figure 17.1.2-3 Concept of the temporal spectrumutilization in the human visual system.Upper frame shows the luminance channel for both theperipheral channels and the channels supporting thefoveola. Lower frame shows the two chrominancechannels superimposed for convenience. See text.

R(t) = F(t).i + G(t). j where Θ = arctan and θ = arctan

( )( )

G tF t

⋅ji

( )( )

G tF t

“Vector form of R(t) and constructs” Eq. 17.1.2-1

Θ is the apparent angle in the new graph and θ is the intrinsic angle associated with the underlying data or graph. Inthis case, the angles in the new graph only equal those in the original if the ratio of the two unit vectors is equal to1.000.

17.1.2.9 Conceptual loading of the signaling channels

Figure 17.1.2-3 provides a cartoon of the utilization of the signaling channels in human vision. The upper framedescribes the luminance channels of vision. The lower frame describes the chrominance channels. In both frames,the solid lines represent the bandwidth capacity of the channels. The dashed lines represent the bandwidth of thesignal content. Although clearly different and supporting different requirements, the similarity of the visual system tothe systems developed by man to provide color television service are striking. Two subcarriers are shown at thenominal frequencies used throughout this work. In the upper frame, only one tremor carrier and one set of sidebandsare shown supporting the foveola. There may be two separate sets of sidebands associated with the foveola andtransmitted in morphologically separate orthogonal channels. These separate channels would support separatevertically and horizontally oriented sections of the AOS. There is probably no signal related to the tremor carrier inmost of the peripheral luminance channels of the signal projection stage. The peripheral signals appear to betransmitted at baseband.

In the lower frame, the two chrominance channels areshown superimposed for convenience. They wouldactually be transmitted over morphologically separatechannels within the chrominance channels of vision. Although not demonstrated, the literature appears tosupport the genetic choice of the wider, and fasterresponding, upper sideband for the signals related tothe M-photoreceptor channels. The S- and L-channelsignals appear to occupy the narrower, and slowerresponding, lower sideband.

The subcarriers associated with the chrominancechannels and the foveola are created by distinctlydifferent mechanisms. One mechanism involvesphysical motion (tremor), the other a free runningelectronic oscillator.


17.1.3 Glossary

Discrete regions of radiant intensity based on the mechanisms of vision

Hypertopic region –The very highest level of radiant intensity tolerated by the visual system inthe absence of pain. The region is characterized by hard signal saturation in one or more of thespectral channels (usually the M-channel). Hard signal saturation implies no change in currentthrough the channel as a function of input intensity. The subject typically perceives a yellowing ofany object in the field of vision.

Photopic region –The operating region of the visual system where all of the adaptation amplifiersof the individual spectral channels are all operating at amplification factors greater than 1.0 butnone have reached their maximum gain.

Mesopia– A clinical syndrome describing the limited performance of the visual system undercertain conditions. See mesotopia and Section 17.3.3.6.1.

Mesotopic region – 1. The operating region wherein one or more of the spectral channels of vision is operating with its adaptation amplifiers at maximum gain. Colorconstancy is lost under this condition.

2.The operating region below the photopic region characterized by the L-channel adaptation amplifier operating at full gain but the L-channel signalfalling more rapidly than in the M- and S-channel signals with fallingillumination levels. Signal to threshold performance is typically limited byquantum noise fluctuations in the illumination. A region of decreasingsaturation in the perceived colors of objects due to a decreasing signal level inthe P & Q chrominance channels relative to the threshold level. See mesopiaand Section 17.3.3.6.1.

Scotopic region –The lowest operating region of vision characterized by all adaptation amplifiersoperating at full gain but a complete absence of L-channel sensitivity in the spectral response ofthe eye. A region of achromatic vision due to the signal level in the P & Q chrominance channelsfalling below the threshold level.

Theoretical Photopic Luminous Efficiency Function

Defined as the threshold performance of the dark adapted eye as a function of wavelength measured with aphotopic intensity probe (typically of 2 degree diameter and a flicker frequency between 1 and 20 Hz.) inthe absence of any background illumination.

Not indicative of operation under actual photopic conditions (unless illumination is at a color temperature near 7053 Kelvin & scene at low contrast--typically below 2:1)

Performance is defined in terms of the perceptual recognition of the test probe in the presence ofthe natural thresholds present in the visual system without any determination of whether the probeexhibited a chromatic aspect (hue or saturation). The threshold is normally probabilistic under


dark adapted conditions. However, it may be deterministic under other states of adaptation and inthe presence of background illumination.

Theoretical Scotopic Luminous Efficiency Function

Defined as the threshold performance of the dark adapted eye as a function of wavelength measured with ascotopic intensity probe (typically of 10 degree diameter and a flicker frequency between 1 and 5 Hz.) inthe absence of any background illumination.

Fairly indicative of operation under actual scotopic conditions due to natural lighting. Not indicative of operation based on low color temperature artificial illumination.

Performance is defined in terms of the perceptual recognition of the test probe in the presence ofthe natural thresholds present in the visual system without any determination of whether the probeexhibited a chromatic aspect (hue or saturation).

Visual Threshold

A term used in a variety of visual situations including both deterministic and probabilistic, absolute anddifferential, and monocular and binocular. Because the threshold model of the visual system has not beenwell defined, most uses of the visual threshold have involved the probability of perceiving a given stimulusor change in stimulus. In that case, the threshold is specified at a given probability value, p. Under moreclearly understood conditions, the alternate approach is to assign a given signal to internal threshold ratio tothe observed external visual threshold, where the internal threshold may be deterministic or probabilistic. In this scenario, the external visual threshold may be a function of the state of the adaptation of the visualsystem (and therefore a transient), a function of the degree of signal integration occurring before perception(and therefore a function of the signal integration capability of the visual system that is in turn a function ofthe size and duration of the applied scene), and a function of the background surrounding the scene.

Metameres–Two color samples that appear identical under identical illumination and surround conditions within thephotopic range because they exhibit identical values of P and Q in the chrominance channels.

Trans-metameres--Two color samples that exhibit identical values of P and Q in the chrominance channels underdifferent illumination and/or surround conditions and that therefore appear identical.

Brightness– The psychophysical perception of the intensity of an image in object space. This characteristic is afunction of the intensity of the irradiance reaching the cornea of the eye and the state of the visual system. Thebrightness can be described in terms of a source of irradiance or as the result of reflectance of a source by an objectin object space. The brightness is a function of the irradiance, the reflectance of the object, the transmission of thelens group and the state of adaptation of the eye, all as a function of wavelength.

Candela– The standard of luminous flux. (Current narrow band definition, 1979) The candela is the luminousintensity, in a given direction, of a source which is emitting monochromatic radiant energy of frequency 540"1012

Hertz (555.016 nm in standard air) and whose radiant intensity in that direction is 1/683 Watt (4.092"1017 photons)per steradian. An isotropic radiator of one Candela produces 0.0184 watts of light at 540"1012 Hertz. (Previousbroad band definition) The candela was the luminous intensity, in the perpendicular direction, of a surface of1/600,000 square meter of a blackbody at the temperature of freezing platinum under a pressure of 10,325 newtonsper square meter (near 2042 Kelvin).

Irradiance, (E)– The absolute intensity of the radiation incident on the cornea of the eye and within the capture


angle of the pupil of the optical system and the spectral passband of the visual system. The units are watts.

Irradiant spectral intensity, E(λ)– The absolute intensity of the radiation incident on the cornea of the eye andwithin the capture angle of the pupil of the optical system as a function of wavelength. The units are watts per unitwavelength.

Irradiant flux intensity F( λ)– The absolute intensity of the photon flux incident on the cornea of the eye andwithin the capture angle of the pupil of the optical system as a function of wavelength. The units are photons perunit wavelength.

Lightness– The perceived relative brightness of an element in a scene relative to a reference element. Generallydescribed using a range from light to dark.

Lumen– (Current definition) The luminous flux of monochromatic radiant energy whose radian flux is 1/683 W(4.092"1017 photons) and whose frequency is 540"1012 Hertz (555.016 nm in standard air).

Modulation– The variation in the lightness of a scene element compared to a reference scene element (that maydescribe the background of object space).

17.1.4 The simplified block diagrams used to define the descriptors of vision

When discussing different aspects of the visual system, it is frequently possible to use a simplified block diagram. Such diagrams are presented in this section. While extremely useful, it must be remembered that some of theparameters associated with these diagrams are functions of the state of adaptation of the system. It is thereforenecessary to specify whether the models are being used in the scotopic, mesotopic, photopic or hypertopicperformance ranges.

The following Sections will examine the performance of the eye in each of the above performance ranges. Each ofthese major sections will use simplified graphical variants of the Top Level Schematic developed in Chapter 11. Sections 17.2, 17.3 and 17.4 will rely upon the block diagram shown in Section 17.1.4.2. Sections 17.5 through17.7 will rely heavily upon the simplified oculomotor servomechanism diagram of Section 7.3.5 and the detailedcircuit diagrams of Section 11.7.

17.1.4.1 The key role of adaptation in the visual process

The phenomenon of adaptation plays a key role in the luminance, chrominance and temporal performance of thevisual system. It, along with color differencing, can be considered keystones in the architecture of the entire visualsystem. The phenomena is associated with three distinct mechanisms within the eye;

• the dynamics of the iris (pupil) of the stage 0 eye,• the dynamics associated with the bleaching of the available chromophores of the stage 1 sensory neurons and• the variable gain characteristics of the adaptation amplifieres associated with each stage 1 sensory neuron.

The remainder of the neural system orthodromic to stage 1 operates in a nominally constant amplification state.

The dynamics of the iris have been presented in detail in Section 2.4.3 of this work.


22Cornsweet, T. (1970) Visual Perception. NY: Academic Press23Wuerger, S. (1996) Color appearance changes resulting from iso-luminant chromatic adaptation. VisionRes. vol. 36, pp. 3107-311824Shevell, S. & Wesner, M. (1989) Color appearance under conditions of chromatic adaptation and contrast. Color Research and applications. vol 14, pp. 309-317

Many textbooks have referred to the conceptual work of Cornsweet22 when describing the effect of bleaching on theperformance of the human eye. Unfortunately, his description was more speculation than the result of research andis inadequate for describing the actual phenomenon involved. He relied upon the duplicity theory of distinct rodsand cones which is shown to be faulty in this work. As an example, his figure 7-11 presents straight lines on a semilogarithmic graph lacking any data points and calculated from an earlier conceptual equation offered by Rushton. Itdoes not differentiate between an external quantum noise limited threshold versus an internal noise limited threshold. A more realistic graph would use a logarithmic abscissa to describe the level of bleaching.. Where he has provideddata, it is largely archaic relative to the more recent literature.

The variable gain intrinsic in the design of the individual adaptation amplifiers found within each photoreceptor cellis also an important feature in dark adaptation.. This portion of the adaptation phenomenon is the result of a uniquecircuit configuration that has been identified in the sensory neurons of virtually all sensory modalities. It is afundamental phenomenon contributing to the extreme operating intensity range of the visual system in object(stimuli) space. When the adaptation amplifiers of all spectral channels change their gain in unison, adaptation todifferent levels of object luminous intensity, without change in spectral content, within a reasonable length of time isachieved (lightness constancy). When the amplifiers change their gain individually over a reasonable length of timeto compensate for changes in the spectral content of the objects luminous intensity, a major degree of colorconstancy is achieved. Whenever, these amplifiers are operating at less than full amplification, they exhibit atransient response in returning to their fully dark adapted operating condition. This response is conventionallylabeled the dark adaptation characteristic of the system. There is also a light adaptation characteristic associatedwith the change in the gain of these amplifiers but it is much more rapid, of less practical importance and less wellstudied.

The pervasive aspects of adaptation cause it to be discussed throughout the vision literature. Wuerger recentlydiscussed its impact on color changes following chromatic adaptation23. Using her paper, one can trace the earlyfirst order proposals of von Kries, through the more advanced proposals of Walraven, el. al. to those of Shevell &Wesner. Each group proposes a better empirical explanation of the observed performance. It can be seen that theseproposals, especially those of Shevell & Wesner24, are converging on the model proposed in this work. Theypropose a variable gain mechanism prior to a subtractive process occurring in a later stage. Unfortunately, most ofthe literature continues to use photometric units where radiometric units are clearly required and many authors areusing tricolor display monitors with phosphors that are not well related to the chromophores of vision. Adaptationfrom the overall performance perspective is developed in Section 17.6 of this work.

17.1.4.2 The signaling matrix applicable to luminance and chrominance descriptors

[Figure 11.6.4-2] presented a simplified block diagram applicable to discussions concerning the luminance andchrominance channels of biological vision. The analysis accompanying that figure showed the first orderperformance of the visual system (avoiding flicker effects, aftereffects, stereo-optic considerations and certainnonlinearities) can be described by the analog electrical signals found at the S-plane of the individual retinas. Exceptfor certain specialized encoding techniques (spatial and diversity encoding to minimize the physical size of the opticnerve), this location corresponds to the output of Stage 2, the signal processing stage.

Figure 17.1.4-1 develops the signaling matrix embodied in the Matrix Theory of Color Vision embodied in this


Figure 17.1.4-1 The luminance, chrominance and appearance channels of the eye of tetrachromats and aphakichumans. The spectral response in the O-, P- and Q- channels are shown as sinusoidal for illustration. The UVphotoreceptor cells are known to be functional in humans of all ages. Research is ongoing to determine if the signalin the O-channel of the aphakic human is typical of tetrachromats. If it is, an aphakic human will be able to tell uswhat “color” other animals perceive in the ultraviolet.

work. This Matrix Theory was initially introduced in Sections 1.5.1 & 1.7.5 as a replacement for earlier ZoneTheories. The matrix shows the analog signals at the output of Stage 2 and their characteristics as a function ofspectral wavelength. This figure will be discussed in detail in Section 17.2-17.4.

17.1.4.3 The block diagram applicable to temporal descriptors

The temporal descriptors of vision include both simple delays associated with transmission of signals over finitedistances and much more complex processes that are functions of multiple parameters. To discuss the temporalproperties of vision, it is necessary to expand the Top Level Schematic down to the circuit level. Particularly withregard to the photoreceptor cells. They are the site of the fundamental transduction mechanism as well as theadaptation mechanism.

Figure 17.1.4-2 illustrates the various signal paths from the photoreceptor cells to the stellate cells at the entrance tothe brain. The multiple Nodes of Ranvier along each signal path within the area defining the optic nerve are notshown in this figure. However, these circuits contribute significant time delay to the overall operation of the visual


system.

The simplicity of the signaling circuits shown is startling in relation to their capability.


Figure 17.1.4-2 The large signal circuit diagram of the fundamental signal paths of a highly evolved animal eye. (A) Generic photodetection module, (B) Generic luminance channel-- R, (C) One of three generic chrominancechannels--O, P & Q. (D) Generic appearance channel--Zn.


Figure 17.1.4-3 Overall Servomechanism of the human visual system. Similar systems are found among thechordates. The significance of the delay associated with signal projection is highlighted throughout the figure.

17.1.4.4 The block diagram applicable to oculomotor performance descriptors

The detailed discussion of the servomechanisms of vision are presented in Sections 7.3-7.5. Figure 17.1.4-3reprints the Overall Servo System of human vision found in those sections. It is required to support the discussionsin Sections 17.7. It is also important in understanding the ability to read and interpret fine detail as developed inSection 17.7.5. This figure labels the major signal path associated with both voluntary (cognitive) and involuntaryeye motions. The involuntary functions are focused on the stereo, alarm and interpretive paths. The interpretivepath includes the inner servo loop consisting of the foveola, POS and oculomotor plant. The major role played bytime delay (related primarily to the signal projection tasks) is highlighted. To minimize the total delay in criticalprocesses, the inner servo loop (foveola, POS, oculomotor plant) does not include the cortex. Not shown in thisfigure is the cerebellum, a crucial element in the inner servo loop called upon extensively by the pretectum.


25Estevez, O. & Spekreijse, H. (1982) The “silent substitution” method in visual research. Vision Res. vol.22, pp 681-69126Volbrecht, V. & Kliegl, R. (1998) The percepton of blackness: an historical and contemporary review.Chapter 10 in Backhaus, W. Kliegl, R. & Werner, J. Color Vision: perspectives from different disciplines. Berlin: W. de Gruyter

17.1.5 Problems with “black,” univariance, “silent substitution” and arbitrarynormalization

Two time-honored concepts of psychophysics are in need of re-conceptualization based on this work. Even thequestion of whether black is a perceptual phenomenon remains open to discussion. The Univariance Principle wasoriginally conceived at the beginning of the 20th Century. It was promulgated more broadly by Rushton beginningin 1959. He subsequently redefined it in 1971. The silent substitution method of exploring the performance of thevisual system has its roots in the same time periods. Both of these concepts rely upon the putative linearity of thevisual system originally proposed by Grassman in the 1860's. Estevez & Spekreijse reviewed these developments in198225. They also presented a comprehensive treatise on their silent substitution methodology based on the rules ofconventional colorimetry. Chapter 12, the equations of Chapter 16 and the above models highlight a series ofproblems with these concepts. The problems become worse as higher precision is sought and narrower spectral bandstimuli are used. These problems will be discussed briefly below with additional details provided in Appendix T.

17.1.5.1 The phenomenology of “black”

Volbrecht & Kliegl have recently revisited the debate concerning the validity of black as a “real” perception26. Theproblem with these discussions is they lack a fundamental model of the visual system. Volbrecht & Kliegl developthe positions of Maxwell versus Hering in the 19th Century. Their arguments are based purely on observationsmostly related to their own vision. A key question in the argument is whether a human perceives black in theabsence of a stimulus. However, there is no discussion of the fact that the human visual system is AC coupled. Thehuman visual system can not deliver a constant signal value to the brain representing an absolute stimulus intensityapplied to the eye (or to the retina). This fact is embodied in the difference between the perceived brightness of animage and the actual lightness of that image. The fact that the human perceives a gray (Eigengrau) in the absence ofany stimulus, whether the eyelids are closed or not, merely reflects the above situation. In the language of thetelevision engineer, the visual system does not possess a DC restoration circuit. Lack of such a circuit is why mosttelevision screens produce a neutral gray screen when the transmitting station sends a black signal. High pricedtelevision sets frequently have a DC restoration circuit and their screens go black when the station transmits black.

Based on the actual circuitry of the human visual system, black as a phenomenon is the absence of any stimulation tothe photoreceptors of the eyes. The perception of black varies with the circumstances. In the absence of anystimulus to the retina, the visual system reports a neutral gray (Eigengrau). Neglect perceptions related to color forthe moment. If a stimulus varying in intensity (of finite contrast) is applied to the retina, the retina will perceive thearea of minimal stimulus intensity as more black than the Eigengrau. Similarly, the retina will perceive the area ofmaximum stimulus intensity as more white than the Eigengrau. As the contrast of the stimulus increases, theperceived difference between black and white will increase until the signal resulting from the stimulus occupies allof the limited dynamic range associated with the luminance channel of vision. This range is typically less than200:1.

At very low stimulus values, the impact of noise must be considered in the above discussion. This noise normallyoriginates in the variation in the photon flux of the stimulus. The contrast-to-noise ratio of the stimulus usuallyexceeds the above dynamic range under photopic conditions. The perception of noise is suppressed in the luminance


27Rushton, W. (1972) Visual pigment in man, In, Handbook of Sensory Physiology, Vol. VII/1,Photochemistry of Vision Dartnall, H. Ed. NY: Springer-Verlag, pp 364-394

signaling channel under this condition. Under mesotopic conditions, the photon noise may dominate the perceptionof both the black and white regions of a scene. Under scotopic conditions, the effect of photon noise associated withthe more black scene elements is usually suppressed by the circuits of stage 3 and stage 4 of the visual system. Thephoton noise associated with the more white scene elements may still be perceived.

17.1.5.2 The Univariance Principle

This Principle was documented in its modern form by Rushton27. It has been promulgated widely within thepsychophysical community and is frequently referenced in their literature. However, it is not always stated in aspecific form. Based on a very simple linear and floating model of the visual system, Rushton proposed that: “Anytwo lights that are equally absorbed by rhodopsin will be equally seen by rods.” Wyszecki & Stiles paraphrasedRushton on page 587 that: “It follows that rhodopsin spectral absorption curve must coincide with the scotopicluminous efficiency curve, V’(λ).” The curve Rushton used to justify this relationship was not the C.I.E. V’(λ). Hisjustification relied upon a sparse set of psychophysical data points (with no direct association with the putative rods)overlayed on a similar curve by Crawford. The original discussion promulgating the principle contained no model ofthe process being discussed and occupied less than one-half page. The top level schematic of the visual system highlights a problem with the Univariance Principle. First, there is norhodopsin in the sense that he used it and “rods” are not a functional designation in vision. Second, omitting theUV- and O-channels of vision for the moment, there are three separate and distinct spectral channels (classes ofreceptors) that are used to absorb photons and generate signals. Rushton recognized this and extended his Principlein 1971 to say “For each class of receptor the result of light depends upon the effective quantum catch, not uponwhat quanta are caught.” Estevez & Spekreijse say that Rushton repeatedly demonstrated the validity and usefulnessof the Principle and built a research methodology entirely based on its validity. However, they provided nodiscussion of the precision of the results obtainable with this methodology. The above model of the completephotoreceptor cell has shown that further clarification of Rushton’s second Principle is needed. The words resultand effective are clearly in need of clarification. To add precision to the concept, it is important to specify what theresult is and where it is measured.

The result can be taken at the input to the neural signal processing, at the output of the adaptation amplifiers, at theS-plane of the retina or as the perceived response after all other second order effects have been included.

1. If the result is measured at the input to the adaptation amplifiers, it is clear that the transfer function of the L-channel exhibits a square law term that is not compatible with the linearity requirement of Grassman’s laws.

2. If the result is measured at the output of the adaptation amplifiers, the variations in adaptation among theindividual spectral channels, impact the effective quantum catch of those channels. However, the square law termrelated to the L-channel is eliminated for signals within the photopic region.

3. If the result is measured at the pedicle of the photoreceptor cells, the exponential conversion of the signal, from acurrent proportional to the flux to a voltage, is not compatible with Grassman’s laws based on a linear system.

There is a further complication within the signal processing of stage 2. The luminous signal and the chrominancesignal are treated differently.

4. If the result is measured at the output of the bipolar neurons of the S-plane, the logarithmic summation introducesvariations in the perceived luminance signal not contemplated by Rushton or others.


28Estevez, O. & Spekreijse, H. (1974) A spectral compensation method for determining the flickercharacteristics of the human color mechanisms. Vision Res. vol. 14, pp 823-830

5. If the result is measured at the output of the horizontal cells of the S-plane, the logarithmic subtraction processimposes a more subtle restriction on the perceived chrominance signals. This restriction negates the additivity andcommutativity laws of colorimetry.

The above realities suggest the Univariance Principle requires restating. To meet current goals inthe precision of visual research, it is suggested that the Univariance Principle be:

Under achromatic adaption and non-flickering small signal conditions within the photopicregion of vision,

the electrical signal at the pedicles of the photoreceptor cells depend upon the effectivequantum catch, not upon what quanta are caught,

the perceived luminance response at the S-plane of the retina is a function of the wavelengthof the quanta caught (particularly for narrow spectral band irradiance),

the perceived chrominance response at the S-plane of the retina is determined by thedifference in the quantum catch by the individual pairs of photoreceptor cells and not by thewavelength of the quanta caught.

17.1.5.3 The silent substitution method

The silent substitution method, as defined by Estevez & Spekreijse, relies upon Grassman’s Laws of linearity asencapsulated in Rushton’s Univariance Principle. However, many of the demonstrations of this method involvebackgrounds that effectively limit the experiments to small signal conditions.

Estevez & Spekreijse discuss the results of Donner & Rushton on page 686. Their results appear to be in agreementwith the above elaboration of the Univariance Principle. They found silent substitution is possible within thescotopic region (the L-channel signal is trivial because of its square law term), fails within the mesotopic region, butwas observed again within the photopic region (the L-channel signal is linear again due to the action of theadaptation amplifier). They also note their puzzlement over the fact that “near the dark adapted state, changes in thesensitivity functions could occur without disturbing silent substitutions.” The adaptation amplifiers within thephotoreceptor cells were performing their function.

Estevez & Spekreijse note that the origin of the term “silent substitution” was a result of the instrumentation used toobserve the firing rate of the ganglion cells of frog. By using an audio amplifier and speaker, they were able to listento the firing rate of the cells. If they could substitute a stimulus without hearing a change in frequency, it wasdeemed a “silent substitution.”

As in the case of the limitations on the Univariance Principle, the silent substitution method requires much greatercare in application as the desired precision is increased or the spectral bandwidth of the stimuli are reduced. Thefundamental difference between the signal processing in the luminance and chrominance channels must berecognized.

There is a significant problem with the first paper of Estevez & Spekreijse28. They used the human corneal spectraldata of Wald (1964). These spectra were derived using the difference spectra technique. These spectra are grossly


29Davson, H. (1962) The Eye, Volume 2. NY Academic Press p 241

different from the electrophysiologically measured spectra of biological vision (both at the S-plane and at the planeof the ganglion cells). This calls into question whether their data was obtained under optimal conditions.

17.1.5.4 Problems leading to expansion of the CIE functions, V(λ) and V’(λ)

The CIE has struggled with the name for the function described by V(λ). In their vocabulary, it is associated withthe inadequately defined Standard Observer dating from the 1920's. While originally designating it a visibilityfunction, adopted the name efficiency function in 1951 in the absence of any physical or mathematical modelshowing it was related to the efficiency of the visual system. It is important to note that because of the abovedifficulties, there are several problems with the the CIE photopic and scotopic luminous efficiency functions(previously visibility functions) of 1951. First, V(λ) is not actually a description of efficiency. It is a relativesensitivity measurements under poorly specified test conditions. Second, V(λ) is not defined in terms of specificstimulus intensity levels. V(λ) is a relative sensitivity function defined in terms of the diameter of the test imageprojected onto the fovea of the eye. The photopic function is defined without reference to a specific stimulusintensity level based on the assumption that the mechanism providing brightness constancy over the photopic regionis operating.

The scotopic variant of V(λ) is defined in the absence of any defined stimulus intensity level. Finally, the nominalscotopic function is defined at a position not less than five degrees from the line of fixation (Wyszecki & Stiles, pg258) while the photopic function is defined at a location centered on the line of fixation.

With the adoption of the Visibility Function in 1924, it became under attack immediately. Judd, a member ofthe committee refused to accept the new function as realistic (Section 17.1.9.2). In 1931, Purdy reviewed theshortcomings of the function again (17.2.6.5.1).

In the 1951 time period, the Visibility function, V(λ), was recognized as a relative function that could beconverted to an absolute function, the Luminous Efficiency Function by introduction of a constant labeled the“Maximum luminous Efficiency,” Km = 680 lumens/watt. This value was subsequently changed to 683lumens/watt. Since the maximum luminous efficiency was a function of the visibility function, the reasoningand analysis were clear examples of circular reasoning.

Marriott, writing in Davson (Don of the visual sciences in his day), noted and discussed the inadequacies ofthe C.I.E. visual and color spaces as far back as 196229. “At the time of this writing,, the data of colorimetryare undergoing re-examination. The results that have been accepted as standards since the C.I.E. adopted thevisibility function V l in 1924 and the “Standard observer” color matching system in 1931 have recently beenquestioned. In all probability, new standard functions for colour-matching will be laid down in the next fewyears; meanwhile, it is difficult to decide what results should be used.” He went on, “The C.I.E. functionshave been officially accepted since 1931 and are adequate for most practical purposes; for theoretical studiesof colour vision, however, they must be regarded as capable of improvement.” The C.I.E. ChromaticityDiagram of 1931 was largely replaced by the new “Uniform Color Spaces of 1976." These remain empiricalin character and attempt to maintain the now obsolete, but widely used, C.I.E. Chromaticity Diagram. Marriot provided additional details in this area.

Marriott went on, “The C.I.E. V(λ) function is a compromise solution to the problem based on an average ofresults of the flicker method, the step-by-step method, and the direct comparison method.” The theoreticalweakness of such a combination of inconsistent results is obvious, but is much outweighed by the practicalvalue of a single visibility function, which ca be used without large discrepancies, for all photopic brightness. In fundamental color research, however, the imperfections of the function must be realized.”


30Sperling, H. & Harwerth, R. (1971) Red-green cone interactions in the increment-threshold spectralsensitivities of primates Science vol 172, pp 180-184

In 1969, Wright, one of the original laboratory investigators, made a parody of the above assertion ofMarriott, when he suggested the accuracy of the values at a given wavelength for the visibility function wereprobably in error by a factor of 10 and in fact no measurements were incorporated into the standard forwavelengths less than 400 nm (Section 17.2.1.6.5).

Finally, all of the above discussions were based on matching energy levels at a given wavelength on theassumption that the sensory neurons were energy-sensitive. It is now totally clear, based on their physicalchemistry and quantum physics that they are quantum-sensitive. This difference introduces another factorinto the calculations and generally indicates all research quality measurements should be made in aradiometric environment rather than a photometric environment.

- - - -

There is another major concern related to the visibility function unknown to previous investigators. The stage 5cognition process evaluates the signals received from the O–, P–, Q– and R–channels in an unknown manner(Sections 11.1.4.2.1 and 11.6.4.4). This unknown function is concatenated with the initial signals, UV–, S–, M– andL–, generated by the stage 1 sensory receptors and the summing and differencing performed by stage 2 signalprocessing. It appears the stage 5 cognition process is not a linear summation because the sensation of “vividyellow,” usually associated with a wavelength of 583 nm is not associated with a peak in the R– signal, and noobvious feature of the Q–signal (Section 17.3.9.3). The vivid yellow perception can also be enhanced by thecreation of the Purkinje effect generally reported to peak at 580 nm (Section 17.2.6).

The clearest way to evaluate the visibility function non-invasively is to evaluate subjects with stage 2 colorblindness, those unable to generate the O–, P– and Q–channel color signals. Such a subject will perceive only theR–channel signal associated with the summation of the stage 1 signals. It is proposed that this perception will be theclosest possible psychophysical perception of the visibility function, V(λ). Invasively, the simplest method is tolocate a neuron projecting an R–channel signal from a stage 2 signal processing engine or a stage 3 signal projectionneuron.

- - - -

Definition: The shorthand notation, V(λ), is more completely, and properly, expressed as Vt(λ, F, area, location,adaptation state) where the F indicates the intensity of the test signal (in quanta per pulse) while the eye is uniformlyadapted with respect to wavelength. As long as it is associated with a Standard Observer, it does not represent thespectral response of a real subject under actual photopic operating conditions.

A new photopic visibility function, Vo(λ), is needed to reflect the actual spectral performance of the visual systemunder photopic operating conditions. The expanded form of this expression would be as above except thebackground level must be specified as well, Vo(λ, F, area, location, background) . The data to support thisdescription is widely available now, although it was not in the first half of the 20th Century. Figure 17.1.5-1, fromSperling & Harwerth, provides a good example of an actual photopic operating visibility function for the youngRhesus monkey obtained psychophysically30. Note, the measurements were made in quantal units, not with respectto energy or power.


31Ikeda, M & Shimozono, H. (1981) Mesopic luminous efficiency functions J Opt Soc Am vol 71(3), pp280-284

As noted by Sperling & Harwerth, “Clearly, the narrowpeak at 610 nm cannot be accounted for by anyadditive combination of the sensitivities inferred fromthese pigment functions (referring to the widelyaccepted sensitivity functions with peaks near 435, 555& 575).” On the other hand, the peaks at 435, 555 and575 are easily obtained from the peaks of the actualphotoreceptors near 435, 535 & 610 nm. Sperling &Harwerth demonstrated this in their differentialadaptation experiments. Curves fitting the data in theabove figure better will be presented later in thischapter.

Thornton has provided similar Vo(λ) data for thehuman, except the experiments have a few caveatsattached to them. See Section 17.2.8.

[xxx rewrite To account for bleaching ]While the quantum efficiency of photodetection ineach of the spectral channels of vision remainsessentially constant below the hyperopic region, theoverall system efficiency is reduced, inversely withrespect to illumination, within the photopic region tomaintain brightness constancy. Within the mesotopic and scotopic regions, the quantum and system efficienciesactually remain constant but the signal to noise ratio of the system degrades. The use by the CIE of a ten degree(scotopic) test field, instead of the two degree (photopic) test field in the CIE protocols is a method of spatiallycompensating for this loss in intrinsic signal to noise ratio. Note that the association of a two degree test field withthe photopic standard of 1951 does not imply all of the data used to determine the standard (in the interval of 1915-1931) was collected using a two degree field.

Definition: The shorthand notation, V’(λ), is more completely, and properly, expressed as Vt’(λ, F, area, location)where the F indicates the intensity of the test signal (in quanta per pulse) while the eye is dark adapted. The functionVt’(λ) is more properly named the Scotopic Threshold Visibility Function. The equivalent operating function,Vo’(λ), exhibits the same spectral characteristic since the feedback mechanism remains non-operational in thisregime. The resulting spectrum does represent the actual spectral performance of the visual system under scotopicconditions.

Ikeda & Shimozono have provided both the operational photopic visibility function and the operational scotopicfunction for a human in one graph31. Figure 17.1.5-2 shows their results on a continuous vertical axis. The CIEthreshold photopic visibility function, Vt(λ), and threshold scotopic visibility function, Vt’(λ), have been added forcomparison. These functions were adopted based on data that had been smoothed to the equivalent of a 30 nm widesliding window filter. It should be noted that the CIE photopic threshold visibility function does not have the samepeak wavelength (555 nm) as the M-channel component of the photopic operational visibility function (532 mm),as assumed since 1931. Similarly, the CIE scotopic threshold visibility function does not have the same peakwavelength (505 nm) as the M-channel component of the scotopic operational visibililty function (532 nm) asassumed since 1961.

Figure 17.1.5-1 A photopic operating visibility function,Vo(λ), for the rhesus monkey. Background was 3000Trolands from a 5500Kelvin source, labeled W. The linesrepresent nominal absorption spectra, in the originalfigure, at 445, 535 & 610 based on the Dartnallmonograph. From Sperling & Harwerth, 1971.


32Nicodemus, F. ed (1976-85) published in parts Self-Study Manual on Optical Radiation Measurements. Wash. DC: National Bureau of Standards Tech Notes 910-1 through 910-833Nicodemus, FE. (1973) "Normalization in Radiometry", Appl. Opt. vol. 12, No. 12, pp 2960-2973

17.1.5.5 Problems associated witharbitrary renormalization

The common practice of plotting a normallizedphotopic threshold function on the same coordinates asthe normallized scotopic threshold function (Fig1(4.3.2) in Wyszecki & Stiles) obscures threesignificant facts. First, the two curves are not obtainedunder similar conditions. The photopic response isnormally obtained on-axis using a two degree diameterprobe. The scotopic response is normally obtained atfive degrees off-axis using a 10 degree diameter probe. Second, the two curves do not exhibit the fact that theintrinsic sensitivity of the S– and M– channels do notchange with stimulus level. Third, the two waveformsare dimensionless in the resultant figure.

As noted in a NBS discussion of the process ofnormalization, each of the above functions has beenpeak normalized32. Each of the functions hasassociated with it a normalizing factor that is notexpressed. Several authors have chosen to renormalizesuch a composite peak normalized graph. A commontechnique is to renormalize the two waveforms at 555nm based on the adoption of this number for the peakof the CIE photopic luminous efficiency function (Fig2(4.3.2) in Wyszecki & Stiles). This processintroduces another pair of normalization functions thatare also not expressed. As a result, investigators havedrawn the inappropriate conclusion that the absolutescotopic luminous efficiency has a higher peak thanthe photopic function by a factor of about 2.5:1. Theyhave gone farther and concluded that the scotopicluminous efficiency function is associated in some waywith a factor described as 1700 lumens/watt. Thisfactor is frequently indicated as associated with thepeak of the scotopic luminosity function, at 507 nm, onthis renormallized graph. No explanation has been provided for the physical meaning of the factor, 1700lumens/watt. Without describing, and accounting for the individual normalization factors used, this result is totallymisleading. A more correct expression would be 1700"(x/y) lumens/watt where x and y are the normalization factorsused in the scoptopic and photopic data collection and presentation process. One of the NBS staff has presented adetailed monograph on the arcane subject of normalization33.

Figure 17.1.5-2 Operational visibility functions shown onthe same graph for HS. Top curve; –2-log photopicTrolands. Bottom curve; +2-log photopic Trolands. TheCIE threshold visibility functions have been added forcomparison (dashed lines). Solid lines from Ikeda &Shimozono, 1981.


34Kokoschka, S. (1972) in German Die Farbe vol. 21, pp39-112. Figure reproduced in Wyszecki, G. &Stiles, W. (1982) Op. Cit. pg 40935Shevell, S. (1980) Unambiguous evidence for the additive effect in chromatic adaptation Vision Res. vol.20, pp. 637-639

This is clearly shown in the data of Kokoschka34. In his plot, the “luminous efficiency,” as plotted at a givenwavelength below 532 nm, actually goes down as the intensity of stimulation increases. His plot is interesting in thathe plotted the scotopic luminosity function along with photopic luminosity data for a ten degree field. A moreappropriate plot would show the two curves normalized to 100% at a wavelength of 532 nm, the peak in the intrinsicM–channel response under both conditions. In this case, the peak in the photopic luminosity function would beapproximately 0.5 log units higher than the scotopic luminosity function. This difference would reflect the largerarea under the smoothed luminosity functions due to the logarithmic signal processing discussed in this work. Thisis the method used in the figures of Section 17.2. This method also highlights the fact that the threshold response isdominated by properties other than the relative efficiencies of the individual spectral absorbers. It is dominated byother computational mechanisms. Specifically, the relative importance of the individual spectral components iscontrolled by EITHER the relative density of the individual spectral absorbers or the signal transfer efficiency at thesynapses leading to the bilateral cells of the retina OR both. The Purkinje Peak in the threshold response is also afunction of the logarithmic signal processing and the color temperature of the stimulus.

The original goal of these normalization procedures was to accommodate the fact that neither of the two functionshad been measured in absolute terms, or under the same conditions. The areas of the test stimuli was grosslydifferent and the scotopic function was measured eccentrically with respect to the line of fixation. This work hasdemonstrated that the intrinsic sensitivity of the photoreceptors of the S– and M–channels have not changed withinthe mesotopic region. The appropriate technique would be to renormalize the two functions at a wavelength whereeither the S– or M–channel photoreceptors are dominant. Using this procedure, the two normalized sensitivityfunctions overlay each other at wavelengths shorter than 532 nm and only diverge due to the operational factorsrelated to the L–channel.

Renormalization at a shorter wavelength is also consistent with the data of Kokoschka. In his plot, the “luminousefficiency,” as plotted at a given wavelength below 532 nm, actually goes down as the intensity of stimulationincreases. His plot is interesting in that he plotted both the scotopic luminosity function and the photopic luminositydata for the same ten degree stimulus field. A more appropriate plot would show the two curves normalized to 100%at a wavelength of 532 nm, the peak in the intrinsic M–channel response under both conditions. In this case, thepeak in the photopic luminosity function would be approximately 0.5 log units higher than the scotopic luminosityfunction. This difference would reflect the larger area under the smoothed luminosity functions due to thelogarithmic signal processing discussed in this work.

17.1.6 Problems with center-surround experiments

While easy to perform, center-surround experiments have produced conflicting and controversial results over a longperiod of time. This has been due to the lack of a comprehensive model of the underlying processes. This hasresulted in analyses based on a long series of inadequate assumptions. The underlying problem came to prominencein 1980 when Shevell wrote a “letter to the editor.”35 The protagonists all assumed a linear visual system, includinga linear detection process, but differed in how to envision the subsequent signal processing. The paper includesmention of many, but not all, of the factors involved in center-surround experiments. It notes the unusual impact ofthe intensity level of long wavelength irradiance (although it does not recognize a square law relationship). It alsodiscusses a largely conceptual “‘two-process’ theory in which the adapting field both causes a gain change (asproposed by Walraven) and also contributes directly to the color signal (this contribution is called the “additiveeffect” since it affects the color signal in the test area by a fixed amount rather than a fixed proportion).”


36Dacey, D. et. al. (2000) Center surround receptive field structure of cone bipolar cells in primate retinaVision Res. vol. 40, pp 1801-181137Taylor, W. (1999) TTX attenuates surround inhibition in rabbit retinal ganglion cells Visual Neurosci. vol.16, pp 285-29038Hart, W. ed. (1992) Adler’s Physiology of the eye. St. Louis, MO: Mosby Year Book. pg. 710

The above quotation provides a direct insight into the problem of center-surround experiments. The visual system isnot linear and the signal processing is fundamentally logarithmic. Depending on the absolute values of the intensityof signals applied to the three spectral channels of vision, the perceived color of the chromatic signals can appear toadd linearly or proportionately. The experimental problem is complicated further by the contribution of the spectralchannels to the luminance signal. The perceived color is a composite of both the chrominance and luminancechannel signals. As a result, the perceived result of center-surround experiments is highly variable, paticularly atlight levels in the low photopic and mesotopic regions. Figure 2 of Shevell highlights the problem. He compares hiscurved representation and the straight line representation of Walraven to a set of data points that can be equally wellfit by a line of opposite curvature. The caveat to Figure 2 presented by Shevell highlights the limited applicability ofboth of their models. The logarithmic signal processing model combined with the square-law detection mechanismrelated to the long wavelength spectral channel of this work provides a better theoretical fit than either of theirsimpler models. It is also applicable over a wider intensity and contrast range than they address.

It is suggested that all center-surround experiments be reviewed in the light of the above discussion before any oftheir associated analyses are accepted.

A recent paper by Dacey, et. al. has broadened the subject of center-surround experiments36. They employed morereasonable light sources for the chromatic aspects of their research work. These were narrow spectral band LED’s at460, 525 & 652 nm. It is not entirely clear whether their dimensions for their test spots were with respect to theretina or an equivalent retina based on paraxial optics in air. They propose the location of chrominance signalgeneration is prior to the ganglion layer of the retina. They describe it as probably occurring in the circuitry of theouter retina. At different points they refer to bipolar cells and amercine cells. Both references appear conceptual incharacter. In section 3.1, they define cells with branching dendritic trees and multiple cone contacts as diffusebipolar cells. Recall that the morphological designation bipolar cells refers to the shape of the cells and not thenature of their output signals. They have traditionally been documented as exhibiting monopolar output signals. Dacey, et. al. note their cells exhibited hyperpolarizing or depolarizing light responses. Cells with the abovecharacteristics are defined as horizontal cells in this work. Unfortunately, they still use the term inhibition for aprocess that involves simple subtraction. They also employ a linear model of the summation process (their equation2) that only provides a precise solution over a very limited range of signal intensities. Their summary is broadranging. They are correct in their summary where they say, “these initial results suggest that the basic spatialstructure of the ganglion cell receptive field ( in macaque) is established at the level of the bipolar cell.” They notethat Taylor has taken a position similar to theirs based on “spiking” amercine cells37. This work suggests the basicspatial structure of the ganglion cell receptive field is established by the horizontal cells located at this level.Conceptually, the amercine cells of Taylor are the same as the horizontal cells of this work. Spiking amercine cellsare seldom reported. Amercine cells are typically electrotonic unless loaded electrically by a test set. The spikesreported by Taylor are probably related to his test set.

17.1.7 Historical composite descriptors of vision

Hart has described the competition in the 19th Century between the early trichromatic theory based on the physics ofthe day and the later opponent theory based on the psychophysics of that day. He summarized in 199238: “However,over the past several decades, it has become apparent that human and nonhuman primate color vision is indeedmediated by an essentially trichromatic process at the receptor level, but is encoded for neural transmission in a


39Uttal, W. (1981) A taxonomy of visual processes. Hillsdale, NJ: Lawrence Erlbaum Associates, pg. 42

physiologic paradigm of the color opponent process.” This work shows that his description was on track but toonarrow.

While the vision of the large chordates is indeed mediated by a degenerate tetrachromatic mechanism that isessentially a trichromatic process at the output of the receptor cells, neural transmission involves separate encodingand signal projection for the luminance information and the chrominance information. Only encoding of thechrominance information can be described as involving an opponent process. Luminance channel encoding is apurely additive (albeit logarithmic) process. Besides encoding, signal transmission also includes the actual signalprojection from the eye to the brain. The asymmetry of the signal projection channels plays a major role in thetransient chromatic performance of the eye. Therefore, four fundamental situations must be recognized tounderstand the operational and performance limits of the human eye:

+ The signal detection stage of the human eye involves four parallel channels that operate independently andperform all signal detection and amplification functions in vision.

+ The physiological optics of the human eye are nearly opaque to ultraviolet light. This causes the netperformance of the signal detection stage to appear to be trichromatic.

+ The signal manipulation stage of the human eye involves two distinctly separate and parallel signalingvenues that all operate under fixed amplitude conditions. There is a fundamental difference in operationbetween the single luminance channel and the two chrominance channels of human vision.

+ The signal projection stage of the human eye transmits the luminance and chrominance information to thecortex over distinctly different types of data channels and the data channels associated with the chrominanceinformation are distinctly asymmetrical.

Uttal has presented a valid question in his 1981 book. “Can valid psychophysical laws be formulated?39” Maninvariably attempts to derive “laws” to describe processes and the results of processes. In the visual science, this hasinvariably involved;

+ the adaptation of laws from other fields according to one analogy or another and

+ the proclamation of a simple law supposedly covering a wide range of a given parameter.

This process has surfaced three significant difficulties. First, the chosen analogy has frequently been inappropriateat a detailed scientific level. Second, the operation of the visual system employs multiple stages, and multiplemechanisms within those stages, that operate according to different algorithms as a function of the exciting stimuli. Third, most of the observed results related to vision are functions of more variables than the investigator explicitlycontrolled. As a result, all of the laws developed in the literature must be qualified as to their range of applicability. This qualification must account for both implicitly and explicitly recognized variables. This requires very carefuldefinition of the test instrumentation and protocols used, more careful than that generally found in the literature. Asan example, it is completely inadequate to give the wattage of an illumination source when it is the spectral output asa function of wavelength (or at a minimum the color temperature) of the source that is the relevant unstated variable.

The unidimensional laws such as those of Fechner, Beer, Grassman, etc. cannot generally be applied to visionwithout considerable qualification. As will appear below, a similar statement can be made concerning the simplemultidimensional hypotheses concerning chromatic theory proposed by Young-Maxwell versus Hering. Finally,one must be cautious when proposing an equality between two processes of grossly different underlying complexity


40C.I.E. (1986) Colorimetry, CIE Publication #15.2, Vienna: Central Bureau of the CIE41Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 310 and 164-16942Gouras, P. (1991) The perception of colour. Boca Raton, FL: CRC Press, Inc. pp 224-24843Fry, G. (1987) Judd’s 1951 color-mixture diagram Color Res. Appl. vol. 12, no. 2, pp 88-9344Partridge, J. & De Grip, W. (1991) A new template for rhodopsin (vitamin A1 based) visual pigments.Vision Res. vol. 31, no. 4, pp. 619-630

such as the simple isotropic absorption spectrum of a retinoid in dilute solution versus the complex and highlystructured absorption spectrum represented by the scotopic luminous efficiency function of the actual human eye (asopposed to the highly smoothed response of the eye of the Standard Observer).

17.1.7.1 The CIE Standard Observer and other (largely archaic) descriptors

This work will show that the standards adopted beginning in the 1920's, and not fundamentally overhauled since atleast the mid 1930's, are archaic. Their original formulation was so convoluted that it was necessary to define a“Standard Observer” that was neither a real person or the average of data from real persons. The averaging of datasets by the CIE was based on broad spectral smoothing to the extent that all information below the level of about a30 nm smoothing window was lost. The fundamental problem was the assumption of linearity in the visual system. The secondary problem was the failure to preserve conformality in the expression of the data available. The C.I.E.began publically recognizing some of these shortcomings beginning in 1976. As they stated in 1986 with specificreference to the XYZ system, “Pending the development of an improved coordinate system, the use of one of thefollowing coordinate systems is recommended whenever a three-dimensional spacing perceptually more nearlyuniform than that provided by the XYZ system is desired40.” [Underline added] Those suggested were the C.I.E.1976 uniform color space, the CIELAB and the CIELUV color spaces. Stiles & Wyszecki stress the lack ofuniformity in the proposed uniform color spaces (UCS)41. Gouras lists and discusses a broad range of studies andcross-comparisons performed in a search for a better system42. Fry reviewed the arguments for and against the CIEand Judd representations but retained the underlying linear assumption and the equal-energy stimuli of the 1924 CIEstandard43. Neither of these efforts have produced a new product. This work presents such a replacement coordinatesystem that is theoretically defendable and satisfies the needs of the research community.

Following presentation of the New threshold luminousity function (aka Luminous Efficiency Function), a discussionof the differences with the old standards will be presented. See Section 17.2.3 for the luminosity function andSection 17.3.1.3 for the color performance. Following the presentation of a New Chromaticity Diagram forResearch, a specific discussion of the shortcomings of the C.I.E. Standards will be presented. See Section 17.3.5 inPart 1b.

17.1.7.2 The use of empirically based standards and templates

Many researchers have used the C.I.E. synthetic tristimulus functions and the templates of Dartnall in the past as anaid. These aids are obsolete for research purposes, particularly when used as a reference in spectral differenceexperiments based on the linearity laws. These difference experiments have consistently computed an absorptionpeak in the human visual spectrum near 565-575 nm that has never been confirmed by electrophysiological data ormicro-spectro-radiometry. Partridge & De Grip review a number of templates previously used in vision prior topresenting data on transverse microspectrography of single photoreceptors44. While Dartnall was able to establishthe slope of the long wavelength side of the photopic spectrum, if not merely the slope of the L-channel absorptionspectrum, as the same as predicted by Fermi-Dirac statistics, he was not able to similarly quantify the slope of theshort wavelength side of these spectra. He generally defined a lesser slope.

The problem with the short wavelength side of the Dartnall templates is that they incorporate an absorption due to


45Wolbarsht, M. (1976) The function of intraocular color filters. Fed. Proc. vol. 35, no. 1, pp 44-5046Ebrey, T, & Koutalos, Y (2001) Vertebrate Photoreceptors Prog Ret Eye Res vol. 20(1), pp 49-94

the β−peak in the ultraviolet. The shape of the cumulative absorption between these two peaks, and the distancebetween these two peaks, in the absorption spectrum does not scale when the principle absorption is used as atemplate and moved along the wavelength axis. Wolbarsht discusses the derivation of Dartnall’s templates andexplores sliding the composite absorption along the horizontal axis while holding the distance between the two peaksconstant in terms of wavenumber45. The results are not compelling. He plots Dartnall nomographs in the same paperthat do not contain any β-peak.

In the case of the overall spectrum and the S-channel spectrum, the psychophysical slope is actually steeper than thatpredicted by Fermi-dirac statistics at the shortest wavelengths due to the additional absorption of the physical optics.

These aids (standards and templates) do not present the effect of the logarithmic summation in the luminancechannel. Any difference experiments that ignore these additional features and employ linear algebra cannot be takenseriously in research.

17.1.8 “Rod intrusion” as a concept

The literature of luminous efficiency measurements frequently describe the steps taken to prevent “rod intrusion” intheir data. However they fail to describe the properties of the rods doing the intrusion or the mechanism of intrusionexcept in the most conceptual way. The CIE has had a special committee, TC 1-43 attempting to formalize thesubject of “rod intrusion” for more than a decade.

CIE TC 1-43, Task Title: “Rod Intrusion in Metameric Colour Matches”

Mission– To write a report giving a step by step procedure for calculating the effect of rod intrusion on atrichromatic colour match. To use the procedure to calculate the effect of rod intrusion on typical industrialmetameric colour matches. It is interesting that this charter does not identify any earlier relevant work.

Unfortunately, being a volunteer organization that requires consensus, deadlines are not set within CIE committeesand it is impossible to say whether TC 1-43 will ever issue a report.

Most discussions of rod intrusion rely in some way upon the interpretation of the dark adaptation characteristic ofHecht as involving separate “rod component.” The expressions cone plateau and rod plateau (level) are based onthis interpretation. This assumption is mathematically unsupportable and has been shown to be untrue in Section16.4.2. Another frequent reason for rod intrusion is the change in color rendition caused either by a broadbandachromatic intrusion by a rod in the overall spectrum or the loss of the L-channel response at low levels as predictedby this work and readily identified in visual spectra as a function of light level (Section 17.2.2.2).

Ebrey & Koutalis, in 2001, presented a great mass of data from a genetics perspective that lacks any organizingstructure46. They closed with the following. “Finally, the kinetics of the gecko rod receptor potential appearsrod-like, despite the rod being filled with an M/LWS pigment. Ebry introduces a wide-ranging analysis of variousenzymes associated with the visual process by the pharmacological community. This discussion is largely unrelatedto the visual (specifically transduction) process. They introduce a section on visual photoreceptors with, “Acontinuing theme in this paper is an attempt to define what is a rod and what is a cone. We have seen that using thetype of pigment in the photoreceptor is inadequate and that so far not enough is known about the other componentsof the transduction cascade to use them as definers, although they may be the reason for the underlying physiologicaldifferences between different kinds of photoreceptors.” They go on, “Some cones, like the human parafoveal cones,


47Stabell, B. & Stabell, U. (2002) Effects of rod activity on color perception with light adaptation J. Opt.Soc. Am. A vol 19(7), pp 1249-125848Stabell, U. and Stabell, B. (1977) Wavelength discrimination of peripheral cones and its change with rodintrusion Vision Res vol 17, 423–426.

closely resemble rods in a light microscope. In addition, cones from the periphery of the retina often have differentmorphologies from those in the central retina. Moreover, there is good reason from the visual pigment workpresented above to think one might want to not lump all cones together but rather distinguish them at least by whichone of the five classes of visual pigments they have. Some efforts in this latter category are starting to appear andinvestigators are trying to delineate the properties of cones more precisely.” One useful distinction they made intheir Table 1 was the spectral sensitivity of the dark adapted scotopic eye ranged out to ~500 nm for weak stimulantsand extended to the red for the photopic eye for weak stimulants. Based on this theory, the statement can be restatedas extending to ~570 nm for the scotopic eye at 50% response (due to the loss of the L-channel sensitivity) and to660 nm for the photopic eye at 50% response with the S–, M– & L–channels active [Figure 17.2.2-3 ].

Ebry & Koutalos made another observation on an unrelated subject. “There is a second important morphologicaldistinction between the outer segments of rods and cones. In cells which are morphologically rods at the lightmicroscopic level, electron microscopy studies have found that most of the membrane area in the outer segment ismodified plasma membrane which has pinched off from the plasma membrane to form disks (see Cohen, 1972). Theplasma membrane, not the disk membrane, acts as the ion selective permeability barrier between the inside andoutside of the cell. Rods can have up to a couple of thousand of these disk membranes. In contrast, all of themembrane area of the outer segments of cones is in contact with the extra-cellular medium. The surface area tovolume ratios are quite different for rods and cones. Thus, in spite of the reservations just stated, the morphologicaldistinction between rods and cones is probably useful. What is most important is to explain and refine thedistinctions between different kinds of photoreceptor cells.” [xxx move this paragraph and reference to thephotoreceptor chapter and interpret]

In section 4.7, they state, “So far, all mammal retinas that have been studied contain no more than three members ofthe five visual pigment families.” This statement does not leave room for any “rod” pigment if the three are assumedto subserve the S-, M- and L- channels.

Their section 5 provides a broad discussion of the electronic performance of the photoreceptors. However, thegraphics do not provide a definitive difference between rods and cones. Their figures 5, 6 & 7 are indistinguishablealthough figure 5 is described as involving rods. [xxx move this paragraph and reference to the photoreceptorchapter and interpret]

They conclude, “With regard to phototransduction in particular, information on cones is quite sparse compared towhat is known about rods. Part of the reason for this disparity is the lack of adequate amounts of cones themselves.” This statement is incompatible with the common assertion that the fovea is “rod free” and therefore must consistonly of cones.

In 2002, Stabell & Stabell47 have presented work building on the work of Hunt during the early 1950's. They alsopresented a relevant paper in 1977 that focused on rod intrusion48. The term rod intrusion does not appear in the2002 paper.

Quoting Stabell & Stabell (2002), Hunt found “The most striking finding obtained was a marked decrease insaturation of the test colors when the adapting light intensity was lowered. As one of several possible explanations ofthis change, Hunt suggested that the color response of the cones was increasingly desaturated by the addition of a‘‘whitish’’ response from the rods. However, when they compared the results of a test field confined within the


49Fotios, S. (2006) Chromatic adaptation and the relationship between lamp spectrum and brightnessLighting Res Technol vol 38(1) pp. 3-17 (including critique)50Shin, J-C. Matsuki, N. Yaguchi, H. & Shioiri S. (2004) A color appearance model applicable in mesopicvision Optic Rev vol 11(4) pp 272–27851Yaguchi, H. (2005) Mesopic color reproduction In Zhao, D. Luo, M. & Yaguchi, H. eds. Illumination,Radiation, and Color Technologies

rod-free fovea with the results obtained with a foveally fixated semicircular test field of 20 deg, the reduction insaturation as light adaptation was lowered was found to be very similar—if anything, slightly morepronounced—when the rod-free fovea was test stimulated. On this evidence the rod desaturation hypothesis wasrejected, and they concluded that the rods could play only a minor role in producing the desaturation effectobtained.” They conclude no systematic study had occurred since Hunt. Therefore, “In the present study an attemptis made to examine anew the contribution of rod activity to chromaticity changes with light adaptation.” Theyexplored the visual field 17 degree nasal of the point of fixation. They used the three primaries, 460, 530, & 650 nmof the Wright colorimeter.

Their primary conclusion was interesting, “The present results are in opposition to the conclusion of Hunt that rodsmay play only a minor role in producing the desaturation effect obtained when the adapting light intensity islowered.” They did describe what they called “the absolute dark-adapted cone threshold of the background light.This threshold was found at 20.7 log photopic Trolands.” See Section 17.1.2.1.1.

While focused on 650 nm light (page 1256), they did establish several “absolute visual levels” based on the Wrightcolorimeter. “Hence, as the background intensity is gradually increased from – 4 log ph td, the sensitivity of the rodsystem to the test light decreases until eventually at 0 log ph td the rod system is light adapted to such an extent thatthe test intensity of 15 ph td is below rod threshold. At this background intensity level, then, only cones areeffectively excited by the test light.” In their interpretation, and words, higher light levels do not cause saturation inthe rods but causes “the test intensity at 15 ph td is below rod threshold.” More appropriately, this observation, ifvalid, can be stated as at 15 ph tr, saturation within the rods has caused their AC sensitivity to fall to a negligiblevalue.

They go on, “However, the analysis is not readily applicable to the results obtained with short-wavelength tests.Thus it will be seen that the chromaticity measurements during the cone-plateau period and following complete darkadaptation are closely similar at 0 log ph td also for the 450-nm test light, despite the fact that the rod receptors arestrongly activated under the dark-adapted condition by the 450-nm test light at this background intensity level.”

They conclude, “Apparently, the desaturation effect of rods depends on the test wavelength used, that is, on therelative response of the different types of receptor triggered by the test light.” Their concluding paragraph is worthyof reading because of the ambiguities left unresolved.

- - - - -

Fotios, an architect, has gotten into the discussion in his recent paper which drew considerable criticism49. Berman’sresponse appears to be far from the main stream, talking about contribution from a broad spectrum photoreceptorphysically on the ganglion neurons and not in the focal plane (Petzval surface) of the optical system. Such aphotoreceptor could not participate in resolving shapes in the far field.

Recent attempts to treat rod intrusion have focused on Yaguchi’s laboratory. A 2004 paper50 describes the threecolor opponent channels of color vision using the descriptions, L–2M, L + M – S and L + M. His 2005 paper merelyinserts a presumed rod element into his equation for the perceived response associated with these three arbitrarilydefined luminance and chrominance channels51.


52Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons

17.1.9 Particularizing the photometry and colorimetry of vision

The discussions in the literature of the photometry and colorimetry of the visual system are complex andcontradictory. Many techniques have been devised to evaluate the photometric and colorimetric performance of thevisual system. However, they are predominantly based on a simple two terminal model of the system as describedby the expression “psychophysical,” the psychological response of the total system to a physical stimulation. Thephysical stimulation is necessarily described in object space (external to the eye). The psychological responsefrequently involve the motor neuron system (pushing a button or providing a verbal response) which involveselements of the neural system beyond the visual system. Interestingly, the sampled-data character of the visualsystem, as required by the employment of action potentials in the signaling channels, has not been addressedsubstantively in the vision literature.

The discussions of the photometry and colorimetry of the visual system have also been based on an archaic premisedating from the 1800's, that the visual system is linear with respect to intensity of stimulation across the visualspectrum and a white light is perceived when the eye is presented with equal portions of a red, green and blue light. This premise has led to the consistent failure of the constellation of photometry and colorimetry techniques to giveconsistent results. It has also led to the inability of the vision community to explain in detail what constitutemetameres.

[xxx combine with the above two paragraphs ]Historically, the visual system has been assumed to be linear and only involve a single signaling channel between theretina and the cognitive neural system. It is now clear that the system involves multiple parallel signaling channels,within both the optic nerve and in higher order elements of the central nervous system. The stage 3 signaling pathsall involve sampled-data signaling. These multiple paths make the design of proper experimental protocols muchmore demanding. It is also clear the system is not linear. It is fundamentally a logarithmic system with the additionof an additional adaptation mechanism that is also nonlinear. Fortunately, a logarithmic system can be approximatedby a linear system under small signal conditions. However, the visual system operates over an extended stimulusintensity range on the order of ten or twelve orders of magnitude. Care must be taken to differentiate between largesignal and small signal conditions in the experimental arena.

Wyszecki & Stiles have provided the most comprehensive material on photometry and colorimetry to date52. Thematerial is now quite old although it is still widely used as a reference. It includes three chapters that appear in thereverse of the natural order in the view of this author, Chapter 3 Colorimetry, Chapter 4 Photometry and Chapter 5Visual Equivalence and Visual Matching. In Chapter 5, they present a wide variety of experimental configurationsfor determining the performance of the human visual system and make the important observation on page 392,

“The results obtained by the different measurement procedures, each with its own particular criterion, usuallydiffer systematically from one another. These differences offer clues toward a better understanding of thefunctioning of the visual mechanism, but they are also disturbing as they put constraints on the validity of thebasic principle of photometry.”

Because of the difficulty in controlling the operating state of the visual system and even different regions of the


retina, it is normally necessary to employ the system as a null detector in intensity differencing experiments. Evenusing the system as a null detector does not avoid the temporal response characteristics or the sampled-data characterof the system.

“The matching of brightness is the fundamental operation in visual photometry” according to Wyszecki & Stiles(page 249). They describe three principle photometric methods.

C Broad-band photometry– “The most widely used method. It involves either a thermal detector or more commonlya photon detector whose relative spectral responsivity has been modified, often referred to as ‘corrected,’ toapproximate the V( l) function.” It should be noted that a thermal detector is inconsistent with the quantum nature ofthe visual system.

C Spectroradiometric photometry– The preferred method if a realistic result is required. It involves measuring thespectral concentration of the appropriate radiometric quantity and then calculating the desired photometric quantity(luminance) in accordance with the appropriate equation of the visual response at that radiometric level.

C Visual photometry– The comparison of two stimuli of similar relative spectral radiant power using symmetricalfields juxtaposed to one another, where the intensity of one stimulus can be varied. The eye is used fundamentallyas a brightness matching device.

They go on to say, “Visual photometry is rarely used in routine photometric measurements. It suffers from lowprecision, and the visual judgements made by individual observers differ somewhat from one observer to the nextand from the (hypothetical) standard photometric observer, characterized by V(λ) and V’(λ).”

17.1.9.1 Stimulus matching methods

Figure 17.1.9-1 shows conceptually the four major matching methods of photometry and colorimetry. The threemethods on the left are static. The subject is usually asked to adjust the intensity of one or more of the componentsshown in order to achieve a “best match.” As a result, the duration of any given observation is usually longer than150 msec. In the technique on the right, the situation is dynamic. The subject is also asked to adjust the intensity ofone or more of the components while the two fields are being alternated at a fixed rate. The flicker frequencybecomes a significant factor in the results.

The “photometric” method on the left is primarily associated with luminance matching between two stimuli ofsimilar spectral content. If the spectral content is not similar, the matching procedure frequently results in multiplematch points and introduces the previously complex problem of identifying and defining metameres.

Figure 17.1.9-1 Three major matching geometries of photometry & colorimetry. In the sequential method, theexperimental components shown on the right using bipartite fields are presented sequentially using the total field at aspecified flicker frequency.. Modified from Wyszecki & Stiles, 1982.


As discussed in Sections 17.1.2.3, 17.2.1 (work of Thornton) & 17.3.4.3, the understanding of metameres iscritically dependent on an adequate understanding of the visual system. Metameres do not exist in object space, theyare perceptual phenomenon resulting from the signal sensing and manipulation mechanisms within stages 1 and 2 ofthe system. They exist in two forms, chromatic metameres and complete metameres. Two stimuli are chromaticmetameres only when both their P channel voltages are equal and their Q channel voltages (technically their O, Pand Q channel voltages) are equal. Two chromatic metameres are complete metameres if their R-channel voltagesare also equal.

The “colorimetric” methods illustrated in the two central frames attempt to match two fields of different spectralcontent by adjusting the intensity of one or more of the components to achieve a precise match. Historically, thesematches have assumed the visual system follows the law of color addition in object space given as R(λ)R-bar + G(λ)G-bar + B(λ) B-bar = WAW-bar. The intensity values given as a function of wavelength are narrowband. The barredvalues are primary stimuli of fixed wavelengths chosen arbitrarily, λR, λG, λB, except for L-bar and W-bar. L-bar is atest stimulus of variable wavelength and W-bar is a fixed stimulus defined as white. The values of R(λ), G(λ) &B(λ) are the tristimulus values obtained for the set of reference wavelengths, λR, λG & λB. Any test wavelength L-bar, can be used in the maximum saturation method. In the Maxwell method, the test source is specified as a white.

There are major problems with the maximum saturation and Maxwell methods.

C The dominant problem is that the visual system does not employ the law of color addition applicable to objectspace.

C The use of three wavelengths in the maximum saturation method does not produce a match if L-bar is a wavelengthshorter than the peak of B( λ). This failure is due to the tetrachromatic capability of the human eye in the regionbetween 400 and 437 nm.

C The use of R(λ)R-bar plus G(λ)G-bar in the upper half of the maximum saturation bipartite field cannot match anarbitrary L(λ)L-bar plus B(λ)B-bar. It is typically necessary to remove the B(λ)B-bar term from the lower bipartitefield and add it to the upper bipartite field to obtain a match. The result is a set of color matching functions thatrequire a negative intensity for the expression, B(λ) (illustrated in W & S, page383). This requirement shows theinadequacy of the underlying hypothesis of linear summation. It is widely noted to be unrealizable. This failure ofthe conventional matching protocol is due to the use of a linear law of subtractive color within the visual system.

C The color matches obtained using either method fail with major changes in retinal illuminance (W & s, pp 376-378).

The criteria for a complete match under the Maxwell method is not that the x & y chromaticity values of the twofields match. The criteria is that the P and Q values of the two fields match to give a chromatic match and that the Rvalues also match to give a complete match (Section 17.3.4.3).

Use of the sequential method shown on the right introduces another complication discussed in Section 17.2.1.5. Thestage 3 chrominance channels of vision are modulated asymmetrically and involve a low pass filter in the decodingcircuits used to recover the information. The result is a significant impact on the measured results as a function ofthe flicker rate. The rolloff flicker frequency is near 3 Hz.

The diameter of the bipartite or sequential fields have a significant impact on the results of the experiments. Theretinas exhibit a significant change in color performance at the edge of the foveola (1.2 degree diameter) asrecognized by Maxwell’s Spot (Section 17.3.1.7.2). Investigators have used a wide variety of bipartite andsequential field shapes. Wyszecki & Stiles describe about ten on pages 288-293. They provide a list of protocols


53Palmer, D. (1967) The definition of a standard observer for mesotopic photometry. Vision Res. vol. 7, pp619-62854Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg 406

using these field configurations in matching experiments on pages 392-394. Many of these require revision to meetthe demands of a multiple parallel channel signaling visual system.

Section 17.3.4.3 develops the subjects of metameres and compliments et al. in greater detail.

17.1.9.2 Problems with luminance descriptors

Lacking a model of the signal processing occurring within the visual system and with only limited knowledge of thenecessary physics and chemistry at the time, the early investigators of the luminance characteristics of the human eyerelied primarily on psychophysical tests to provide the luminance transfer function of the eye. To obtain comparableresults in different laboratories, test conditions were standardized to the maximum amount possible at the time. Thisstandardization did not generally include the filter bandwidth on the various spectrometers used because many ofthese were locally constructed. Similarly, the spectral characteristics of the illumination was not well standardizedamong laboratories (see background in Section 17.1.5.4).

Lacking a sophisticated model of the eye, the available luminance response information was collected and basicallyaveraged for each spectral wavelength. This was the genesis of the C.I.E. Luminance Response of 1924 (2 degreeStandard Observer). The technical shortcomings of this standard were reported in the literature almost immediatelyby Judd, the Chairman of the Committee responsible for its creation. This standard only applied to the “photopic” orhigh light level response of the human eye. It was only in 1951 that the C.I.E. expanded its standard to recognize thetwo extreme conditions. The 1924 Standard was renamed, the CIE Photopic Observer Curve of 1924 (2 degreeStandard Observer), and the new Standard was named, the CIE Scotopic Observer curve of 1951 (2 degree StandardObserver). These standards still did not specify the light level at which they were applicable for they did notrecognize the continuous transition occurring with illumination level. Palmer53 made an effort to define thistransition. However, his effort was basically an attempt to define a linear interpolation of these two Standards as afunction of illumination level. His efforts provided several insights but used so many different parameters thanused for the C.I.E. Standards that the works are not comparable. In addition, the Standards were prepared withoutspecifying the color temperature of the source used to collect the data. Wyszecki & Stiles review the experimentalevidence of why Palmer’s linear summation hypothesis is not acceptable54.

17.1.9.3 Problems with chrominance descriptors

Investigations of the chrominance response of the eye have been hampered by two problems; lack of a detailedunderstanding of the operation of the eye and the assumption that the luminance and chrominance functions wereclosely related. Without a model based on a significant amount of electrophysical evidence, many of the earlyhypotheses can only be described as conjectures. After these two basic problems, there were two more significantproblems; the assumption that the eye was fundamentally a linear device and that the sum of the responses from theindividual chrominance channels represented the luminance response (at least under photopic conditions). Embedded in the linearity assumption is the related assumption that the signal levels in the various chromaticchannels track each other regardless of illumination levels. Following the above axioms, the basic hypothesisenshrined by the C.I.E., has been that color vision involved a trilateral process and the process was stable over asignificant range of illumination levels. The first corollary is the color performance of the human eye can berepresented on a trilateral diagram with the corners approximated by the generally accepted and semantically definedprimary perceived colors of red, blue and green.

The above rational has resulted in the C.I.E. Chromaticity Diagram of 1931 and its progeny. These diagrams are


known to be poor representations of the performance of the eye for scientific purposes. However, they have gainedwide commercial use and are destined to be used for a very long time in that regime. For scientific purposes, a moreaccurate and precise diagram is needed. The C.I.E. has struggled to provide more useful chromaticity diagramsbased on empirical factors.

This work looks at the complete model of vision and defines a different set of fundamental conditions. Thefundamental conditions are two; the chrominance signaling system is fundamentally separate from the luminancesignaling system, and the chromatic signal processing of vision involves mathematical differences between pairs ofchromatic signals.

Although the chrominance and luminance signaling channel share the same photon detection channels, they arecompletely separated within the analog signal processing regime of the retina. Their perception within the brain isindicative of this fact. The perceived color of an image is separate from its perceived brightness. Unfortunately, theexperimental procedures to demonstrate this situation are difficult. Suggested procedures will be highlighted below.

The chromatic difference signals are independent of each other and are therefore best represented as orthogonalcomponents on a composite graph. This postulate applies to tetrachromatic vision as well as trichromatic vision.

There are two complications that arise within the above context. First, each chromatic detection channel involves ahighly non-linear electronic gain mechanism, dependent on the signal level received from the transduction functionand incorporated into the dendritic structure of each photoreceptor cell. The transduction process itself, as definedherein, for the L-channel is fundamentally and significantly different than that of the other channels. It involvesdifferent parameters and mechanisms.

Because of these two complications, the resultant amplitude transfer functions associated with the variousphotoreceptors do not track each other when the illumination level is changed. The individual channels responddifferently with regard to signal intensity delivered to both the chrominance differencing circuits and the luminancesummation circuits.

A satisfactory theory of human, as well as animal, vision must utilize a model that can account for the fundamentalchromatic perceptions reported by the subject and also account for the long list of special effects noted by variousinvestigators. Previous theories of vision have not reached that stage of sophistication. This work appears able toexplain these effects. Because of time and page limitations, only a few of them can be discussed in detail.

17.1.9.4 Threshold performance descriptors

Many investigators have sought to describe the threshold performance of the human eye. This has been extremelydifficult without a clear understanding of the photodetection process and the signal manipulation within the visualsystem. As a result, most experiments to date have relied upon psychophysical perceptions. A significant result ofthis work has been the recognition that the threshold performance of the system in the photopic and hypertopicregions is primarily determined by the dynamic range capability of the signaling channel. The threshold in theseregions can be considered a “hard” or deterministic level. It is only in the mesotopic and the scotopic regions thatrandom noise becomes significant. In this region, the threshold level can be considered “soft” or statistical incharacter. The noise threshold in the scotopic region is significantly different than the noise threshold in themesotopic region.

There has been a common attempt to consider the photoreceptors of the eye as thermal noise limited devices such asphoto-conductors. However, a clear understanding of the photoexcitation process would show that photodetection in


55Foster, D. & Snelgar, R. (1983) Test and field spectral sensitivities of colour mechanisms obtained onsmall white backgrounds: action of unitary opponent-colour processes: Vision Res vol 23, pp 787-79756Snelgar, R. Foster, D. & Scase, M. (1987) Isolation of opponent-colour mechanisms at incrementthreshold Vision Res vol 27, pp 1017-1027

vision is a quantum statistical process similar to that of photo-emission rather than photo-conduction. As in aphotomultiplier tube where a photon above a certain energy will cause the ejection of an electron into free space, aphoton must be above a certain energy in order to excite a visual chromophore. Also as in a photomultiplier tube,the quantum mechanical process of exciting an electron into a higher energy state is a thermal noise free process. For typical photomultiplier tubes, photographic films and visual sensors in animals, the thermal noise energyassociated with the detection process is at least an order of magnitude lower than the energy required of the photons. The result is an essentially thermal noise free detection process. The important question with regard to vision iswhen does noise, other than quantum statistical noise, become a factor in vision. As will be shown below, theperformance of the visual system is determined differently in the photopic, mesotopic and scotopic regimes. Theperformance is also slightly different in the L-channel compared to the M- and S-channels.

In the photopic regime, the performance of the visual system is not noise limited. Instead, it is limited by thedynamic range of the signaling channels. In both the mesotopic and scotopic regimes, the visual system in animalsis stochastic noise limited. In the mesotopic regime the predominant noise is that associated with the quantum noiseof the input illumination. In the scotopic regime, the noise is primarily of cortical origin. This stochastic noiselimited performance in a two dimensional array of detectors can cause a problem when the data is processed in thebrain. The result is perception of various shadowy hazards in the field of view, which need not actually exist, undervery low light conditions.

17.1.9.5 Internal calibration of the human visual system

At least two internal calibration procedures can be identified based on the author’s experience. Upon awakening in aa dimly or reasonably lighted room, but before the eyes are opened, two distinct conditions are regularly observed.

C A uniform field of pale blue dots is observed across the entire perceived field of view. The dots appear to be at ornear the size and density of the S–channel photoreceptors. The typical duration of this event is a few to ten seconds

C A field of short, rose–red (almost neon like) lines is observed where the orientation of the lines appears to bepredominantly vertical and horizontal relative to the normal axes of the eyes. The lines have a minimal width(similar to the diameter of the pale blue dots) and to have an aspect ratio of about 10:1. The lines have a moving, asif boiling) appearance. The lines are not uniformly distributed. There is clearly a greater density of lines (probablyby 3:1) in the region defined by the 1.2 degree diameter foveola. There does not appear to be any delineation of thelarger fovea. This pattern is also observed for a period of 10-20 seconds unless the eyes are opened.

Upon opening the eyes, both of these calibration routines are obscured by the higher contrast information in theexterior scene.

17.1.10 Other individual descriptors

Foster and Snelgar have discussed the separation of the descriptors of vision in order to relate to the chromatic-opponent and achromatic (luminosity) mechanisms55,56. Such a separation is key to the understanding of vision. It


57Sharanjeet-Kaur, (no initial). Kulikowski, J. & Walsh, V. (1997) The detection and discrimination ofcategorical yellow Ophtha Physiol Opt vol 17(1), pp 32-3758Kelly, D. (1979) Motion and vision. II. Stabilized spatio-temporal threshold surface. J. Opt. Soc. Am. vol.69, pp 1340-1349

is totally supported by this work. It bridges the chasm between spectral sensitivity curves of human vision and the πparameters of Stiles. Sharanjeet-Kaur et al. have also explored the spectral responses of vision at slow (1 Hz) and 25Hz flicker rates57. Their work shows additional subtleties of the visual process and bridges the chasm between the“fundamental spectra” of the Stockman school and the “spectral sensitivity curves” of Foster and Snelgar (and Stiles)and this work. See Section 17.2.1.5 for further discussion of the Stockman material.

17.1.10.1 Frequency Domain Descriptors

In vision, the frequency domain is unusual in that includes both the temporal frequency domain and the spatialfrequency domain. While this has not caused difficulty for the majority of investigators working in only one of thesedomains, it requires careful definition if the properties of both domains are to be correlated. It is also important tonote that the performance associated with each of these domains is a function of the location within the field of viewof the retina. Even more significantly, the laboratory results are strongly influenced by the spectral character of thestimuli used.

Traditionally, it has been easier to perform psychophysical experiments related to the contrast performance of thesystem versus frequency than it has been to explain the results. The number of variables involved in the explanationis quite large. It requires a detailed knowledge of the system to annotate these variables and describe theirinterrelationships.

Frequently, investigators have used a graphic to present their threshold sensitivity functions with respect tofrequency that has resulted in loss of perspective on exactly what was being presented. It frequently appears that thefunctions are crossing the horizontal axis at a very high angle. In fact, the horizontal axis is an absolute limitcorresponding to 100% contrast, i. e., a black and white test target of the highest possible contrast. The distancefrom this asymptote is actually a measure of the threshold level within the signaling channel relative to a 100%contrast situation at the specified excitation level.

17.1.10.1.1 Specific definitions related to contrast functions versus frequency

As a starting point, the term contrast sensitivity function, CSF, frequently has different meanings in different papers. To solve this problem, the term will be modified to the Contrast Spatial Frequency, CSF, and the Contrast TemporalFrequency, CTF, functions. Beyond these two terms, the additional relevant parameters will be indicated either by asubscript or parentheses. The temporal frequency response is usually given in terms of Hertz. The spatial frequencyresponse is frequently given in angular measure, cycles per degree in object space. Care must be observed when thedata is referred to the retina or to image space in terrestrial eyes. The frequency in cycles per degree is not the samein these two spaces due to the difference in the index of refraction between air and the vitreous humor of the eye, and Snell’s Law.

It will become apparent below that, at least in the HVS, most of the mechanisms affecting the spatial frequencycontrast are in fact temporally based mechanisms. Only the spatial performance of the lens group of the eye is basedon a purely spatial mechanism. As a result, the CTF and CSF show a familial resemblance. This has beendocumented in Kelly58. In that paper, Kelly declares: “retinal image motion is the sine qua non of vision.” However, They did not factor this fact into the low frequency portions of some of his figures. The interface betweenthese two domains is closely related to the seldom studied tremor of the visual system. This aspect will be addressed


59Kelly, D. & van Norren, D. (1977) Two-band model of hereochromatic flicker. J. Opt. Soc. Am. vol 67, pp1081-109160Miller, N. & Newman, N. (1998) Walsh and Hoyt’s Clinical Neuro-Ophthalmology, 5th ed. vol. one. Baltimore, MD: Williams & Wilkins pg 165

in Section 17.1.2.3.2. The actual performance related to the CTF and CSF will be presented in Sections 17.6 and17.7 respectively.

17.1.10.1.2 Attempts to differentiate between temporal and spatial contrast

Kelly introduced his study of the spatio-temporal performance of vision by modeling the spatial and temporalperformance of the eye as orthogonal functions (his equation 1). He then insisted that approach did not work andproceeded to introduce alternate formulations that all included a cross product between the performance in the twodimensions (his equation 2). He then reverted to a template approach not supported here. His figures 13 & 15provide a reasonable description of the modulation of the signal presented to the cortex by the luminance channel butit lacks mathematical precision. His graphical work focuses on a conversion factor of 2 degrees/second between thetemporal and spatial domain (his figure 15) that will be compared to other sources in Section 17.6.3. It must benoted that his test set had an angular RMS sensitivity of “about one minute of arc” and was unable to sense theamplitude of the tremor of the eye. His statements concerning a stabilized image must be interpreted in terms of aresidual motion being present for which he did not fully account (his figure 6). In the context of this work, his datarelated to an image moving at a constant velocity relates to the tracking mode of Section 15.2.5. For his data relatedto an image moving at zero velocity, the actual motion is that associated with tremor and represented by theanalytical mode of Section 15.2.5.

Experiments have also been performed to quantify the spectral contrast performance of the visual system59. To avoidconfusion with the above acronyms, the term Chromatic Contrast Frequency (CCF) function will be used whendiscussing these experiments. The same function has been described using the term chromatic flicker in Wyszecki &Stiles. (1982). These experiments have been performed in both the temporal and spatial frequency domains. If thetest samples are carefully chosen to minimize the luminance difference between the samples, the luminance channel,R, does not participate in the signaling process and only the P and Q chrominance channels are involved. This resultsin a more complicated situation than recognized by Kelly & van Norren. Since these are orthogonal differencechannels with asymmetric temporal frequency characteristics, there are a multiplicity of different test protocols thatcan be implemented. In general, each of these protocols will generate a different form of chromatic contrastperformance.

Most conceptual models of the mechanism underlying the contrast performance of the system versus frequency havegenerally relied upon a series of quasi-independent band pass filters60. Kelly generally follows this approach. Nomorphological or electrophysiological signs of such filters have ever been found and no such conceptual model hasbeen reduced to practice. The following material will demonstrate that only low-pass filters are used in the visualsystem.

Kelly has attempted to fit a single equation to his data using a function in the frequency domain that Hodgkinapplied to a related visual model in the temporal domain. In both cases, the generic equation only applied to aspecific data set. It did not describe the general situation. Both authors relied upon auxiliary equations tomanipulate the original equation to apply over a wider range. This work has shown that all of the frequencyselective filters of the system are low pass filters. There are no bandpass filters within the visual system. However,in two cases, individual low pass filter stages are employed in feedback circuits. As a result, these overall circuitsexhibit a high pass characteristic. By serially combining the low pass and high pass filter elements of the variousStages of vision, an equation can be derived that does describes the correct contrast performance of the system overa wide range of conditions.


61Kelly, D. (1979) Op. Cit.

The models discussed in this chapter will be limited to first order models. Several mechanisms in vision requiremore sophisticated models for their complete description. The operation of the iris is particularly complex but ofrelatively little experimental interest. It can be described in detail using a hysteresis loop of nearly parallelepipedproportions and two opposite sides exhibiting different time constants. The method of encoding employed in thechromatic signal projection paths of stage 3 are asymmetric with respect to signal level where the signal level is achromatic difference. This feature complicates the detailed discussion of the performance of the chromatic contrastperformance of the system.

Kelly, et. al. have provided the results from an extensive set of carefully (but not adequately) planned experiments. The range included the temporal, spatial and chromatic contrast performance versus frequency. His use of an equal-energy light source, instead of the prefered equal-photon-flux source, in some experiments without careful controlof the color temperature leads to some uncertainties in the interpretation of his data. However, he did define thechange in operating regime between the scotopic/mesotopic and the photopic as well as the change between thephotopic and the hypertopic. His work has clearly demonstrated the similarity of the spatial frequency and spatialfrequency characteristics suggested by the theoretical model of this work61.

Kelly & van Norren summarized the conflicts in the literature in their 1977 paper. This literature is generally basedon the use of photometric units. They said: “Unfortunately, no two of these techniques yielded the same results, so itis not certain than any of them succeeded in measuring the characteristics of independent cone classes.” In thatpaper, they deviated from their earlier use of an equal energy source in the use of a mixture of red and greendesigned to produce a broadband yellow. The red and green was derived from a 3400 Kelvin tungsten halide lightsource (neither equal energy or equal photon flux) using filters. They continued to use a 1.8 degree field in objectspace (roughly the size of the foveola) and a 2.3 mm artificial pupil. This effort produced a low frequency portion ofthe CTF at an illumination of 860 Trolands that did not exhibit a horizontal component. It would be useful to repeatthis experiment using a narrowband yellow at 572 nm (see next section). There is a null in the chromatic contrastcharacteristic at this wavelength. Use of this wavelength would insure there was no component of chromaticcontrast introduced into the experiment as a function of illumination level.

In all of the located experiments, the experimenters did not compensate for the loss in absorption associated with thelong wavelength spectral channel in the scotopic and mesotopic ranges. As a result, the test contrast generated bythe test set was not the same as the test contrast sensed by the visual system, particularly at levels below about sevenTrolands.. This fact led Kelly & van Norren into a series of experiments exploring the “Silent-Green” and Silent-Red flicker effects. It is suggested that these effects were largely spurious and due to the use of a stimulus that didnot correlate with the actual sensitivity of the chromatic channels. Their proposition that the visual channelexhibited both an opponent color response and a achromatic response is supported by this work but on entirelydifferent grounds. They presented eight corollaries based on their proposed dichotomy. This work will present amore general continuum. Portions of this continuum can be correlated with some of their corollaries. Future lowlevel tests should differentiate between the test contrast based on the absorption of the chromophores of vision andthe incident test contrast calculated using an arbitrary spectral band.

17.1.10.1.3 Lack of attempts to differentiate between chromatic and temporal or spatialcontrast

In reviewing the literature, it is abundantly clear that the psychophysical community has paid little attention to thespectral quality of the illumination used in spatial and temporal contrast threshold measurements. The unstatedassumption being that their test protocol only excited the subject’s luminance channel of vision. This has led tomuch of the difficulty and confusion in correlating various investigators data that was noted by Kelly & van Norren.


Lacking an adequate model of the visual system, these investigators have made minimal efforts to excite only asingle signaling and/or perception channel of the visual system. As a result, it has been impossible to separate andcontrol the relevant variables during the experiments. Lacking this control, it has been impossible to de-convolvethe data and obtain explicit insights into the operation of the system.

It is critically important that future experiments not rely upon photometry in the representation of their stimuli. It isperfectly clear from the Overall Block Diagram, the spectral characteristics of each chromophore and the NewChromaticity Diagram for Research presented in this work that more precise radiometric and temporal conditionsmust be met in future experiments:

+ The experiments must seek to excite either the temporal, the spatial or the chromatic channels of the visual systemindividually. The design of such experiments is not a trivial problem. There is considerable crosstalk between thesedifferent domains as noted by Kelly.

+ The experiments must recognize that the performance of the system depends on the mean flux level absorbed bythe spectral channel associated with each individual type of chromophore. This includes the irradiation of thechannel before each test as well as during each test. Adaptation is a spectral channel specific function.

+ The experiments must recognize that the signal and data processing capabilities of the visual system are differentfor the foveola and the rest of the retina (as clearly defined by Maxwell’s spot (Section 17.3.1.7.2) and the nature ofa large selection of after images).

The New Chromaticity Diagram for Research, especially when drawn with the auxiliary axes defining thediscrimination capability of the P– and Q–channels is particularly valuable in designing well controlledexperiments. [Figure 17.3.3-12 in Section 17.3.3.6]. By comparing the new diagram with the spectral content of theP–, Q– & R– channels, it is clear how the spectral content of the stimuli must be controlled. It is also clear that thereare two fundamentally independent chromatic difference channels and that each exhibit an independent chromaticcontrast function.

As an example, to determine the chromatic contrast function of the Q channel, the intensity of thestimulus must always be high enough to cause operation of each chromatic channel in the photopicregion. Maximum differentiation in the data requires that the mid wavelength stimulus not containany spectral content at wavelengths longer than 572 nm and the long wavelength stimulus notcontain any spectral content at less than 572 nm. When making threshold experiments, best resultswill be obtained when the mean of the mid wavelength stimulus spectrum is as close to 532 nmand the long wavelength stimulus spectrum is as close to 640 nm as practical.

As explored in Chapter 11and as to be discussed below in Section 17.6, the temporal frequency characteristics ofthe P– and Q–channels are quite different from those of the R–channel. Furthermore they are temporallyasymmetrical. This makes determination of the chromatic contrast functions between red and blue and betweengreen and magenta particularly demanding.

Failure to recognize these temporal frequency differences in the past has contributed to the pollution of experimentsdesigned to measure only the temporal or spatial contrast frequency functions. This fact is highlighted in acomparison of figure 1 of Kelly & van Norren in 1977 and figure 4 of Kelly in 1961. The 850 Troland curve in the1961 paper is essentially the sum of the two distinct curves in the 1977 paper measured at 860 Trolands but usingspectral filters matching the absorption spectrums of the chromophores of vision. The use of these filters seriouslyimpacts the integrity of the photometric intensity measurements.

17.1.10.1.4 Temporal Frequency Domain Descriptors


The temporal description of the human eye has suffered from neglect compared to the static and quasi-staticluminance and chrominance descriptions. First, because of instrumentation difficulties, there have been almost nocharacterizations of the transient response of the human eye to the onset of illumination. Second, thecharacterization of the transient response of the human eye following cessation of illumination have not beencomprehensive in terms of original illumination levels or spatial location within the field of view.

During the early scientific characterization of the temporal response following cessation of illumination, usuallydescribed as the adaptation curve, two relatively distinct zones were frequently observed in graphs of the luminancesensitivity versus time. Lacking any other confirmation, these two levels were assigned relationships to thecontemporary relationships being discussed verbally in the morphology arena, e.g. there appeared to be two generalclasses of photoreceptors, rod shaped and cone shaped ones. Although this morphological difference has sufferedwith time and has not been correlated with the visual performance of the eye to this day, the “adaptation curve”portion of the complete temporal response is still shackled with the “rod & cone” terminology, even though manyadaptation curves fail to present two distinctly different sensitivity plateaus. As will be seen below, the transientresponse following illumination onset has never exhibited two plateaus. No correlation between the onset transientand any morphological feature of the eye could be found in the literature.

With the development of the field of electronics and the field of the Response of Physical Systems behind them, theearly experimenters might have come to a different conclusion concerning the “adaptation curve.” In this era,anyone trained in the above fields and looking at this curve would quickly recognize it as the performance of a single2nd order physical system. The mathematical description of a 2nd order system involves two arguments and severalinitial conditions. The arguments are a time constant and a natural frequency. By varying these arguments, theexperimenter can describe the adaptation curve as a function of the spatial position in the field of view. It is true thatthe observed response is not precisely that of a 2nd order system. However, this is due to the non-linear gaincharacteristic of neuron incorporated in the photoreceptor cells, specifically the adaption amplifierActivas associated with the dendritic structure. When this characteristic is factored into the equation, the result predicts the characteristics of the signal at the pedicels of the photoreceptors with excellent precision.

Using the model developed herein, the complete transient response of the eye to illumination can be defined for anyillumination level or change in level. The dominant feature in the response is the performance of the adaptionamplifier Activas of the Photoreceptor cell and the diffusion parameters associated with the bioenergetic materialproviding power to those Activas.

17.1.10.1.5 Spatial Frequency Domain Descriptors

Many investigators have measured the spatial performance of the HVS, usually allowing the eyes to fixate on thestimulus. As a result, most of the data refers to the performance of the analytical channel associated with thefoveola. Most past attempts to model the spatial frequency response of the visual system have sought to locatelumped constant filters or in some cases sampled-data networks that can account for the variations in the spatialfrequency response of the system without recourse to the temporal domain. These attempts have not gone beyondthe conceptual stage. This work will introduce an alternate approach wherein the spatial performance of the eye is aresult of a conversion of spatial position and motion into a temporal signal related to relative phase and to frequency. This alternative is implemented differently in different areas of the retina. Within the foveola, the approach is basedon the mechanism called tremor and its ability to modulate the spatial information into a temporal data stream.

As a result of this change in approach, it is proposed that Kelly’s quote in Section 17.1.2.3 be modified to includetwo additional words: “retinal image motion is the sine qua non of imaging in vision.” The visual system operates


perfectly well as a change detector in the time domain without any retinal image motion. It is also able to sensemotion intrinsic to local elements of a scene. However, to form an image, the image projected by the lens mustmove relative to the retina. This requirement explains why the blood vessels on the surface of the retina areessentially invisible. Their shadows do not move relative to the retina.

Kelly has presented significant data in his 1979 paper. No model is associated with the data in that paper. Only atemplate solution. More recently, a multi-institutional team have been collecting spatial contrast performance as afunction of spatial frequency under the designation MODELFEST. All of this data will be reviewed in Section17.6.3. 17.1.10.1.6 Chromatic Frequency Domain Descriptors

Some interesting but complex experiments have been performed in the spatial chromatic frequency domain. Only afew noteworthy experiments have been performed in the temporal frequency domain of vision. There is a largerarray of data available with respect to the transient chromatic domain as it appears in flicker experiments. This datais addressed in Section 17.6.1 & 17.6.2. Kelly & van Norren provided additional data on the chromatic responseversus frequency in their 1977 paper. They did not associate a model with their experimental results.

17.1.10.2 Parametric properties clarified

This Chapter brings together considerable disparate data. This action provides clarification of a number ofproperties related to the model that could not be defined in isolation. These include the nominal signal levelsoccurring in the signal processing section of the retina, the effect of various photoexcitation, vascular (hydraulic),and channel related (temporal) time constants.

One of the most important properties involves the signal levels at the pedicels of the photoreceptors. The signalmanipulation subsequent to the pedicels is designed to process constant peak amplitude signals.

The chromatic channels of the visual system are designed to employ constant peak amplitude voltage signals at thislocation (the logarithms of the current through the axon diode). The perception of chromaticity will be seen to becritically dependent on this condition. Further, the lateral cells related to the two chrominance signaling channels areseen to provide signal differencing without any difference in amplification between the pairs of input signals.

The very strong implication from the above situation in the chromatic channels is that all photoreceptors creategenerator currents and generator potentials of equal size at the pedicels, within the gain capabilities of theirindividual adaptation amplifiers.

The luminance channel appears to involve different relative amplitudes between the various chromaticphotodetection signals. It is quite easy to account for these different amplitudes within the signal processing stage. Therefore, it will be assumed, lacking adequate data to the contrary; that under steady state, non chromaticallyadapted conditions, the output voltage of all of the photodetection channels is nominally the same. Any differencebetween them suggested by the perceived luminosity function or luminance equation is due to differences inamplification within the signal manipulation stage. More specifically, the signals at all pedicels can reach the samemaximum voltage. However, different amplitude voltages may be applied to the bipolar cells of the luminancechannels. This is accomplished using different impedance synapses at the input to the common emitter terminal ofthe Activas within the bipolar cells.

The above conditions with regard to both the luminance and chrominance channels suggest that the mosaic ofphotoreceptors in the retina of all Chordata during genesis consists of groups of four different chromaticphotoreceptors in a repetitive pattern. Some chromatic photoreceptors may be represented more than once in each


62Douglas, R. Bowmaker, J. & Kunz, Y. (1987) Ultraviolet vision in fish. In Seeing Contour and Colour,Kulikowski, Dickinson & Murray, Ed. NY: Pergamon Press pp. 601-61663Luckiesh, M (1922 & 1965) Visual illusions. NY: Dover Publications. [in my personal library]

group. In large animals, the ultraviolet photoreceptors are vestigial. In some species, the ultraviolet photoreceptorsappear to disappear in early life. Douglas, et. al62. have traced this phenomena in brown trout Salmo trutta androach Rutilus rutilus, both fresh water teleosts. For human, the result is that there are at least vestigial ultravioletphotoreceptors, as seen in aphakic subjects, and the density of each chromatic photoreceptor type is essentiallyequally distributed throughout the retina. Their figure 7(b) shows the mosaic pattern underlying the Outer Segmentsof trout.

The mosaic nature of the chordate retina implies that the flux density received from an 7,053 K scene, by thephotoreceptors related to each chromophore, are the same or in proportion to the presence of each chromophore typein the basic group of the mosaic and in their relative cross-section within each group.

17.1.10.3 Anomalies and Effects

Based on the explanation of the luminance, chrominance and temporal characteristics of the human eye developed inthis Chapter, a straightforward explanation of most of the unusual situations reported concerning the operation of theeye can be provided. Frequently it is necessary to separate effects due to external anomalies, frequently introducedby a magician, from those caused by computational anomalies within the visual system. A number of books haveaddressed this separation63. A technical discussion of these explanations will be grouped in a later Chapter.

17.2 The Luminance Characteristic of the human eye

This Section will address two distinct performance descriptors; one displaying the (absolute) sensitivity toillumination versus wavelength of the eye, and the second displaying the differential sensitivity to illuminationversus wavelength. Both of these will be presented first in a theoretical context, second by the perceivedperformance in these two areas as memorialized in the current C.I.E. Standards and third in a new proposed form. The relationship between the theory and the empirically based standards will also be developed in detail. This isparticularly important because of the significant difference in performance between the normal and aphakic humaneye.

There is little data available on the color performance of the human eye as a function of field angle. It has onlyrecently been shown that the human retina is tetrachromatic like the retinas of other chordates. Recognition of thisfact places a different perspective on understanding the operation of the human visual system.

Because the spectral sensitivity of the retina and many other parameters related to the photoreceptor cells arevariable, it is useful to address the architecture of the visual system as prior to and subsequent to the formation of thesignals at the pedicles of those cells.

The signaling system subsequent to the pedicles of the photoreceptor cells operates in a fixed gain, large signalmode. With the exception of certain asymmetries in stage 3 of the chrominance channels, this portion of thesignaling system is symmetrical with respect to time. This portion is also characterized by fixed gain coefficientsbetween individual circuit elements (given labels based on the letter K).

The portion of the visual architecture prior to the pedicles of the photoreceptor cells operates in an environmentcharacterized by variable input signal amplitudes and variable amplifier gains individualized with respect to spectralchannel. While individual circuit gains within this portion of the system may be characterized by constants (and


quasi-constants) labeled with the letter K, the overall performance of the complete system is better characterized byan auxiliary group of parameters using the label C.

The significantly different performance of the aphakic eye in the ultraviolet influences the fundamental interpretationof how the human visual system works. This characteristic will be discussed in Section 17.2.2. The obviousconclusion is that the human retina is tetrachromatic throughout the lifetime of the individual. However, the lensgroup absorbs virtually all of the light in the ultraviolet band between 315 and 400 nm. Whereas, the humanretina is tetrachromatic, the complete eye is largely trichromatic, except for a potential cusp in the area of300-315 nm.

To define the luminance performance of the eye requires considerable care in defining what is desired. One goal isto define the quantum efficiency of the photodetection process in both absolute terms and in relative terms for agiven background irradiance. A second goal is to define the perception threshold of the overall visual system undera specified set of conditions. Measurements of these types are very difficult to make in practice. One of the easiermeasurements to make is the spectral absorption characteristic of the eye as a function of wavelength. However,there are a variety of parameters that affect the results obtained. A specific test should be labeled as belonging toone of the following test environments.


64North, A. & Fairchild, M. (1993) Measuring color-matching functions. Part II. Color Res. Appl. vol. 18,no. 3, pp. 163-170

Figure 17.2.1-1 (Color ln) The tetrachromatic luminousefficiency function of human vision along with itscomponents and variations. The figure highlights theimportance of logarithmic signal processing in vision.

The visual system was designed to accept low contrast signals modulating a slowly changing average irradiancelevel in each of the spectral channels. Most of the unusual transient effects observed in the laboratory are a result ofthe asymmetries in the system that were not anticipated, or accepted as a tradeoff, in the overall design. Theseresults include those associated with the Retinex theory.

The nonlinearities and asymmetries of the visual system related to intensity and time make precise determination ofits luminance parameters particularly challenging. These luminance (more properly radiance) parameters will bediscussed in Section 17.2. The variation in these same parameters on a spectral channel basis makes measurementsof the chrominance performance equally challenging. These chrominance parameters will be discussed in Section17.3. The underlying temporal characteristics will be summarized in Section 17.4. The details of the spatialperformance of the visual system will be discussed in Section 17.5. The spatial parameters related to the process ofreading will be introduced in Chapter 19.

As discussed above, the luminosity function varies significantly with the state of adaptation of the eye, withirradiation level (Section 7.2.4), with the color temperature of the source irradiation and to a lesser extent with age. Little data is available relative to age (less than 40 subjects). However, what is available suggests the transmissionof the lens group varies less with age than the dispersion in performance due to other variables64. Figure 17.2.1-1provides an overview of the subject matter for the complete eye. Section 17.2.1.4 will provide a similar figure forthe retina only. The luminous efficiency function is a continuous variable as a function of illumination, although itdoes exhibit two regions of reasonably constant shape, the photopic and scotopic regions. The spectral absorptioncharacteristics of the chromophores of long wavelength trichromats are shown normalized at the bottom of thefigure. The function is a direct function of these underlying spectral absorption characteristics, although this is notobvious because of the logarithmic signal processing employed. This signal processing also results in the twoauxiliary peaks at 487 and 580 nm known as theBezold-Brucke and Purkinje peaks respectively. Theauxiliary peak at 580 is frequently reported as theactual peak in the absorption function of the longwavelength chromophore. It is not. The hatching onthe left is indicative of the absorption introduced by thelens group of large terrestrial chordates. Thisabsorption is a function of the thickness of the lensgroup. The larger the animal, the longer wavelengthfor the cutoff wavelength of this mechanism..

The material developed in this section is being


65Saito, M. Adachi, N. & Kondo, H. (2007) Full-color illumination that neeeds no electric power OpticsExpress vol 15(4), pp 1621-162666Babucke, H. (2007) private communications67Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation. J. Opt. Soc.Am. vol. 43, no. 6, pp 485- , fig 3.

accepted in the literature65, and confirmed through independent computations66, on a daily basis. See Section17.2.2.5.1.

17.2.1 Determination of the luminosity related functions of the visual system[xxx edit entire section to consolidate ]The luminosity related functions of the eye are highly state dependent. If all three spectral channels of the humaneye are not fully dark adapted, it is important to quantify the exact state of adaptation of each channel separately. Asan example, the luminosity function data of Hurvich & Jameson clearly shows a distinct change in the adaptationstate of the L-channel between experimental run #1 and #967. Apparently, the subject caught sight of a pilot light orthe reflection of some red light source while relaxing.

Under completely dark adapted conditions, all of the adaptation amplifiers of the eye are operating at their maximumgain and are stable. All other parameters of the eye, except for the translation function in the L-channel are alsostable. Under these conditions, the perceived sensitivity of the eye is a direct function of the spectral content and theintensity of the irradiation applied to the eye. Because of the unique characteristic of the L-channel translationfunction, the human eye exhibits four distinct luminosity functions. Two are stable with radiant intensity, thephotopic and scotopic luminosity functions. The mesotopic luminosity function is a continuous variable withintensity. The hypertopic luminosity function represents an overload condition and will not be developed here. Very carefully defined experimental procedures must be used to obtain accurate graphs of these functions.

To obtain a luminosity function that is independent of the input illumination conditions, it is necessary that the inputirradiance contain an equal number of photons per spectral wavelength interval. This can be done by using a sourceoperating at a color temperature of 7053 Kelvin. For any other source temperature, the resulting luminosity functionis a function of the source temperature and it should be properly labeled to reflect this fact.

Since the luminosity functions for each illumination regime are each complex functions of the input irradiance, theydo not vary in a smooth manner with changes in color temperature. It is only after sufficient smoothing to removeall of the local maxima, minima and inflection points that a curve similar to the C.I.E. standard luminosity functionsare obtained.

17.2.1.1 Historical determination of the luminosity function

The visual community began making significant efforts to define the luminosity function of human vision with thearrival of the early electrical age, nominally the 1850's. In that time period, the only known materials subject tophotoexcitation were considered photo-conductors. This name was as much colloquial as scientific. The photo-emissive effect was unknown, and the internal energy levels associated with the various components of a moleculewere also unknown until the 1920's. Today, the effect observed in different materials would be described by themore global photoelectric effect which includes both the photo-conductive and photo-emissive effect. As will beshown in the next paragraph, the chromophores associated with photodetection in vision are photo-emissive incharacter, employing the internal photo-emissive effect. Unfortunately, when discussing photometry andcolorimetry, the visual community has continued to assume the visual system is based on photo-conductive materialto this day. All data, models and theories in the literature to date are based on the use of an equal-energy per unit


68Science of Color, 3rd printing (1963) Jones, L. Ed. and Chairman, Committee on Colorimetry, Wash.D.C.: Optical Society of America pp. 223-23269Foster, D. & Snelgar, R. (1983) Initial analysis of opponent-colour interactions revealed in sharpened fieldspectral sensitivities In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pp 303-311 70Thornton, J. & Pugh, E. (1983) Hue cancellation and increment thresholds In Mollon, J. & Sharpe, L. edsColour Vision NY: Academic Press pg 366 71Hood, D. & Finkelstein, M. (1983) A case for the revision of textbook models of color vision: thedetection and appearance of small brief lights In Mollon, J. & Sharpe, L. eds Colour Vision NY: AcademicPress pp 387+

bandwidth illumination source.

As the field of photometry advanced into the 20th Century, the human eye was assumed to be a linear device withrespect to wavelength. At the time it was frequently used as a null detector in many experiments. As developed inWyszecki & Stiles; “The matching of brightness is the fundamental operation of photometry...The observer’s eyefunctions are [sic] little more than a sensitive null instrument that could be replaced by wholly physical lightsensitive devices with response properties deviating widely from those of the human eye, including a different andunrelated spectral responsivity.” Unfortunately, the above characterization is much too broad. The complexity ofthe signal processing in the eye makes it a very poor scientific instrument, even when used as a null instrument inphotometry. As noted elsewhere herein, experimenters have great difficulty in separating the response of thesubjects with regard to chromatic and achromatic responses. These two responses do not correlate well. In addition,it does not operate in the same mode as photo-conductors and the Uni-variance principle only applies to individualspectral channels (not the visual spectrum as a whole).

Because of the poor understanding of the mechanisms of vision up through the present, it has been difficult for thevision community, both science and engineering, to develop well founded terminology with respect to the sensitivityof the eye to radiation. The Science of Color68 includes some information on this situation. The performance wasgenerally couched in terms related to “visibility data.” Early investigators spoke of the visibility function of the eyewhen actually referring to the sensitivity of the human eye to narrow band equal energy radiation as a function ofwavelength.. This term was superceded in 1939 by the term luminosity function. In 1951, this term was subdividedinto two terms recognizing the difference between the photopic and scotopic levels of excitation. Up to now, thesefunctions are defined based on empirical measurements using instrumentation of poorly (or unspecified) spectralbandwidth and light sources of unspecified color temperature (generally in the 2400 to 6000 Kelvin range. The bulkof the data was collected using temperatures near the lower value and the results were clearly deficient in the “blue”portion of the spectrum.

The so-called luminous efficiency functions embraced by the C.I.E. are actually measures of the response of thenominal eye to radiation, not illumination, as a function of wavelength. The highly smoothed data collected todescribe this relationship has been arbitrarily defined as the luminosity function of the eye at an undefined radiationlevel thought to lie within the scotopic and the photopic operating ranges of the subjects eyes. These functions havebeen used to define the filter characteristic placed in front of a broadband, photoconductive detector of radiation. The combination of filter and (generally photoconductive) radiometer was thereby renamed a photometer.

Up until the present era, the most precise descriptions of the spectral sensitivity of the human eye date from 1983. Foster and Snelgar measured the spectral sensitivity under a variety of conditions and noted the peak longwavelength sensitivity moved from 570 nm to 610 nm in the presence of a white conditioning illumination spatiallycoincident with the test field69. In the same volume, Thornton & Pugh provided spectral sensitivities showingdistinct peaks at approximately 430 nm, 530 nm and 615 nm70. Hood & Finklestein presented data showing thedrastic change in spectral sensitivity with exposure interval and spatial diameter, essentially from a single peakfunction for small brief stimuli to tri-peaked sensitivity to larger, longer stimuli71. Krastel et al. show similar


72Krastel, H. Jaeger, W. & Braun, S. (1983) An increment-threshold evaluation of mechanisms underlyingcolour constancy In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pp 545-552

variations with test conditions, including a peak long wavelength sensitivity near 610 nm, in the same volume72.

Wyszecki & Stiles describe more than ten methods of determining the luminosity function of the visual system, mostof which are not compatible with the more precise terminology of luminous efficiency function. Some of themprovide data that can be interpreted as a relative luminous efficiency functions. Most of the methods involvedifferential measurement techniques which are normally less precise than absolute measurement techniques. TheAbsolute Threshold Method is described in subheading (vi). This method can provide a true luminous efficiencyfunction and is compatible with the derivation of both the absolute and relative theoretical luminous efficiencyfunctions of this work. The comments of LeGrand in that paragraph are not supported by the model and equationsof this work. The equations and graphs of the following sections will clearly demonstrate that multiplephotoreceptors are active under threshold conditions and it is their cooperative responses that actually determine thedetailed shape of the luminous efficiency function. This work provides the framework necessary to broaden anddefine the “envelope” of the sensitivities of the individual photoreceptor mechanisms discusses by Pirenne in thatparagraph.

The next paragraph will also show the importance of separating the above methods into those associated with thethreshold performance of the system and those only providing relative amplitude performance relative to an arbitrarypeak response.

There has been little recent discussion of the theoretical foundation of the luminosity function. It has been assumedfor decades to be a linear summation of the light absorbed by three photoreceptors. This has been formalized by thesame equation used in deriving the chromatic characteristics of the eye.

C = xR + yG + zB Eq. 17.2.1-1

where C is the “total color” and x, y & z are in percent

As discussed in detail in Section 17.3.3, this equation is a complete mis-statement of the signal manipulation withinthe human eye. The appropriate equation is developed in the next Section.

17.2.1.2 Theoretical Background

17.2.1.2.1 Energy related matters

There are very significant theoretical and practical differences between materials with a very narrow band gapbetween their valence and conductance bands and materials with a wider band gap. Materials with a very narrowband gap exhibit a finite resistivity at room temperature. This resistivity is often a function of temperature, and thistemperature can be raised by the irradiance of the material by light. Such materials are called photo-conductors. They are sensitive to the energy deposited on them by the radiation received. A current passing through suchmaterials typically exhibits a noise component whether the material is irradiated or not. This noise component isnormally described quite accurately using Gaussian statistics.

A wide band gap material will not exhibit a significant resistivity at room temperature and will be classified as aninsulator. However, upon irradiance with photons of high enough energy, i.e. actinic irradiation, nearly all materialswill exhibit a current upon the application of a voltage. This current may be between two terminals of the material,(due to the solid state photo-emissive effect) or between a terminal attached to the material and a second electrodenearby but separated from the material by a vacuum (due to the vacuum photo-emissive effect). The second case


73Baylor, D. Lamb, T. & Yau, K.-W. (1979) Responses of retinal rods to single photons. J. Physiol. vol.288, pp. 613-634

was the subject of the Einstein Photoelectric Effect of 1905, for which he won a Nobel Prize in 1921. This workushered in the quantum physical era. This Effect was later shown to equate the “photoelectric work function” of thesurface with the internal bandgap of the material. These materials are sensitive to the number of quanta of actinicphotons deposited on them by the radiation received. Materials with a wide bandgap generally exhibit a noisecomponent, associated with any induced current, that is quite different from that of photo-conductors. The noise isnormally due to the quantum statistical characteristics of the incident radiation. At the theoretical level, this noise isdescribed by Bose-Einstein statistics. For irradiation by photons of less than a critical energy, no current isgenerated by the photo-emissive effect.

Making the assumption that the visual system employed photo-conductors, early investigators began using equalenergy per unit bandwidth, sometimes per unit frequency, light sources in their experiments. The assumption wasthat this type of energy source would excite the different photoreceptors of the eye equally. Unfortunately, thevisual system does not employ photo-conductors. The chromophores of vision are wide band gap materialsexhibiting the internal photo-emissive effect. In the absence of irradiation by photons of sufficiently high energy, nosignal is generated, and no noise is generated. Under actinic radiation, the signal generated is related to the numberof photons per unit area received times the absorption coefficient of the material at that photon energy. Singlephoton events are easily recorded using photo-emissive materials. The photo-emissive characteristic of thephotodetectors of the toad, Bufo marinus, was beautifully demonstrated in the electrophysiological experiments ofBaylor, et. al73. Although aware of the phenomena, those investigators did not appreciate completely the nature ofthe randomness, given by Bose-Einstein statistics, associated with their experiments.

[xxx Rewrite ]Today, a fundamental determination is made as to the type of photo-electric material or device under study beforeany experiments are designed to evaluate that material or device. In the case of vision, this determination is mademore difficult by the “square law” operation of the visual detector associated with the L- channel. Because of thissituation, the only real method of determining the “quantum efficiency” of the visual photodetectors as a group isbased on signal to noise ratio calculations. These are difficult to quantify in themselves. For quantum based events,they must be based on Bose-Einstein and not Gaussian statistics.

This section will present a series of graphical descriptors capable of defining the theoretical sensitivity of thenominal human eye to radiation and to a more abstract term, illumination.

17.2.1.2.2 Noise related matters

When measuring the luminous performance of the visual system, it is important to distinguish betweenmeasurements made relative to some high level of response, generally the peak response in the 532-550 nm region,and measurements made relative to a low level, such as the noise level of the system. The latter approach results ina luminous threshold function which is an absolute descriptor of the system.. The former approach only provides arelative response of little theoretical significance. Each of the eleven approaches mentioned above needs to beexamined and categorized against these criteria.

17.2.1.3 Operational considerations

The animal eye was shown in Chapter 16 to operate in four distinct illumination regions and to incorporate a numberof non-additive mechanisms. The human eye operates similarly but effectively in only three illumination regions. This makes it necessary to evaluate the luminance performance of the human eye separately for each of these


74Langley, K. Simmons, D. & Welchman, A. (2002) Visual Adaptation Spatial Vision vol 16(1), pp 1-3

regions. The complexity of the signal detection, signal processing, signal projection and signal interpretation circuitry makes it extremely important to understand the functional aspects of the entire system before attempting toevaluate its response to radiation.

Because of the automatic adaptation characteristics of the eye, it is difficult to discuss the absolute sensitivity of theeye except at the lowest irradiation levels, i. e. the scotopic and mesotopic regions. At higher irradiation levels, thesignals presented to the circuits proximal to the photoreceptor cells are not indicative of the absolute performance ofthe photodetection process. This is due to the changing amplification factor of the adaptation amplifier of eachphotoreceptor cell. Once the radiation level becomes sufficiently high, the hypertopic region of operation is reached. There is further circuit saturation in this operating region and it is even more difficult to describe performance insimple terms.

To obtain accurate sensitivity data, it is absolutely mandatory that the color temperature of the radiation source bewell characterized and the spectral bandwidth of any filters be well known.

17.2.1.3.1 The relationship between dark, light and chromatic adaptation

A one-day conference was held on March 20, 2000 devoted to the study of adaptation from a largely psychophysicalaspect. The conference suffered from a lack of a sufficiently accurate physiological model of the visual system andfrom a poor definition of the terms involved. The models were largely conceptual and floating. The preface by theorganizers describe the less than desirable framework available for the conference74. As they note, “This conferencewas motivated by the identification of a need to satisfy these goals.” However, some useful data was presented.

It is useful to review the relationship between dark adaptation and white light adaptation. Under dark adaptationconditions, all of the adaptation amplifiers of the eye are operating at full amplification factor (gain). The eyecontinues to operate in this mode as the irradiance level is increased until the variation in gain due to the avalanchegain mechanism becomes significant. This typically occurs at and defines the lower limit of the photopic region. Upto that level, the state of adaptation in each of the spectral channels will remain independent of the spectralcharacteristics of the illumination. Above this level, the gain of each of the spectral channels will be reduced. However, these gains tend to track each other up to the point where one of their gains reaches unity. This leveldefines the top of the photopic region. From that point up to higher irradiance levels, the signal level at the pedicleof the photoreceptor will change considerably between the spectral channels.

Within the photopic region, the action of the adaptation amplifiers will maintain the relative signal amplitudes at thepedicles of the photoreceptors constant for any light source that is nominally white, i. e., has a photon flux per unitwavelength that is reasonably constant --typically daylight at 7053 Kelvin. Below the lower limit of the photopicregion, the square law response of the long wavelength channel will cause the signal level at the pedicles associatedwith that channel to drop regardless of the gain of the associated adaptation amplifiers. As a result, the eye willexhibit a scotopic spectral response at light levels significantly below the lower limit of the photopic region (even ifa nominally white light sourc is used as a source).

17.2.1.3.2 A chromatic spectrum for reference

It is useful, when analyzing the spectral sensitivity of the eye, to have a continuous multicolor background spectrumavailable as a reference. It is virtually impossible to produce such a background using conventional “process color”printing techniques, even with the use of additional spot colors. A marginally more effective background can beprovided using photographic prints of photographic negatives. In both cases, the spectrums are prepared usingsampling techniques (three separate but highly overlapping channels). The best available backgrounds found by the


75The Photonic Spectrum Reference Wall Chart. © copyright 1992 Laurin Publishing Co., Inc. Pittsfield,Mass.76Dowling, J. (1987) called in Gouras, P. (1991) Vision & Visual Dysfunction, Vol. 6. Boca Raton, FL:CRC Press plate 977Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate visualcortex. J. Neurosci. vol. 4., pp. 309-356

author are the wall chart produced by Laurin Publishing Co.75 and the plate in Dowling76 reproduced in Gouras. Thedifference in the intensity of the yellow region of the spectrum is pronounced between these two examples. Sincethe reproducible color range of both the photographic and process color techniques are limited compared to animalvision, they can not be relied upon for quantitative purposes. The region between 400 and 450 nm is particularlypoorly reproduced.

All of the spectral peaks in the overlays shown in Dowling, except for the L-channel, are in agreement with thistheory. The L-channel peak should be at 610 nm. The half-amplitude widths are not defined on the Dowling plateand the individual spectra are represented by approximately Gaussian waveforms. They are shown as havingdifferent half bandwidths. This theory calls for the waveforms to be shaped according to Fermi-Dirac statisticswhich gives them a flatter top and more defined skirts. The new half-amplitude values are at 400 & 475 nm., 500 &565 nm., and 595 & 655 nm. the spectral peak associated with the ultraviolet sensitivity of the human retina is notavailable in any reference spectrum. The Laurin chart appears to be poor in the region between 650 & 700 nm.where it shows the color of red to continue to become “redder” as it fades to black, instead of reverting toward thehue of the 600-650 region.

17.2.1.3.3 Chromatic filters for laboratory use

The proper choice of chromatic filters and light source are critical in precision visual spectral measurements. When using broad band filters, it is important to use test sources with spectral content that is carefully chosen tomaximize the difference in signal amplitude between the channels being evaluated. The optimum filters are differentfor short-wave trichromats, tetrachromats and long-wave trichromats. Livingstone & Hubel77 and Kelly & vanNorren have used filters suitable for the long-wave trichromats. However, their choices did not recognize thetheoretical shape of the chromophores involved. A slightly different set may be better able to avoid undesired cross-excitation of the channels by the filters. Table 17.2.1 compares the two sets.

TABLE 17.2.1SPECTRAL FILTERS FOR VISUAL RESEARCH ON LONG-WAVE TRICHROMATS

Livingstone Kelly & This & Hubel van Norren work

UV — ---S 47B 47 30 & long wave blockerM 58 61 74 or 99 are better*L 29 29 or 70 22 & long wave blockerYELLOW 16 106CYAN 45

Numbers are for Wratten filters. All filter sets should include an IR blocker since the eyes are more sensitive in theIR than conventional photographic film.


78Stiles, W. (1949) Increment thresholds and the mechanisms of colour vision Doc Ophthalmol vol 3, pp138-165

* Built from a #57 or #53 & a short wave blocker.

17.2.1.3.4 A light source for laboratory use

As discussed in some detail in Section 1.3.4, the use of an adequate light source is mandatory for precise spectralmeasurements in vision. For measurements involving the complete eye, and overlooking the residual ultravioletsensitivity, a 7053 Kelvin black body light source is required. Such a source provides an equal photon flux per unitspectral bandwidth within +/- 5.7% across the spectrum of interest in long-wave trichromat research. If morecomplete measurements of the eye are desired or the response of the retina is sought, a blackbody light source with atemperature above 8000 Kelvin is required. A source with a temperature of 8683 Kelvin provides a uniformity offlux within +/- 7%. In both cases, the deviation from nominal is predictable. The use of a source of considerablylower temperature than recommended will result in significantly erroneous measurements in the short wavelengthmeasurements. Even the C.I.E. defined “illuminant C’ is inadequate.

17.2.1.3.5 The systemic variation in retinal sensitivity with spatial position

Stiles provided Figure 17.2.1-2 which characterizes the threshold incremental sensitivity of the human retina at fourdifferent wavelengths78. The figure is important for several reasons. First, it shows the distinct separation of thefoveola (nominal diameter of 1.18 degrees) and the fovea (nominal diameter of 8.68 degrees but shown here at 4degrees). Second, it shows the relative perceptual sensitivity of the photoreceptors with position. The perceivedsensitivity is strongly impacted by the number of photoreceptors that are summed in the process of generating theluminance (R-channel) signals of vision. In the area near the point of fixation, summation is minimal. In fact, thiswork proposes that no summation occurs within the foveola.

Many authors have referred to the absence of S-channel sensitivity in the fovea specifically and by inference thefoveola. Notice this figure shows only a 2:1 or 3:1 loss in perceived sensitivity of the S-channel within the foveolarelative to the fovea. It shows essentially the same loss in perceived sensitivity between the S-channel and the M-channel (using 475 nm light as a reference) for both the fovea and foveola. Thus, there is no indication that theretina is blind to blue light in the foveola or fovea under threshold conditions. The loss between the fovea and theperipheral regions is shown as near 100:1. However, this value is highly dependent on the size of the source. Forpoint sources, the value is much closer to 1:1. This is easily demonstrated by looking at the stars at night. The starswithin the foveola and fovea do not appear significantly brighter than those outside of the fovea. Wyszecki & Stilesdiscuss the relevance of the test protocol in determining threshold sensitivities (page 523-525)


Figure 17.2.1-2 Variation of increment threshold in traverses through the dark-adapted foveal and parafoveal areawith monochromatic test stimuli of different wavelengths. From Stiles, 1949.


17.2.1.3.6 The systemic variable related to ageing

In the past, it has been common to define the eyes of the subjects as “young eyes” or to give the age of the subjectswithout any quantification of the significance of age. The effect of Rayleigh scattering within the physiologicaloptics of the eyes can be quantified. This effect exhibits an inverse fourth power relationship with wavelength andbecomes more prominent at a rate of about 0.5% per year. Because of the fourth power relationship, it ispredominant in the short wavelength spectral channel and can be largely ignored in the other channels. In practice,this change in short wavelength performance is not normally noticed. This is because of the compensation providedby the adaptation amplifiers. However, the range of the photopic region, as defined here, is systemically reducedwith age. This fact should be considered in experiment planning for research purposes.

17.2.2 The relationship between brightness and luminance in vision

The relationship between the luminance applied to the eye as a stimulus and the perceived luminance, the brightness,reported by the visual system has not been discussed in detail in the literature. The major problem has been the lackof a framework within which to discuss this subject. Studies of the hearing modality have proceeded further in thisarea and they may offer insight. Vision involves a more complex stimulus environment than does hearing. Thehearing environment can generally be resolved into a small set of individual sources within the external spatialenvironment. Vision, on the other hand, typically involves a large number of significant sources that exhibit spatialvariation themselves, and are embedded in an even more complex background environment. However, by restrictinga test stimulus sufficiently, it is possible to draw analogies between the visual and auditory sensory modes.

The additional dimensions of vision, compared to hearing as an example, make measuring and interpreting theoverall amplitude sensitivity range of vision quite difficult. These dimensions result in a wide proliferation ofdifferent test stimuli.

At a very fundamental level, the difference between stimulating the visual system with an active source (a light)versus stimulating it with a passive intermediary (reflection by a surface illuminated by an unseen source) leads toadditional complexity in exploring the amplitude sensitivity range of vision.

Finally, the dynamic accommodation capability of vision, known as adaptation, plays a major role in nearly allexperiments related to the overall amplitude sensitivity range. While adaptation is primarily a temporal effect, itdoes contain a spatial component. The spatial component is due to the sharing of energy resources among thephotoreceptors within the hydraulic environment of the retina.

Because of these complexities, most of the work aimed at evaluating the sensitivity performance of the visual systemhas been focused on a limited range (the photopic region). Even within this range, most of the activity has beenrestricted even more narrowly to the largely qualitative range defined by the Munsell Values of zero to ten. Thisrange incorporates a range of only xxx:1 in luminance intensity.

Most of the activity in determining the sensitivity range of vision has involved differential tests employing pairs oftest targets. These test targets generally have a minimum spatial dimension of two degrees or more in order toachieve an adequate signal to noise ratio in tests involving one individual and reasonable correlation amongindividuals.

The description of the test target configuration used in amplitude sensitivity experiments is itself complex. This islargely because of the number of dimensions involved, as discussed above. Historically, the test targets have beendescribed using the terms unrelated and related. In this work, the same situations will be described by the clearerterms, isolated and embedded respectively. an isolated test target is viewed against a dark background. An


79Fulton, J. (2006) Biological Hearing: A 21st Century Tutorial. Vancouver, BC, Canada: Trafford

embedded test target is surrounded by a single area of either a nominal luminance level (of the same chrominance asthe test target) or an even more complex surround of multiple luminance and chrominance levels. When comparingtest targets in embedded environments, the data reduction and interpretation tasks become even greater.

17.2.2.1 The perceived intensity of sound versus its actual intensity

By restricting the stimulus to a single audible tone, it has been possible to describe the perceived response to thattone over a large dynamic range in humans as characterized in Figure 17.2.2-1 from Fulton79 (figure 5.4.4.-1 ofmanuscript).

The individual performance regions of the auditory system are readily distinguished in this figure. Below theadaptation range, in the scotopic region, the loudness increases in direct proportion to the intensity of the sound. Within the adaptation range, the phonotopic region, the gain of the adaptation amplifier decreases in proportion tothe stimulus. This results in an apparent increase in loudness with intensity given by an exponent of 0.6. When the

Figure 17.2.2-1 The perceived audio loudness as a function of sound intensity in humans ADD. The thin dashedlines indicate the gain of the adaptation amplifier circuit (which varies with the state of adaptation before a givenstimulus is applied). From Fulton, 2006.


adaptation amplifier gain has reached its minimum value near 1.0, it can no longer suppress the loudness versusintensity function. The function proceeds to increase linearly with intensity in the hypertopic region.

17.2.2.2 The perceived intensity of light versus its actual intensity

Within broad limits, the above figure can be used to predict the performance of the human visual system. Figure17.2.2-2 shows such a conceptual representation. The operating regions are correlated with the luminance levelbased on the values in Section 2.1.1. The ordinate is arbitrary but will be related to the Value scale of Munsell asthe discussion proceeds. The figure will be definitized further by specifying the size of the isolated test target usedto acquire the data in the figure. Based on the previous figure and the observations of Stevens, the solid curved lineintersecting with the dash-dot line labeled compression can be expected to describe the overall response of the visualsystem to a luminance stimulus in the absence of any adaptation mechanism. If the feedback employed by thesensory neurons was 100% effective in limiting the growth in the neural signal above a specific cut-in value, thecurve labeled 100% adaptation asymptote would be achieved with the introduction of adaptation. However, thefeedback employed in vision, like in hearing, is not designed to provide a hard limit on the brightness response. It isdesigned to expand the brightness range associated with a given luminance range over a limited operating rangeknown as the photopic region. The result is the dashed line through the middle of the shaded box labeled “NormalOperating Regime.” The following material will attempt to quantify the scales of this figure more completely.


80Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 493-499

Wyszecki & Stiles have provided a broad overview of the brightness versus luminance response of human vision80. However, the material is difficult to interpret because it lacks an underlying framework. Note that no two figuresamong these pages use the same scales. The data of Bodmann, et. al. (W&S, page 495) shows one piece of isolatedtarget response data and a second piece of embedded target response data, without information on the state ofadaptation of the eye. The test targets had an angular subtense of two degrees. The surround in the embedded caseis described as 180 degrees, which may or may not have been full field in actuality. The statement that the test targethas a given subtense is incomplete. Is the target round, square or otherwise. If square, is the subtense equal to thediagonal or the side. Neither eye has a field of view of 180 degrees in either the horizontal or the vertical aspect. However the pair of eyes has a horizontal field of over 180 degrees. Was the specification meant to describe asurround covering the full field of view of the eye(s) involved. The abscissa of the data covered 1 to 105 candles persquare meter without any discussion of what operating ranges this luminance range corresponds.

Figure 17.2.2-2 Proposed template for the perceived visual brightness as a function of luminance intensity inhumans ADD. The dashed line within the Normal Operating Regime is called the terminal brightness locus byStevens & Stevens. The Compression line is called the Dark adaptation line by them.


81Bridgeman, T. (1963) Inversion of the Munsell Value Equation J Opt Soc Am vol 53, pg 49982Romney, A. & Fulton, J. (2006) xxx (In Press)

Wyszecki & Stiles have provided a figure of considerable interest that is reproduced here in modified form as Figure17.2.2-3. The term Y is that of the CIE coordinate system for the luminous reflectance for an opaque sample orluminous transmittance for a transmitting sample.

The abscissa of the upper half of this figure only coversa linear luminance range described by 0 to 100. Thishalf describes the relationship between the perceivedbrightness of a test tablet when illuminated understandardized conditions as measured by severalinvestigators. The functions shown are actually theequations recommended by those investigators torepresent this response. The mathematical descriptionof these functions are given on page 823 of Wyszecki& Stiles. The best fit to the data is represented bycurve 4. This curve was first proposed by Newhall,Nickerson & Judd using the first five terms of aninfinite series and using a magnesium oxide tablet asthe reflecting surface (reflectance taken as 97.5%). They used a source at a color temperature of 6700Kelvin. As noted rather cryptically on page 823, thisgives Y=102.568 for V=10 although no units wereassociated with this value. In the original paper, thenumeric was given in percent. The proposal was partof the Renotation activity related to the Munsell ColorBook. Their equation was awkward because the valuewas the independent variable in the equation for Y. Bridgeman attempted to provide an equivalent equationfor Y in terms of β, where β was expressed in terms ofeach of the three CIE tristimulus values81.

Two facts need to be noted about the Wyszecki &Stiles figure. First, it is an expansion of an earlierfigure in Newhall, Nickerson & Judd (figure 14). SeeSection 17.3.8. Second, the curves described as fittinga cube root equation well do not fit a cube rootequation well by the graphic standards of today. Theywere probably drawn manually.

The Newhall expression was converted to a cube rootexpression and adopted by the CIE in 1976 in their first excursion into a non-linear expression for brightness. Theydefined L* / V over a limited range. The same curve can be expressed as a simple natural logarithm (or a Briggslogarithm to the base 10) based on the theory of this work. If the limited range of V = 0 to 10 of the upper verticalaxis applicable to a Relative Munsell Color Space is redefined in an Absolute Munsell Color Space, the exponent ofthe luminance parameter of the lower vertical axis can be used as a scale factor in a 3D Color Space as in Figure17.4.2-1 & -2. As a logarithm, the expression precisely relates the reflectance of the achromatic set of chips in thematte version of the Munsell Color Space quite precisely over the value range from V=2 to 10 as shown in thefollowing figure from Romney & Fulton82.

Figure 17.2.2-3 Relationship between lightness-scalevalue V and luminance factor Y plotted in accordancewith different formulae. See text. Upper quadrant fromWyszecki & Stiles, 1982.


Based on the success of the logarithm in matching the measured values of the Munsell chips, it can be said that theequations suggested by other investigators on page 492 of Wyszecki & Stiles are now obsolete. The theoreticallysupported expression is V=kClnY - kClnY0+C =kCln(Y/Y0)+C where C is a scale factor related to any arbitraryluminance level Y0. In the Absolute Munsell Color Space, Y0 is nominally equal to 300 Lux when reflected from a100% reflective surface.

Luminance covers an immensely wider range than shown in this upper half, normally described better using alogarithmic function of much greater extent. To introduce this larger range, the figure has been extended in thebottom quadrant. This new graph provides a broader view of the operation of the visual system. It allows adiscussion of the potential equations listed by Wyszecki & Stiles as candidates for describing the brightness (orlightness) versus luminance relationship in vision. The intent is to allow the operation of the visual system over itsentire range of operation, including the range expanding feature of the adaptation system, to be displayed on onegraph .

- - -

Wyszecki & Stiles have discussed the repercussions of using high luminance levels on visual color-matchingperformance in a variety of contexts (pp 374-379) including adaptation to one broadband light source followed byobserving a different broadband stimulus. Their definition of a photopic Troland is a surface illuminated at 1Candela/m2 viewed through a 1mm2 pupil. Unfortunately, this definition and their data is presented based on anembedded CIE visibility function (V(λ)) instead of a more realistic representation of the sensitivity profile of thehuman retina (Section 17.2.3.5.1). They do not reach a useful conclusion after presenting the data. They use a redtest source at 572 nm but a white source including red source component at 645 nm without any discussion of why. Their blue and green sources were the same for both test sources and their composite white source. Neither 572 nm(a yellow or greenish-yellow) or 645 nm (a reddish-orange) is usually associated with a saturated red sensation. SeeSection 17.3.9.1. The Troland is only applicable to the on-axis (thin lens) model of the eye (Section 17.1.2.1.1).

- - - -

Romney & Indow have recently published a new calibration of the matte achromatic chips in the Munsell ColorBook of 1976. Their results are in excellent agreement with the theory of this work. As a concept used by manyempiricists, they attempted to fit a cube root to their data points instead of using the more appropriate naturallogarithmic function suggested by theory. Figure 17.2.2-4 shows their results when their measured values are fittedwith a logarithmic function, U(M) = Ln L(M) plotted on linear scales. AA1 corresponds to the xxx They originallycollected and fit the data only between a Munsell values of 2 and 10 with a cube root curve. That curve (red line) isunderneath the logarithmic curve and can be seen at the very toe of the curve. The logarithmic curve continues onboth sides of the experimental region as shown. Using the Romney & Indow data, the value range from xxx to xxxcorresponds to a reflectance change of xxx:1. This information can be used to calibrate the overall Munsell Valuerange. [xxx continue ]


83Romney, A. & Indow, T. (2002) A model for the simultaneous analysis of reflectance spectra and basisfactors of Munsell color samples under D65 illumination in three-dimensional Euclidean space PNAS vol99, pp 11543-11546 doi/10.1073/pnas.162368999

Almost simultaneously, a second Romney & Indow paper83 appeared confirming the above results in a somewhatbroader context (370 color samples and the use of a D65 illuminant). They employed an extensive statisticalanalysis using singular value decomposition (SVD). “In the present paper, the analysis is limited to a sample of the360 most representative Hs, namely, (5R, V/C), (5YR, V/C),..., (5RP V/C), where V covers 2, 2.5, 3, 4, 5, 6, 7, 8,8.5, 9V, and C covers the whole range of chroma.” It confirms the axes proposed in this work for the Munsell ColorSpace, at a slightly less precise level, and discusses minor differences from earlier work.

“Jameson and D’Andrade have drawn attention to this discrepancy between the axes posited by opponent processtheory and the axes in the Munsell color system. They say that opponent process theory ‘. . . can never be patchedup as long as unique hues are maintained as unitary sensations and antagonist channel zero-crossings. In light ofthese facts it seems wise to pursue alternate hue axes that model the empirical data more closely, and we suggest that

Figure 17.2.2-4 The human visual response based on the Munsell Color Book using a box plot. The plot shows therelationship between Munsell Value levels (the y-axis) and the axis AA1 as in the right panel of Fig. 2 (the x-axis).Values of AA1 of colors of constant Value are not exactly constant. Red dots represent means, boxes contain 50% ofcases and median line, whiskers contain the range of values that falls within 1.5H spread of the hinges, and asterisksshow outliers. The fitted red curved line is described in the text. [xxx put horizontal reflectance scale back in sothe change in reflectance can be associated with the change in Munsell value. See text. Figure modified fromshaded box and data points from Romney & Indow, 2003.


84Stevens, J. & Stevens, S. (1963) Brightness function: effects of adaptation J Opt Soc Am vol 53(3), pp375-38585Jones, R. (1963) Teminology in photometry and radiometry J Opt Soc Am vol 53(11), pp 1314-1315

one such model may be provided by a maximized interpoint-distance formulation in, for example, the Munsell colorspace, or in some other perceptual scaling space.’”

Stevens & Stevens have provided a large volume of data supporting the proposed template for describing vision84. That paper should be reviewed in detail by the serious reader. The work provides absolute scales for both theordinates and abscissa. However the units used are unconventional or unknown in vision research. S. Stevens hadlong been working in hearing at the time of this paper. In moving into vision, he did not appear to appreciate thevast difference in wavelength of the energy involved versus typical source sizes. Where point sources are the normin hearing because the wavelength is much greater than the typical dimensions of a speaker, the situation is quitedifferent in vision. The wavelength of light is much less than even the smallest element in a scene. As a result,sources are typically large in area and the energy radiated by these sources must be accounted for on a per unit areabasis. Their use of lumens as a unit of energy, equivalent to a watt is not appropriate. This energy could be spreadover an unspecified source area and result in any luminance desired. This oversight may be due to the situationhighlighted by Jones in the same volume of the same journal85. “In describing the calibration or use of a radiometer,it is customary to say something like: “Basically , a radiometer measures irradiance, nor radiance, even though it iscalibrated in terms of radiance.’” the proper use of such a radiometer or photometer requires careful attention to theinstructions in the user’s manual. Stevens & Stevens defined a logarithmic scale, similar to that used in hearing,based on 10-10 lumens = 0 dB. They asserted this value was near the threshold of vision. They also defined a unit ofpsychophysical response they called a brill. They defined it as the brightness seen (? perceived) under the standardconditions when the target has a luminance of 40 dB re 10-10 L or 1 μL. (Unfortunately, they later used the term mLwhich is the standard abbreviation for millilambert rather than millilumen). They did not define any linearityrelationship between the brill and the Lumen. However, they did present a graph of the brightness in brills(perceived luminance) as a function of the “luminance” of the source based on their dB scale. In this figure, a 10 dBchange in brills equaled a 30 dB change in luminance, resulting in a slope of 0.333 for the depicted relationship. Thebrill has not survived in modern vision literature. It is fortunate that the data reported can be converted to a moreappropriate luminance scale because of the linearity between lumens and cd/m2 for a given test configuration. Thelabeling of their light source as 150 watts is superfluous. This is the power into their lamp and is unrelated to theamount of light illuminating their test target.

Figure 17.2.2-5 shows figure 7 of the Stevens & Stevens paper based on their definition of luminance as related tolumens. This figure shows a strong familial relationship to the previous template. There is an asymptote labeled“dark” that corresponds to the compression line of the template. There is also a dashed line below the darkasymptote that they describe as the equilibrium condition following adaptation. It corresponds to the dashed line inthe template where it has the same significance. However, in the template, any variable element in the impressedsignal results in a variation in perceived brightness in accordance with this curve. The Stevens & Stevens figureshows the individual responses converging in the upper right toward a value at 130 dB luminance (1000 brill). Thetheoretical template was developed for isolated stimuli and does not show this condition although it does notdisparage it.

The Stevens & Stevens test configuration involved an embedded stimulus of 5.7 degrees diameter within a surrounddescribed as limited by a second aperture to 58 degrees. This allowed testing under different levels of centralillumination while using a controlled surround. As a result, curves were obtained similar to that of Bodmann et. al. They systematically fell below the dark line that was equivalent to Bodmann, et. al’s. isolated stimulus and thecompression line of the template.


86Craik, K. (1940) The effect of adaptation on subjective brightness Proc roy Soc (London) vol B128, pp232-247

The term adaptation level in this figure should probablybe defined more clearly as the surround brightnesslevel. It does not relate directly to the adaptation levelof the circuitry within the photoreceptor cells.

Figure 9 of Stevens & Stevens replots the curves offigure 7 on linear-linear scales. The resulting curvesshow a generic exponential character and a equilibriumbrightness that is essentially horizontal. This is acharacteristic of the feedback loop associated with thesensory neurons which is designed to perform aclamping function (Section xxx). It suggests the clamplevel is near 50-100 brill for a target luminance of 20-100 millilamberts. (It is not clear why millilamberts areused in this figure rather than their Lumens in dBparameter). For levels above this value, the perceivedbrightness remains nominally constant within theadaptation range of the photoreceptor cell. They notedCraik confirmed this equilibration level held up to aluminance of 75,000 ft-L (119 dB) using a Maxwellianview test set86.

Stevens & Stevens give no data points, other than one in their figure 8 with a wide range bar (one order ofmagnitude), to substantiate the verticality of the individual curves they show under low luminance conditions. However, the depiction agrees with that suggested by the theoretical template.

In discussing their figure 7, Stevens & Stevens made several critical observation (page 381). First, they noted theequilibrium curve did not follow a power law as the operating point changed. Second, they noted, “The terminal orequilibrium brightness function shows that, if the visual receptor is allowed to adapt to the level of the stimulus, theinput-output relation may approximate a logarithmic function more closely tha a power function, at least over someof the range.” They also note “the changing ‘operating point’ of the visual system that results from different levelsof adaptation can thus obscure the basic form of the psychophysical function.” This last statement appears to bepoorly constructed. The changing of the operating point is also a fundamental property of the visual system.

17.2.2.3 Analysis of the brightness/luminance relationship

[xxx end with a new template with specific scales. Show or claim the theoretical template is exact for the isolatedstimulus The Stevens & Stevens case shows the theoretical template with an embedded stimulus]

A new theoretical performance graph for the visual modality is shown in Figure 17.2.2-6. It is calibrated using theexperimental data of Romney & Indow and Stevens & Stevens. It applies specifically to the isolated stimuluscondition. Verification of its precision awaits further experimental investigation using modern instrumentation.

As developed in both vision and hearing, the line labeled compression is an asymptote defining the nominalmaximum signal output of the photoreceptor neurons under high stimulus conditions. The heavy curved lines areactually one line that represents the logarithmic conversion performed in the axon circuit of each photoreceptor.

Figure 17.2.2-5 Brightness functions for various levels ofadaptation. The dashed line shows the terminal brightnesslocus–the level of sensation reached when the eye comesinto full equilibrium with the luminance it is viewing.


87Stevens, S. (1961) The psychophysics of sensory function In Rosenblith, W. ed. SensoryCommunications NY: Wiley & Sons pp 1-33. NY: Wiley

This line moves in this representation as the gain of the adaptation amplifier changes. The gain levels shown refer tothe gain of the adaptation line before the latest stimulus is applied. When that stimulus is applied, the adaptationamplifier gain will change in an attempt to bring the output voltage at the pedicle of the photoreceptor into thenormal operating range.

The maximum operating range is shown as 200:1. This value is in good agreement with the maximum operatingrange under photopic operating conditions as suggested by Munsell Color Book. Based on the work of Romney &Indow, this range corresponds to a Value range in the Munsell Color Book of about xxx.

The theoretical performance does not predict the heavy curved lines converge at a point equal to 130 dB as shown inStevens & Stevens. However, these lines below the compression line are temporally dynamic. Second order effectsmay cause the curves to converge, or Stevens & Stevens may have documented a dynamic condition with a timeconstant of about 2 minutes.

17.2.2.4 Compression factors found in other sensory modalities

The above paragraphs have described the variation in the exponents associated with the perceived versus appliedstimuli. Compression factors are found in all sensory modalities. They typically expand the area of response withinthe range of primary interest. Stevens has provided estimates of the slopes of the response functions within theadaptation ranges of several sensory modalities87. He lists the slopes in these areas as; loudness, 0.67; brightness,0.33; smell, 0.6; taste based on salt, 1.4; and heaviness(?), 1.45. The precise meaning of a slope greater than onemay not be interpretable using the same model as used here for vision and hearing.


17.2.3 The luminance threshold (AKA luminous efficiency function) of the human eye

This section will discuss the methodology required to define the luminosity function, the perceptible luminancefunction and the luminance discrimination function of human vision and then review the experimental techniquesrequired to obtain precise verification of the theoretical functions. Because of the number of variables involved,several specific forms of the above theoretical functions will be presented to allow easy comparison with theaccepted functions in the literature and those standardized by the C.I.E.

It should be noted that the entire field of photometry, as opposed to radiometry, is founded on a set of highlyunrealistic assumptions. First, it assumes a series of symmetry and proportionality laws based on linear addition inthe signal processing channels of the eye. This condition is clearly not met except for small signal conditions. Second, it assumes a fixed relationship between the perceived spectral sensitivities of the three individualphotodetection channels of vision. This condition is not met in a real eye except under totally dark adaptedconditions. Because of these difficulties, it is frequently hard to correlate the psychophysical data and theelectrophysical data in the literature. The psychophysical database is based primarily on photometric units and theelectrophysical database is based primarily on radiometric units.

Figure 17.2.2-6 The theoretical performance of the visual modality with adaptation as a parameter. The curvedheavy lines reflect the state of adaptation prior to the application of a new stimulus. Upon application of thatstimulus, the adaptation gain will change to bring the performance into the normal operating regime shown.


88Griswold, M. & Stark, W. (1992) Scotopic spectral sensitivity of phakic and aphakic observers extendinginto the near ultraviolet. Vision Res. vol. 32, no. 9, pp 1739-174389Tan, K. (1971) Vision in the ultraviolet. Ph. D. thesis. Utrecht, Holland: Rijksuniversiteit te Utrecht, alsoUniversity of Missouri (Columbia) Library, call no. QP481.T16. Also available in a review by Stark, W. &Tan, K. (1982), Photochem. Photobiol. vol. 36, pp 371-38090Boettner, E. & Wolter, J. (1962) Transmission of the ocular media. Invest. Ophthal. Vis. Sci. Vol. 1, pp776-78391Van den Berg, T. & Tan, K. (1994) Light transmittance of the human cornea from 320 to 700 nm fordifferent ages. Vision Res. vol. 34, no. 11, pp 1453-1456

17.2.3.1 The tetrachromatic spectral sensitivity of the human retina

Surgery to remove the lens of the human eye has frequently been necessary in the past. It has been found that thehuman eye exhibits significant ultraviolet sensitivity after such an operation (in the absence of a prosthetic that itselfabsorbs in the ultraviolet). Griswold & Stark have provided excellent spectral data on such eyes down to awavelength of 315 nm88. Figure 17.2.3-1 presents their data, and that of Tan89, in the context of this work. Alsoshown are the set of theoretical absorption spectra defined in this work for the human eye. The spectra are drawn forthe nominal peak wavelengths and an arbitrary quality factor of Q=4.8. The spectra must be considered illustrativeuntil better data becomes available for the half amplitude values for each individual spectrum (Section 5.5.10).

The one data set is labeled as “with B & W.” This notation refers to the studies by Boettner & Wolter of theabsorption of the other elements of the physiological optical system, Stage B, except for the lens90. The Tan data isalso “with B & W.” A recent paper by Van den Berg & Tan provide additional data relative to the Boettner &Wolter paper. While published in 1994, it reports on the mining of data collected in 1967-6891. It is unknownwhether Boettner & Wolter included the absorption and scattering within the neural layer of the retina (the field lensof the physiological optics, and potentially the source of macular absorption).

Griswold & Stark made considerable effort to perfect and calibrate their test instrumentation. However, there are anumber of theoretical problems with their analytical procedure. First, they discuss their work in terms of scotopicsensitivity measurements. However, they use a stimulus that is only 38 minutes in diameter. This differs from theC.I.E. suggested diameter. The C.I.E has adopted a stimulus diameter of two degrees for photopic measurementsand ten degrees for scotopic measurements. Their figure 1 shows the nominal C.I.E. scotopic luminosity functionoverlayed on some of their data. As shown in [Figure 17.2.2-9], the difference between using the C.I.E. scotopicand photopic characteristics would be small at this wavelength relative to their ordinate. Their figure 3 shows thenet absorption of the lens based on their experiments. This data will be discussed in the next section. It shows amaximum absorption of slightly over 4 log units (a transmission of only 0.01% at 360 nm). This peak wavelength isconsistent with other literature.

Second, they attempt to relate the absorption in the region of 350 nm to the cis-peak in the dilute isotropic absorptionpeak of the retinoids (not actually limited to the cis-peak of rhodopsin) in their results section. In their discussionsection, they back off from this position and posit the possibility of a separate UV sensitivity mechanism (based onother work within their group). As seen from the above figure, the anisotropic absorption of Rhodonine(11) whenconfigured as a liquid crystal within the Outer Segment of the photoreceptor cells is a much better match to the datathan an isotropic cis-peak. Furthermore, the literature does not explicitly define a cis-peak for the retinoidsassociated with vision (See Chapter 6).


92Saszik, S. & Bilotta, J. (1999) The effects of temperature on the dark-adapted spectral sensitivity functionof the adult zebrafish. Vision Res. vol. 39, pp 1051-1058, fg 2 & 3

Figure 17.2.3-1 (Color ln) Comparison of aphakic vision and the theoretical model. The data curves werenormalized with respect to each other by Griswold & Stark. The theoretical spectra are normalized with respect toeach other but separately from the data. The four chromophore absorption curves are shown normalized separatelyas a reference. The composite theoretical curves are for a quality factor of 4.8 and are only illustrative. See text fordiscussion. Data points from Griswold & Stark, 1992.

While the experimental data in the figure appears to be quite good, it must be noted that at the scale of the figure, thedifferences between Griswold & Stark and Tan are generally greater than 2:1. Some points differ by 3:1. Thetheoretical curves proposed by this work can easily be drawn within the envelope of these combined works asshown. Besides the reference absorption curves at the bottom of the figure, two composite spectral sensitivity curvesare shown. The upper line is for photopic vision and the lower is for pure scotopic vision. These two curves weredrawn using the parameters of the Standard Eye presented in the appendices except for the following parameters.

The spectral responses for the human retina presented above are not unexpected or unusual within biological vision. In fact, they can be overlaid directly with the spectral response of the zebra fish as reported by Saszik & Bilotta92. For the size of fish used (4-5 cm in length) the absorption of their lenses in the ultraviolet would be expected to beminimal. The peak sensitivity for these fish in the UV was also within a factor of three of the peak sensitivity in the500 nm region.

Temperature = 310 Kelvin, λss = 405 nm, λms = 505 nm, λls = 600 nm and kuv:ks:km:kl::500:330:1000:330 for the


93Jacobs, G. Neitz, J. & Deegan, J. (1991) Retinal receptors in rodents maximally sensitive to ultravioletlight. Nature, vol. 353, pp 655066694Stark, W. Wagner, R. & Martin-Gillespie, C. (1994) Ultraviolet sensitivity of three cone types in theaphakic observer determined by chromatic adaptation. Vision Res vol. 34, no. 11, pp 1457-1459

photopic curve. For the scotopic curve, kl was effectively zero and the other parameters remained unchanged.

The adjustments of 5 nm in the above wavelengths were made for two reasons. The main reason was to moreprecisely fit the data points on the assumption that the dip in the data near 425 nm was not due to any variation in thetest set. This dip is at a slightly shorter wavelength than expected by this theory. However, this theory depends onparameters for the ultraviolet chromophore that have never been measured before. The parameters chosen weredeveloped within the theory itself. The second reason was to more precisely track the data points in the area of thepotential Bezold-Brucke anomalies near 487 & 580 nm. The data of Griswold & Stark and of Tan vary by a factorof between 2:1 and 3:1 in this area. By adjusting the difference between λsl and λms, the data of either investigatorscan be matched precisely. However, the preferred approach is to obtain a more statistically relevant data set so theactual wavelength difference can be specified precisely.

Griswold & Stark noted that their threshold measurements always appeared colorless to their subjects. This causedthem to relate their data to the C. I. E. scotopic luminous efficiency function. However, sensitivity threshold testsalways appear colorless to the subject, whether scotopic or photopic. Whether the tests were performed within thescotopic range is determined by a variety of conditions. However, the primary condition is whether the longwavelength signaling channel is functional or not due to the square law mechanism in its translation process. Bycomparing the data points and the theoretical curves, it is clear that they were operating in the scotopic visual region. However, both their data points and those of Tan deviate from a Fermi-Dirac slope in the long wavelength skirt ofthe measured sensitivity functions. This deviation suggests the presence of some sensitivity due to the longwavelength signaling channel. Such sensitivity is probably due to the long wavelength signaling channel. Suchsensitivity would be an example of a failure in the univariance principle.

The theoretical curve demonstrates clearly that the measured sensitivity functions contain significant componentsdue to three of the four chromophores of vision operating via separate signaling paths. This fact completely negatestheir reference to the data “making it fairly certain that our spectra are largely pure rod spectra.” In fact, their datais very compatible to a tetrachromatic eye containing no achromatic photoreceptors (rods) of any kind.

It would be interesting to expose their subjects to a checkerboard or other pattern of various intensities orreflectances over the range of 320 nm to 490 nm in order to elicit the perceived colors of the patterns at higher lightlevels. This would allow the determination of the wavelength of the neutral point within the ultraviolet-shortwavelength color space. These tests would provide a preliminary answer to the age old question of “What doanimals see in the ultraviolet, and how do they describe ‘white’.” These answers would also allow a furtherdefinition of the complete tetrachromatic color space defined in Section 17.3.3.

It would also be interesting to expose their subjects to chromatic adaptation similar to that of Jacobs, et. al.93. Such atest would demonstrate that the ultraviolet sensitivity was due to a distinctly separate ultraviolet absorber. Figure 6in Jacobs, et. al. demonstrates this clearly for the mouse. Note the very rapid fall off in sensitivity indicative of aFermi-Dirac edge in the absorption spectrum. Such a test would quell the idea that the ultraviolet sensitivity was anextension of the short wavelength spectral channel or a b-peak due to one of the other channels.

Stark, et. al. (1994) have provided additional data based on the in-vivo aphakic subject (WSS)94. Higher stimuluslevels were used that allowed chromatic adaptation to be employed. In that paper, they again suggested the UVresponse might be a cis–response associated with the normal three chromophores. However, they also confirmed the


95http://www.atofinachemicals.com/atoglas/technicalinfo/Arch/PLA17c3.cfm96http://www.bbc.co.uk/iplayer/episode/b00rqgh4/Richard_Hammonds_Invisible_Worlds_Out_of_Sight/97Hambling, D. (2002) You don't have to come from another planet to see ultraviolet light. GuardianThursday May 3098Anderson, R. (1983) Visual perceptions and observations of an aphakic surgeon Percept Motor Skills vol57, pp 1211-121899Kraft, J. & Werner, J. (1994) Spectral efficiency across the life span: flicker photometry and brightnessmatching," J Opt Soc Am A vol 11, pp 1213-1221

earlier findings of the team that the UV response exhibited a higher peak sensitivity than any of the longerwavelength chromophores. This finding is not compatible with the idea of a secondary sensitivity peak, a β-peak,whether due to a cis–response or otherwise. An unexpected feature of their protocol was the use of a “frosted UVtransmitting Plexiglas.” No specifics were given concerning this Plexiglas. This product normally exhibitsnegligible transmission at wavelengths below 350-365 nm95.

Richard Hammond presented a TV program over the BBC on 23 March, 2010 involving a man with his biologicallenses removed who discusses his resulting UV vision96. The program should be available in the USA on theDiscovery Channel in the near future. He claimed that after the operation he started to see bright purplish and bluelight emitting from scanners used to scan currency notes. He also said that rainbows had far more color in them nowthan he had seen before. This is completely expected. No information was provided on the types of replacementlenses he was using. He did not demonstrate his ability to see at wavelengths shorter than 400 nm. Hamblingpresented an article in the popular press on UV vision, citing Stark as a specific example97. Much of the content isanecdotal and the concepts questionable.

Anderson provided a first hand account of aphakic vision from a medical surgeon98. However, he was not anophthalmologist or an optician. As a result, his observations are those of a educated individual but not an authorityin what he is talking about. Many of his observations are useful in the hands of one with a better understanding ofthe eye-brain system. His observation of an exhibit of rocks under ultraviolet illumination at the SmithsonianInstitution is very instructive concerning the operation of the aphakic eye versus his other normal eye. While normalobservers saw a well organized display of rocks against a dark background, his aphakic eye say a highly illuminateddisplay in total disarray (crude tables built on saw-horses for legs, electrical cords running aimlessly), and not readyfor public display. His observations of the geometric performance of the human eye/brain system are even moreuseful and demonstrate the conformal transformation of circles on the retina into straight lines on area 17 of thecerebral cortex and the resulting perception of straight lines where intuition would say circles or circular arcs shouldhave been observed. See Section 15.2.5.7. His familiarity with reduction telescopes as used in surgery was at bestcursory from an opticians perspective. The shortcomings he discusses are easily overcome with two features he didnot discuss, a telocentric telescope design and an aspheric version of a reduction telescope.

Kraft & Werner have provided extensive data comparing the sensitivity of the eye with and without the presence ofthe lens for 50 subjects99. [xxx may not be correct interpretation ] Their data (Figure 17.2.3-2) is reproduced (witha false color background) in Backhaus et al. (page 26) and follows the earlier data of Tan, of Stark and of Babucke. The graphic printing technique used does not represent wavelengths less than 460 nm and longer than 625 nm at all. Thus the color background is stretched to cover 400 to 700as an artistic devise. Note the increasing sensitivity of theretina at short wavelengths. This increase can be expected to continue with a peak near 342 nm. (in the absence ofany limits within the instrumentation) and rise above the peak of the short wavelength receptors near 437 nm.


100Bowmaker, J. & Kunz, Y. (1987) Ultraviolet receptors, tetrachromatic colour vision and retinal mosaicsin the brown trout, Salmo trutta; age-dependent changes. Vision Res. vol. 27, no. 12, pp 2102-2108

17.2.3.1.1 Effect of aging on ultraviolet vision

Bowmaker & Kunz have suggested, but did not demonstrate, that tetrachromatic fish lose the ability to see in theultraviolet as they mature due to atrophy of the ultraviolet photoreceptors100 (see Section 1.2.1.2). The data ofGriswold & Stark do not support such atrophy in humans. Their aphakic subjects varied in age from 22 to 43 yearsof age. These subjects all had normal eyes until surgery at ages exceeding 10 years. Based on this work, the loss ofUV vision in fish is due to their growth in size and the thickening of the lenses of their eyes. These lenses areparticularly thick in grown fish relative to the diameter of their eyes. It is how they achieve a high f/# opticalsystem. The lens is particularly absorbent of UV light.

The figure strongly supports the tetrachromatic hypothesis of this work based on the Rhodonines. The correcteddata of both Griswold & Stark and of Tan in the ultraviolet portion of the measured spectrum match the predicted

Figure 17.2.3-2 Heterchromatic brightness sensitivity change per decade is plotted as a function of wavelength atthe cornea (black circles) and at the retina (whilte squares). The horizontal line at zero denotes no age-relatedchange. The thicker horizontal line at +0.05 shows the mean increase in brightnes sensitivity per decade between420 and 560 nm. Note the false color used as a background. See text. From Kraft & Stark, 1994.


spectrum of Rhodonine(11) very well. The match is good with respect to both center wavelength and width of theabsorption characteristic. It also appears to be good relative to the quality factor, Q. For the nominal Q = 4.8, thecrossover between the theoretical chromophores is lower in the 400 nm region and higher in the 600 nm region thanin the region of 500 nm As a result, the theoretical luminous efficiency function (not shown) would be expected tohave a larger dip in the region of 400 nm than at either 500 (494) nm or at 600 (580) nm. Of course, whether this dipis observable under dark adapted conditions would depend on the relative contributions of the spectral channels tothe luminance equation. It would also depend on the statistical precision of the data. Although Griswold & Starkused only a few subjects, the error bars provided suggest their data is quite precise. Whether it is indicative of alarger population is still an open question. Their data does exhibit a number of relative maxima, relative minima andinflection points that suggest it is compatible with the complete luminous efficiency function of this work. This iseven true in the long wavelength region where there appears to be an inflection point near 600 nm and a change inslope (at least in the data of Tan) supporting the presence of a long wavelength chromophore at reduced absolutesensitivity. This would mimic the situation found in normal eyes.

Griswold & Stark suggest that the sensitivity of the ultraviolet spectral channel in the aphakic human is even moresensitive than the short wavelength channel and approaches the sensitivity of the mid wavelength channel. Bennett& Cuthill summarize the work of several investigators an say that “Birds appear if anything, to be more sensitive toUV than to light in the ‘human visible’ part of the electromagnetic spectrum.” If both of these statements are true,one would not expect any auxiliary peak near 400 nm (due to a pseudo-Bezold-Brucke Effect) under dark adaptedconditions. However, under conditions where the ultraviolet sensitivity was reduced by about a factor of five, it ispossible such a peak would be observed. Bennett & Cuthill have referenced peaks in the vicinity of 380 nm thatmight relate to this pseudo-Bezold-Brucke Effect. A similar peak was referenced in the vicinity of 415 nm. Thesepeaks were obtained using less precise psychophysical techniques.

The above discussion and data makes it abundantly clear that the aphakic human retina is tetrachromatic even inmiddle age and beyond. The performance of the overall system is limited by the absorption of the lens towavelengths longer than 400 nm. The data strongly supports the theory and model of this work. It is particularlyuseful in supporting the proposed spectral performance of the Rhodonines, even supporting the Q = 4.8 proposal. Whether the O-channel of the chrominance signal processing path is functional in the human remains to bedetermined.

Kraft & Werner addressed the change in sensitivity of the human eye in both the broad and ultraviolet portion of thespectrum in the paper cited above.

17.2.3.2 The spectral characteristics of the physiological optics of the human eye

Figure 17.2.3-3 provides an overview of the spectral limitations of the physiological optical system. The outsideenvelope is due primarily to the absorption of water. This absorption limits biological vision to the region between340 and 1400 nm. Within this range, there are a series of other absorbers that impact or control the absorptioncharacteristics of vision. The most important of these in the large chordates (including man) is the absorption by thelens group in the region of 350 to 400 nm.

The complete description of the equivalent optical density of the physiological optics is given in Section 16.3.3.2.1. A precise description is complicated by two factors. First, the transmission path is that of a converging refractingoptical path. The optics involves curved surfaces that are not properly represented by an equivalent slab of constantthickness homogeneous material. Hence, measurements are a function of the size and position of the light bundleused to calculate the optical density. These variations are codified by one of Stiles-Crawford Effects (see Section17.3.7). Second, the portion of the overall optical system related to the macular region exhibits an additionalabsorption mechanism that is not shown in the above figure.


Figure 17.2.3-3 CR Light transmission through thephysiological optics of humans. From Miller,1991.

Figure 17.2.3-4 “Equation for optical density ofphysiological optics” Eq. 17.2.3.1

17.2.3.2.1 The primary in-band spectralabsorption of the physiological optics

As noted in Sections 16.3.3.2.1 and 17.2.2, it is theabsorption of the lens, with an absorption edgeoverlaying almost precisely the long wavelengthabsorption edge of Rhodonine(11) that causes thehuman eye to be limited to that of a long wavelengthtrichromat.

The popular literature has occasional references to theability of the human eye to see light down to 300 nm. This feature is due to two factors. First, the presenceof ultraviolet photoreceptors in the retina, as shown inSection 17.2.3. Second, the small rise in thetransmission of the lens in the area of 320 nm. This rise is more clearly identified in the following figure describingthe equivalent optical density of the lens.

The equation for the optical density of the physiological optics, without the reflectance term associated with the air-cornea interface and without a scaling constant is given in the Figure 17.2.3-4. The reflectance loss is about 2.5%across the visual spectrum. The total attenuation is described by three terms. The first term is an absorption due toan alcohol ligand within the lens and humors of the eye. The second term is an absorption due to an aldehydeligand within the lens and humors. The third accounts for the Rayleigh scattering within the medium. The twoligand terms, ao( λ) and aa( λ), for the alcohol and aldehyde respectively, are each given by a two-sided Fermi-Diracexpression defined in terms of a quality factor of nominally Q = 15. The first term has a peak absorption near 325nm and the second a peak absorption near 357 nm. These wavelengths are the presumed peaks for these materialsin-vivo, as opposed to in ethane or hexane--the solvents associated with in-vitro spectral evaluations.

Figure 17.2.3-5 shows the theoretical loss overlaid on the data points of Griswold & Stark. The fit appears to beexcellent. The fit in the area of 330 nm can be improved by adjusting the Q and peak wavelengths slightly. However, it is not likely the data is as accurate as the theoretical curve in this area. The data points were derivedfrom measurements on only a few eyes and only a few data points in this area.

The two Fermi-Dirac expressions are not coupled. This suggests the individual ligands are not in quantum


Figure 17.2.3-5 The equivalent optical density of thephysiological optics of the eye, disregarding theabsorption peculiar to the macular region. The data pointsare from Griswold & Stark. The smooth curve is thetheoretical optical density of this work. The region below400 nm is dominated by ligand absorption. It is thisabsorption that limits the human eye to trichromaticperformance even though the retina is tetrachromatic. Atwavelengths greater than 400 nm, performance is limitedby Rayleigh scattering.

mechanical communications with each other, i. e., theyare probably entirely separate molecular structures. The Q is probably due to the temperature of thematerials.

The scatter term is the major source of loss within thevisual spectrum from 400 to 700 nm. It is also theprinciple loss factor that is a function of age. Theequivalent optical density due to this factor is believedto increase about 0.55% per year. Such a change isnearly negligible year to year.


101Brown, P. & Wald, G. (1963) Visual pigments in human and monkey retinas Nature vol. 200, pp 37-43

Figure 17.2.3-6 (Color ln)The theoretical absorption ofthe macular. Compare with the empirical data of Wald.

17.2.3.2.2 The spectral absorption of the macular area

The absorption of the neurological material within the optical path associated with the macular has been presented inSection 3.2.1.3. This absorption is well characterized by conventional bulk absorption by the molecules forming thelayer. Figure 17.2.3-6 presents the results of the theoretical analysis. The equation of a two-stage, stagger-tunedelectronic circuit well emulates this type of absorption as measured by Brown & Wald101.

17.2.3.3 The tetrachromatic spectralsensitivity of the complete human eye

With very precise theoretical relationships for thespectral absorption of both the retina and thephysiological optics of the eye, it is possible tocalculate the theoretical spectral absorption of theoverall eye and compare it to the available empiricaldata. This can be done for both the macular area aswell as the surrounding area.

17.2.3.3.1 The spectral sensitivity of thecomplete human eye (except in macular)

By combining the theoretical spectral absorption of the retina with the optical density of the physiological optics(other than in the macular), a theoretical spectral absorption function for the complete human eye is available. Thisfunction is presented by the solid lines in Figure 17.2.3-7 along with the best available empirical data. The humaneye exhibits a significant sensitivity in the ultraviolet region that is not normally measured in the laboratory becauseof the use of glass optics and light sources of low blackbody temperature. To measure the complete sensitivityfunction of the human eye, the use of quartz optics and a light source at a nominal color temperature of 8683 Kelvinis required.

The use of crystalline quartz optics is preferred since many fused quartz glasses have limitedspectral transmission due to additives introduced for other purposes. The Infrared Handbookprovides an easy source of data on these materials.

The ultraviolet sensitivity peaks in the vicinity of 300 nm due to the high absorption of the physiological optics inthe 325-357 nm region as developed above. Note this spectral sensitivity of the human eye in the ultraviolet regionis not the result of fluorescence within the materials of the eye. It is a real and conventional sensitivity.


Figure 17.2.3-7 (Color ln) Calculated tetrachromatic spectral sensitivity of the normal human eye compared withthe best data available. The green curve represents the scotopic response. The photopic response is given by the redextension of the green curve. The coefficients, kuv:ks:km:kl::500:330:1000:330, were used to generate this extension. The value of kl is higher than in the standard eye (typically 100) in order to emphasize the response and a smallBezold-Brucke Effect near 580 nm. When working within the macular area, the correction shown by the dotted lineis appropriate. All curves include the absorption and Rayleigh scattering associated with the physiological opticsof the eye. The data points of Griswold & Stark are also shown.

Figure 17.2.3-8 provides a comparison between the aphakic and phakic (normal) eyes based on the data of Griswold& Stark. The absorption of the aphakic eye has been extended based on the absorption of the viscous humor near300 nm. The 1000:1 additional attenuation of the phakic eye in the ultraviolet is in good agreement with theestimate by Wald. As noted earlier, the label B & W refers to the data of Boettner & Wolter related to otherelements of the physiological optics (the macular specifically). The axial length of the normal human lens is 4.5 mm(Section 2.4.1). Individuals with lenses of significantly shorter axial length can be considered partially aphakic (ordysphakic) from an absorption perspective. For a dysphakic eye with a lens of only 2.25 mm axial thickness, theattenuation would be expected to be only about 30:1 or one and one-half log units. Such dysphakic subjects reportsignificant ultraviolet perception under daylight conditions (color temperature of illumination near 6500 Kelvin).


102Rodieck, R. (1973) The Vertebrate Retina. San Francisco, CA: W. H. Freeman pg 290

17.2.3.3.2 The spectral absorption of thecomplete human eye in the macular

The macular introduces a significant attenuation of theinput irradiance in the region of 430 to 490 nm. As aresult, the overall sensitivity of the human eye issignificantly different in the foveola and fovea than itis in the more peripheral areas. This difference isillustrated by the dashed line in the above figure. Thisfact requires more careful documentation of the area ofthe retina observed when laboratory results arepresented in the literature than has occurred in the past. The macular has introduced a generally unknownfactor in the performance of the eyes presented in thepast. It may account for the suggested changes in theobserved sensitivity reported by Judd and discussed inChapter 17.

17.2.3.3.3 The measurement of thereflectance of the retina through thephysiological optics

The measurement of the spectral properties of the retina by microspectrometry through the lens is clearly impactedby the absorption of the lens. The impact is compounded by the light passing through the lens twice. This limits theobserved spectral characteristic to wavelength longer than 400 nm and introduces twice as much Rayleigh scatteringas normally involved. The physiological optics does not attenuate the light at wavelengths shorter than 300 nm. However, the viscous humor absorbs strongly below 300 nm. As a result, a small response in the region near 300nm may be recorded using the double pass approach if quartz optics and suitable stimuli are used.

There is an even more important consideration when observing the retina microspectrographically. It is that theimpact of spectral absorption by the individual photoreceptors is merely summed algebraically. The result is aspectrum that is completely unrelated to the electrophysiological and psychophysical spectrums. It does not reflectthe “filling in” of the spaces between the skirts of the spectral absorbers provided by the logarithmic processing.

17.2.3.4 Comparison with the ultraviolet research literature

The above figure shows the data points provided by figure 1 of Griswold & Stark that include the ultravioletsensitivity of the complete human eye (curve labeled phakic w /B & W). As mentioned earlier, Griswold & Starkwere very careful in the design of their experiments. The range bars associated with their data is generally smallerthan the symbols in the above figure. As a result of this fact, the concordance of the theory and their data givesconsiderable credence to the adequacy of the theory.

Additional credence is provided by Rodieck102. He references Goodeve, et. al. of 1942 as showing that aphakics cansee down to 298 nm. He also noted that Wald had shown in 1945 that the sensitivity of the aphakic at 365nm wasabout 1000 times higher than the normal eye.

Figure 17.2.3-8 A comparison of aphakic and phakic eyesbased on Griswold & Stark. The designation w/o B & Wcan be ignored. A normal eye has an axial lens thicknessof about 4.5 mm.


103Lamb, T. (1995) Photoreceptor spectal sensitivities: common shape in the long-wavelength regions. Vision Res. vol. 35, pp. 3083-3091104Stockman, A. Sharpe, L. & Gach, C. (1999) The spectral sensitivity of the human short-wavelength conesderived from threshold and color matches. Vision Res. vol. 39, pp 2901-2927105Baylor, 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

17.2.3.5 Comparison with the photopic research literature

There is a large volume of research literature on the shape of the absorption characteristic in the photopic region. Most of it is psychophysically based and much of it relies on difference spectrums. Much of it relates to themacular area. Only a few papers, such as Griswold & Stark, et. al. recognize the ultraviolet capability of the humaneye. Lacking an appreciation of the ultraviolet capability of the human visual system, most of the literature isarchaic with respect to research.

Lamb provided a review of selected portions of the database with some adjustments in values as part of theinterpretation103. The data is presented initially as a function of spectral frequency instead of wavelength. Whenthe data is normalized and fit to Lamb’s series expansion in the exponential of frequency, all of the data shows acommon low frequency (high wavelength) asymptote given by 70loge units per unit of normalized frequency. Whenconverted to a graph of normalized spectral sensitivity versus wavelength, the long wave responses all exhibit aslight curvature as found in this work (compare with Sliney in a later Section). He concludes that the half amplitudespectral width of the chromophores is a constant when calculated with respect to frequency in support of Mansfield,instead of wavelength as calculated by Dartnall and others. In this work, the spectral half amplitude bandwidths ofthe individual chromophores are found to vary in the manner suggested by Mansfield. However, the reasoning isquite different. The Fermi-Dirac spectral bandwidth for each chromophore is calculated with the wavelength in thedenominator of an exponential expression. Thus, a variable half amplitude spectral bandwidth as a function ofwavelength is obtained without resorting to a normalized calculation based on a series expansion based onfrequency.

Stockman, et. al. have recently provided another series expansion as a template for the absorption characteristic ofvision104. However, it is a general expansion of the second order in terms of wavelength with no theoreticalrelationship to absorption. They assumed the visual system was linear prior to their application of this expansion. By just letting a digital computer run, they provided 5-place accuracy parameters (based on 18 place calculations)that appear unjustified.

The isotropic absorption characteristic of the Rhodonines given by Baylor, Nunn & Schnapf can also be compared to this figure105. xxx Their data was collected using radiation with its e-vector perpendicular to the length of theOuter Segment. Although the caption of their fig. 4 says rods, the data actually represents the isotropic spectrum ofall photoreceptors.

17.2.3.5.1 The photopic research literature–normal broadband

The available animal data on the individual spectral channel absorptions agree very well with the derivationspresented here. Most of the human data prior to 1975 is poorer for several reasons. The general prohibition againstinvasive experiments has largely prevented acquisition of precise electrophysiological data. The resulting focus onpsychophysical techniques has introduced its own group of problems. The psychophysical data has been collectedusing a variety of methods and protocols. Several of these protocols are clearly inadequate. They generally do notemploy sufficient suppression of the mid wavelength spectral channel when trying to isolate the long wavelengthchannel. Thus, the preponderance of the putative long wavelength data shows the Purkinje Peak in the region of 580nm. One investigator recorded a peak at 610 nm and then placed an unsubstantiated comment in the caption saying


106Boynton, R. (1979) Human Color Vision NY: Holt Rinehart & Winston fig 6.14, pg 195107Weale, R. (1953) Spectral sensitivity and wave-length discrimination of the peripheral retina J Physiolvol 119, pp 170-190108LeGrand, Y. (1972) Spectral luminosity In Jameson, D. & Hurvich, L. eds. Handbook of SensoryPhysiology, vol VII/4 NY: Springer-Verlag pg 422

“The peak near 610 nm cannot be due to a cone pigment.106” He offered no alternate explanation for the data. Indifferent parts of the same figure, he showed both a peak and a valley at 580 nm. This feature is easily explained bythe logarithmic summation process used in chordate vision.

When collecting composite spectral data, the color temperature of the light sources used were invariably below 3600Kelvin. As a result, the data generally under represents the performance of the human eye in the blue.

Both human and animal data recorded before 1975 usually shows significant smoothing of the spectral responses dueto the use of spectral filters wider than 15 nm. The result is a broadening (and smoothing) of the recorded spectrabecause of the Central Limit Theorem. Most investigators did not specify the precise location of the retina exploredor anticipate any effect due to a variation in the length of the outer segments in that region. The intrinsic compositespectra show detail at the 5 nm level.

One of the earliest measurements of sensitivity illustrating all three spectral peaks (ignoring the ultraviolet) was byWeale107. Figures 17.2.3-9 shows his data as presented by LeGrand108. The point of measurement was 25 degreesfrom the foveola and just beyond the blind spot. The long wavelength peak is at 612 nm . The state of adaptationresulting in this data was not clearly described. However, incandescent sources were used to control the backgroundsurrounding the 50 minute test apertures.

Figure 17.2.3-9 Early spectral sensitivity curves. Weale,c, shows sensitivity peaks at 612 nm, 535 nm and near440 nm. The state of adaptation was not clearly defined. The response by Moreland clearly illustrates a Bezold-Brucke peak near 510 nm. From LeGrand, 1972.


109Wald, G. (1964) The receptors of human color vision Science vol. 145, pp 1007-1016

Figure 17.2.3-10 Comparison of theoretical and empiricalspectral sensitivity functions (luminous efficiency functions). Theoretical functions for relative coefficientsfor the S:M:L channels of 100:1000:300 from Fulton(1984). Data points from Wald, 1964.

Neglecting the ultraviolet sensitivity defined in this work, there is excellent agreement between this work and thetrichromatic based photopic research literature as shown in Figures 17.2.3-10 and 17.2.2-10. The data points in thefirst figure are from Wald using a 10-15 nm bandwidth spectral filter109. The theoretical curve is based on relativecoefficients for the S:M:L channels of 100:1000:300. The data points differ from the theory by less than a factor oftwo except in the most rapidly changing area, where averaging due to the finite width spectrometer is mostsignificant. No smoothing of the theoretical function has been incorporated into this figure. Such smoothing will beintroduced below. The primary remaining question concerns the precise difference in wavelength between the longwavelength half-amplitude point of the M-chromophore and the short wavelength half-amplitude point of the L-chromophore at in-vivo temperature in human. Two cases are shown, where the difference is 30 nm. and where it is35 nm. (a matter of 5 parts in 600 or less than one percent). The difference corresponds to a slight difference in thepeak spectral height of the theoretical luminous efficiency function near 572 nm. This slight difference causes thesmoothed theoretical function (discussed below) to exhibit a peak that varies but is near the C.I.E. Standard of 555nm found using the average response over a 2° field. As calculated, this peak was for an equal flux source ofillumination at 7053° Kelvin. More detailed laboratory analysis will be required to determine the precise edges ofthe two absorption bands. However, this data is critically important in determining that the two absorption edges areseparated by less than 35 nm at 37 Celsius.


110Piantanida, T. & Sperling, H. (1973) Isolation of a third chromatic mechanism in the deutranomalousobserver Vision Res vol. 13, pp 2049-2058, fig 1

Figure 17.2.3-11 Incremental threshold spectralsensitivity of two normal human subjects (circles). Averaged six ascending and six descending readings foreach observer after adaptation to a 3000 td white light. Lines are predicted spectra based on this work for theparameters shown. Data points from Piantanida &Sperling, 1973.

The highest precision spectra for the perceived spectral sensitivity of the human eye is that of Piantanida &Sperling110. Their data for a one degree diameter spot centered on the point of fixation is presented in Figure17.2.3-11. The test set provided a 50 msec flash of light. This data was collected without reporting a colortemperature (although their 1971 work was reported at a color temperature of 5500 Kelvin). A color temperature of5500 Kelvin would account for the high sensitivity they show at short wavelengths. A 14 degree diameterbackground illumination, described as 3000 Trolands, was drawn from the same source. It was described as an“equal energy source” but its color temperature was not specified. The filters used had a 0.5 nm half-band widthand a spacing of 10 nm was used. Although their text indicates the experiments covered 400 to 700 nm, they did notprovide values at 400, 410 & 420 nm. Nor did they report values for 680, 690 and 700 nm. The figure has beenreplotted from a non linear abscissa. Only two subjects were evaluated and no range bars were provided. Noexplanation could be found in the paper as to why TP showed a sensitivity four times lower than TW at allwavelengths.

The relatively smaller downturn in the shortwavelength response of TP is interesting. It wouldsuggest that the eye of TP was somewhat smaller thanthe eye of TW and/or TP was younger than TW. Iftrue, the effect could have been due to less absorptionof light by the lens of the subject. The data required toanswer this question was not given in their paper.

The lines drawn through the data points are obtainedfrom the equations of this work using the coefficientsand parameters shown in the figure. Even better fitscould be obtained if the range bars for the data wereavailable. At this level of precision, the length of theouter segments of the photoreceptors must be known ifthe actual spectral response of the averagephotoreceptor of each spectral type is to be calculated.

The best fit to the test data that could be obtained underthe current circumstances suggests a mean spectralabsorption for the spectral channels of 437.5, 531.5 &631.5 nm and relative sensitivities ofkS:kM:kL::350:1000:625. This was achieved using atheoretical calculation at five nanometer spacing and asmoothing factor (called ksmooth in Mathcad byMathSoft) of 40 nm. The smoothing factor is the onlyarbitrary constant in the entire calculation.

Note the peaks near 470 nm and 580-610 nm are notrelated to the presence of an actual chromophore. These peaks are due to the logarithmic summation process causedby the output structure of the photoreceptor cells. They are related to the Bezold-Brucke and Purkinje Effectsdiscussed in the next section.


It is important to note that the perceived luminous channel sensitivity for both TW and TP include an absolute S-channel contribution about 35% as high as the M–channel contribution. This percentage is recognized due to thehigh color temperature source used. It is also in great conflict with the typical psychophysical measurementsreported in the literature and based on a color temperature between 2000 and 2800 Kelvin.

A larger data set and a more precise description of the light source would allow more precise definition of the meanabsorptions and the variations from the mean for these two humans. The problem of a small data set is highlightedin Section 17.3.1 where the nonuniformity of the color sensitivity of the eye, in the area of the fovea is noted.

Note carefully the shoulder on the long wavelength skirt of the overall functions. This hump occurs at the actualwavelength of the L–channel chromophore. It is found in all precision spectra of all primates.

The remainder of the two papers by Paintanida & Sperling on protonomalous and deutranomalous subjects agreeswell with the theory of this work presented in Chapter 18. The protonope lacked an L-channel chromophore andthe deutranope exhibits normal spectral performance in the long wavelength region. The deutranope exhibits anormal spectral sensitivity (using all three chromophore types) but a failure in the signal processing associated withthe Q–chrominance channel.

An earlier Sperling & Harwerth graphic of the visual sensitivity of the rhesus monkey is shown in Figure 17.2.3-12. It shows the typical “three humps” recorded by many (Thornton, 1992). All show a L-channel peak in the 607-620nm region.

Figure 17.2.3-12 Visual sensitivity of the rhesus monkey. The vertical line at 600 nm is provided only as a visualaid for the reader. From Sperling & Harwerth, 1971


111Kurtenbach, A. Meierkord, S. & Kremers, J. (1999) Spectral sensitivities in dichromats and trichromats atmesopic retinal illuminances J Opt Soc Am A vol 16(7), pp 1541-1548112Babucke, H. (2007) Personal communications.

Kurtenbach et al. have provided mean spectral sensitivity data for groups of three individuals, who were eithertrichromats, deuteranopes or protonopes, using 4 nm wide filters within the mesotopic regime (0.05 to 14.98 td)111. Averaging the data from three individuals obscures the spectral response slightly due to the incorporation of subject-specific variations in the absorption of the macula. However, the data does show fine variations indicative of thetheoretical spectra of this work. Figure 1 of the paper shows the progressive loss in the L-channel response oftrichromats with reduced illuminance (note the distinctive shelf at 575 nm and 0.47 td). It also shows that thedeuteranope is not missing any spectral component (figure 2 is nominally identical to figure 1) and that theprotonope is missing the L-channel spectral component (no shelf appears in the long wavelength region at anyilluminance and the long wavelength sensitivity is reduced at all illuminances). Their analysis depended entirely oncurve-fitting using a set of templates from Smith-Pokorny fundamentals (obtained using 7-15 nm wide filters). Thecited Smith & Pokorny paper did not propose a unique set of spectral responses (see text associated with their figures6 & 7).

Babucke has collected new data for individual single humans with a test set designed to show the fine detail in thespectrum under mesotopic conditions112. Figure 17.2.3-13 shows his data for a single subject. The collected datanot only shows all of the predicted curves and shoulders in the spectrum, it clearly shows the predicted “computational peak” at 0.58-0.59 microns. This peak can only be obtained by logarithmic summation within theneurological system. A similar but less pronounced effect is seen at 0.465-0.475 microns. Additional experimentsare under way to acquire more statistically relevant data for this and other subjects (note the large deviation about themean at short wavelengths). The theory suggests the data will be different for different subjects due to minorvariations in disk diameter within the retina. By collecting the data separately, it may be possible to determine thesubject-to-subject variation in this experiment.


Figure 17.2.3-14, from a more recent private communication from Babucke (2008), has provided some very precisespectral data for subject KM. With one exception, the data points are within ±30% of the theoretical response usingthe equation and standard parameters of Section 5.5.10 when using spectral filters on the order of 10 nm wide. Babucke is concerned about the data points at 590 & 600 nm and at 520 & 530 nm. The fact the points at 520 & 530nm are above the best fit curve using the standard parameters (blue line) can not be explained by this theory and willrequire more analysis of the test protocol. Unusually high values have been measured on multiple subjects. At leastfor SG, the height of the values above the nominal blue curve are proportional to the eccentricity of the light appliedto the retina.

The points at 590 & 600 nm are consistent with the Purkinje Effect described in Section 17.2), except the peakappears to be shifted slightly toward the red.

Figure 17.2.3-13 A human spectral response confirming all of the curves and shoulders predicted by the theoreticalmodel. The data points are the average of seven readings. Additional data is needed to establish the mean andstandard deviation at each wavelength. The blue curve is the absorption function developed in this work with thecoefficients shown. The red curve is the absorption function after allowance for the absorption of the macularmaterial. Except at the longest wavelengths, the data points are within +/– 26% of the theoretical function in blue. From Babucke, 2007.


Attempts to fit the data points more closely using a different set of parameters suggests subject SG has outersegments that are smaller in diameter (and possibly shorter in length) than the subjects used to obtain the original setof parameters. As noted in Sections 5.4.2 & 5.4.3, the Pauli Exclusion Principle determines the precise width of thespectral absorption bands of the chromophores. In developing the original theoretical spectrum, it was assumed thecenter wavelengths of the chromophores were at 437, 532 and 625 nm. It was further assumed that the width of theabsorption spectra were broadened according to the Pauli Exclusion Principle resulting in the above centerwavelengths ±n nm where n equaled 25-30 nm. The best values to fit the data of Section 5.5.10 were tabulated inTable 5.5.10-1. Attempting to fit the theoretical equation to a data set using values with less than 5 nm spacing istedious. It will not be pursued here unless the data is known to be accurate to such fine tolerances.

By changing the value of n, it is possible to move the peak of the Purkinje peak toward the red. The dashed red lineshows a fit based on n closer to 20-25 nm (at least for the M- and L-channels). The parameters used are shown in themiddle of the figure. A set of data developed using Mathcad and known as c_human_spec_b.MCD was used. Nosmoothing was used in the calculation. Several smoothing routines are available to use with the above Mathcadprogram. However, they do not use a kernal based on a Boltzmann Function.

The theoretical formula allows the data points to be matched arbitrarily well by the theoretical equation using

Figure 17.2.3-14 High precision spectral data for SG. The dashed overlay shows the theoretical fit to the curveusing the parameters shown in the middle of the figure. From Babucke, 2008, unpublished.


different values for the wavelength parameters and smoothing comparable to the width of the filters used to collectthe data. A better match will not be attempted until the statistical ranges for each wavelength of the data set for SGis determined.


113Sperling, H. & Harwerth, R. (1971) Red-green cone interactions in the increment-threshold spectralsensitivity of primates Science vol. 172, pp 180-184114Harwerth, R. & Sperling, H. (1971) Prolonged color blindness induced by intense spectral lights in rhesusmonkeys Science vol. 174, pp 520-523115Harwerth, R. & Sperling, H. (1975) Effects of intense visible radiation on the increment-thresholdspectral sensitivity of the rhesus monkey Vision Res vol. 15, pp 1193-1204116Sperling, H. Crawford, M. & Espinoza, S. (1978) Threshold spectral sensitivity of single neurons in thelateral geniculate nucleus and of performing monkeys Mod Probl Ophthal vol. 19, pp 2-18

Sperling & Harwerth have provided data similar to the Paintanida & Sperling data for the rhesus monkey, Macacamulatta113,114. The data shows that the spectral performance of man and the rhesus monkey are nearly identical. They extended their study to include degradation performance following intense illumination. Unfortunately, theyused a two degree diameter test target (which introduces some inhomogenuity if their foveola has the samedimensions as in humans. The effect is noted in Section 17.3.1 but they did specify the color temperature of theirsource as 5500 Kelvin.

Unfortunately, they attempted to match their data to a linear summation of three spectral channels based only on aDartnall nomograph and peak absorptions at 445, 535 and 575 nm. The latter number is actually associated with thePurkinje peak found in the logarithmic summation mechanism and not a chromophore of vision. Because of theirassumption, a simple summation of spectral channels was not possible. They reverted to a 2x2 matrix with fouradditional arbitrary coefficients to take differences between the 535 and 575 nm values in order to arrive at a set of pseudo-absorbers in the long and medium wavelength regions. Interestingly, these pseudo-absorbers had peakabsorptions near 625 nm and 535 nm. Under their assumptions, they had to revert to a piece-wise linear model,based on a curve fitting activity. They describe their final spectral envelope as an “upper envelope model,” togenerate an overall absorption spectrum.

In 1975, Harwerth & Sperling provided additional empirical data which is excellent115. However, their curve fittingefforts used the same techniques as in the above papers. The discussion and the results based on their modeling arenot satisfying to this author. Sperling et. al. provided additional data in 1978 116. The data provided both apsychophysical response as well as an electrophysical response measured at the output of a ganglion cell (their figure12). The agreement between the psychophysical and electrophysical data is convincing that the Luminance channelmeasured at the ganglion cell of the luminance channel is representative of the perceived luminance of the monkey. However, they continued to employ their pseudo-absorbers. This was necessary because they continued to relyupon the data reported by Marks in 1964. Marks, in his apprentice paper as a researcher, provided one spectral tracethat appeared to peak at 575 nm. As a result of this trace, Sperling et. al. assumed “the generalized absorptionspectra of the three classes of primate cones” occurred at 445, 535 & 575 nm. Their larger data set is shown inFigure 17.2.3-15. The graph has been replotted with a linear horizontal scale. The vertical scale is shown as thelogarithm of the reciprocal of the photon count to the base 10.


Figure 17.2.3-15 Increment-threshold spectral sensitivityfor rhesus monkeys. Data points; mean and 1 standarddeviation of 72 threshold determinations per wavelengthusing 5 monkeys. Protocol used an 18 degree, 5,650Kelvin neutral background of 3000 td and 2 degree testflash for 50 msec. Xxx Continuous lines based on theparameters shown and a smoothing factor of xxx found inMathCad. From Sperling et al., 1978.

The figure is drastically different from what would beexpected based on the current CIE luminous sensitivitystandard for humans. The same is true of the curves forthe humans TW and TP of the previous figure. For themonkey data, the peak sensitivity in the blue, near 437nm, is only about 25% lower than the peak in the green. Similarly, the peak near 610 nm is actually higher thanthe peak in the green near 532 nm. The overall plotalso shows a tilt relative to the peak values that mightsuggest the investigators did not correct for thevariation in quantum flux per unit wavelength due tothe color temperature of their source. It may be theyonly calculated a quantum flux per unit wavelength atone wavelength and assumed it was constant at allwavelengths. This would likely be the case if theycontrolled the flash intensity using calibrated filtersalone (without an associated radiometer). Their test setappears to be the same as that reported earlier byHarwerth & Sperling in 1971. In that paper, theydescribe their test set usign terms like watts/steradianand watts/cm2 for their measured intensity. They alsodiscuss their calibration using an integrating radiometer. This notation and instrumentation would indicate theydepended on the calibration of the counter-rotatingneutral density wedge filters to control their intensity regardless of the quantum flux in the 50 msec pulse as afunction of wavelength.

If their double monochrometer maintained a half-amplitude width of 0.5 nm as in the previous papers, their actualexcitation was somewhat reduced at short wavelengths relative to what was intended. This is shown by the 5650Kelvin line in the figure. It is shown for a color temperature of 5650 Kelvin although their article was somewhatambiguous. 5650 Kelvin is the value shown in their captions but 5500 Kelvin is stated in their text.

The Sperling, et. al. paper did not present a “conclusions” section. Their conclusions were included in the runningdiscussion. Their conclusion that “the peak at 610 nm is too narrow and much too far toward the red, and the 535nm peak is too narrow to be accounted for as either the envelope or the sum of the cone sensitivities.” is based ontheir adoption of the pseudo-absorbers used in the previous papers and the . The reference to “envelope” refers totheir piecewise linear model labeled “upper envelope model” of the previous papers. That model includes fouradditional coefficients selected arbitrarily to provide good the best fits to their data. Their concern about the widthsof their peaks is based entirely on their assumption that the spectra of Marks were theoretically correct. Theircontinued use of a piecewise linear envelope and an auxiliary 2x2 matrix with four arbitrary coefficients appearsbased on the same assumption.

The theoretical spectral response of this work has been fitted to the above with a deviation of no more than a factorof two from any of the mean values. However, it is not shown here because of the following discussion. It is shownlater in this chapter. Figure 17.2.3-16 shows the above figure of Sperling et al. (1978) corrected for the assumed


Figure 17.2.3-16 Increment-threshold data for Rhesusmonkeys corrected for color temperature. Data as inprevious figure except for adjusted quanta per flash. Solidline is theoretical performance based on parameters inTable xxx.

nonuniformity in quantum flux due to color temperature. The human and unadjusted monkey data, along with thisfigure, are all unusual in that they show nearly equal peak amplitude near 437, 532 and 625 nm. This is in utterconflict with the CIE Standard Luminosity Function. Granted, some of the data is for a rhesus monkey and it mayalso suffer from a color temperature calibration error. However, with or without the correction for colortemperature, all of the data shows the same detailed features as a function of wavelength. While only for twohumans and five monkeys, the separate data sets show distinctive features that have not been erased by averaging. This situation suggests that testing more individuals would not change the precision of the results from this singletest set. This is not to say that more thorough calibration would not improve the accuracy of the results.

The color corrected figure no longer shows a higherpeak sensitivity in the red than in the green. In fact,the three peaks achieve the same sensitivity within afactor considerably less than two (near 1.4:1). Inaddition, the theoretical spectral sensitivity equation ofthis work fits the data extremely well. It remainswithin the plus or minus one standard deviation limitsof the data at nearly every wavelength. It alsoreproduces all of the features associated with the data without relying upon any arbitrary constants.

The fit of the theoretical equation to the data can bemade better. However the effort is not warranted dueto the limitations within the test protocol and testequipment that generated the data. The theoreticalcurve does not include any compensation for theabsorption and scatter of light within the lens groupand humors of the monkey eye. Because of this, theshort wavelength half-amplitude point for the S-channel should not be relied upon. It is probably closerto 400 nm as in the nominal value of this work for thehuman. Similarly, the peak absorption in the region of437 nm channel is probably not 80% of that in the 532 nm region. No correction for absorption by the macular hasbeen included.

Because of these remaining questions, the nominal values shown in the table are the best available for the rhesusmonkey but differ marginally from those for the human. The mean peak absorption wavelengths, calculated fromthe half-amplitude values of the in-situ chromophores, are 438.5, 539.5 and 637.5 nm at the fixation point of the eye. While the photochemistry of the visual process does not support the difference in the long wavelength region fromthat of the human standard of 625 nm, it does support the need to repeat the tests of Sperling, et. al. under animproved protocol and calibration procedure.

Sperling, et. al. did confirm that the perceived (psychophysical) and luminous channel (electrophysical) responsesare the same in the monkey. They are both given by a single function based on a logarithmic summation of theelectrical response generated by the transduction process of each spectral type of photoreceptor. This fact is alsouseful in Chapter 15. It provides good confirmation that the stellate cells of the brain perform a linear decoding ofthe stage 3 signals (which are logarithmically encoded). The result is a luminance (R-channel) signal provided to thebrain (after decoding) that remains a logarithmic summation of the signal applied to the photoreceptors.


117Wilson, B. (1964) An experimental examination of the spectral luminosity construct. Ph.D. dissertation,New Your University. Ann Arbor, Mi: University Microfilm118Krantz, D. (1975) Color measurement and color theory. II Opponent-colors theory J Math Psych vol 12,pp 304-327119Blackwell, H. & Blackwell, O. (1961) Rod and cone receptor mechanisms in typical and atypicalcongenital achromatopsia. Vision Res. vol. 1, pp 62-107120Stockman, A. Sharpe, L. Merbs, S. & Nathans, J. (2000) Spectral sensitivities of human cone visualpigments determined in vivo and in vitro Meth Enzymol vol 316, pp 626-650

Wilson also provided a spectral response in good agreement with this theory in 1964117. It is reproduced in Krantz118

and here as Figures 17.2.3-17. Re-plotting this figure using a photon-catch criterion, rather than an energy criterionwould cause the short wavelength spectra to be emphasized more in this figure. The short and long wavelengthshoulders would then be of equal threshold. The spectral peaks can be determined relative to the theoretical valuesshown based on this work and shown by the vertical lines. Those peaks are at 437, 532 and 625 nm.

The inset shows the stimulus configuration used toachieve identical viewing conditions. During boththreshold determinations and brightness matches, thesurround was illuminated with 5500K light and half thebipartite field was illuminate with 550 nm light, both at10 mL luminance.

Blackwell & Blackwell have provided a variety ofspectral data related to the various illumination regionsgathered in the clinical environment119. This datainvariably shows detailed structure that is absent fromthe C.I.E. Standard and other excessively smoothedcurves. It should be noted that several of their patientswith achromatopsia show a relative peak near 460 nm. This does not appear to be a true Bezold-Brucke peak. It may be due to a bias error in the signal processingsystem of these patients as discussed in Section 18.8.2. Although their material is now dated and they discussseveral features in terms of discovery, most of thefeatures were already well documented in othercommunities. References to these discussions appearat appropriate points in this work.

The above data is in strong disagreement with thepsychophysical data originally published by the SanDiego school of the 1980's, typified by the data ofStockman et al120. They have frequently presentedspectral data that presumes to show the spectralsensitivities of the S-, M- & L-channels. The high degree of overlap between the M- and L-channels is similar tothat obtained by Wald in the 1940's based on incomplete differential adaptation using an adapting light ofinsufficiently long wavelength (typically 485 nm to suppress the M-channel photoreceptors). The data is also similarto that obtained very early for protanopes and deuteranopes, where the assumption was made that the completespectrum of the deuteranope represented only the L-cone sensitivity (when it in fact is the logarithmic sum of the M-and L-channel absorption spectrums). The long wave portion of the protanope’s sensitivity is represented by the M-channel chromophores only. Their calculations are based on a linear visual system consisting of a single zone

Figure 17.2.3-17 Comparison of luminous efficiencyfunctions for absolute threshold and for heterochromaticbrightness matching. The plot is for the relative energythreshold rather than the relative photon flux threshold. The latter would cause the curve to emphasize the shortspectral region and de-emphasize the long wavelengthregion. See text. From Wilson, 1964.


121Lewis, A. & Zhaoping, L. (2006) Are cone sensitivities determined by natural color statistics? J Visionvol 6, pp 285–302 (avail. on the Internet)122Kalloniatis, M. & Harwerth, R. (1990) Spectral sensitivity and adaptation characteristics of conemechanisms under white-light adaptation JOSA A vol 7(10), pp 1912-1928

model, linear matrix algebra, and the CIE assumption that the luminance visibility function is equivalent to thestandardized mid wavelength photoreceptor function.

Several authors have commented on the less than optimum separation of the M- and L-channel sensitivities impliedby the Stockman et al assertions. The most recent of these has been Lewis & Zhaoping121.

No record has been found of anyone using the putative Stockman et al. spectra in an operational robot attempting tosimulate human vision. The Stockman et al. spectra are not used in television transmission systems.

Kalloniatis & Harwerth have collected Increment-threshold spectral-sensitivity (ITSS) functions and similarthreshold versus intensity data using 10 nm filters at higher intensities with a uniform background of unspecifiedcolor temperature using monkeys122. The paper deserves additional editing for readability. No background colortemperature was given. The stimulus interval was long, 50-500 msec (equivalent to 10 to 0 Hz flicker frequency). Figure 17.2.3-18 shows their data with overlays based on cone fundamental responses and using the logarithm of thesums and differences of these responses. The logarithm of the absolute difference describing their proposedopponent function leads to a discontinuity in the region of 570 nm that is not present in the data or the modelproposed here. There is a small notch of variable wavelength in the data and theoretical model of this work thatvaries with adaptation level. To alleviate the significant notch, they switch to a logarithm of the sum in this interval(as opposed to the sum of the logarithms used in this work). Their final proposal uses a logarithm of the absolutedifference in the cone fundamentals plus a logarithm of the sum of the cone fundamentals (with a variety ofconstants chosen to fit their data) to describe the spectral region from 550 to 580 nm. Outside of this region, theyomit the contribution of the logarithmic summation. No explanation was provided as to how or why the neurologicalsystem would employ this methodology and introduces so many arbitrary constants. Their paper provides abackground on why the earlier assertion of three fundamental cone responses near 440-460, 530-545 and 600-610nm by Stiles and Crawford (which was correct) was dropped by Stiles in 1978.


Kalloniatis & Harwerth conclude their introduction with the statement; “The underlying mechanisms may not be thecone fundamentals; more important, however, is that the hypotheses proposed by Stiles have not been adequatelytested.“ In their discussion, they assert, “It appears Stiles was correct in hypothesizing shape invariance of theindividual color vision mechanisms and suggesting that the differences in adaptation characteristic of thesemechanisms resulted in the overall changes in shape of the spectral sensitivity function under white-light adaptation. However, the underlying detection mechanisms are not the fundamental cone response, as was originallyhypothesized.”

Kalloniatis & Harwerth encountered some of the subject to subject variation (figure 8) also reported by Babucke.

17.2.3.5.2 The photopic research literature–infrared

The performance of the visual system in the infrared is dominated by the long wavelength absorption edge of thelong wavelength spectral channel combined with the losses due to absorption by the lens group. The absorption of

Figure 17.2.3-18 Piece-wise fitting of human absorption spectra using cone fundamentals. Dark lines with asignificant dip at 570 nm represent attempts to emulate the measured data (crosses) using a logarithm of the absolutedifferences between the cone fundamentals. The notches are not present in the empirical data. Dark lines without thedip employ a logaritmic summation approach. From Kalloniatis & Harwerth, 1990.


123Charman, W. (1991) Limits on visual performance set by the eye’s optics and the retinal cone mosaic, inVision and Visual Dysfunction, vol. 5 Boca Raton, FL: CRC Press, Inc. Chapter 7124Geeraets, W. & Berry, E. (1968) Ocular spectral characteristics as related to hazards from lasers andother sources. Am. J. Ophthalmol. vol. 66, pp 15-20125Walraven, P. & Leebeek, H. (1963) Foveal sensitivity of the human eye in the near infrared xxx(probably JOSA) vol. 53, pp 765-766126Sliney, D., Wangemann, R. Franks, J. & Wolbarsht, M. (1976) Visual sensitivity of the eye to infraredlaser radiation. J. Opt. Soc. Am. vol. 66, no. 4.127Lamb, T. (1995) Photorecepor spectral sensitivities: common shape in the long wavelength region, VisionRes. vol. 35, no. 22, pp 3083-3091, fig 3

Figure 17.2.3-19 The predicted dark adapted photopicluminosity function in the infra-red compared to the datapoints of Sliney. Upper curve for RH = 685 nm. Lowercurve RH = 655 nm. Dashed curve shows averagecorrection for seven eyes (ages 23 to 78) from Geeraets &Berry, 1968. See text.

the lens group has been reproduced in Charman123

based on data from Geeraets & Berry124 (See Section17.2.2.2).

Measuring the sensitivity of vision in the infrared isdifficult because of both the range and the equipmentinvolved. Walraven & Leebeek summarize the dataavailable prior to Sliney and assemble a curve ofindividual segments125. No one investigator exploredthe entire range prior to Sliney, et. al.

When the above factors are combined, the agreementbetween the measured data and the theoreticalequation is quite good. Figure 17.2.3-19 presents thesame equation extended into the infra-red. Theequation, represented by the solid lines, is thepredicted sensitivity versus wavelength. The lowercurve represents the nominal equation with the longwavelength parameter of Rhodonine(5) at the nominalvalue of 655 nm. The upper curve is for the sameparameter at 685 nm. The dashed line represents thereduction in sensitivity due to absorption by the optics. These curves agree well with the measured values ofSliney, et. al126. over a range of ten orders ofmagnitude. The data points of Sliney suggest that thesubject was not completely dark adapted. The lowamplitude of the data point at 480 nm suggests that thesubject was violet adapted with coefficients of100:1000:400. This situation would place the long

wavelength data points about 0.5 to 1.0 orders of magnitude too high relative to the peak at 550 nm. In either case,the predicted characteristic, modified by the data of Geeraets & Berry, differs from Sliney by less than 10% perdecade over ten decades. Interpreting Fig 2 of Walraven & Leebeek is difficult It appears they mis-drew the loss insensitivity due to the lens. A loss in sensitivity would normally lead to a larger number for the absolute sensitivity. Itshows the sensitivity of the complete eye, with the absorption of the lens, as higher than the sensitivity of the retinain the absence of the lens. The absicca is missing a label in the published figure. This figure also shows a sensitivityabout one order of magnitude less than the other investigators. See Also the data of Lamb127.

Sliney, et. al. note the many reports of perception of a blue-green color after stimulation with long wavelengthinfrared. They accept it as fact but question whether it can be due to frequency doubling. They say frequency


128Aurebach, E. & Wald, G. (1954) Identification of a violet receptor in Human color vision, Science, vol.120, pp 401-405129Wald, G. (1964) The receptors of human color vision. Science, vol. 145, pg. 1009

doubling is too inefficient a process to give the result observed. This work claims that the normal S-channelresponse to infra-red light is due to a 2-exciton process (where the energy of two photons is summed in order toexcite an electron-hole pair in the base of the adaptation amplifier Activa). Since the threshold level of alladaptation amplifier Activas are nominally 2.0 eV, the same 2-exciton process is also able to excite M-channelActivas. This mechanism does not require the matching of energy band widths and levels as frequency doublingdoes. However, the sensitivity of the M-channel chromophore to light at these wavelengths must be considered. While the sensitivity of the M-channel chromophore may be reduced by a factor of at least 100 at these wavelengths,its relative availability may compensate for this.

17.2.3.5.3 The photopic research literature–chromatic adaptation (A MAJOR PROBLEM)

When discussing chromatic adaptation, it is important to remember the time constants involved in vision. Measurements of the spectral response of vision under differential adaptation must be accomplished within aneffective time interval of less than one minute following adaptation128.

Wald presented a series of chromatically adapted spectrums in 1964 that form a milestone in the psychophysics ofvision129. Instead of the nominal two-degree stimulus field, he used a one-degree field designed to remain within thefoveola. The data provides a long wavelength spectrum that is claimed to be and frequently associated with the longwavelength chromophore of vision. Although widely reproduced, that claim is erroneous. Figure 17.2.3-20reproduces his figure 4 with a dashed overlay based on this work. He used the data points and curve labeled “greenadapted” to support his claim that the peak in the long wavelength absorber was at 575 nm. The short dashed curvethrough these same data points uses the overall spectral response equation of this work. The equation usesks:km:kl::1000:110:275 to fit this data at least as well as the freehand line drawn by Wald. The equation is based onpeak wavelengths for the photoreceptors of human vision of 437, 532 and 625 nm. To precisely fit the data requiresan exact knowledge of the difference in half-amplitude wavelengths of the middle and long wavelength absorbers forthe subject. The values used in this calculated curve were λsl = 455, λms = 490, λml = 560, λls = 595 and λll = 645nm.. These half-amplitude difference impacts the depth of the notch near 520 nm and the shape of the peak near600 nm. Hence, additional iterations of the calculation could provide a better fit if the data was statistically moreaccurate. The data of Wald does not support his claim for the peak wavelength of the L–channelphotoreceptor of human vision. The overall sensitivity equation indicates that the peak near 575 nm was formedprimarily by the Bezold-Brucke Peak resulting from a mixture of M– and L– receptors in the ratio of 110:275. These values suggest the “blue” adapting light only suppressed the M–channel by a factor of 10 relative to the L-channel. While Wald describes his “green” adapting light as based on a Ilford 604 filter, he fails to note that his“field lamp” was incandescent and of unspecified color temperature. Since the incandescent source is deficient inthe blue, such a combination actually provides a peak radiation intensity near the long wavelength cutoff of the filter. In this case, the peak was probably near 530 nm This explains why the S–channel receptors were not significantlysuppressed in his figure 4. To isolate the L–channel receptor would have required chromatic adaptation of theM–receptor by an additional order of magnitude. This is shown by the long dashed line labeled “Alternateadaptation.” At this level of adaptation, km:kl::10:275, the true peak wavelength of the L–receptor is seen. The peakabsorption of the L–channel receptors is at 625 nm.

The above discussion combined with that in Section 5.5.10.4.1 have serious ramifications. Virtually all of the experiments in psychophysics of the last 50 years have assumed the longwavelength chromophores of vision peaked in the region of 575 nm. They have relied upon afalse assumption! It is unfortunate that the proposal of Wald was not questioned or theexperiment performed under a more strenuous protocol for over 40 years. The peak spectral


130Augenstein, E. & Pugh, E. (1977) The dynamics of the Π1 colour mechanism: further evidence for twosites of adaptation J Physiol vol 272, pp 247-281131Tansley, K. Copenhaver, R. & Gunkel, R. (1961) Spectral sensitivity curves of diurnal squirrels. VisionRes. vol. 1, pp 154-165

Figure 17.2.3-20 Wald figure 4 with overlay. Wald usedthe curve labeled green adapted to justify his claim thatthe long wavelength photoreceptor had a peak absorptionat 575 nm. The short dashed curve through the samepoints contains ks:km;kl::1000:110:275. The two peaks inthe measured data are actually due to the Bezold Effect. The short wavelength peak is near 460 nm and the longwavelength peak is near 575-580 nm. The alternate (longdashes) adaptation curve correctly isolates the peakabsorption of the S–channel at 437 nm and the L–channelat 625 nm. See text.

absorption of the L-channel in human vision is at 625 nm. If it is not near 625 nm in humans,humans are the only known chordate exhibiting a chromophore in their long wavelength visualchannel at such a short wavelength. A repetition of Wald’s experiment using a more demandingM-channel suppression protocol will clearly demonstrate the peak spectral sensitivity of theL–channel.

Augenstein & Pugh have provided a number of spectra resulting from differential bleaching that show the signatureof a chromophore with a peak sensitivity near 625 nm130. These spectra cannot be synthesized using onlychromophores with peak wavelengths shorter than 580 nm.

Tansley, et. al. have provided many spectrums ofsquirrels, based on ERG techniques, under variousstates of adaptation131. The work is an excellentexample of exploratory research lacking an adequatemodel. This is highlighted by their use of theamplitude of the ERG as a reference. This approachfails to note the variability of the adaptation amplifierthat is the ultimate source of the ERG waveforms. Thework suffers from the instrumentation of the day,particularly the use of a “100 watt Sylvania” lightsource and only a few narrow band filters. Thediscussion is a model of objectivity. Equal quanta perunit wavelength were used to obtain the data. It clearlyshows a Bezold-Brucke peak near 490 nm along withthe normal shoulder near 437 nm and the normal peakat 532 nm associated with trichromatic vision. It alsohighlights the difference between the amplitude ofthese components as a function of chromatic adaptationand intensity. They describe the presence of acomponent in the 450-460 nm region as capricious inits appearance but statistically significant. Althoughthe reference in Davson says Tansley, et. al. used equalquanta per unit wavelength in their experiments, no


132Davson, H. (1990) Physiology of the Eye, 5th Ed. NY: Pergamon Press, pg 442133Stockman, A., Sharpe, L. & Fach, C. (1999) The spectral sensitivity of the human short-wavelengthcones derived from thresholds and color matches. Vision Res., vol. 39, pp. 2901-2927

Figure 17.2.3-21 The spectrum of the “bluemonochromat” and a yellow adapted trichromat shownagainst theoretical performance. See text for details.Theoretical curve (solid line) at 10 nm. precision for bothfully and partially chromatically adapted trichromat. Monochromat data (dashed line) from Stockman, et. al.(1999). Chromatically adapted trichromat data (crosses)from Wald (1964).

claim to this appears in the paper132. It is also highly doubtful based on the instrumentation used.

Stockman, et. al. have recently provided the spectrum of what appear to be true monochromats. They exhibitsignificant sensitivity to radiation only in the spectral region of the S-channel133. Figure 17.2.3-21 shows their data (dashed line), compared with the spectrum of Wald (crosses) and two theoretical responses according to this work. The solid line beginning at 370 and terminating near 650 nanometers represents the theoretical S-channel responseonly. The theoretical response beginning at 370 and terminating near 680 nanometers represents a partially adaptedeye. It follows what Wald described as a yellow adapted trichromatic human eye (solid line following the datapoints of Wald). The data is plotted on the scales of Wald. The data of Stockman was truncated at 575 nm. forconvenience. The half amplitude points of the theoretical model are 400 & 475 nm. at a temperature of 310K. Theresponse of the theoretical normal trichromatic eye was reduced approximately 1000:1 in the M- and L-channels tocorrespond to the Wald data. There appears to be excellent agreement between the two sets of data points and thetwo solid lines. The theoretical solid line following Stockman is for the M- and L-channel coefficients set to zero. The data points would probably be in better agreement with the theoretical line if the number of adjustments to theraw data made by both Wald and Stockman in order toremove irrelevant factors were reduced. Datamanipulation invariably leads to a Gaussian final shapein accordance with the Central Limit Theorem. Thedeviation of the data points from the theoretical line aretoo small to warrant a change in the half amplitudepoints of the theoretical curve which must also becompatible with other, particularly vernier, data. Thetheoretical curve as presented may be too high in theregion between 380-425 nm because it does notcontain any absorption term to account for the opticalsystem of the eye.

Wald presented data on a series of individuals underdifferent states of adaptation in the above paper. Thatdata is well represented by the theoretical model whenthe coefficients describing the state of the adaptation of


134Fulton, J. (1985) The perception of luminance under various state of adaptation. Los Angeles, CA:Hughes Aircraft Co. Research Report (available from the author)135Wooten, B. Fuld, K. & Spillman, L. (1975) Photopic spectral sensitivity of the peripheral retina. J. Opt.Soc. Am. vol. 65, pp. 334-342136Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones. J. Opt. Soc.Am. A, vol. 10, no. 12, pp. 249-2521

each chromatic channel are assigned appropriately134. The theoretical equation of this work can also be used topredict the set of curves for different states of adaptation presented by Wooten, Fuld & Spillman for an observer at30 degrees retinal eccentricity135.

17.2.3.5.4 The photopic research literature–Difference spectra

Comparing psychophysical luminosity functions, acquired under different states of adaptation, algebraically has beena common technique for over a century. However, the technique fails to take into account two major considerations. First, the underlying processes involved are not linear. Second, there are multiple parallel spectrally sensitive signalpaths involved in vision that do not perform in a coordinated manner. This has led to what might be calledpsychophysically acquired spectra. Most of these spectra have been obtained using differential chromatic adaptationtechniques that were less than aggressive.

The psychophysical community has given these spectra the name fundamental cone spectra or cone fundamentals. Although these fundamental spectra are discussed in terms of specific cone spectra, they are not. These spectragenerally show structure indicative of their actual origin, particularly the presence of S-channel receptor absorptionin the case of the M- and L-channel fundamental spectra. They also show a strong resemblance to the underlyingluminosity function. Two recent empirical difference spectra, presented by Stockman, et. al.136, are shown in Figure17.2.3-22. The upper frame shows their data points compared to the previous curves presented by Smith & Pokorny(solid curves) and Vos & Walraven (dashed curves) for the fundamental M-cone spectrum. The C.I.E PhotopicLuminosity Standard (dash-dot line) is also shown for comparison. Based on this work, it is seen that the so-calledfundamental M-cone spectrum is only a luminosity function obtained under a slight condition of chromaticadaptation. This condition can be described in either of two ways. The most appropriate is the suppression of theM-channel signal by about a factor of three relative to the S-channel and an additional suppression of the L-channelby a factor of three relative to the M-channel. This explanation is consistent with their test procedure. An alternateexplanation based only on the graphics would suggest the L-channel was suppressed by a factor of three relative tothe M-channel while the S-channel was enhanced by a factor of three. Determination of a peak wavelength for thedata points of Stockman, et. al. is difficult because of the wide spacing of the data points.


137Stockman, A. MacLeod, D. & Vivien, J. (1993) Isolation of the middle- and long-wavelength-sensitivecones in normal thrichromats. J. Opt. Soc. Am. A, vol. 10, no. 12, pp. 2471-2490138Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and500 nm. Vision Res. vol. 15, pp. 161-171

Figure 17.2.3-22 Comparison of difference spectra withthe CIE Photopic Luminosity Standard of 1924. Upperframe shows the “fundamental” M-cone spectrum ofStockman and others. The lower frame shows the“fundamental” L-cone spectrum of Stockman and others. The dash-dot lines represent the CIE Standard. All otherlines and data points are from Stockman, et. al. (1993). See text.

The lower frame shows their data points and the curvesof the other authors, as described above, for the so-called fundamental L-cone spectrum. Stockman, et.al’s. data points (with their error bars) are seen tomatch the C.I.E. Standard Luminosity Function at leastas well as they match the curves of the other authors. The only deviation is in the very short wavelengthswhere the C.I.E. function is known to be inappropriate. If the modified C.I.E. Standard as proposed by Judd isused, all of the data points and curves of other authorsrepresenting the “fundamental L-cone spectrum”display a remarkable agreement with the C.I.E.Standard. There is no sign of significant chromaticadaptation. The broadness of all of the data points andcurves in this frame make determination of a peakwavelength indeterminate.

The poorly defined maxima of all of these curves,approximately 542 in the upper graph and 560-565 inthe lower graph (See below) do not contribute newinformation to the art. The poorly defined peak in thelower curve appears to be the source of the valuefrequently found in the literature, of 560-576 nm forthe L-cone fundamental. Stockman, et. al. used anunusual arrangement of 4 degree diameter adapting andbackground lights, alternating between a red light at678 nm and a blue light at 485 nm at 0.5 Hz. Thespectral width of these lights was not specified. Theblue light was used to suppress the putative M-cones. The red light was used to suppress the L-cones. Thealternative light was used as a background duringprobing with a 2 degree narrow spectral band lightflickering at 17 Hz. They also introduced a secondviolet light to suppress the S-cones during M-coneisolation. This suppression was apparently notsuccessful. Note the plateau in the 450 nm region of the empirical data showing the functional presence of the S-channel chromophores.

Based on this work, the choice of wavelengths of the adapting and background lights as well as the rate ofalternation and the intensity of the adapting light used by Stockman, et. al. appears questionable. Their logic forthese choices is provided in a separate paper137. This paper is meticulous and exhaustive but based on empirical dataand a conceptual rather than precise understanding of the mechanisms of the visual system. Although equation 2 ofthat paper includes logarithmic notation, following a proposal of Smith & Pokorny138, the summing process is a


139Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons pg 565

linear one within one logarithmic term.

The Stockman paper compares their results with that of many other psychophysicists over the years. Excellentagreement is obtained. However, both groups employ a variety of adjustments to their data. Both the Stockmangroup (page 2476) and the psychophysicists also rely upon the linearity assumption. The first paragraph of theintroduction to the paper also develops the crux of their problem. The second paragraph develops theirunderstanding of the problem. The problem is that the psychophysical spectra assigned to the photoreceptors of theeye are grossly different than those measure by the electrophysiologists. This problem is compounded by theanisotropic absorption spectrum of the Rhodonines in the liquid crystalline state. Most of the electrophysiologicalmeasurements before 1998 were made using transverse illumination applied to an individual Outer Segment. Theresult was the isotropic absorption spectrum of the chromophores, with a peak near 500 nm regardless of thechromatic type of photoreceptor measured. Stockman, et. al. used narrow band filters for the probes used toestablish the spectral sensitivity but only collected data at well spaced points. The filters were described as 7 to 11nm half-bandwidths. They did not use, but their discussion supports, the more specific term, half-amplitude-bandwidths. Their data was collected at relatively wide spacings, generally 30 nm. Although they did not connectthe points in their graphs, they used the lines of other investigators as overlays to connect the points. The result isthat their data presentation is compatible with a smoothing of the sensitivity curve. No narrowband structure is seenin the graphs. After all data reduction, they gave the peak absorption wavelengths for their proposed 2 degree conefundamentals as 445, 545 &570 nm.

The Stockman et al. data are combined and annotated further in Figure 17.2.3-23. Symbols have been added todescribe the spatial quality of the conditioning (adaptation) and the test spectrum. The 1993 test protocol involved avery complex conditioning regime. It combined both multiple spatial parameters and multiple temporal parameters(page 2475). The spatial parameters are shown. A disk-shaped four degree conditioning stimulus was usedconcentric with a two degree test stimulus for the M– and L–channel tests. The test stimulus flickered at 17 Hz forthe M– and L– channel tests, with a 50% duty cycle between a test wavelength and an additional background of 561nm. The result was data based on a chromatic discrimination criteria rather than a threshold brightness criteria.

For the S–channel tests, the conditioning field was 16 degrees in diameter with a test field of two degrees flickeringat 1 Hz. The parameters of the test stimulus appear to have been of variable wavelength at 50% duty cycle against acontinuous conditioning field. This simpler pattern resulted in a threshold brightness criteria regardless of teststimulus wavelength.

The shape of the S–channel (S-fundamental) response agrees completely with the theoretical response ofRhodonine(9), both in center wavelength and the slope of its skirts. This response can be associated with theabsorption spectra of the S– chromophore as projected to the entrance aperture of the eye, a so-called S-fundamental.Both of the M– and L– channel responses show residual S– channel sensitivity. The L–channel response short waveskirt also suggests significant M– channel sensitivity as well. These problems appear to be due to inadequateintensity in the conditioning signals and the high flicker rate causing the results to be based on chromatic differencecriteria rather than an intensity threshold criteria. This difference is due to the flicker frequency exceeding thecritical flicker frequency of three Hertz documented by de Lange Dzn139.

[xxx include comments brought forward from the new comparison section, 17.2.3.5 ]


Contrary to the position of Stockman, et. al. in theirfirst 1993 paper, in the absence of aggressivechromatic adaptation such as used by Wald in the1950's and the Stockman group in their 1999 paper, thespectral response of the individual chromatic channelsof subjects with normal vision cannot be obtained bypsychophysical means. In the 1999 paper, thespectrum of the S-channel is easily recognized in thosewith normal vision by comparing the spectrum tosubjects who appear to be true S-channelmonochromats.

17.2.3.5.5 The photopic researchliterature–Foveal

Although there is considerable discussion in theliterature concerning whether the fovea is color blindor not, there is little substantive data, at least in the last50 years. The nominal luminous efficiency function is obtained using a two degree diameter (in object space) lightsource. The area of this source more than covers the fovea of the human eye and the resulting average response maybe hiding important details of the function. It would be of interest to the research community to have luminousefficiency data as a function of wavelength for only the fovea (more precisely the foveola) to settle the luminosityaspect of this question. Similarly, it would be useful to have chromatic discrimination data for this same portion ofthe retina. Careful experimental design could produce interesting new information concerning this area. It mightshow that, because of the difference in the signal path for foveal photoreceptors connecting to the cortex, both theluminous efficiency function and chromatic discrimination function are fundamentally different for this region of theretina.

17.2.3.6 Interpretation of the photopic standards literature

17.2.3.6.1 State of the Photopic Standard

As indicated above, the state of the CIE Photopic Standard is poor, to the extent that some authors have begun usingsubscripts to denote quasi-official (?, quasi-accepted) modifications to the archaic standard. The problem iscomplicated by the use of questionable procedures in the collection of data for both the old and new data bases. SeeSection 17.2.1.3.1. It is further complicated by the communities continued reliance on a variety of questionableconcepts. These include the lack of recognition of the dependence of the visual system on photon flux instead ofintegrated energy, the assumption that the photopic luminosity function is independent of the spectral content of theillumination used, the lack of appreciation of the importance of data smoothing in obscuring the contributions of theunderlying mechanisms, and the assumption of the Univariance Principle across the visual spectrum of the eye.

The CIE has struggled for a long time over the correct name to use in describing the sensitivity of the human visualsystem under typical daylight operation. The original designation visibility function of 1924 was dropped in favor ofphotopic luminous efficiency function in 1951 concurrent with the adoption of the first scotopic luminous efficiencyfunction. Looking closely at the visual system and the test methodology described, it is clear that the measuredfunctions have little to do with the efficiency of the system. They in fact describe the threshold sensitivity of thesystem as a function of wavelength under various conditions of stimulation. Because of the concurrently operating

Figure 17.2.3-23 Annotated Stockman et al. datacompared to the proposed theoretical peaks. See text.


140C.I.E. (1978) Light as a true visual quantity: Principles of measurement. Publ. CIE No 41 (TC-1.4) Paris,FR: Bureau Central de la CIE

adaptation process, the measurements do not reflect the efficiency of the system, only its performance under theconditions specified. Because of this situation, the term luminous efficiency function will only be used as part of thetitle in the official CIE Standard. A more appropriate title would be the overall threshold visibility function (as afunction of wavelength). This terminology separates the performance of the eye from the photometric terminologybased on the lumen.

The current standard differs significantly in the long wavelength region compared to most of the data in the researchliterature as suggested by the work of Wald and of Sliney reviewed above. The deviation is so large as to questionwhether further consideration of the C.I.E (1924) Photopic Luminous Efficiency Function is warranted in a researchenvironment. The C.I.E140. published a summary of more recent work in 1978 that included a curve described as theWeighted Mean for each of several methods of measurement. The wide disparity of the results of individualinvestigators continues to disparage the concept of using a weighted mean. Several of the investigators recordedfeatures that are instantly associatable with the theoretical function of this work. This includes the peak near 580 nmand the inflection point near 487 nm shown in the data of Sperling & Lewis using the absolute-threshold method. The absolute threshold data of both Guth & Lodge (1973), Sperling & Lewis (1959), and the Weighted Mean showpeaks at 540 nm (or slightly less in the case of Guth & Lodge by interpolation). This is 15 nm lower than in theStandard and conventionally quoted 555 nm.

There have been numerous calls for revision to the Standards by researchers. However, the Standard occupies afundamental position in the industrial applications of illumination and is not likely to be changed soon. It isprobably more useful to consider a separate standard for purposes of research. This standard would recognize thevariability of the results based on color temperature of the illumination and would memorialize an equal photon fluxper unit bandwidth source as the test standard. The standard would also recognize the importance of data smoothingdue to finite width spectrometric instrumentation. It would also redefine the Standard Observer based on this newstandard luminosity function for research.

The magnitude of the deviation between the smoothed CIE luminous efficiency functions fora standard observer and those for a real person (whether using the theoretical function ormodern measurements) is so large (frequently over 30% at specific wavelengths) that theCIE functions should never be used as a real standard or to represent an average subject.

Without a usable Univariance Principle, the precise conversion of the graph of the current standard luminosityfunction to an equal photon flux per unit wavelength basis is a significant activity. The ratio of the width of thevisual spectrum to its center wavelength is significant as in the highly asymmetric contribution of the physical opticsof the eye to the overall characteristic. Because of the nature of the equations, it is also necessary to consider thethree absorption regions separately.

17.2.3.6.2 Individual factors not addressed in the CIE Standard

There is more than sufficient information available to demonstrate the defined luminosity function is a continuousvariable with respect to spatial position across the retina, to average radiant intensity, and a complex function of thespectral content of the radiant intensity. To fully describe the luminosity function at a given instant is difficult andrequires several lines of mathematical formula to be evaluated for a specific set of parameters. To avoid thisproblem, the luminosity function of the literature was originally restricted to a specific, normally poorly defined , set


141Wyszecki G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley, Chap. 5

of parameters.

The empirical concept, if any, was that these parameters determined one particular edge of the multidimensionalparameter space. It soon became clear that this was impossible and two separate and distinct edges of that spacewere defined, still without total definition. Thus evolved the photopic and scotopic luminosity functions. Theempirical protocol for determining these functions were defined to eliminate, rather than control, as many variablesas possible. There are two facets of the protocol. One defines the state of the visual system as fully dark adapted. The other specifies, at least partially, the test probe to be used. This probe employs small spatial field conditionswith respect to the fovea, illumination centered on the point of fixation, and nominal duration pulses of illuminationderived from a light source via a spectrometer. The diameter of the illuminating probe is usually defined in terms ofangular field in object space and has converged on two values. For photopic conditions, the diameter is normallytaken as 2° circular. Recognizing the significance of, and the necessity of exceeding, the noise threshold (at leastimplicitly) the diameter for the scotopic condition is normally taken as 10° circular. These are the sizes recognizedin the CIE Standards. The parameters of the illumination source have never been adequately specified or controlled. Their specification has usually been defined as “depend on the experimenter to use the best instrumentation availablebased on his experience or available funds.”

Although not commonly discussed in matters involving luminance, the variation in the performance of the retinawith spatial field, and the nature of the surrounding field, is widely recognized. Wyszecki & Stiles141 devote anentire chapter to the philosophy and procedures of visual sensation matching. Lacking a detailed model of the visualsystem, the discussion is superficial.

The signal flow schematic diagram of the eye related to the luminance channel is shown in Figure 17.2.3-24. Thisdiagram stresses the summation process used in the luminance channel. It omits completely the discussion of thespatial encoding that occurs at the input to the parasol ganglion cells of the projection neuron subsystem. Adiscussion about the relative contribution of each photosensing channel in the signal sensing stage, 1, to theluminance signal in the signal manipulation stage, 2, will follow below.


Figure 17.2.3-24 The signal flow schematic used for calculating the luminance function of human vision. Spatialencoding is omitted from this elementary diagram. Photoreceptor cells in foveola (also) connect directly toindividual bipolar and parasol ganglion cells projecting to the Pretectum.

It is very difficult to measure the spectral sensitivity of the human eye directly, and with precision, as a function ofirradiation level and spectral interval. As listed and graphed above, the human eye incorporates a variety oftechniques to achieve its very wide dynamic range with respect to radiation intensity. In this situation, apsychophysical experiment must be very carefully defined. Since the eye incorporates state variables in the signalpath, both a prior and an instantaneous condition must be prescribed in any experiment. There are very few clearlydefinable states of the eye. One corresponds to the fully dark adapted condition. Another corresponds to theboundary between the photopic and mesotopic ranges. At this level, all of the photoreceptors are operating at fullsensitivity and neither the (individual) adaptation amplifiers or the iris have begun to modify the signals delivered tothe brain. These are the two conditions normally chosen to measure the photopic luminosity function. The testcriteria is usually based on detection of a short pulse. This criteria is basically a signal to noise ratio criteria that is a

function of test exposure area. As long as the dark adapted state is not disturbed, it is possible to use short testpulses of radiation at higher irradiance levels. However, if the total flux absorbed begins to impact the amplificationof the adaptation amplifiers, different psychophysical results will be obtained.

The theoretical concept derived from this work recognizes the many parameters involved explicitly and the dynamicperformance of the visual system based on the instantaneous state of the variables associated with those parameters. There are substantially fixed parameters and a set of parameters that vary automatically in an attempt to provide anominal perceptual performance optimal for the species. The key factor is the tendency of the individual


photoreceptor channels to adjust the net amplifier gain in each stage 1 channel (using negative internal feedback) toproduce a nominally constant signal level at the nodes (pedicels) of all of the photoreceptors. This tendency isstrongly affected by the ability of the vascular-electrostenolytic system to maintain the quiescent condition withvariations in illumination. The theoretical concept also provides an explanation of what the luminosity functionactually represents from a system perspective. It represents the minimum photon flux per unit angular area(normally in object space) required to exceed the effective noise threshold of the luminance channel of the visualsystem (the noise threshold divided by the effective gain of the amplification system) sufficiently to be perceived bythe individual. The minimum photon flux per unit area may be obtained from a source of radiation that is narrowlyfiltered spectrally or less narrowly filtered. Since an integral is involved, the more filtered the radiation, the greaterthe precision of the determination.

The theoretical concept provides a much better framework for defining one or more states for measuring a singleresponse to a set of conditions that could be considered the nominal luminosity function of the visual system. Several conceptual conditions become clearer.

Being a function derived from psychophysical data, the luminosity function relies on fivemajor parameters or processes;+ the nature of the radiation used to excite the eye+ the absorption of light by the physical optics of the eye+ the anisotropic absorption of radiation by the Outer Segment (Poynting vector of radiation

parallel to the long axis of the OS), + the adapted state of the photoreceptors individually, and+ the logarithmic processing of the photoreceptor signals.

The luminosity function cannot be obtained by reflective microspectrophotometry throughthe aperture of the eye or by invasive techniques employing transverse irradiation ofindividual photoreceptors.

In summary, the theoretical luminosity function is the normalized reciprocal of the perceived sensitivity threshold asa function of wavelength of the human eye to pulse irradiation, of equal photon flux per unit wavelength, of aspecified spatial extent, and with a specified on-pulse duration (and specified off-pulse duration if repetitive), underdark adapted conditions. In practice, the CIE Photopic Luminosity Function is a characteristic based on a smoothedand distorted version of the above fundamental function, due primarily to the limits of the test instrumentation usedto determine it. The CIE Function displays filtering by a nominally 30 nm. wide spectral filter and use of a nonequal-flux irradiation source, typically an incandescent lamp with a soda glass envelope. The lamp was generallyoperated at an effective black body temperature of about 2800 degrees Kelvin. However, it was deficient in the bluedue to absorption by the soda glass envelope.

When discussing the luminosity function and the processes that contribute to it, it is important to recognize that thepeak spectral response of each process is different. The peak wavelength of the cumulative response moves tolonger wavelengths starting with the response of only the Outer Segments of the retina. When calculated using anequal photon flux per unit spectral wavelength, the peak absorptance of the Outer Segments of the retina as acomplete in-vivo array under dark adapted conditions occurs at 537 nm. After including all of the physical optics ofthe eye in the calculation, the peak absorptance of the eye at its aperture, based on equal flux conditions, occurs at aslightly longer wavelength, depending on the pupil size and the age of the subject. It is only when the spectralperformance is smoothed using a spectral filter of about 30 nm and then replotted on an equal energy per unitwavelength basis that the peak is seen to occur near 555 nm, the accepted value in the literature.

There are two distinctly different groups of quasi-constant contributors to the complete luminosity function. Theelements of the physical optics of the eye contribute a radiation transfer characteristic that varies only slightly with


142Hart, W. ed. (1992) Adler’s Physiology of the eye. pg. 710143 Weale, R. (1954) Light absorption by the lens of the human eye, Optica Acta. vol . 1, pp. 107-110 144Ruddock, K. (1963) Evidence for macular pigmentation from colour matching data. Vision. Res. vol. 3,pp. 417-429145Wald, G. (1945) Human vision and the spectrum. Science, vol. 101, pp. 653-658

Figure 17.2.3-25 Equations for the spectral absorption ofthe physiological optics of the eye. Solid lines areabsorption of the outer lens group as a function of age(only applicable at wavelengths greater than 400 nm). Dashed line is the absorption of the field lens (generallylabeled the macula)in the region of the fovea.

pupil size and age. They vary more significantly with the angle of the chief ray through the optical system. Thisvariation involves the effective thickness of the outer lens group with angle and the variation in absorption of thefield lens adjacent to the Outer Segments. This variation is usually described in terms of the macula or macula luteasuperimposed between the vitreous humor and the retina. Most recent data shows that it is not a unique layer but avariation in the optical density of the neural tissue related to the movement of as much neural tissue as possible outof the optical path leading to the fovea. In this context, the macula lutea is a portion of a conglomerate retinal tissuein front of the photosensitive surface that contains a reduced amount of neuron material.

The lens system of the eye makes a significant contribution to the overall luminosity function of the eye. The outerlens group, the cornea and “lens,” absorb significantly in the short wavelength portion of the spectrum. The totalabsorption of the outer lens group is a function of angle with respect to the optical axis and the pupil diameter inprecise measurements. The field lens, consisting of the neural material overlaying the photoreceptors, exhibitssignificant absorption as a function of retinal position, and is particularly important in the foveal area of the retina.

[xxx revise this to show aldehyde absorption in Section 16.3.3.1 ]Equations derived in Chapter 16 from the best available data for the absorption of the outer lens group (as afunction of age) and the field lens are shown in Figure 17.2.3-25. See also [Figure 17.2.3-3] for alternate data inthe region of 300-400 nm. The absorption of the field lens, frequently described as a separate layer known as themacula or macula lutea in early work, is seen to be quite significant in the short wavelength region of vision. Thecurve represents in-vitro data from only nine subjects. Only near age 63 does the absorption of the outer lens groupequal that of the macula. The impact of the outer lens group on the overall absorption is more significant in themiddle and long wave region as age increases.

The equations shown are based on the data presentedin Adler142 and drawn from the work of Weale143 (lens)and from Ruddock144 (macula). Weale’ data is basedon color differences for living subjects and notspectrographic data. By comparing Ruddock’s data tothe earlier data of Wald145 that has been widelyreproduced, it is apparent that Wald was using a widespectral bandwidth spectrometer as would be expectedfor his time period. Wald was also working in-vitrowith the macula from 9 subjects in chloroform. [thisparagraph probably moves to Chapter 16]

As discussed in Section 16.3.3.2.1, the more recentdata of Griswold & Stark would suggest, a differentfundamental equation is needed to conform to theFermi-Dirac characteristic of the optical absorption ofthe lens group in young eyes.

The equation for the lens group absorption exhibits a single peak near 350 nm. The literature has frequentlyassociated the retinenes with this UV wavelength peak. However, most creditable references show retinal with a


146Wald, G. (1945) Op. Cit.

peak near 380 nm and retinol with a peak near 330 nm. Only the average of these two values would approach 350nm. The data supporting the equation clearly show a single peak at 350 nm (see Chapter 6). The material of themacula is fundamentally different, it exhibits a double peak in its absorption spectrum. The peaks occur at 440 and487 nm and exhibit the same resonance factor, or Q, even though their amplitudes are slightly different. Early workby Wald146 claimed “the human macular pigment was shown to be a carotenoid, apparently lutein or leafxanthophyll.” These early demonstrations appear to have shown a degree of correlation but not exclusivity relativeto the immense biochemical family.

By combining the impact of the outer lens group and the field lens on foveal vision, it is seen that the light associatedwith the S-channel of human vision suffers an attenuation of between 4:1 and 9:1 before reaching the photoreceptorswhile the M- and L-channels encounter much less attenuation depending on age. This attenuation is encounteredwithout any additional factor due to inadequate short wavelength irradiation due to an inappropriate light source.

The synaptic network between each photoreceptor cell and each bipolar cell of the luminance channel also impactsthe contribution of each chromatic type of photoreceptor cell to the overall luminance signal. It can do this in twoways. It can sum the signals from different numbers of photoreceptor cells based on their chromatic performanceand/or it can employ different size synapses in order to control the amplitude of the signal passed to the bipolar cellfrom each photoreceptor. The synaptic size determines the proportion of the pedicel voltage that appears at theemitter terminal of the Activa of each bipolar cell.

Little data could be mined from the literature on the impact of the first synaptic network on the formation of thesignal in the luminance channel. Only global estimates could be made based on the many different spectralcharacteristics of the visual system, under both dark adapted and chromatically adapted conditions. These estimatesgenerally converge around ratios between the S:M:L channels of 10:100:10. More specific ratios will be reviewed inthe following sections.

There are also a variety of time variant contributions to the luminous efficiency function. These have occasionallyinfluenced the experiments revolving around this function.

The high degree of negative interior feedback in the adaptation amplifiers is the primary variable in the luminousperformance of the visual system. Since these amplifiers operate independently as a function of the input current tothe base terminal of each Activa, but tend to a common gain due to the hydraulic properties of the IPM, they play acrucial role in the luminosity function. The role is particularly important in explaining the role of absorption by theouter lens group. Although the absorption by the outer lens group can be described by continuous functions, theradiation transmitted by the group is absorbed differentially by three different classes of narrowband absorbers. As aresult, the signal level at the base terminal of each chromophore related Activa is different. However, the negativeinternal feedback of these amplifier tends to eliminate this variation. As a result, the role of the absorptioncharacteristic of the lens group, and of the macula lutea, are minimized for signals within the high gain operatingrange of the adaptation amplifiers.

17.2.3.6.3 Light versus dark adaptation

Based on the above discussion, it is clear that the operating conditions of the visual system are quite different underdark and light adapted conditions. Under light adapted conditions, the gain of the adaptation amplifiers associatedwith the shorter wavelength channels will tend to be higher in order to compensate for the absorption by the physicaloptics of the eye. Because of this fact, the shorter wavelength channels will transition from the photopic to themesotopic regime at higher illumination levels. While the S-channel photopic regime will normally be narrower due


to absorption by the macula lutea, both the S-channel and the M-channel will further narrow with age due toabsorption by the outer lens group. Under conditions still within the photopic regime of all of the spectral channels,the first order spectral response of the visual system will remain independent of the absorption by the physicaloptical elements. The shape of the luminosity function will be defined by two components; the inherent spectralabsorption of the chromophores of the signal sensing stage and the logarithmic summation process within the signalmanipulation stage.

Under totally dark adapted conditions, the situation is different. All of the adaptation amplifiers are then operating atmaximum gain. The adaptation amplifiers do not compensate for the variation in effective signal gain due toabsorption by the outer lens group and the macula lutea. This is true as long as the product of probe illumination andtime is small enough that the vascular supply is not impacted. The shape of the luminosity function will now bedefined by the three components; the absorption characteristics of the lens group, the inherent spectral absorption ofthe chromophores of the signal sensing stage and the logarithmic summation process within the signal manipulationstage.

Under fully dark adapted conditions, the recorded luminosity function will be lower in the shorter wavelength regionthan it will be in the longer wavelength region. If the illumination source used in the probe is at a lower colortemperature than 7053° K, the recorded reduction will be exaggerated but artificial.

17.2.3.6.4 Calculation of the neural component of the CIE luminous efficiency function

The literature does not present any calculation of the CIE luminous efficiency function based on a physical model ofthe visual system. The previous calculations have been based on a mathematical model based on the use ofconceptual (and known to be imaginary) tristimulus values.

The summing circuit shown combining the voltages at the output nodes of the amplifiers (the pedicles of thephotoreceptor cells) in the above signal flow schematic is critically important in determining the neural componentof the luminosity functions of vision. The fundamental summing circuit is shown in Figure 17.2.3-26. This circuitis a simplification of the right hand part of (A) and the left hand part of (B) in [Figure 11.7.2-1]. The voltage ateach of the pedicles of four chromatically distinct photoreceptors are shown on the left. The 1st generic synapseassociated with the pedicle of each photoreceptor cell has been replaced by a an equivalent diode labeled Zsubscript. Similarly, the input circuit of the Activa of the first bipolar cell has been replaced by a simple diode labeled Zeg. Zegis not a simple diode strictly speaking because, it includes the effect of the base impedance of the bipolar cell. Thisbase impedance provides a common path for the current in both the input and output circuit of the bipolar cell andtherefore contributes to a negative feedback component that is being ignored here.

Considering the impedance, Zeg, to be a simple diode here, the circuit can be seen to consist of a “soft” analog “OR”circuit. It has the same topology as the “OR” circuit found in digital combining circuits. However, the signals beingsummed are analog. It is important to note that if the voltage, Veg , becomes greater than any of the individualpedicle voltages, the diode in that circuit becomes a very high impedance. Of greater importance, the diodes must beconsidered real diodes and not idealized switching diodes. This is because the voltages involved have similarmagnitudes to the equivalent threshold voltage of each diode, ηVT. Thus, the switching is labeled soft. Note thateach diode is labeled. This is to emphasize that these are not ideal diodes. They each exhibit a distinct impedancecharacterized by their reverse cutoff current. This parameter also describes their forward current capability at agiven voltage, i.e., their effective forward impedance.


Figure 17.2.3-26 The summing circuit at the outputterminals of four photoreceptor cells. It can be describedas a “soft” analog “OR” circuit. See text for details.

Being a psychophysical function, the luminosityfunction is an end-to-end representation of all of thesignal detection, signal processing, and signalperception occurring within the HVS. In some caseswhere the subject is asked to respond to a stimulus, themeasured function may even include a componentrelated to the motor system. The complete luminosityfunction for human vision, ignoring the contribution ofthe cognitive and motor circuits, is given in closedmathematical form by a complicated logarithmicequation multiplied by a complex absorption functiondue to the physical optical system. This function isdeveloped in the Block Diagram of [Figure 17.1.4-1]showing the method of separation of the luminancechannels and the chrominance channels leading to theperception of a scene. Neglecting the UV-channelentirely and the physical optics for the moment, thecomplete function describing the sensitivity of thesignal manipulation stage is derived from thephotodetection signals and the synapses and is given insymbolic form as:

R = lnC = ln xL2 + ln yM + ln zS Eq. 17.2.3-2

where S, M, & L are the integrated product of the scene irradiance, the absorption of the physicaloptics, and the spectral absorption characteristic of the chromophores, all as a function ofwavelength; x, y, and z are functions of the state of adaptation due to the magnitude of theirradiance in their respective channels. They need not sum to a specific value.

When the scene irradiance is above the mesotopic level, the above equation is transformed into:

R = lnC = ln xL + ln yM + ln zS Eq. 17.2.3.-3

by the dynamic adjustment of the adaptation amplifier in the L photodetection channel. In both of these equations,the terms are shown in the order generally agreeing with the order in the above, linear equation. In these equations,R is the signal level at the output of the bipolar cells. In the absence of any spatial encoding, it also can represent theinput to the parasol ganglion cells. It represents the symbolic form of the signal that can be measuredelectrophysiologically by sampling the axoplasm of the bipolar cell or the dendroplasm of a parasol type ganglioncell. C is the perceived illuminance after recovery of the signal transmitted over the signal projection sub-system tothe cortex, assuming the simplest possible decoder. This signal is also measurable by electrophysiologicaltechniques at the collector (axon) terminal of the decoder neuron within the cortex.

When the above equation is multiplied by the equation for the absorption of the physical optics (for a specific regionof the retina) and the resulting equation is transformed into absolute units, C describes the complete LuminosityFunction as a function of illumination for the HVS. The resulting Luminosity Function is correct for any


147Fulton, J. (1985) The perception of luminance under various states of adaptation. Unpublished, availablefrom the author.

illumination level.

To evaluate the equation under fully dark adapted conditions, it is necessary to evaluate the individual voltage levelsand gain parameters associated with the above figure. Under fully dark adapted conditions, the output of thephotoreceptor cells are at their dark adapted set point voltage of -25 mV relative to the INM. To a firstapproximation, all of the offset voltages are the same. The precise voltage of the dendroplasm of the First BipolarCell is not known but is more negative than the above set point. This condition assures that the 1st generic synapsesare all operational and they can be represented by the diodes shown on the left.

It is necessary to assign gain coefficients to the circuit elements forming the voltages at the photoreceptor pedicelsand to the diodes forming the summing network. The circuit elements associated with the transducers and thephotoreceptor cells determine the signal amplitude associated with the dark adapted set point for the photoreceptorcells. It is also necessary to assign values to the input irradiance and the state of adaptation of the individualphotosensitive channels. By using a 7053 Kelvin temperature source, the impact of the source of radiation iseliminated. The design of the Outer Segment insures the absorption coefficient in each chromophoric channel isgreater than 95%. Similarly, the stabilizing influence of the IPM as a common vascular supply network insures thatall of the gain coefficients of the adaptation amplifiers are essentially equal under dark adapted conditions. Thisincludes the linearization, with amplitude, of the signal emanating from the long wavelength chromophoric channel. At this point, the absorption function of the lens will be assumed to be a constant of 1.0.

The only remaining variables are the actual coefficients of the diodes associated with the summing network of thebipolar cell. Each of these diodes has a coefficient, an impedance, related to the active junction area of thesynapses.

The coefficient of the diodes representing the individual chromophoric channels depend on two parameters that arepoorly known. The first parameter is the actual junction area of the individual synapses between the photoreceptorcells and the first bipolar cell. The second is the number of photoreceptors of a given chromophoric type that areconnected to a given bipolar cell. It is the total equivalent area of the synapses associated with a givenchromophoric channel that determines the coefficient of the summing diode in that channel.

There is an additional complication here. Although, it is appropriate to count all of the photoreceptors activating asingle bipolar cell, normal experimental procedure is to illuminate a specified area of the retina without regard to theactual field of individual bipolar cells (or parasol cells for that matter). This introduces an additional unknown intothe calculations. However, an extensive analysis of the available data for both the dark adapted and “color adapted”human eye has provided a consistent, but simplified, set of these coefficients147. For the dark adapted condition, therelative gain coefficients of 100:1000:100 can be used initially for the L:M:S coefficients in computing the photopicluminosity function, including the contribution of the physical optics. The magnitude of these values are chosenbecause of a peculiarity of logarithmic summation when using natural or base 10 logarithms. The absolute value ofeach logarithmic term in the summation must remain positive for each spectral wavelength of interest. Therefore, ifthe relative spectral response of a specific chromophoric channel is to be used down to the 1% point, the coefficientof this term must exceed 100. To avoid any confusion with versions of the color equation in the literature, equation17.2.3-2 will be re-written as:

R =LnC = [Ln(KL x L) + Ln(KM x M) + Ln(KS x S)]/Const. Eq. 17.2.3-4


148Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate visualcortex. J. Neurosci. vol. 4, no. 1, pp. 309-356, pg. 349

This equation still suffers from one defect. Note the result of one pedicle becoming considerably more positive thanthe other two. Under this condition, the node labeled Veg becomes more positive than the other two pedicle nodesand the intervening diodes become reverse biased. Only the signal from the dominant pedicel is sensed by thebipolar cell. This situation is very unlikely in nature. However, it is encountered in the laboratory and must berecognized in the protocol for determining the dark adapted photopic luminosity function.

If the diodes in the summing circuit were perfect switching diodes, the terms R = LnC could be set equal to thelarger of the right hand terms. However, the resulting equation would be fatally flawed and would not represent thetotal dark adapted photopic luminosity function or the Purkinje and Bezold-Brucke Effects properly. The regionwhere two or more of the terms are nearly equal is critical to the computation. The more appropriate interpretation isto discard a term on the right when it becomes less than 10% of the dominant term. Because of the logarithmicrelationship, such a term becomes negligible in the summation, and subsequent exponentiation to obtain C. In thepreparation of the figures in this work, a more complex approach has been used. The computer program, MathcadPlus, version 6.0, has been used to introduce an “exclusive or” function in the equations. This eliminates thepossibility of a negative value for any logarithm and essentially implements the diode relationship into the algebra.

The theoretical formulation of the above equation 17.2.3-3 is very similar to that derivedempirically by Land in his Retinex Theory of vision, including the limitation to positive logarithmsin the summation. This is not unexpected based on Land’s background in photography whereintensity is normally measured on a logarithmic scale. Most people found it difficult to followLand’s description of his methodology. A readable description of the methodology appears inLivingstone & Hubel148.

Figure 17.2.3-27 presents the theoretical photopic luminosity function of the Standard Human Eye based on theabove scenario. Note the five individual lobes in the theoretical luminous efficiency function prior to anysmoothing. Three of these are directly related to the absorption spectrums of the chromophores but two are the resultof mathematical manipulation within the retina. The spectra of the three chromophores of human vision, as recordedunder operational conditions, are shown at the bottom of the figure. They are all plotted to the same nominalmaximum absorption. It is important to note that (contrary to remarks in the psychophysical literature related to theso-called "fundamental cone spectra") there is little overlap between the individual spectra when they are all plottednormalized to a common peak relative absorption. The horizontal dash-dot line represents the half amplitude pointlevel. The degree of overlap is a critical parameter in the overall photopic luminosity function due to the logarithmicaddition employed in the signal manipulation stage of the visual system. Since the actual densities of the differentspectral types of photoreceptors within the retina are unknown, and the relative sizes of the diodes formed by thesynapses are also unknown, only the relative magnitude coefficients derived above (which include the contributionof the physical optics) are available. When the relative contributions of the various chromatic channels are plotted,the overlap between the M- and L-channels and the signal processing within the signal manipulation stage results inan apparent peak in the theoretical luminosity function in the region of 579-580 nm. The presence of the physicaloptics in the signal channel has negligible effect on the wavelength of this peak. This peak is generally associatedwith Purkinje (See Section 17.2.3.5.1). The Purkinje Effect is generally associated with the transition between themesotopic and photopic illumination regime. A similar peak is seen in the region described by the overlap of th S-and M-channels near 487 nm. This peak is one of two generally associated with the Bezold-Brucke Effect. Theother peak in this effect is that associated with the above Purkinje Effect under different circumstances. The Bezold-Brucke Effect is generally associated with the hypertopic illumination regime or under abnormal mesotopicconditions. The wavelengths of these peaks are a function of the state of adaptation of the individual eye asdiscussed elsewhere in this work.


Figure 17.2.3-27 The theoretical photopic luminosityfunction of the complete human eye. The dotted linerepresents the fully dark adapted relative luminosityfunction of the eye in response to a photopic level equalphoton flux per unit wavelength probe. The dashed linerepresents the above function smoothed to correspond tothe use of a finite spectral bandwidth probe typical of the1950's. Further smoothing can be employed to achievethe equivalent of the spectral bandwidth common in the1920's. The result is a very good emulation of the C.I.E.(1924) Standard. The individual absorption spectra at thebottom of the figure are those of the S-, M- & L-channelsin human at 310° K.

In this figure, the gain ratios are ks:km:k l::60:1000:60. The operating temperature was 310°K. The spectralparameters are those of the Standard Human Eye provided in this work. Note how narrow the notches are at 495and 562 nm and how abrupt the corners are at 470 and 622 nm in the absorption spectrum for this set of gainparameters. The heights of the mathematically derived peaks are quite sensitive to the gain ratios and to thetemperature.

The above luminosity function is calculated without regard to any source of exciting radiation. In practice, it can bereproduced from laboratory data obtained using a source of uniform photon flux per unit spectral wavelength intervaland a spectrum selection filter no wider than 5 nm. Such a source has a black body color temperature of 7053Kelvin. The theoretical curve does depend on a set of amplitude coefficients in the equation for the R channel signalamplitude. These coefficients were chosen to include the affect of absorption by the physical optics of the eye. This theoretical function can be compared with three different empirical functions, the C.I.E version based on theaveraging of data aquired with 30 nm smoothing in the 1920's, the data acquired by Wald with 10-15 nm smoothingin the 1950's, and more recent data taken with 5 nm smoothing. The agreement between the theory and the database improves as time progresses. It appears that the data at 5 nm displays all of the features predicted by thetheoretical photopic luminosity function.

Because of the logarithmic summation, the theoretical function exhibits five relative maximums, that are documentedin the literature based on 5 nm spectrography, and very specific slopes to the skirts of the total waveform.

If this theoretical function is smoothed by to anequivalent 25-30 nm. wide spectral filter width, theresulting curve corresponds to the C.I.E. photopicluminosity function standard. It should be noted thatboth of these curves exhibits a peak that is not relatedto the actual chromophores of vision. This peak (andothers discussed below) is an artifact of the logarithmicaddition employed in the signal processing circuits ofthe retina. In the absence of absorption due to thephysical optics, the peak occurs near 537 nm. in thetheoretical equation. The overall theoretical luminosityfunction peaks at a slightly longer wavelength for equalflux irradiation after introducing the absorption of thephysical optics. It is prescribed as occurring at 555nm. in the C.I.E. Standard. This value can be obtainedafter additional smoothing of the theoretical function tocorrespond to the bandwidth of the spectrometers usedin the 1920's and earlier.

Comparing the results of this work with the literaturecan be done under either of two conditions. The resultsof most research activity associated with the sensitivityof the visual system is presented on graphs using alogarithmic vertical scale in order to present a greaterdynamic range. However, the C.I.E. StandardLuminous Efficiency function (1924) is frequentlypresented using linear coordinates. In either case, thevertical scale is a measure of the sensitivity of thevisual system to a stimulus at a particular wavelength. The linear form of the C.I.E. Standard, figure 1(4.3.2) in


Wyszecki & Stiles, presents an impression that the photopic and scotopic spectrums are distinctly separate and thateach of these portions of the visual spectrum is functionally much narrower than it actually is. It also suppresses theinflection point associated with the short wavelength portion of the photopic Standard. The similar inflection pointassociated with the long wavelength portion of the visual spectrum is difficult to see even in the logarithmic form ofthe 1924 Standard. This inflection point is omitted in figure 1(5.7.2) of Wyszecki & Stiles although it is clearlypresent in the tabular data in their Appendix and when re-plotted by computer.

It will be most useful in this work to utilize sensitivity graphs with a logarithmic vertical scale. When plotted in thisway, the C.I.E. Standard correlates directly with the signal in the R-channel of the visual system. In its linear form,the CIE Standard correlates with the perceived signal in the cortex, but only under dark adapted conditions and smallsignal conditions. This signal was defined as C to conform with earlier notation concerning the archaic colorequation. In that equation, C = rR+ gG + bB as discussed above. This formulation does not represent the measureddata under general conditions. In this work C equals the antilog of R and R is the logarithmic sum of S-, M- & L-channel signals after adaptation and logarithmic conversion. For a limited dynamic range and conceptualdiscussions, the difference between these two definitions of C are small. However, the difference is large in theresearch arena and under large signal conditions. The expression on the right varies with both wavelength and thephoton flux intensity, F, applied to the eye. To avoid confusion with other uses of the letter C, the term C will bereplaced with the broader expression X(8,F) in the remainder of this work. It is worth repeating that “the sum of thelogarithms is not equal to the logarithm of the sum.” Information about the visual system is lost when this inequalityis ignored.

There is an additional challenge in the fact that the theoretical sensitivity of the visual system contains theillumination level in the long wavelength term. This makes the entire luminous efficiency function a function of theillumination level. It is only within the psychophysical photopic regime, where the adaptation amplifiers arecontrolling the signal level applied to the signal manipulation stage, that the luminous efficiency function isindependent of the illumination level. This fact has not generally been acknowledged in the literature but hascontributed to the difficulties of standardization between laboratories. It is also useful to note that the luminousefficiency function has nothing to do with the quantum efficiency of the chromophores while the eye is operatingwithin the psychophysical photopic regime.

To avoid this variability introduced by the adaptation amplifiers, the so-called photopic luminous efficiency functionis nearly always determined under dark adaptation conditions. Under these conditions, all of the adaptationamplifiers are operating at their maximum gain. The visual system is then probed by a short duration, narrowspectral band, illumination source intense enough to elicit a perceived response from all of the spectral channels ofthe eye. The diameter of the test probe was standardized at 2°. It was normally centered on the fixation point of theeye. While standardized, the sensitivity recorded under these conditions is only indicative of the performance of theeye near the lower limit of the photopic regime in response to radiation of a specified, or unspecified but controlling,color temperature. If the source is deficient at a specific wavelength, the recorded response will reflect thisdeficiency. The sources used in the 1920's were grossly deficient in the short wavelength spectrum. This is thefundamental fact underlying the proposal, of Judd and others coalescing up into 1950's, to update the C.I.E. 1924Standard. The CIE chose not to act on these recommendations. To alleviate such suggested changes, the C. I. E.defined a Standard Observer in 1931 whose visual system actually performed according to the above StandardLuminous Efficiency Function. This Observer is clearly not a normal human, or the average of a group of normalhumans.

In 1951, the C. I. E. introduced the Standard Scotopic Luminous Efficiency Function along with a Standard ScotopicObserver. The function was defined under the conditions defined above except the intensity of the probe had to bemaintained at a level low enough to avoid exciting the L-channel photoreceptors significantly. Such a signal couldnot normally be perceived using a 2° diameter test field. Therefore, the field was increased to 10° diameter in orderto raise the signal to noise level in the visual system and insure perception. The result was a function that described


149Wald, G. (1945) Human vision and the spectrum. Science, vol. 101, no. 2635, pp. 653-658150Judd, D. (1931) The 1931 I.C.I. Standard Observer and coordinate system of colorimetry, J. Opt. Soc.Am. vol. 23, pp. 359-374151Wright, W. (1969) The Origins of the 1931 CIE System Color Group Journal (G. Britain) As reproducedin Boynton, R. (1979) Color Vision NY: Holt, Rinehart Appendix, Part II

a fully dark adapted visual system responding to radiation of a specified, or unspecified but controlling, colortemperature. This function is more in agreement with normal human vision. Although, the C. I. E. also defined aStandard Scotopic Observer, it has been much less controversial than its photopic partner.

The critical nature of the color temperature of the illumination source is seldom discussed in the literature.

17.2.3.6.5 Extended remarks on the familiar C.I.E. Luminosity Standards

[xxx condense this section ]In developing the C.I.E. Standards related to the Luminosity function (1924 & 1951for the 2° field, also 1964 for the10° field), the community has been left with an unfortunate legacy. Following exploration of the function in avariety of subjects by different laboratories, a consensus was arrived at and the standards promulgated. In theprocess, the standards defined the functions with great precision as a function of spectral wavelength. This precisionis hollow. The original experiments were performed with spectrometric equipment with a bandwidth of nominally30 nm. This bandwidth integrated all of their measurements over this interval, essentially averaging out any featuresoccurring within this interval. The resulting smoothed values from individuals were then averaged over a group ofsubjects. The resulting average of the smoothed responses were then accepted as the new standard. There was asignificant difference in data from different laboratories, particularly in the blue region of the spectrum. Thatdifference, as great as 9:1 at some wavelengths149, was discarded and suppressed in preparation of the final standard. Some of the data was collected with a significantly higher color temperature light source that gave more weight tothe data in the blue region of the spectrum.

Following selection of the standard spectrum, tabular values were calculated by interpolation of the original datapoints. Whereas most of the original data was collected in steps of 10 nm. or coarser, and using spectrometers withbandwidths of 30 nm. or greater, the tabular values were presented at an interval of 1.0 nm. These values arepresented in Judd150 in an official report. This report does not include his later personal comments suggesting theinadequacy of the Standard. The report does include a conceptual explanation of why the color temperature of thesource and the state of adaptation of the observer is unimportant. It includes the statement, “Colorimetry is based onthese properties of the normal visual mechanism which make it a satisfactory null instrument.” Unfortunately, forpurposes of research, this is a naive conclusion.

Of greater importance is the accuracy of the published values for the CIE Luminosity Function. Wright has someimportant remarks on this subject in 1969151.

“The CIE Colorimetry Committee recently in their wisdom have been looking at the old 1931observer and have been smoothing the data to obtain more consistent calculations with computers. This has also involved some extrapolation and, in smoothing, they have added some additionaldecimal places. When I look at the revised table of the x (bar), y(bar), z(bar) functions, I am rathersurprised to say the least. You see, I know how inaccurate the actual measurements really were.(Laughter from audience) Guild did not take any observations below 400 nm and neither did I,and neither did Gibson and Tyndall on the V(8) curve, and yet at a wavelength of 362 nm, forexample, we find a value y(bar) of 0.000004929604! This, in spite of the fact that at 400 nm the


value of y(bar) may be in error by a factor of 10 (Laughter).”

Although not addressed significantly in the early literature, there has also been a problem related to the spectrum ofthe light used in vision experiments. The Planck Radiation Formula was only promulgated within the theoreticalphysics community in 1900. It appears that most of the experimenters working in vision up through at least the1930's lacked an adequate understanding of the importance of the spectral distribution of light in their experiments. They were primarily concerned with the total integrated energy, which might be called the photopic energy, enteringthe visual system and typically used lamps with a color temperature in the 2400-2800°K range. The specific problemrelates to the relationship between the amount of energy radiated by a source per unit spectral bandwidth versus thenumber of photons, the photon flux, radiated by that same source per unit bandwidth. As late as 1963, theCommittee on Colorimetry of the Optical Society of America (erroneously) defined an equal energy spectraldistribution as one characterized by equal flux per unit wavelength interval. Wyszecki & Stiles gave a correctinterpretation of this relationship on page 4 of their 1982 work. The term “equal-energy” source began appearing inthe vision literature in the 1950's. The term was frequently shown as above in quotation marks and was seldom ifever defined rigorously. In reading the articles of that period, the typical experimenter was using a nearly fixedspectral bandwidth spectrometer to filter the luminance of a commercial tungsten lamp. The goal was to control thetotal integrated energy entering the eye in accordance with Stefan’s Law, rather than concern themselves with theuniformity of the flux entering the eye in accordance with the more detailed Planck Distribution Law. This lack ofdefinition leads to considerable difficulty in correlating the early data to the real world and any theory.

As a result, the current C.I.E. Standards represent the average values obtained from smoothed data collected withinadequate light sources and interpolated to a precision exceeding that of the original data by ten to one.

The problem is actually worse if Wyszecki & Stiles are correct on page 395. Quoting, “Thevalues adopted in 1924 were those suggested by Gibson and Tyndall (1923) who composed asmooth and symmetrical V(λ)-curve from the data cited above. The final result was not anaverage of the experimental data, but a weighted assembly of the different sets of data. From400 to 490 nm, the V(λ)-curve represents roughly the results of Hartman (1918); from 490 to540 nm, those of Coblentz and Emerson (1918); from 540 to 650 nm, those of Gibson andTyndall; and above 650 nm, those of Coblentz and Emerson (1918).”

It is also noteworthy that there have been fundamental revisions (greater than 7%) in the relationship between theCandela and the Watt during the period 1920-1970.

More recently (1979), the appropriate national standards laboratories have chosen to re-define the standard units ofluminous intensity (the candela)and luminous flux (the lumen) in terms of monochromatic light instead of ablackbody source. They chose the frequency of the monochromatic source as 540x1012 Hz. This frequencycorresponds to a wavelength in dry air of 555.016 nm. This wavelength corresponds to the nominal peak in theC.I.E (1924) Standard Luminous efficiency Function.

Wyszecki & Stiles present three figures, their 1(5.7.2) through 3(5.7.2), that highlight the difficulties encounteredlater. Figure 2(5.7.2) illustrates the range associated with the data from 52 subjects accepted as the Standard. Figure1(5.7.2) shows the correction recommended by Judd in 1951 (that was not adopted). The caption of figure 3(5.7.2)requires careful reading. The Judd recommendations for a 2° field are compared to the newer alternate C.I.E (1964)Standard for a 10° field. Judd’s recommendations raise the short wavelength region of the 1924 Standard but can beinterpreted erroneously as lowering the alternate 1964 Standard. The situation becomes consideerably morecomplex if one addresses the UV sensitivity of the human retina presented by Tan and by Griswold & Stark. Bycombining their data (Figure 17.2.3-1) with the more current data on the absorption of the physiological optics ofthe human (Figure 17.2.3-4), a much more realistic estimate of the true spectral characteristic of human vision.


152Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones. J. Opt. Soc.Am. A, vol. 10, no. 12, pp. 2491-2521153Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley, pg. 331-410154Special metamerism index: change in observer. CIE Publ. no. 80. Vienna: Central Bureau of the CIE155Hardle, W. (1991) Smoothing techniques with implementation in S. NY: Springer-Verlag

Stockman, et. al152. have discussed this issue in detail and adopted what they call the CIEJudd 2° color-matchingfunctions153. The intent appears to be to redefine the CIE Luminosity Standards even though Judd had beenunsuccessful in such an endeavor some 40 years earlier. Although they collected sensitivity data based on 7-11 nmspectral bandwidths, they reported data with error bars of ±1-2 nm precision.

Recently, C.I.E. committee TC 1-07 has proposed a C.I.E. Standard-Deviate Observer to represent the individualvariations in luminous efficiency function among “color-normal” observers154. The decomposition procedure usedresulted in four sets of deviate functions.

Modern statistics theory would suggest there are two additional problems with both the older and more recentluminous efficiency data155. First, the theory in this work suggests there is significant detail in the spectral sensitivityof the human eye at intervals of less than 5 nm. Most of the data in the literature has been collected at an interval ofmultiples of 10 nm. Generally the spectral bandwidths used have been greater than 15 nm. The early data wascollected with bandwidths that appear to be about 30 nm. Considering the spectral bandwidth equal to the statisticalbinwidth, a binwidth greater than the interval suggests considerable loss in information. An interval greater than theminimum detail spacing also suggests considerable loss in information. In addition, it suggests that the data pointscannot be connected by straight lines, or even gently curving lines. The graphic presentation should be limited torange bars, and confidence bars if available, at the test intervals.

Second, the various features of the theoretical luminous efficiency function are not well correlated with a scale givenby multiples of 10 nm. As Hardle says so clearly:

“The choice of the origin, xo, of the bin mesh is arbitrary; the consequences for the interpretationof the histogram are drastic.”

His figures 1.14 and 1.15 dramatically illustrate this problem. It would be useful to collect new data in support of anew luminous efficiency function at a bin mesh of less than 5 nm. and a spectral width of less than 5 nm. If a binmesh of 5 nm is used, it might even be useful to collect some of the data at the same bin mesh but with an offset of2.5 nm from the previous set to uncover any significant detail. The expected improvement in the resulting data isillustrated in figure 1.16 of Hardle.


156Hardle, W. (1991) Smoothing techniques with implementation in S. NY: Springer-Verlag, Chap. 2.157Hardle, W. & Schimek, M. ed. (1994) Statistical theory and computational aspects of smoothing. NY:Physica-Verlag, a Springer-Verlag imprint.

The following discussion will address two additional aspects of the problem, how the theoretical luminosityfunctions can be degraded in order to emulate the current Standards or how the current standards should be recast forpurposes of research to better represent the real world of vision. This problem is complicated by the manynonlinearities in the system. An ideal situation would allow the original data from a large number of investigators tobe reprocessed in order to recover the original spectral absorption function in spite of the above problems with thedatabase. This appears to be impossible. The interval in the database is too large relative to the expected underlyingfunction. An alternate approach is to attempt to degrade the theoretical function marginally until the resultingfunction passes within the confidence interval associated with all of the data points in the above database. Unfortunately, it appears the systemic errors among the different experiments occupy a significant portion of theindividual data ranges. The only option left is to degrade the theoretical function until it passes within the range barsat each data interval. Because of the size of these range bars (See Wyszecki & Stiles, pages 402 and 405), this is nota difficult task. When degrading a function, it is very important that the main features of the original function beretained to the greatest extent possible. Hardle156 explores this problem in some detail. Of the half dozen kernelsthat could be used to emulate the shape of the spectral passband of the filters used in the 1920's, the Gaussian, theuniform (rectangular) and the triangle are not likely candidates. However, most researchers will be tempted to usethe Gaussian kernel. Before doing so, they should review Hardle & Schimek157. The extreme sensitivity of thesmoothing parameter, h, for a Gaussian kernel is demonstrated in figures 2.10 & 2.11 of Hardle. Three digitaccuracy and a nominal value near 0.500 is required. If a relatively large amount of degradation is used (a deviationof only 0.007 from 0.500), the function can be made to pass through the median value of nearly every range bar ofthe above data. The resulting function would then correspond to the weighted mean in the 1978 CIE data on page402 and/or 405, or the Standard Observer of the 1924 CIE Standard. However, this function and the weighted meanhave little relevance to the intrinsic luminous efficiency function of human vision.

17.2.3.6.6 Obtaining the familiar C.I.E. Luminosity Function by smoothing T(8,F)

As an example of the above discussion, Figure 17.2.3-28 shows the results of smoothing a specific theoreticalluminance threshold sensitivity function (reflecting the Bezold-Brucke Effect, see Section 17.2.3.5) until itresembles the C.I.E. (1924) Luminosity Function for the Standard Observor. The figure shows two degrees ofsmoothing with common smoothing functions provided in the MathCad package. The function labeled ui + 3 isnamed ksmooth and uses a Gaussian kernel to compute the local weighted average of the input waveform. Thefunction labeled yi + 2 is named supsmooth and uses a more complicated kernal based on a symmetric k-nearestneighbor linear least square fitting procedure to compute the local weighted average of the input waveform. In bothcases, the kernal represents the spectral bandwidth of the spectral filters used to collect the empirical data. Bothexamples will lead to a smoothed graph with a nominal peak near 580 nm even though the underlying functionexhibits no peak associated with this wavelength.


Figure 17.2.3-28 Comparing a theoretical human spectralsensitivity function and its smoothed counterpart (omittingany ultraviolet contribution) to illustrate how a spectrumsimilar to the C.I.E. Luminosity Function is obtained froma much more complex data set. Note the convergencetoward a peak near 580 nm (the Purkinje Peak) assmoothing continues and the complete obliteration of thecontributions related to the short and long wavelengthabsorption spectrums.

17.2.3.7 Comparison with the photopicstandards literature

The theoretical visibility function is seen to include avariety of variables that suggest there is no onestandard function that fits all variants of the HVS. The most significant variables appear to be thoserelated to age and the source of illumination used intesting. The absorption of the outer lens groupappears to increase at 0.55% per year across the visualspectrum compared to the reference year of age 21. Due to the nature of Rayleigh scattering, thisabsorption is of primary importance with respect tothe short wavelength portion of the visual spectrum. Within the photopic illumination range, the adaptationamplifiers of the S-channel photoreceptors canaccommodate almost completely for this shortfall. However, at lower illumination levels, complete compensation is not available. At levels above the photopic range,the saturation inherent in the adaptation amplifiers lead to significant narrow peaks in the overall absorptionspectrum that are not represented in the C.I.E. Standards at all.


17.2.3.7.1 State of the theoretical description

The theoretical description developed in this work is an analytical expression that can be evaluated with any desireddegree of granularity. The basic form of the expression applies to the retina and neural system without the physicaloptics of the eye or the illumination source. Expressions for the absorption parameters of the physical optics areavailable and can be combined with the basic expression. The visual system is fundamentally a photon detector andnot an energy detector. If a non-equal-photon-flux per unit wavelength source is used in empirical measurements, acorrection factor for this source can also be calculated.

The photopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye inperceptual space under a specific set of conditions. The conditions are that the threshold level is determined by thedynamic range of the signaling channel, and not quantum noise or a cortical threshold, and that the adaptationamplifiers in all of the three spectral channels are maintaining a constant average signal level at the pedicels of thephotoreceptors. Under these conditions, the gain coefficients maintain a fixed relationship with each other. Thisrelationship is typically kS:kM:kL::50:1000:30 when including the absorption of the lens group. Since the adaptationamplifiers have a dynamic range of about 10,000:1, the achievable photopic range is approximately 10,000:1 inintensity.

All of the parameters in the analytic expression of the human luminosity function are readily measurable. Thoserelated to the chromophor controlled absorption spectra have been determined, based on data in the literature, tobetter than ±2 nm. The analytical expression makes it clear that the Uni-variance Principle is only applicable to theP/D process within the individual S- and M- absorption channels of vision. It does not apply as a single Principleapplicable to the overall visual process. It does not apply to the individual or groups of complete photoreceptorcells.

The above corrections can be calculated individually and then combined, or the total effective signal gain of eachphotodetection channel can be determined by curve fitting to the best available empirical data. This latter approachwas used in Section 17.2.3.2.1 using the empirical data of Wald. It appears that this data was obtained with aspectrometer bandwidth of 10-15 nm, considerably better than the data of Gibson & Tyndall that was used in theC.I.E. Standard. Many other data sets are available, some using spectrometer bandwidths slightly better thanWald’s, based on a variety of test methodologies. Wyszecki & Stiles provide comparisons between and referencesto these studies through 1982. The data from some of these studies exhibit the fine detail predicted by this work,particularly Sperling & Lewis (1959).

From Section 17.2.3.2.1, the relative gain coefficients for the human eye, operating within the photopic regime andfor the illumination conditions used by Wald, are for the S:M:L channels respectively 100:1000:100. More than oneplace accuracy is difficult to justify without repeating the experiment, and those mentioned above, under morestringent conditions of control. See the results of similar NTSC studies in Section 17.3.3.1.4.

17.2.3.7.2 Comparison of the theory and empirical data

Because of the poor state of the Standards for the human photopic luminosity function, some assumptions must bemade concerning any comparison between the theoretical photopic luminosity function of this work and theempirical data base. Comparing the theoretical function and the current standard is awkward. The theoreticalfunction does not exhibit any dependence on the illumination environment. The measurement of an equivalentfunction depends on the use of an equal photon flux per unit bandwidth source, nominally at 7053° Kelvin. Thecurrent standard has (at least in the recent literature) assumed an equal energy per unit wavelength illuminationsource.


Several comparisons are illustrated in Figure 17.2.3-29. The unfiltered theoretical luminosity function is shown bythe short dashed line. This function is the result of logarithmically summing the individual absorption functions,shown at the bottom of the graph all normalized to the same maximum value and a set of spectrally specificabsorption coefficients, kS:kM:kL. The curve is computed at a spacing of 0.5 nm with straight line segmentsconnecting the data points and spectral coefficients in the ratio of 50:1000:30.

Note the distinct separation of the three chromophores as plotted at 10 nm spectral interval. The curves were plottedfor the half amplitude wavelengths documented in the Standardized Human Eye and a body temperature of 310Kelvin (37 Celsius). The individual spectral curves also illustrate the variable Q (average, or peak wavelengthdivided by width between half amplitude values) associated with these spectra using the best available halfamplitude values. Note also the appearance in the theoretical luminosity function of two additional features due tothe logarithmic summation. The higher peak near 590 nm is due to the slightly greater overlap between the M- andL-channel chromophores. The lower peak near 490 nm is due to the overlap between the S- and M-channelchromophores.

Smoothing of the theoretical photopic luminosity function has been performed using a variety of mathematical filtersfound in Mathcad Plus, ver. 6.0. Using this program and the filter “ksmooth,” the theoretical photopic luminosityfunction can be fit with precision to the C.I.E. (1924) Standard and to Judd’s recommended (1951) modification. This requires that the same assumptions be used with regard to the source temperature used to collect the data. Thelong dashed line represents the above theoretical function smoothed using a Gaussian kernel with a parameter ofb=0.06 (~30 nm). The Gaussian function appears to be a reasonable approximation of the spectral filtercharacteristic implicitly included in the C.I.E. (1924) Luminosity Function. Note how all of the distinct peaks andplateaus of the original function are lost at this degree of smoothing. The two theoretical curves have been adjustedin amplitude so that the smoothed curve has a peak value of 1.0.

The C.I.E. (1924) Luminous efficiency function was plotted as a solid line after conversion to an equal flux per unitwavelength condition. This calculation was based on the assumption that the original C.I.E. function was obtainedunder true equal-energy conditions. The dash-dot line is the above luminous efficiency function modified asrecommended by Judd. Both of these functions are for a 2° diameter illumination field in object space. This sizewas determined to be the smallest field giving consistent results in the laboratory.

Note how the smoothed theoretical function falls between the C.I.E. and Judd functions in the short wavelengthregion when they are all plotted with the same peak amplitude. It is clear that the smoothing parameter, b, need beadjusted only slightly to cause the smoothed function to emulate either the C.I.E. or Judd function.

After smoothing of the theoretical function to approximate the spectral bandwidth of the instrumentation used toprepare the standard, there is good agreement between the form of the graphs but there is a systematic error. On theshort wavelength side of the graph, both the C.I.E. and Judd functions tend to be lower than the theoretical functions. On the long wavelength side of the graph, both the C.I.E. and Judd functions are higher than the two theoreticalfunctions by a factor that grows with wavelength. The presence of this difference questions the recent association ofthe term equal-energy with the C.I.E. (1924) Luminosity Function. It would suggest that the original data obtainedto define the function were not obtained under equal-energy conditions but with light sources that were of distinctlylower black body temperature, probably near 2400 Kelvin on average. There is negligible difference between theoriginal C.I.E. function and the smoothed theoretical function in the long wavelength region if the 2400 Kelvinassumption is used. However, this assumption would require replotting of the short wavelength portion of thisfunction. The resulting difference between the C.I.E. and the smoothed theoretical function can be made quite smallby selecting the parameter, b. If the proposed Judd modifications are included, an even better fit can be obtained inthe short wavelength region. If the data of Sperling & Lewis is accepted, the deviation in the short wavelengthregion is negligible and the predicted inflection point in the long wavelength region is seen in the data. By replotting


the C.I.E. Standard, the Judd modification, and the Sperling & Lewis data for the equal flux condition based on areasonable estimate of the source temperatures used to collect the data, it becomes difficult to see the differencebetween the smoothed theoretical function and these data.

The peak of the smoothed theoretical and the C.I.E. Standard luminosity functions occurs at a wavelength independent of that of any of the chromophores present. The standard graph of the C.I.E (1924) function exhibits apeak near 555 nm. If the data for this graph had been collected under truly equal energy conditions, the peak wouldhave been nearer 551 nm. Under equal flux conditions and a narrower spectral passband spectrometer, the peakwould have depended on the state of adaptation. It would have approached the peak of the M-channel chromophore,532 nm, in the absence of the peak at 590 nm (See the following Section on the Purkinje Effect).

In 1964, the C.I.E. issued another Photopic Luminosity Function, or Luminous Efficiency Function, based on a 10°field stimulus in object space, V10(λ). It is interesting to note that this function has been smoothed to the point thatit does not show any inflection points, even those of Judd. This function has little theoretical significance.

In summary, the luminosity standards of the C.I.E. are now 50 to 75 years old. The theoretical luminosity functionshows a number of inflection points not found in the C.I.E. Standard. It is clear that the C.I.E. (1924) Standard waspromulgated before the vision community understood the impact of quantum physics on the performance of thehuman eye. The Standard includes the implicit assumption that the eye is responding to an incandescent light sourcewith a color temperature near 2400 Kelvin.

By smoothing the theoretical function, and incorporating the absorption of the physical optics and the colortemperature of the source explicitly, a very good agreement with the C.I.E. Standard can be obtained.

The methods of empirically determining the photopic luminosity function also play an important role. The testresults may be significantly skewed by a light source with a true blackbody temperature of less than 7053 K. It isalso clear from the graph that the logarithmic summation process leading to the luminosity function of the human eyeis not compatible with the so-called Univariance Principle.


158King-Smith, P. & Carden, D. (1976) Luminance and opponent-color contributions to visual detection andadaptation and to temporal and spatial integration J Opt Soc Am vol 66(7), pp 709-717

Figure 17.2.3-29 Comparison of the theoretical and empirical Photopic Luminosity Functions. The individualhuman absorption spectra (for the Rhodonines) have been shown on a relative basis at the bottom of the figure forreference. The horizontal dash-dot line represents the half amplitude level. The theoretical function (short dashedline) has been calculated using the absorption coefficients, kS:kM:kL::50:1000:30. The theoretical function has beenmathematically smoothed (long dashed line)using a 50 nm. Gaussian filter. The difference between the C.I.E.Standard (solid line) and the modification of Judd (dashed-dot line) is highlighted by these comparisons.

17.2.4 Resolving the difference between spectra of the chromophores and other spectra

17.2.4.1 Comparing the long pulse versus flicker photometry

King-Smith & Carden have provided valuable data comparing the spectra recorded psychophysically under bothpulse photometry and flicker photometry158. They suffered from the lack of a theoretical model. Hence many of their


propositions are not supported by this work. They did rely upon a zone model to generate a luminance signal andtwo chrominance channels. They did note there was no accepted understanding of how the threshold detectionfunction was accomplished in the CNS, whether it was based on luminance or chrominance channel information.

They did present a figure 2 describing the detection thresholds and color determination thresholds being essentiallythe same as a function of wavelength for 200 ms test flashes. Both functions showed a 3-peaked response. Theydescribed their criteria for determining the color of the test flashes and how they arrived at the conclusion the resultswere valid.. Their figure 4 showed that the peak at 530 nm moved to 555 nm and the peak at 440 nm (due to theS–channel photoreceptors) is eliminated for either brief or small flashes. The 555 nm peak is obviously acombination of the M– and L–channel responses.

Their figure 5 is particularly important and is reproduced as Figure 17.2.4-1. This figure is important because it wasbased on only one individual being evaluated under both conditions in only one laboratory. Only a few questionscan arise regarding the differences in the protocols used. The data was collected using nominally 10 nm wide (athalf transmission) filters. However, data was only collected at roughly 20 nm intervals so some information mayhave been lost. The important point is that there is a significant loss in sensitivity in the blue region, and quitepossibly in the red region (see their figure 6), when using flicker photometry at 25 Hertz compared to the singlepulse technique. King-Smith & Carden associate this loss with a difference in integration time for the blue and redphotoreceptors. This work describes a different situation. It shows all types of photoreceptors exhibit the sametemporal characteristics (except for the 2–exciton process associated with the L-channel photoreceptors). However,the subsequent signal propagation techniques used for the luminance and the chrominance channels within stage 3of vision are totally different. These techniques provide a longer time constant circuit for the recovery of anadequate copy of the signal originating at the S–channel and the L–channel photoreceptors relative to the M–channelphotoreceptors.

Figure 17.2.4-1 Comparing spectral sensitivity based on 1o 10 ms test flashes and flicker photometry. The 10 msflashes (open squares) were centered on a four degree diameter, 3200 Kelvin, 1000 td, white background. The thickline (labeled L) determined from thresholds for detecting 25 Hz flicker on a similar 1000 td white background. Thethin line determined from flicker photometry on a dark background. Both curves shifted vertically to match thesquares at about 555 nm. From King-Smith & Carden, 1976.


159Kranda, K. & King-Smith, P. (1979) Detection of coloured stimuli bey ndependent linear systems VisionRes vol 19, pp 733-745160Thornton, W. (1999) Spectral sensitivities of the normal human visual system, color matching functionsand their principles . . . . Color Res Appl vol 24(2), pp 139-156

Their figure 6 is more complicated. However, it does clearly show the presence of three spectral peaks in the pulsephotometry spectra but only a single-peaked broad response based on their deduced spectrum from flickerphotometry data. This representation would support the assumption that both the blue and red channel responseswere suppressed in flicker photometry spectra. their figure 2 also shows three spectral peaks obtained based on aone degree field stimulus of longer (200 ms) pulse duration.

In 1979, Kranda & King-Smith provided another paper that included a graph of the suppression of the S– and L–channel sensitivities under flicker at 25 Hz159. They were using 16 nm FWHA filters at 10 nm spacings. As a result,their data integrated out the finer variation in the overall spectra compared to the work of Babucke using narrowerfilters. Their figure 13 shows a three-peak overall spectrum with peaks at ~440, ~530 & ~610 nm. The various solidand dashed lines appear to have been extended arbitrarily without any data points in the segments below the overallresponse. While not presenting a graphical model of their work, they were clear that they “assumed a multiplechannel system, responding linearly to threshold stimuli, up to the visual stage where the responses to differentcolours are combined.” This appears to conform to the small signal model of signaling. They also assumed theXYZ chromaticity diagram was linear in X and Y and draw straight loci representing various color mixtures. Theydid a lot of curve fitting and determined the luminance function was the sum of the R and G fundamentals of Vos &Walraven.

The conclusion proposed here, confirmed largely by the work of King-Smith’s team, is that spectra obtained usingflicker photometry suppress the blue and red spectral channels in flicker photometry in the 25 Hz region. Thespectra obtained by pulse methods in the 10 ms to 200 ms more correctly represent the actual spectral sensitivity ofthe human eye. This proposition divides the following discussions into two distinct classes. The results based onpulse photometry appear to provide more complete and less adulterated spectra reflecting the individual spectra ofthe three spectral classes of photoreceptors.

17.2.4.2 Reviewing other the measurements based on long pulse photometry

[xxx edit into above theme ]17.2.5 Predicted versus measured spectra and color-matching functions

The subjects of this section are color-matching functions as opposed to the color-difference functions appearingwidely in the literature. Wyszecki & Stiles review various matching experiments on pages 278-306.

Thornton has recently obtained a large set of color-matching functions (CMF) of vision aimed at extracting thespectral parameters of the visual process. His methodology employs a different protocol and more modernequipment than that of previous investigators. They consist of six papers in 1992 reporting on laboratory workperformed in 1990 plus additional discussion in 1999. His important series of papers are cited in the culminatingpaper of 1999160. The 1992 papers share a common outline and list of figures and can only be considered as a group. In addition, certain abbreviations such as to Color Science, 2nd Ed. by Wyszecki & Stiles (describes as CS followedby a page number) and to Sources of Color Science by MacAdam (described by SCS followed by a page number)are used throughout the set but only defined when first used.

It is important to know that the Thornton data carries with it at least two technical problems that are not


161Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones J Opt Soc Am vol 10(12), pp 2491-2521162Fairman, H. Brill, M. & Hemmendinger, H. (1997) How the CIE 1931 color-matching functions werederived from Wright-Guild data. Color Res. Appl. vol. 22, no. 1, pp 11-23

obvious. The simplest problem involves the age of his limited number of subjects. Their average age was 56with only one subject younger than 35. Their data skews the S-channel peak significantly from the area of437-445 nm to his claimed peak at 452 nm. The more sophisticated involves his use of metameres in hiscolor matching function experiments. Most modern spectral data is obtained by direct psychophysical orelectrophysical measurements using either dark adapted eyes or uniform white backgrounds illuminated witha source with a color temperature near 6500 Kelvin, Thornton takes a different approach. He seeks completemetameric matches between two reflected lights. What he refers to as a standard light may consist ofmetameres of a 6500 Kelvin source, specifically fluorescent sources or a mixture of three 15 nm wide lightsfrom a stabilized xenon lamp source. This methodology introduces additional variables into the problem. His procedure can be described as matching complete metameres where one of the metameres is itself acomplete metamere of a 6500 Kelvin source.

He makes a very important observation (p. 153). “The practice of freely transforming these CMF’s (associated withthe CIE 1931 & 1964 Standard Observers) among primary sets has, I think, led to a widely held notion that the truespectral sensitivities of the normal human visual system are unknowable and even irrelevant.” It has also led to thecommon assumption that the peaks in the normalized color-matching functions of the Standard Observers (based onthe CIE 2° color matching procedure), or of a selected set of these transforms (445, 545, & 570 nm according toStockman, MacLeod, Johnson161) derived from these two sets represent the absorption spectra of the photoreceptors. His set of papers describes the differences (and relationships) between CMF’s and photoreceptor spectral responses. When adjusted as described below, his values and those of this work are in excellent agreement.

Thornton has pointed out some important conditions present in the earlier work of the community, starting withMaxwell’s paper of 1857. “Maxwell credits Young as the first to look toward the human visual system to suggestthat each of three types of nerves in the eye is affected chiefly by rays from one sector of the visible spectrum, ‘butto some degrees also by those of every other part of the spectrum.’”

Thornton takes time to stress how much manipulation was performed on the spectral power distributions (SPD) collected during the first half of the 20th Century to reach a consensus that could be memorialized in the current CIEStandards. He references an important review by Fairman, Brill & Hemmendinger162. As a result, he notes severalkey points (p. 140). “ These manipulations, along with several at-the-time inspired assumptions have led to adifficult situation.” “. . . today the investment of a large amount of intellectual labor on the part of an individualdetermined to understand the system often fails to be adequate.” He notes his purpose is to clarify the situation andease the problem of understanding it.

Thornton makes two important assessments of the currently accepted CIE methods. “One problem is that perceivedbrightnesses are not even approximately additive.” “The second problem is that when the use of the CMFs of eitherStandard Observer as weighting functions on the SPD of a viewed light is stressed by strong metamerism theStandard Observer often fails.”

Thornton reviews the Maxwell-type of color match (using a broadband source in a bipartite field as a reference) tocompare with a an alternative known as the maximum-saturation color match method (where the reference was amixture of “colors of the spectrum” in a bipartite field) The spectral lines were as narrow as he could produce withadequate brightness. In both cases, the reference light was called the “standard light.” He noted that a variant of themaximum-saturation color match method is the basis of the current CIE Standard Observers. This variant uses onlynarrow band spectral colors. Thornton explored two experiments. The first matched three narrow band lights to a


163Aguilar, M. & Stiles, W. (1954) Saturation of the rod mechanism of the retina at high levels ofstimulation Optica Acta vol 1. pp 59+

standard light from a fluorescent source. Using a fluorescent source as a surrogate for a broadband equal energy perunit wavelength source is unusual. He justifies the surrogate on the basis that it looks “white” and apparently excitesthe spectral photoreceptors to the same degree as a broadband source. Such a surrogate cannot generally be used inmetameric experiments because of its non-uniform energy spectrum. The second involved matching two pairs,“doublets,” of narrow band lights in a bipartite field. This technique does not attempt to match a standard light tothe sum of three spectral lights. As he notes, this technique avoids the awkward idea of negative powers frequentlyencountered when the experiment seeks to sum three lights to match a fourth. It avoids the awkwardness by theobvious solution of rearranging the individual lights so that the appropriate two are on each side of the matchingequation.

[xxx does the following need to be split into two parts; standard light and the doublet matches. ]Thornton introduces a variation that is key to the success of his work. While earlier methods have kept the power ofthe three test lights constant and varied their wavelength to achieve a match. He keeps the power of the StandardLight constant and varies its wavelength. To achieve a match, he varies the power of the three other spectral lights. As a result, he obtains a spectral power distribution for each of the three test lights as a function of wavelengthduring a color match with the standard light. While certainly conventional, Thornton errors in measuring the powerin watts in his matching experiments, rather than the applied photon flux applied. While, making his matches whilereading a power meter does not affect the individual match, it does distort the relative powers needed to achieve amatch (since power is not a constant as a function of wavelength in a photon detection experiment). The effect ofthis problem will be developed below. While Thornton attempts to define some of the parameters of the visual system (and their relationships to eachother), he does not define any model of the visual system. He only briefly refers to a Stiles-Aguilar model163. Thiswas a very early model assuming a linear visual system. A description of the characteristics of the filters used intheir early apparatus has not been located. Thornton makes a number of sweeping statements designed to build confidence in his analyses. However, these alsopoint to the lack of any model of the visual and neurological system behind his assertions. This work takesexception to his plea to “. . . recognize that the operating point of ‘trichromacy’ (again from the standpoint ofcolorimetry) is at the rear of the visual system.” His desired to “discuss the colorimetry that goes on deep in thenormal human visual system” in the context of R, G & B signals (p. 153) can not be supported. An appropriatemodel of the visual system shows these signals are converted to P & Q difference signals before the informationleaves the retina. This work also takes exception to several of his fundamental assumptions, whether stated orimplied.

<He assumes the visual system is linear when it is not.<He does not recognize the square-law performance of the long wavelength spectral channel.<He only addresses the three commonly recognized spectral channels without accommodating the fourth.<He does not factor in lens system attenuation as a function of wavelength (particularly as a function of age).<He treats the photoreceptors of the eye as energy detectors instead of quantum-mechanical photon collectors.

While these constraints are significant, his work still provides a clear mechanism for determining the approximate spectral peaks of the S-, M-, and L-channel photoreceptors of the visual system. With straight forwardmodifications, his values will be shown to agree well with the theoretical values provided in this work. However, alarger data set than that from only six elderly subjects (only three subjects in many crucial experiments) is needed toachieve the statistical accuracy he suggests for his current values.


Figure 17.2.5-1 (top) shows his approach in caricature using the solid lines. The vertical line at 500 nm was used todescribe his approach at a specific wavelength in detail. The standard light was held at a fixed power (normalizedhere to one watt) and the three spectral sources were adjusted in power to achieve the best bipartite color match. Thefield diameter was described in the 1992 paper as xxx. The actual power level used for the standard light was xxx. Under the linearity assumption, the concept is clear. When the power required for two of the three lights is zero, thepower of the third light should equal the power of the standard light. This should occur at the wavelength of theunderlying photoreceptor channel. In this case, the wavelength of the S-channel photoreceptor would be 444 nm. The M-channel photoreceptor peak response would be at 526 nm and the L-channel peak response would be at 645nm (although the last value is poorly delimited). At other wavelengths, one of the test lights must be added to thestandard light to achieve a match with the remaining two test lights.

Figure 17.2.5-1 (bottom) shows Thornton’s actual test data averaged for six subjects. The null points are quiteclean suggesting the underlying photoreceptors have peak sensitivities (prior to any other adjustments) atwavelengths of 452, 533, & 607 nm. However, the location of these null points is highly dependent on the precisionof the curves of low slope near the null. His expanded graphs show he is relying upon these crossing to a precisionof better than one percent. If his measurements from six subjects have a statistical error in amplitude of over onepercent, he should be reporting a range of nullwavelengths rather than a specific number. He defineswavelengths determined using this method as the primecolors of human vision. The broadness of theabsorption characteristics of the photoreceptors in the1964 CIE data set are shown in his figure 22. Thesame broadness is shown in his Figure 25 using hismodern data set. These curves show broad spectralpeaks (in the absence of any correction for lensabsorption) centered within 15 nm of the theoreticalvalues of this work.

Thornton isolated the color reversal phenomenon foundin the extreme red region of human vision. His figure10 gives the wavelength of the color reversal as 645nm. It is 607 nm in figure 13 and 610 nm in figure 17. He also stresses the importance of the short wavelengthlight in achieving a match in the spectral regionassociated with deep red. This requirement is in goodagreement with the new Perceptual ChromaticityDiagram of this work.

Thornton compared his 1990 data with that of the CIE1931 and CIE 1964 Standard Observers in a table andwas astounded by the agreement. Figure 17.2.5-2summarizes his data and some other relevant material. The electrophysiological data from the monkeys is

Figure 17.2.5-1 Three-color matching functions for afixed power “standard light.” Top; a caricature of thetechnique described in the text. Bottom, raw un-normalized unmanipulated modern (1990) visual datacollected from six subjects as described in the text. Dotted lines show the relative number of photons per wattof light as a function of wavelength. Each of the curvesneeds to be adjusted in height to reflect the match pointsbased on photon flux instead of power and new null pointsdetermined. Original data from Thornton, 1999.


164Padmos, P. & Norren, D. (1975) Increment spectral sensitivity and colour discrimination in the primate,studied by means of graded potentials from the striate cortex Vision Res vol 15, pp 1103-1113165Govardovskii, V. Fyhrquist, N. et al. (2000) In search of the visual pigment template Vis Neurosci vol 17,pp 509-528

quite rare164. This data shows the R-channel (brightness) of vision as recorded at the occipital lobe of the cortex.

Govardovskii et al. have recently measured the spectra of a variety of fresh water fish (based on vitamin A2chemistry)165. Their spectra were not statistically different from that of humans and other saltwater-based species(based on vitamin A1 chemistry).


The precision of the psychophysical values should not be taken too seriously based on the absorption characteristicsof the photoreceptors. Figure 17.2.5-3 shows the shape of these characteristics based on power measurements madeby Thornton. An overlay has been added to show the situation if a constant photon flux criteria had been used. Small but significant changes in the location of the equal signal crossover points are involved. Additionalmodifications to the graph are needed to account for lens absorption and the 2-photon requirement of the L-channel. The lens absorption is comparable to the change introduced by the power to flux conversion. Accounting for thisabsorption would shift the empirical crossover points farther to the long wavelength by a similar increment.

Figure 17.2.5-2 Tabular comparison of peak absorption wavelengths. The psychophysical data assumes a linearvisual model and includes the absorption of the lens system. The electrophysiological data includes the lens andassumes a linear visual model. The theoretical values assume a square-law model for the L channel and do notinclude any lens absorption.


Thornton noted (p.155) that the shape of the absorption characteristics were crucial to his analyses. Figure 17.2.5-4shows a comparison of his spectra and the theoretical spectra of this work. Although he did not measure the skirts ofthe characteristics in detail, the spectra are quite similar. The short wavelength skirt of the S-channel was eitherlimited by the optics used or his subjects had excessive absorption in their lenses at wavelengths shorter than 440nm. This assertion is supported by the fact his subjects had an average age of 56 (only one subject was under 53). “Young eye” played no role in this study. The shape of the two M-channel spectra are quite similar. The two L-channel spectra are quite similar although the measured curve occurs at a shorter wavelength. The reducedamplitude of the theoretical curve (also seen in the M-channel characteristic) is due to the narrowness of the spectrain relation to the Fermi-Dirac defined edges of the characteristic.

[xxx working here ]

17.2.5.1 Interpretation of the Thorntonwork

[xxx begin my interpretation of the situation.

Thornton has offered a massive psychophysicalinvestigation of the spectral performance of the humaneye. Its content within that field is of monumentalimportance. His background in lighting andknowledge of the idiosyncracies of the CIE StandardObserver are if great value to the community. The

Figure 17.2.5-3 Absorption spectra based on powermeasurements. The crossovers at 487 and 568 wouldmove to the right (489 & 570) if the measurements werebased on equal photon flux measurements as shown by thedashed construction lines. Data (solid lines) fromThornton, 1999.

Figure 17.2.5-4 Comparison of measured and theoreticalspectra. Solid lines are spectra from Thornton, 1999. Dashed lines are theoretical values from this work. Thedifferences between them are discussed in the text.


meticulous repetition of experiments, both of his own and others, in order to confirm specific characteristics isseldom found in the vision literature. This is particularly apparent in his repetition of certain experiments to seek ordemonstrate the absence of “rod intrusion” into his data. However, he has occasionally strayed from his area ofstudy and made remarks in the vernacular that are uncalled for. For example, his repeated statements concerning theseat of chromaticity being located at the rear of the visual system (implying the rear of the brain). His interpretationof a paragraph from Wyszecki & Stiles is similar. “The careful choice of words in the Wyszecki-Stiles quotesuggests that deposing the retina as the seat of trichromacy is timely.”

He has made a number of statements that are blatantly unsupported. The last paragraph on page 253 of his Part III isan example. “The Stiles-Wyszecki attempt to correlate the tristimulus values of colorimetry to retinal absorptionsresulted in a persistent sensitivity much deeper in the red than a retinal cone absorption can be.” He did not describewhat the limit was that he invokes.

In the realm of statistical analysis, he has provided nominal values with deviations attached. However, no definitionof the meaning of these deviations was offered. In general his deviations represent deviations in repeatability of theexperiment and do not represent the precision of the data. This becomes obvious when deviations of one or twonanometers are attached to a value obtained from a binning operation using spectral filters with widths and meanseparations of 15 nanometers.

As seen in the discussions of visibility functions (Section xxx), the use of filters wider than 5 nm at their half-amplitude point can introduce significant errors into spectral diagrams obtained by binning. The Fermi-Diracfunction describing the edge of all known “undoped” photo-electric devices changes by 80% within 15 nm in the redregion of the spectrum.

As in any major study (and this work), the results point to a specific set of values that become the cornerstone of thework. Thornton settled on the spectral values of 452,533 & 607 and reiterated these specific valuesthroughout the material as his prime color regions(PC). His figure 65, reproduced as Figure 17.2.5-5with a reference line added at 611 nm, is highlyinstructive. It shows that his values of 450 and 533 aresharply defined (repeatable) by dual crossings of theabscissa while the value in the long wavelength regioncan vary considerably. Note also the unexpectedamplitude of the functions in the long wavelengthregion determining the nominal sensitivity of thatchannel (the values go off the expected grid). Theconfluence of the curves in this figure might suggest anull in the red region closer to 625-650 than to 607. The value of 452 is obviously determined by the age ofhis subjects as noted above.

Thornton presented a table including the systematicchange in parameters reflected in the figure. The longwavelength primary varies between 580 and 650 nm inthat table while the short and medium wave primariesare fixed at 450 nm and 530 nm. Thus, each curve inthis figure is the metamere of a set of his primaries andnot matched to a fixed source. The curves passingthrough the reference line at 611 nm begin at the top

Figure 17.2.5-5 Color matching functions of eightprimary-sets (J-Q of his Table XV) obtained bytransformation from the PC primary-set averaged observerA. A vertical line has been added at 611 nm for reference. See original for details. From Thornton, 1992, fig.65.


166Thornton, W. (1997) Toward a more accurate and extensible colorimetry: Part IV Color Res Appl vol22(3), pp 189-198

matching a 650, 640, 630, 580, 590, 620, 600, 610 nm source. Placing a grid over the figure and enlarging it, asThornton has done for other figures, it is seen that the long wavelength crossover occurs at the value of the primaryused in the patching experiment. There is no convergence on a unique solution other than that of the three primariesused as a reference. However, this convergence appears quite distinct.

Thornton also settled on a set of four wavelength that he defined as anti-primes (AP) This set consists of a regionin the violet, the blue-green near 500 nm, the yellow near 570-580 nm and the deep red. He frequently defines thetwo dips in the visual spectrum as near 497 and 579 nm. These psychophysical values are in good agreement withthe theoretical values of 494 and 572 developed in this work.

His discussion of the goal and reality of defining metameres in terms of the CIE Chromaticity Diagram is of greatvalue since it is virtually unique in the published literature. The discussion appears in his section IV. Discussionand the graphics extend from his figure 11 to figure 30.

His development of an alternate description of brightness (discussion in his section IVB, with concept developmentin his section IVD3 & IVD4) is of immense value to the theoretician. It offers an entree into the empiricaldescription of brightness not found elsewhere in the literature. His analyses is nearly a perfect overlay (except for alack of boundaries) to the theory of this work. His descriptions and relationships on pages 246-250 will be exploredmore fully in Section 17.4.2. That section develops a new three-dimensional color space compatible with, butproviding new levels of detail concerning the Munsell Color Space. It does not pursue the modified CIE color spacethat Thornton suggests.

Thornton actively pursued, and did not find any rod intrusion into his experiments166, by repeating them at 30 cd/m2

and 100 cd/m2 (regions associated with sunset and typical indoor reading environments in Section 2.1.1.1).

His figure 67 is of great value to the community in allowing comparison between the various color indices currentlyin use. It shows significant differences between the color-discrimination index (CDI), the color-rendering index(CRI) and the color-preferences index ((CPI).

Thornton’s comments on page 183 of the 1992 set of papers surfaces something not previously found in theliterature.

“The wonder is that, in view of the three independent channels in the human visual system, recognized sincePalmer (1777) and Young (1802), we have countenanced not only the concept but the prescription of a one-component, one-dimensional visual-sensitivity curve. The promulgation of a one-component weightingfunction. representing visual sensitivity, as characteristic of a visual system with three independent inputs,has always been insupportable. To teach that a one-input device, as the foot-candle meter, can substitute forthe three-input normal visual system has caused enormous confusion.”

His practical answer to this problem was the development of a three channel “brightness-meter” with a sensitivityprofile (his figure 74) equivalent to the theoretical profile of this work for the human as a blocked tetrachromat,shown in Figure 17.2.1-1 xxx.

17.2.5.2 Reviewing the measurements supporting “cone-fundamentals”

The vision community is divided into two groups with grossly different estimates of the peak wavelengths of the


167Schanda, J. (1998) Current CIE work to achieve physiologically-correct color metrics In Backhaus, W.Kliegl, R. & Werner, J. eds. Color Vision” Perspectives from different disciplines. NY: Gruyter Chap 17168Thornton, W. (1999) Spectral sensitivities of the normal human visual system . . . Color Res Appl vol24(2), pp 139-156169Ikeda, M & Shimozono, H. (1981) Op. Cit.170Smith, V. & Pokorny, J. (1971) Spectral sensitivity of the foveal cone photopigments between 400 and500 nm Vision Res vol 15, pp 161-171171Vos, J. & Walraven, P. (1970) On the derivation of the foveal receptor primaries Vision Res vol 11, pp799-818172Wald, G. Brown, P. & Smith, P.(1955) Iodopsin J Gen Physiol vol 38, pp 623-681

spectral mechanism of vision. The one group has obtained spectra using physiological techniques and relying upondifferential adaptation to separate the spectra. Various titles have been used for these spectra, including actionspectra, cone sensitivities and cone fundamentals. Schanda, in reviewing recent CIE committee work, has definedthe concept of “fundamentals” as the spectral sensitivities obtained psychophysically and referred to the outer layerof the eye167. He defines “photopigment absorption spectra or cone-excitation spectra” as the spectra associated withthe physico-chemico-biological photopigment absorption/photo-signal excitation process.

Stockman, MacLeod & Johnson have been the most active investigators in this area in recent times. They havefocused primarily on re-computing earlier results of several groups relying upon psychophysical experiments. Theother group has used both psychophysical and electrophysical techniques to obtain total spectra exhibiting theindividual peaks associated with each spectral channel. Thornton168 and Ikeda & Shimozono169 have been active inthis group recently. This author has also offered theoretical spectra based on the photo-chemistry of thephotoreceptor neurons (Chapter 5).

Textbooks commonly cite one of three groups when discussing the spectra obtained from psychophysicalexperiments; Smith & Pokorny170, Vos & Walraven171, or Wald, Brown & Smith172. Each of these investigatorsfollowed a different experimental protocol. As a rule, these groups did not factor out the role of the lens in limitingthe spectral performance of the intrinsic chromophores. However, this factor is only important in defining thedifference between the psychophysical performance of the S-channel and the actual absorption spectra of thechromophore.

Wald, Brown & Smith explored visual performance of trichromats under differential adaptation conditions sufficientto eliminate the S-channel, but apparently not sufficient to eliminate the M-channel, from their psychophysicalexperiments. This shortcoming has been demonstrated by the more recent controlled differential adaptationexperiments of Sperling & Hawerth that will be discussed below.

Neither Smith & Pokorny or Vos & Walraven based their work on trichromats. They both accepted the spectraobtained from protanopes and deuteranopes and relied upon the early concept of color blindness attributed toHelmholtz. While Helmholtz suggested deuteranopia as due to the absence (or possibly the failure) of the M-channel photoreceptors, Fick suggested an alternative. Fick suggested the cause of deuteranopia could be due to afailure in the signal processing associated with the “red/green” Hering type signaling channel. His proposalsuggested the fusion of the M – and L–channels. Both the Helmholtz hypothesis and the Fick Hypothesis werebased on the original trichromatic theory. A variety of intermediate situations can be defined between the hypothesisof Helmholtz and that of Fick. Stiles addressed the fact that erythrolabe and chlorolab were both known to bepresent in deuteranope retinas. This fact led him to the idea that the M-channel photoreceptors contained a mixtureof the two chromophores, leading to a failure in the ability of the subject to resolve reds and greens, depending onthe ratio of the two chromophores within the outer segment of the photoreceptors.

The Vos & Walraven paper was an entirely mathematical analysis based on a significant variety of arbitrary (butcarefully drawn) qualitative choices and the use of a zone theory model of vision that is more complicated than that


173Vos, J. Estevez, O. & Walraven, P. (1990) Improved color fundamentals offer a new view on photometricadditivity Vis Res vol 30(8), pp 937-943174Vos, J. (1982) On the merits of model making in understanding color-vision phenomena Color Res Applvol 7, pp 69-77

of this work. Their spectra (“experimental courses not data points”) were obtained from Hecht (1949), Wright(1947), Hsia & Graham (1957) and Boynton et al. (1959). The additional complexity of their model was because ofa lack of definition of the names and spectral range of colors and their specific role in the zone theory. It was basedentirely on linear matrix algebra and did not account for the square-law performance of the L-channelphotoreceptors. Their proposed spectra in figure 5 shows a component of the short wavelength spectra incorporatedin the proposed L-channel spectra. Their proposed L-channel spectrum is essentially the full spectrum of adeuteranope. This spectrum is shown to consist of both the L- and M-channel photoreceptor channels in this work(and in agreement with the Fick hypothesis). Their M-channel spectrum is nominally that of a protanope. Their S-channel spectrum appears to be that of a normal subject limited by the lens of the eye at short wavelengths. All threeof the spectra show this limitation at wavelengths shorter than 420 nm.

A second Vos & Walraven paper promised in 1970 finally appeared in 1990 as Vos, Estevez & Walraven173. This isan important paper corroborating the work presented here. It addresses the potential for the luminance channel ofvision to be represented by the sum of the logarithms of the individual spectral responses for the first time outsidethe writings of this author dating from the 1960's, although this mechanistic approach was mentioned in a 1982 paperby Vos174. However, the concept is only described superficially and their figure 6 should not be relied upon. Theirformulations do not address adaptation within the visual system. While continuing to rely upon the HelmholtzHypothesis, the work relies upon a negative S–channel input, or no S–channel input, to achieve a satisfactorydescription of the visibility function.

Vos, Estevez & Walraven also identify the Bezold-Bruecke hue shift region in close association with the peak regionof their putative L–channel spectrum (figure 5). Their putative L–channel spectra is actually the summation of thereal M–channel and real L–channel spectra under one state associated with the Bezold-Bruecke effect. Theiranalysis also surfaces the fact that the exponent associated with the photon to electron conversion process in theL–channel of vision is twice that associated with the M–channel (0.68 versus 0.34 or 0.34x2 versus 0.34). Thisfeature of vision is discussed in Section 12.5.2.4. The factor 0.34 is actually an approximation to the naturallogarithm conversion. This approximation has frequently been described as the 1/3 power rule.

The Smith & Pokorny paper also relied upon the spectra of protanopes and deuteranopes. While the paper includedthe results of original work, the choice of filters used was unfortunate. While narrow band filters were used, theirspacing was not contiguous or adequate in the critical 496-658 nm region. Thus, they were unable to resolve the finedetails in this region of the spectra. While they did not rely upon differential adaptation as part of their test protocol,the use of a Kodak (Wratten) #47B filter leads to un-quantified differential adaptation. The spectral peak for theirprotanope was at 540 nm with no other measured value within 38 nm of that value. The spectral peak for theirdeuteranope was at 580 nm with no other value within 40 nm of that value. While their spectral data was collectedin terms of energy versus wavelength, they converted the data to quantal sensitivity as a function of wavenumber intheir concluding figures.

Two major problems appear in the Smith & Pokorny paper. The first concerns the precision of their empiricalcurves. It is critically important to note their figures 6 & 7 describing the “quantal sensitivity of the proposed humanvisual photopigments” do not contain any data points. The curves are smoothed and populated with open and closedcircles for identification. More circles are included than there were filters in the original experiments. Only twocurves are shown in each figure. The long wavelength curve is that of a deuteranope, which they propose is thetheoretical spectral response of the L-channel chromophore of a normal trichromat. The shorter wavelength curve is


175Padmos, P. & Norren, D. (1975) Increment spectral sensitivity and colour discrimination in the primate,studied by means of graded potentials from the striate cortex Vision Res vol 15, pp 1103-1113176King-Smith, P. & Webb, J. (1974) The use of photopic saturation in determining the fundamental spectralsensitivity curves Vison Res vol 14, pp 421-429177King-Smith, P. (1975) Visual detection analysed in terms of luminance and chromatic signals Nature vol255, pp 69-70178Sperling, H. & Harwerth, R. (1971) Op. Cit.

that of a protanope, which they propose is the theoretical spectral response of the M-channel chromophore of anormal trichromat. No discussion of failure modes within the visual system leading to color blindness appears in thepaper. The Helmholtz hypothesis is implicit in their proposals.

The second problem concerns their assertions concerning figure 6. Their figure 6 has the title, “Panel (a) Logrelative quantal sensitivity of the proposed human visual photopigments.” This figure has been widely reproducedbased on this inappropriate assertion. In their discussion, they say, “Figure 6 shows the proposed visual pigmentabsorption spectra and their predicted tritanopic coefficients without a differential macular pigment correction. It isclear that these coefficients are completely incorrect, the pair of pigments lie too close together to predict thetritanopic coefficients.” They refer the reader to a corrected figure 7. In both figures 6 & 7, the labels are reversedbetween the long and mid wavelength sensitivity functions! Figures 6 & 7 are arrived at from figure 1 where thecurves were calculated, using a template, and “are slid along the horizontal axis to provide a good fit to the symbolsont eh long-wavelength slopes.” This data hardly qualifies as a reference source for the spectra of the chromophoresof human vision.

Several authors have provided data that can help resolve this situation. Padmos & Norren have provided a papershowing electrophysiological data that displays both types of data from the same subjects and describes the way thedata was obtained175. Similarly, two papers by King-Smith have presented both types of data from the samesubjects176,177. Sperling & Harwerth have provided key data from their experiments involving differential adaptationto show the spectra of Stockman et. al., originating with Smith & Pokorny in 1975, can be obtained from the morefundamental spectral channel data of Thornton, Ikeda & Shimosono and others 178. However, they assert, and thisauthor concurs, the opposite is not true. The real long wavelength spectral characteristic of the photoreceptors cannot be obtained from the smoothed spectra peaking in the 575 nm and 555 nm regions. The broad spectra of the so-called mid wavelength cone spectrum (mws) and long wavelength cone spectrum (lws) generally attributed to Smith& Pokorny, are not the spectra of the actual photoreceptors of vision.

A careful examination of the documents referenced in the previous paragraph, from the perspective of the modeldescribed in Section 17.1, will show that the composite visual spectrum, that is the R-channel or brightness channelof vision, can be measured directly under photopic conditions without requiring any form of adaptation. Because ofethical problems, it is more direct to perform the direct experiments on other primates. However, the results are thesame. The human visual spectrum exhibits four peaks in sensitivity in the absence of the lens and three peaksensitivities in the presence of the lens. These peaks are found in the vicinity of 342, 437, 532 & 625 nm. If thelight level is reduced to scotopic conditions, the long wavelength sensitivity is lost due to the square-law operationof the L-channel photoreceptors.

By introducing differential adaptation at either the photopic or scotopic level, it is possible to suppress either one ortwo of the spectral channels of the human and thereby isolate the remaining spectra. Completely suppressing the L-channel artificially under photopic conditions will result in obtaining the scotopic spectral response and thechromatic sensitivity of a protanope. Completely suppressing the S-channel artificially under photopic conditionswill result in both an abnormal spectrum and chromatic sensitivity generally associated with a tritanope. Completelysuppressing both the S- and M-channels under photopic conditions will isolate the L-channel and result in thechromatic performance of a true long wavelength monochromat (if such exists). However, this condition has seldom


been achieved in the past because the adapting light wavelength has been significantly shorter than 510 nm. If ashorter wavelength is used under photopic conditions, a hybrid spectrum not unlike that achieved with total S-channel suppression will be reported and color performance similar to that of a tritanope will be reported.

Based on this discussion, it appears clear that the human and other species share three common spectral channels(omitting the ultraviolet channel). These channels are centered at spectral wavelengths near 437, 532 and 625 nm. The spectral peaks at 505, 555, 575 are easily generated based on the 437, 532, 625 set of wavelengths. The 505 nmpeak called the scotopic visibility function will be reported under dark adapted conditions where the test light levelreaches the scotopic (but not the photopic) light level and the response is window filtered by a 30 nm filter. Underthis condition, the L-channel is inactive because of its square-law operating characteristic. This performance isusually recorded using a 10° diameter test field to achieve adequate signal-to-noise ratio.

The 555 nm peak called the photopic visibility function will be reported under dark adapted conditions where thetest light level reaches the photopic light level and the response is window filtered by a 30 nm filter. Under thiscondition, the L-channel is active. This characteristic is usually recorded using a 2° diameter test field because ofthe higher available signal-to-noise ratio.

17.2.5.3 Rationalizing “cone-fundamentals” and π-parameters with other spectralparameters

The profusion of different representations of the human visual spectrum are due to at least two distinct concepts ofdata gathering and a wide variety of protocols related to each of these concepts. The term fundamental sensitivityspectra (or briefly fundamentals) are used by the psychophysical community to describe spectra obtained fromsignals passed through the entire visual modality (stages 0 through 6, see Section 14.1.3) but referred to a plane atthe external surface of the eye. These “fundamentals” are subject to any limitations imposed by the neural system(logarithmic signal conversions and spectrally asymmetrical signal processing) and cannot report on the ultravioletperformance of the retina (except in the rare case of an aphakic subject). The term absorption spectra or cone-excitation spectra are used to describe spectra obtained by more clinically intrusive techniques at the cellular orneural path level. These spectra are still frequently limited by the stimulus spectra being limited by the transmissionproperties of the eye forward of the retina (stage 0). Thus, the ultraviolet performance of the human eye is onlyavailable by in-vitro measurements or by using aphakic subjects.

17.2.5.3.1 The design and interpretation of spectral sensitivity experiments

The protocols used to gather spectral data vary significantly in both spatial characteristics and temporalcharacteristics. The spatial characteristics of the stimuli seldom are matched to the variation in retinal performancecharacteristics. Including the transition between the foveola and the parafovea at 1.8 degrees diameter is a particularproblem). Similarly, the temporal characteristics (limitations) of the neural system are seldom considered whenplanning the temporal characteristics of the stimuli. The use of flicker photometry introduces a particularly limitingcharacteristic into obtaining realistic fundamental and excitation spectra. In addition, the precise state of adaptationof each spectral group of sensory neurons must be known if meaningful overall spectra, or relative spectra, are to beobtained.

When discussing any conditioning, or pre-adapting, broadband stimulus, it is critically important that the colortemperature of that stimulus be described. The chordate eye is subject to chromatic (differential) adaptation. Thus,the relative quantum flux at a given wavelength is critical to the adaptation or conditioning process. An adaptinglight at 6500 K for the complete eye (or 7053 K for the aphakic eye) provides near uniform quantum flux stimulationat all visible wavelengths.


179Sharanjeet-Kaur, (no initial). Kulikowski, J. & Walsh, V. (1997) The detection and discrimination ofcategorical yellow Ophtha Physiol Opt vol 17(1), pp 32-37180Foster, D. (1981) Changes in field spectral sensitivities of Red-, green- and blue-sensitive colourmechanisms obtained on small background fields Vision Res vol 21, pp 1433-1455181Foster, D. & Snelgar, R. (1983) Test and field spectral sensitivities of colour mechanisms obtained onsmall white backgrounds: action of unitary opponent-colour processes: Vision Res vol 23, pp 787-797182Snelgar, R. Foster, D. & Scase, M. (1987) Isolation of opponent-colour mechanisms at incrementthreshold Vision Res vol 27, pp 1017-1027

The temporal limitations of the mammalian eye must be understood if maximally precise measurements are to beobtained. The visual modality involves a considerable number of time constants, particularly related to the sensoryneurons.

The longest time constant is the second time constant of the hydraulic system controlling the dark adaptationprocess. It is on the order of 20-30 minutes. For subjects who have recently been exposed to conditions leading to“snow blindness” or “beach blindness,” it is appropriate to wait for multiples of 30 minutes before attempting anyhigh precision measurements. The next longest time constant due to lesser bright light is on the order of threeminutes. A dark adaptation time of ten minutes is needed and conventional in this case. The first Activa of thesensory neurons of vision includes a low pass filter with a time constant of about 1.6 ms. Following any pre-testconditioning or adaptation stimulus, it is desirable to wait at least 8 ms after stimulus termination before applyingany test stimulus in order to allow the output potential of the neuron to stabilize. For a lesser period, the experimentshould be interpreted as measuring incremental sensitivity rather than absolute threshold sensitivity.

The spectral channels of vision are uniquely designed to integrate the photo current related to short flashes andpresent an appropriate signal at the pedicle of the sensory neurons. However, the achromatic and chromatic channelsof vision propogate signals to the CNS using different modulation techniques. The achromatic (brightness) channelcan deliver an initial action potential to the CNS (stage 4) with a delay determined primarily by the distance betweenthe retina and the stage 4 element (either the PGN or the LGN) of the diencephalon. However, the chromaticchannels operate differently. They typically require the delivery of multiple action potentials, at pulse intervals of 20ms or longer in the M– spectral ranges (60 ms or longer in the S– and L– spectral ranges). Thus a test stimulus of atleast 200 ms is needed to precisely notify the brain of a change in chromatic stimulation. A test stimulus interval ofat least 60 ms is required to precisely notify the CNS of a change in achromatic stimulus.

Flicker colorimetry experiments introduce a more complex situation. The above test and conditioning stimulusintervals can be obtained at low flicker frequencies; and by operating at lower than 100% duty cycle, dark intervalsof 8 ms can be achieved between the stimuli to allow settling of the output of the sensory neurons before beginningthe next stimulus interval. However, at flicker frequencies above even three Hz, these conditions cannot beachieved. As a result, the experiments must be considered either incremental threshold measurements or more likelyincremental color discrimination sensitivity experiments.

The protocol must make clear whether it is attempting to determine the threshold sensitivity or the incrementalsensitivity associated with the brightness (luminous) channel of the neural system, or whether it is attempting todetermine the chromatic difference sensitivity of the chromatic channels of the neural system.

In comparing the various spectral characteristics in the literature, the above considerations must be respected. Section 17.2.5.5.4 [xxx ] will illustrate some of these differences following the discussion in this section.

17.2.5.3.2 Background from the literature

Sharanjeet-Kaur et al.179, Foster180 and Foster & Snelgar181,182 have provided a set of papers that help rationalize the


various visual spectra found in the literature, and the theoretical spectra of this work. The Foster paper is extensiveand comprehensive. As noted earlier, Foster and Snelgar have discussed the separation of the descriptors of visionin order to relate to the chromatic-opponent and achromatic (luminosity) mechanisms. This separation is importantin the following discussion. Figure 17.2.5-6 from Sharanjeet-Kaur et al. shows human luminosity spectra obtainedunder two different flicker-photometry conditions. The upper curves at 1 Hz show the typical spectral response alsoreported by Thornton, and most recently with excellent precision by Babucke (Section 17.2.1.3 xxx). Spectral peaksare reported in the regions of 437 nm, 532 nm and 600-625 nm. Using 2700 K background, the notch, which is theapproximate location of the null in the M–L chromatic channel, occurs near 574 nm. With the 6800 K background,this notch shifts to around 565 nm. The nominal theoretical value of 572 nm at 6500 K, based on this work, is inexcellent agreement with these values. “There is no appreciable effect of colour temperature on the 25 Hz curve.”

Sharanjeet-Kaur et al. assert, “The 25 Hz presentationproduces a luminosity spectral sensitivity functionwhereas the I Hz reveals the sensitivity of theblue-yellow and red-green systems.” That is to say, the25 Hz presentation is unable to separate the M– and L–channel signals successfully under their protocol.

When the flicker frequency is increased to 25 Hz, thereis a significant loss in detail within the luminosityfunction at both 2700 and 6800 K. While suggested bythe inflection points in the overall response, the relativepeaks near 437 nm and 600-625 nm are lost in this testregime. This response corresponds to the M-channel“cone fundamental” response of Stockman, MacLeodand Johnson (1993) measured at 17 Hz flickerfrequency, a two degree circular test spot at fixation,and a 4 degree diameter background field.

Thus, a single subject can display the multi-peakedluminosity function found frequently in the literatureand the less detailed single peak response of Stockman,Sharpe and MacLeod at the same time, with only achange in the flicker frequency. In this comparison,the M-cone fundamental of Stockman, MacLeod and Johnson is taken to be the actual luminosity function of theirsubject in the presence of some, but minimal, L–channel suppression (see their isolation procedure). In subsequentexperiments focused on isolating the S–cone fundamental, Stockman, Sharpe and Fach (1999) used a flicker rate of 1Hz.

Figure 17.2.5-7 from Foster and Snelgar shows recent attempts to isolate the three spectral channels of vision whilecomparing them with the luminosity function of the same individual using flash techniques. The graph has beenreplotted with a linear abscissa to conform to the convention in this work. [The original art for figures 1 in the 1981and 1983 papers are not clear. The notation includes a period before the last zero in each ordinate value.] The zeroafter the decimal point has been dropped in this reproduction. Note the straight line character of the skirts of thevarious functions when using this abscissa.. These skirts conform to the theoretical model based on the Helmholtz-Boltzman equation and Fermi-Dirac statistics of the absorption process (Section 5.5.10). The one exception isassociated with the 608 nm experiment where the dotted line probably represents the actual situation. The top box ofeach inset shows the size of the test field; it was nominally 1.05 degrees (entirely within the foveola). The bottombox shows the background field diameter; it was 10 degrees. All fields were concentric and centered on the point of

Figure 17.2.5-6 The effects of flicker frequency on theobserved spectral sensitivity curves in humans. Thecircular test spot was 1.2 degrees in diameter centered onthe fixation point. The surrounding field was 10 degreesin diameter centered on the fixation spot at 1000 Trolands. Subject; SK. From Sharanjeet-Kaur et al., 1997.


fixation. A two millimeter artificial pupil was used in all tests. The upper pair of curves shows the smoothing effectof using a large background field (during flash experiments). The “white” background had an intensity of 1000Trolands and color temperature of 3400 K in the upper curves.. The test flash had a duration of 200 ms with rise andfall times of less than 2 ms. When appropriate for spectral isolation, a ten degree diameter variable intensitymonochromatic conditioning field was used at the wavelength specified for each curve. The upper pair of curves show the significantsmoothing encountered when a large background fieldis used in this type of experiment. It is best to use aconditioning field the same diameter as the teststimulus. Optimally, both should be less than 1.2degrees in diameter when presented centered on theline of fixation. The magnitude and the shape of thenotch shown is predicted in detail by the “sum of thelog absorptions” representation for the luminosityfunction proposed in this work. The specific shape ofthe notch can not be accounted for using a linearsummation hypothesis (such as a linear differencing ofthe M– and L– channels defined by Stockman et al.).

Foster and Snelgar describe their lower spectra as fieldaction spectra (using the earlier terminology of Stiles). Note the insets. Foster and Snelgar used a fixed testwavelength and a variable surround wavelength in athreshold experiment. Unlike, the Stockman group,Foster and Snelgar used conditioning fields very closeto the peak sensitivity wavelengths of the spectralchannels to be suppressed; they used 422 nm, either521 or 531 nm and 608 nm. They describe theisolation of a specific spectral component using theterm spectral sharpening. As the pre-adaption intensityincreases, these spectra begin to approach thetheoretical absorption spectra of the chromaticchannels (with appropriately straight skirts on a semi-logarithmic graph). The short wavelength field action spectra approaches the theoretical absorption spectra quiteclosely at wavelength shorter than 500 nm. Beyond that wavelength, the subject in this psychophysical experimentreports some residual sensitivity due to the M– channel. The mid wavelength field action spectra shows a peakresponse near the theoretical 532 nm with residual sensitivity below 475 nm due to the sensitivity of the S-channeland above 580-590 nm due to the L–channel. The long wavelength field action spectra shows a clear peak in theregion beyond 600 nm. Another data point is needed between 620 nm and 640 nm to determine the precise locationof the peak. The long wavelength action spectra shows a clear relative peak near 532 nm due to the residualsensitivity of the M–channel which was not suppressed adequately. Additional suppression of the M–channel wouldisolate the L–channel spectra completely, although the intensity of the adapting light might involve some discomfortfor the subject.

Comparing the two figures, it is clear that the luminosity response of an individual is unchanged between a 1 Hzflicker based stimulation and a 200 ms flash stimulation, and the three spectral peaks of the individual absorptionspectra can be isolated using appropriate differential chromatic pre-adaptation. The peaks in the field action spectraagree very well with the theoretical absorption spectra of the Rhodonines in the liquid crystalline state (Section5.xxx) and when behind the lens of a normal eye to eliminate the UV channel sensitivity of the retina.

Figure 17.2.5-7 The luminosity function and partiallyisolated spectral responses of the human eye (with lens)based on flash stimulation. Data is for the right eye of thesubject (one author). Tics have been added along theabscissa at 437, 532 and 625 nm for reference. See text. Redrawn with linear abscissa from Foster & Snelgar,1983.


183Stiles, W. (1939) The directional sensitivity of the retina and the spectral sensitivities of the rods andcones Proc Roy Soc (London) series B vol 127, pp 64-105 (beginning on page 81)184Stiles, W. (1959) Color vision: the approach through increment-threshold sensitivity PNAS vol 45, pp100-113

Snelgar and Foster provided more data in their paper. It opens with a statement. “There are three characteristicpeaks at approximately 440, 530, and 610 nm in the spectral sensitivity curve obtained by increment thresholdmeasurements of a long-duration, circular, monochromatic test flash presented on a large white conditioning field.The three peaks have been demonstrated for the human eye in many studies (about a dozen citations).” “Evidencesuggesting that the peaks at about 530 and 610 nm result from relate to (this author) activity in the red-greenopponent-colour channel of an opponent-process system has been reviewed in Foster and Snelgar (1983a).” Thepaper focuses on the characteristics of the notch near 580 nm.

The π-parameters of Stiles have left many investigators perplexed for many years. Their traceability to the actualabsorption spectra of human vision have been difficult to demonstrate. The problem began with the early Stileswork itself183,184. He began with a discussion of the foveal stimulus threshold (at a test wavelength) versusconditioning intensity with a different spectral profile. This function when plotted is known as a t.v.i. curve. Itexhibited three branches. “The three branches are provisionally ascribed to three component mechanisms, denotedby the neutral symbols π4, π1 π3 as marked in the figure.” His interpretation of the t.v.i. curve was based on theexistence of a “rod mechanism” as well as multiple cone mechanisms. When the functions associated with theneutral symbols were presented on a sensitivity versus wavelength graph, the data space became confusing. Whileπ1 could be associated with the S-channel absorption spectra, the other symbols were more difficult to associate withany reasonable aspect of the visual system. In his table 1, he associated π0 with an undefined rod mechanism “absentfrom the fovea.” π1, π2 and π3 were all associated with a “‘blue’ cone mechanism.” π4 and a π4' were associated witha “‘green’ cone” with a maximum sensitivity in the 540 nm region. π5 and a π5' were associated with a “‘red’ cone”with maximums in the 575 and 587 nm region respectively. He left two major questions outstanding on page 109 ofhis 1959 paper. The specific test protocol was not clearly defined in the 1959 paper. The 1953 paper and thediscussion in Wyszecki & Stiles (pages526-544) suggest the test stimulus was of short duration and imposed on asteady, larger spatial diameter, conditioning stimulus.

Foster and Snelgar also interpreted their data relative to the π-parameters of Stiles with useful results. They note,“One of us has recently shown (Foster. 1979, 1980, 1981) that if the field spectral sensitivity curves of the medium-and long-wavelength sensitivity mechanisms, corresponding normally to Stiles’s mechanism π4 and π5 are obtainedwith a long-duration test flash superimposed on a steady monochromatic ‘auxiliary’ conditioning field, spatiallycoincident with the test field. then the resulting curves may appear narrowed or sharpened with their peaks shifted inopposite directions along the wavelength scale. Thus, the field spectral sensitivity curve of the long-wavelengthsensitive mechanism π5, normally rather flat-topped with maximum sensitivity at about 575 nm {Stiles. 1959).becomes attenuated on the short-wavelength side and acquires a relatively sharp peak at about 605 nm (Foster 1980,1981). The field spectral sensitivity of the medium-wavelength sensitive mechanism π4,. also fairly flat-topped withmaximum sensitivity at about 54O nm (Stiles. 1959). becomes attenuated on the long-wavelength side and peaksmore sharply at 530 nm (Foster. l981).” It is proposed the same results will be obtained if the Stockman et al.experiments were repeated at lower flicker frequency and greater degrees of differential adaptation.

17.2.4.5.3 Conclusions

It is concluded that the luminosity function of the human eye is best described by flash or low frequency flicker(below 3 Hz) experiments. At higher flicker frequencies, the luminosity function becomes distorted due toattenuation of the sensitivity in both the short and long wavelength regions. At a flicker frequency in the 15 to 25Hz region, the luminosity function can be separated into two components, a short wavelength component with


185Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons

energy at wavelengths shorter than 494 nm and a longer wavelength component with energy at wavelengths longerthan 494 nm. The longer wavelength component can be further separated into two components, one at a wavelengthshorter than 572 nm and a second at a wavelength longer than 572 nm. With more intense, differential chromaticadaptation, these two components can be sharpened significantly. The shorter wavelength component can besharpened until it exhibits a peak wavelength at 532 nm and straight skirts when the responses are plotted on a semi-logarithmic graph. Similarly, the longer wavelength component can be sharpened until it exhibits a peak wavelengthin the vicinity of 610-625 nm and straight skirts when the responses are plotted on a semi-logarithmic graph. Thethree resulting spectral components are in agreement with the theoretical absorption spectra of the Rhodonines ofthis work when in the liquid crystalline state and dimensionally configured as in photoreceptor outer segments. Bothof these conditions are required.

The reason for the reduction in luminance sensitivity at large distances from 532 nm in high frequency flickerexperiments is complex. For flash and low duty cycle flicker experiments (where the stimulus interval is inthe 150-200 ms range), the experiment calls on the neural system to perform a threshold detection experimentbased on the stage 3 luminance channels (regardless of the chromaticity present). For higher duty cycleflicker experiments (50% duty cycle and test stimulation interval less than 200 ms), the neural system iscalled upon to make a chromatic discrimination experiment. The stage 3 chromatic difference propagationcircuits employ a biphase modulation mechanism encoding a nominally 30 Hz pulse carrier. For wavelengthsshorter than 494 nm or longer than 572 nm, the performance of these circuits deteriorates in proportion to thewavelength difference from these nominal values and the amplitude of the signal at the pedicle of thephotoreceptor neurons. These are the mechanisms that cause the apparent psychophysical sensitivity of thehuman eye to deteriorate in high flicker rate experiments. For flicker rates approaching the critical chromaticflicker frequency (CCFF), given by the above 30 Hz pulse carrier frequency, a chaotic situation arises in thestage 3 propagation channels leading to fusion of the stimulants present during the two flicker phases. Themeasured flicker frequency sensitivity relative to the human CCFF obtained by de Lange Dzn in 1958 isgiven on page 565 of Wyszecki & Stiles185. He showed an attenuation of 8:1 at 17 Hz compared to 1 Hz for achromatic flicker consisting of alternating fields of 615 and 549 nm. A similar result can be expected for anexperiment using fields near the S-channel peak at 437 nm and a more central wavelength associated with theM–channel (example, 515 nm).

The low “carrier frequency” of 30 Hz can be considered a sampling frequency based on the principles of Information Theory. Based on this interpretation, flicker frequencies above one-half of this value (15 Hz)will result in phase ambiguity (distortion) in the reconstructed signals delivered to stage 4.

The so-called cone-fundamentals of Stockman et al. are protocol limited (flicker-rate dependent) measures ofperceived (psychophysical) color sensitivity. The cone-fundamentals do not represent the spectral absorptioncharacteristics of the chromophores of vision or the output of the photoreceptors of vision. Their measurements at17 Hz are significantly limited by the stage 3 neural pathways of vision. These pathways impose an attenuation inthe apparent sensitivities of the S– and L–channels for protocols employing flicker frequencies above about 3 Hz. As a result, the L-channel cone-fundamental is actually a function of the flicker-rate given by 625 x f(flicker rate)nm. This function, and the overall L-channel cone-fundamental function is described conceptually in Section17.2.3.5.4. The peak spectral responses of the primates are better represented by probe data obtained at the outputof stage 1 or stage 2 circuits. Such data is shown for the rhesus monkey in Section 17.1.5.

The human luminance spectra measured with narrow band filters (less than 10 nm FWHA) using flash or flickertechniques below 3 Hz, correctly point toward the peak wavelengths of the underlying absorption spectra (except forthe UV spectra). By employing differential chromatic adaptation within the above constraints, the individualabsorption spectra can be isolated more precisely (to levels of ±5 nm or better). Precise measurement of the


L–channel absorption spectrum (peak and skirts of the absorption spectrum) requires careful attention to the protocolused. Effort is required to insure the measurement represents an intensity threshold rather than a chromaticdiscrimination. In general, the protocol should employ a chromatic adaptation interval of over 500 ms followed afterat least 30 ms by a test stimulus of at least 150 ms.

17.2.4.5.4 Graphic comparison of spectral characteristics

The spectral characteristics found in the literature fallinto two distinct classes.

Figure 17.2.5-8 provides a graphic comparison of thevarious spectra claimed to represent the performance ofthe human visual system. The ordinate for curves E, F,G & H are as presented by Foster. Curves A throughD are scaled to the same relative scale but aredisplaced vertically for clarity.

The key functions to understanding these spectra arecurves C and D from Sharanjeet-Kaur et al. Theyshow a complex curve obtained using flickerradiometry (frequently mislabeled photometry but notinvolving the visibility function) at 1 Hz and a highlysmoothed curve obtained with the same subject andtest set at 25 Hz. As developed in the abovediscussion, both the S-channel and L-channelcomponents of the overall curve are suppressed athigher flicker rates, with the critical flicker frequencyat 3 Hz. As noted, the color temperature of thebackground has minimal impact on the responseobtained at a given flicker frequency. Thus the overallspectral performance of the human eye is a function ofboth the spectral channel of interest and the flickerfrequency of the protocol. The data of Sharanjeet-Kauret al. confirms the earlier data of King-Smith &

Figure 17.2.5-8 A comparison of various spectra claimedto represent human vision. Curves C & D from the sameindividual are key. Curve C at a flicker frequency aboveCCFF is distorted compared to Curve D acquired at afrequency below the CCFF. Curve D and below provide abetter representation of the spectra of vision. See text.


186King-Smith, P. & Carden, D. (1976) Luminance and opponent-color contributions to visual detection andadaptation and to temporal and spatial integration J Opt Soc Am vol 66, pp 709-717 [xxx Thornton pg183 ]

Carden186.

Curves A and B were acquired by Stockman et al. using flicker radiometry at 17 Hz in a complex stimulus protocol. xxx Their selection of conditioning wavelengths was based primarily on anecdotal evidence (page 2473 & 2475). Theamplitudes of these conditioning wavelengths appear to be arbitrary, and in hindsight inadequate. The preferredconditioning wavelengths would be close to the peak wavelengths of the channels to be suppressed. Some variationis desirable to avoid interfering with measurement of the skirts of the spectrum of interest.

While obtained at 17 Hz instead of 25 Hz, the Stockman et al curves are smoothed even more than curve C fromSharanjeet-Kaur et al. They give a peak wavelength of 545 nm for the M– fundamental and 570 nm for the L–fundamental at 17 Hz. These peaks were obtained using a modest degree of chromatic adaptation. They providedno curves obtained at higher degrees of adaptation. As noted above, by increasing the degree of chromaticadaptation, the peaks in the L-fundamental response moves closer to 625 nm and the peak in the M-fundamentalresponse moves closer to 532 nm. These considerations extend the overall spectral performance of the human eye toa function of the spectral channel of interest, the flicker frequency of the protocol and the level of chromaticadaptation. The limitations are not restricted to mechanisms within the photoreceptors. The “fundamentals” ofvision should not be associated with the terms “cones” or photoreceptors. The “fundamentals” of vision relate to thespectral channels of vision.

In 1999, Stockman et al. provided an S-fundamental response based on an entirely different protocol at one Hertz. The resulting curve is shown dashed. Note, the peak sensitivity occurs very near the theoretical value of 437 nm, itstwo skirts are symmetrical and the skirts exhibit a slope predicted by the Helmholtz-Boltzman equation. Byreducing the flicker frequency below CCFF, the researchers have obtained an S-fundamental response that isdependent primarily on the characteristics of the S-photoreceptor. It is equivalent to the photoreceptor excitationspectra.

While the expression “cone” is a convenient semantic shorthand for photoreceptor, the term is misleading inthat it implies there are non-cone photoreceptors.

The set of two curves labeled E and curves F, G & H were obtained by Foster and Snelgar from a single subjectusing 200 ms flash stimulus techniques (essentially zero flicker frequency). The complete spectrum obtained underflash conditions is very similar to curve D obtained under 1 Hz flicker conditions. The measured S-channelspectrum (curve H) peaks very near 437 nm and is equivalent to the theoretical S-channel absorber for wavelengthsshorter than 500 nm. The measured M-channel spectrum (curve F) peaks very near 532 nm but its skirts aredistorted by the inadequate suppression of both the S-channel and L-channel responses. The measured L-channelresponse (curve G) peaks near 615 nm, very near the theoretical value of 625 nm. Unfortunately, its shortwavelength skirt is distorted due to inadequate suppression of the M-channel and its long wavelength skirt isdistorted (not obvious in the original data plot using a different format) by one data point that is probably extraneous.

The data of Foster and Snelgar as well as the S-channel response of the Stockman group is clear; the use of flashradiometry, or flicker radiometry below the CCFF, leads to photoreceptor fundamentals that are representative of theunderlying photoreceptor excitation spectra (the actual absorption spectra of the photoreceptors). Data collectedunder these conditions differ significantly from the M-fundamentals and L-fundamentals of the Stockman groupcollected at a flicker frequency of 17 Hz. The M-fundamentals and L-fundamentals of the Stockman group properlyportray the overall performance of the M-channel and L-channel under high frequency flicker conditions but do notrepresent the performance of the photoreceptors alone.


- - - -The flicker method of spectral measurement used by the psychology community is an end-to-end measurement. It isnot confined to the measurement of only the spectra of the photoreceptors. The fundamental problem with theflicker method of luminance and chrominance spectral measurements is that it introduces a condition that the visualsystem was not designed to process. A flickering light source does not occur in the natural world (except due toforest fires and possibly the reflection of sunlight off of moving water). The visual system employs a pulse basedstage 3 signaling system. The chrominance encoders of the stage 3 neural circuits employ a carrier frequency that isnominally 30 Hz and phase modulated (Section 14.xxx). This frequency is closely related to, but not the directsource of, the critical flicker frequency (CFF). It is the source of the critical color flicker frequency (CCFF) of thevisual system (Section xxx or other ref). The recovery of the chrominance information by the stage 3 decodercircuits is enhanced by the use of a low pass filter with a nominal 3dB point of 3 Hz..

The mathematical description of stage 3 chrominance signaling is complex but the system can be considered ananalog modulation scheme or a sampled-data modulation scheme. Consider it a sampled-data modulation schemefor the moment. When the frequency of the flickering illumination approaches the sampling frequency of the stage 3chrominance channels (30 Hz), the output of the stage 3 system is indeterminante and the number of pulses per unitinterval propagated to stage 4 tends toward zero, e. g., little or no information is forwarded to the CNS.

A feature of the stage 3 signaling system is that the more inhibiting the stage 2 signal applied to the stage 3 encodersof the O–, P– & Q– channels, the fewer the number of pulses within the nominal integration interval associated withthe CNS and represented by its reciprocal, the CFF. Because of the univariance principle, this means the longer thewavelength of the L–channel stimulus or the more saturated that stimulus, the less information propagated to theCNS within the integration interval. Similarly, the shorter the wavelength of the S–channel stimulus or the moresaturated that stimulus, the less information propagated to the CNS.

As seen in the discussion above, using the flicker method of colorimetry in an end-to-end psychologticalmeasurement leads to a change in the reported peak spectral frequency of both the M & L spectral channels as afunction of the flicker frequency. Figure 17.2.5-9 shows a conceptual graph of the reported peak wavelength of thelong wavelength (L–channel) photoreceptors as a function of flicker frequency. The long pulse measurements ofSperling & Harwerth, Thornton, many others and more recently Babucke (Section 17.2.1xxx) have generally given apeak wavelength in the 610-620 nm region while thehigher flicker frequency approaches have reportedpeak wavelengths in the 560-580 nm region. Thetheoretical peak at 625 nm is in agreement with thevalues reported for a variety of non human chordates(Sections 5.5, 5.7, & 17.1.5). Any theoretical value isalways subject to perfection of the model, but itappears the current value is defendable.

Figure 17.2.5-9 Predicted long wavelength peak versusflicker frequency.


Figure 17.2.5-10 provides an alternate form showing the independent variable, flicker frequency, on the ordinatescale. The data shows the theoretical value for the peak wavelengths at zero frequency along with the reportedvalues of Stockman et al. at 17 Hz using a 561 nm pre-conditioning stimulus and a 2 degree field centered on thepoint of fixation. It is interesting that the Stockman et al. values appear to be converging on the wavelength of thepreconditioning stimulus. This suggests the neural system is losing its ability to ascertain individual colors as theexposure interval is being reduced. As a result, the reported wavelength is a weighted average of the pre-conditioning and test stimulus wavelengths. The curves suggest the reported stimulus for both the M– and L–channel photoreceptors would converge on 561 nm at frequencies equal to and above the critical flicker frequency.

Also shown is the 3 dB bandwidth of the stage 3 signal projection channels. As noted above, others primarily of theUniversity of Chicago psychology school report values similar to those of Stockman et al. Many others reportedvalues are along the curves shown at locations within the gray box. These values were obtained using long pulse orlow frequency flicker techniques. Stockman, Sharp & Fach have recently provided a value for the S–channelphotoreceptor at 1 Hz flicker frequency. While the data is primarily graphical, for both central and peripheralfixation, the peak value is given as 440 nm at a granularity of 5 nm in their Table 3.

No empirical values for the peak UV wavelength were found in the literature, except those deduced from thecomplete visibility spectra. The individual spectral responses typically have broad peaks. As a result, the reportedpeak wavelength is subject to the mathematical approach used to define the peak.


In summary, the term “cone fundamentals” is a misnomer as discussed in detail on the web page,http://sightresearch.com/files/conefundamentals.htm The spectral responses defined by this label do not relate to theintrinsic spectral responses of the chromophores or photoreceptors of human vision.

17.2.6 The performance of the eye under unusual illumination conditions

The community has found it difficult to define the transition points between the various regions of vision based onstimulation intensity. Wyszecki & Stiles review the literature. For general purposes, the transition between thephotopic and mesopic regions can be defined as 3-5 cd/m2. The transition between the mesopic and the scotopic isgenerally taken as near 10-3 cd/m2.

17.2.6.1 The full eye at very reduced irradiance (Scotopic region)

Figure 17.2.5-10 The flicker frequency versus peak spectral wavelength relationship. The values at 17 Hz are thoseof Stockman et al. of 1993, using a 561 nm pre-conditioning stimulus. Values along the curves falling within thegray box have been reported by many investigators (see text). The tabulated 1 Hz value of 440 nm for the S–channelis from Stockman, Sharpe & Fach of 1999. The 3 dB bandwidth of the stage 3 signal projection channels isestimated from this work.


187Crawford, B. (1949) The scotopic visibility function Proc. Phys Soc B vol. 62, pp 321-334188Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons, pp. 395-396189Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg. 396190Brown, P. & Wald, G. (1964) xxx Science vol 144 pp 45-52

17.2.6.1.1 Comparison with the scotopic research literature

There has been very limited laboratory research on the scotopic performance of the human eye. Determination of thescotopic luminosity function is much more difficult than for the equivalent photopic function. It was not until the1940's that experimentalists achieved reasonably repeatable results187. To achieve repeatable results, i. e., achieve anadequate signal to noise ratio, it was necessary to expand the size of the stimulus to a larger diameter object field. The tests were still performed with incandescent illumination sources and, as found for the photopic case, these lowtemperature sources were a better approximation of an equal photon flux source than they were of an equal-energysource. The current standard was derived from tests on less than 100 subjects and the statistical variation wassignificant188. The subjects were dark adapted for one hour before the experiments. One hour is a reasonable periodfor convenience but does not meet the normal criteria for full dark adaptation. Although various references suggestthe C.I.E. function is for a field located at least five degrees from the fovea, the data was not collected under thatcondition. Crawford collected the original data using a 20° diameter bipartite field with a vertical dividing line189. The subject was asked to fixate on the top of the dividing line and compare a “white” field with the test field. Thewhite field had a nominal luminous intensity of 3 x 10-5 candela per square meter and was viewed through the naturalpupil.

The scotopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye inperceptual space under a specific set of conditions. The conditions are that the threshold level is determined by thecortex, and not quantum noise, that the adaptation amplifiers in all of the three spectral channels are operating atmaximum gain, but the incident radiation level is so low that the gain coefficient of the L-channel is negligiblerelative to the coefficient of the M-channel, due to the square-law term in the L-term in the luminance summationequation. Under these conditions, the S- and M-channel gain coefficients maintain a fixed relationship with eachother and this relationship is typically kS:kM:kL::50:1000:(<1) when including the absorption of the lens group. Theabsolute value of these coefficients decrease with radiant intensity level and the signal to threshold ratio of thesystem decreases continuously with radiant intensity. This is measurable at the output of the pedicles where theaverage signal level decreases with decreasing radiant intensity. The dynamic range of the scotopic region isconstrained at the lower radiant intensity by the signal to threshold ratio at which the subject can perceive a changein the stimulus. Perception at this level is strongly dependent on spatial integration of the signal in the cortex. Thiscondition is controlled primarily by the size of the stimulus in object space.

Brown & Wald190 have provided their measurement of the scotopic response in Figure 17.2.6-1. No range barswere provided. The measurement was performed under psychophysical conditions using a large field of view. Suppression of the L–channel photoreceptors was by bleaching with a “yellow light.” This curve differsconsiderably from the CIE adopted standard discussed in the next paragraph. It can be matched by a theoreticalcurve where the L–channel response was nearly completely eliminated and the M–channel response was reducedrelative to its normal sensitivity relative to the S–channel. As a result, the curve shows a peak as expected by theBezold-Brucke Effect near 494 nm. The peak would have changed to 532 nm if a bleaching light with less radiationat wavelengths shorter than 600 nm had been used, i.e., a red light. The resulting difference response would havemore closely matched the calculated scotopic response and the CIE standard.


Figure 17.2.6-1 The difference spectrum recorded psychophysically in the human retina (parafoveal region). Thespectrum was obtained by recording the dark adapted spectrum and then subtracting the spectrum obtained byrecording response after a brief exposure to a very bright yellow light. The .spectra were recorded in a darkenedroom using very low light intensities. Note the inflection points suggestive of the summation of the S– andM–channel responses. Note also the major peak near 494 nm indicative of the theoretical peak described by theBezold-Brucke Effect. From Brown & Wald, 1964.


Figure 17.2.6-2 Comparison of the theoretical and otherscotopic data. Solid line, theoretical scotopic luminosityfunction with kS:kM:kL::50:1000:(<1). Short dashed line,kS:kM:kL::50:1000:5. Long dashed line, C.I.E. ScotopicLuminosity Function (1951) The relative absorptionspectrums of the Rhodonines are given in the bottom ofthe figure.

17.2.6.1.2 Comparison with the scotopic standards literature

The current C.I.E. (1951) Scotopic Luminous Efficiency Function for a 10° field is shown by the long dashed line inFigure 17.2.6-2. It is slightly asymmetrical but exhibits no inflection points.

Also shown in this figure is the theoretical scotopic luminous efficiency function based on this work. This functionis computed similarly to the theoretical photopic luminous efficiency function at a spectral interval of 0.5 nm. Thethree absorption spectrums of the visual chromophores, the Rhodonines, are shown normalized at the bottom of thegraph based on the half amplitude absorptions parameters of the Standard Human Eye.. The half amplitude value forthese spectrums is shown by the horizontal dash-dot line. The L-channel chromophore is shown dotted since thebaseline assumption is that it does not participate in scotopic vision. Based on this assumption, the theoreticalfunction is computed by logarithmic summation using the same absorption coefficients as for the photopic functionexcept the L-channel coefficient has been set very low. The result is the solid line in the figure. The theoreticalfunction shows several important features. As in the photopic case, there is a perceived peak in the spectrum near490 nm that is not directly related to either of the absorption spectrums alone. Second and as expected, the functionshows a rapid drop in sensitivity for wavelengths beyond 565 nm. Third, the long wavelength skirt of the functionis defined by the Fermi-Dirac equation.

When compared to the theoretical function, the C.I.E. Standard shows two characteristics. First, the longwavelength skirt of the function cannot be represented by a Fermi-Dirac function or the templates of Dartnall. Thelong wavelength skirt does resemble a mesotopic luminosity function as shown by the short dashed line blendinginto the solid line near 570 nm. This line was calculated for a set of absorption coefficients, kS:kM:kL::50:1000:5. The long wavelength skirt of the C.I.E. Standard matches the long wavelength skirt of this mesotopic function quitewell. This suggests that the test procedure used in acquiring the data for the standard was not entirely adequate. Thestimulus was in fact a factor of five too high in intensity for the purpose of evaluating the scotopic luminosityfunction. To achieve an accurate scotopic luminous efficiency function for research purposes, the experiments needto be repeated even if the test stimulus size must be expanded beyond 10°.

Second, the C.I.E. Standard has been smoothed to ahigh degree in the process of averaging the spectralresponses of the individual test subjects. A theoreticalfunction based on the coefficients, kS:kM:kL::50:1000:5and smoothed with a 35 nm wide Gaussian filterprovides an accurate portrayal of this empiricalfunction, the current Standard. However, thecalculated peak wavelength is at 525 nm, not theStandard value of 507 nm. The functions are quite flatin the region between 507 and 525 nm and thespecification of the peak value is subject to how thedata was interpolated.

17.2.6.2 The full eye under transitionconditions (Mesopic and Mesotopicregions)

This work makes a distinction between the overall


mesopic region and the more carefully specifically defined mesotopic region (Section 17.1.1.2.1). The clinicallydefined mesopic region relates to a variety of phenomena due to a series of underlying mechanisms. The mesotopicregion relates only to the neurologically based mechanisms supporting these phenomena. In the past, these regimeshave been separated experimentally by using a small artificial pupil (typically 2mm in diameter). With the artificialpupil, only the mesotopic region is explored.

Discussion of all of the changes in variables occurring within the mesopic range, and only the variables changingwithin the mesotopic range, is complicated. While the visual system is largely dynamic range limited at the top ofthe mesopic and mesotopic ranges, and largely internal noise limited at the bottom of these ranges, the intermediaterange exhibits limitations depending on a variety of mechanisms in the individual spectral channels and the resultingluminance channel. Precisely mapping all of these phenomena and mechanisms is beyond the scope of this work.

There is little precise data relating to the mesopic or mesotopic range in human vision. This is largely because theCIE protocol for measuring the spectral sensitivity of the human eye (the so-called luminous efficiency function) isnot amenable to direct measurement as a function of stimulation level.

Recent data for DG taken by Verdon, Haegerstrom-Portnoy & Schneck have provided calibration for the loss of longwavelength sensitivity as a function of stimulus intensity. DG exhibited normal photopic spectral sensitivity at 3.4log scotopic Trolands. However, his sensitivity in the red was reduced by between 30:1 and 100:1 at both 1.9 and2.4 log scotopic Trolands. Figure 17.2.6-3 shows this data in greater detail. The reference spectra were notsummed logarithmically to show the theoretical photopic and scotopic spectra as shown in the previous figure. Noaccommodation was made for the absorption of the lens of the eye in the short wavelength region. Section 18.8.3.6discusses the vision of DG in greater detail.

17.2.6.2.1 The physiological mechanismsassociated with the mesopic region.

There are two major situations related to thephysiological optics that impact performance in themesopic region. The secondary role of the operation ofthe iris in controlling the stimulus intensity applied tothe retina has been discussed in Section 2.4.3.1. Themore critical role of the iris in controlling the quality ofthe image projected onto the foveola, and describedusing the Stiles-Crawford Effect, is discussed inSections 2.4.2 & 2.4.5. The Stiles-Crawford Effectitself is discussed in Section 17.3.7. While thediameter of the pupil determines the mean stimuluslevel of the image applied to the retina, it alsosignificantly impacts the spatial contrast of that image(see Section 17.6.3.4).

The physiological component of the mesopic region isnominally described as beginning at 104 cd/m2 with thebeginning of the iris opening and ending at 3"10-3 cd/m2

with the completion of the opening process. This is a broad range. However, the actual change in stimulus intensityat the retina due to the action of the iris alone is only a factor of 16 to 1.

Figure 17.2.6-3 ERG data showing the change in spectralsensitivity with stimulus level in the achromatope, DG. No data points were obtained at wavelengths below 500nm for the trichromat or for DG. From Verdon et al.,1997.


17.2.6.2.2 Brief summary of the neurological phenomonology and mechanisms

[xxx rewrite concerning efficiency ]The mesotopic luminosity region represents a major part of the transition between the photopic and scotopic regions.The performance of the visual system within the mesotopic intensity region can be described rigorously. All of thephotodetectors of the eye continue to exhibit the same quantum efficiency in the mesotopic region under the theoryof this work. However, the psychophysical luminosity function changes continuously in the mesotopic region as afunction of the photon flux rate absorbed by the L-channel photoreceptors. As a result, the long wavelength portionof the luminosity function changes form continuously as the stimulus intensity changes. The transition between thescotopic and photopic regions is a smooth, although not linear one. The L-channel performance rises according to asquare-law relationship.

The mesotopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye inperceptual space under a specific set of conditions. The conditions are three. First, that the pupil size is constrainedto a fixed diameter. Second, that the threshold level is largely determined by the quantum noise associated with theradiant intensity of the stimulus, on an individual spectral channel basis, and not on the threshold level of the cortex. The third condition relates to the gain of the adaptation amplifiers associated with the individual spectral channels. The loss in color constancy occurs when the adaptation amplifiers associated with at least one of the spectralchannels reaches their maximum gain. This point establishes a technical definition of the photopic mesopictransition. However, there is no data showing at what point the human is able to perceive this loss in colorconstancy. It probably occurs at a lower stimulus.

In the mesotopic region, both the gain coefficients and the RMS noise threshold associated with each spectralchannel are changing with stimulus level. The amplitude portion of the theoretical mesotopic luminosity function iseasily calculated by logarithmic summation as were the photopic and scotopic functions of earlier paragraphs. Under these conditions, the gain coefficients maintain a fixed relationship with each other, however, the quantumnoise is different in each spectral channel and the quantum noise in the L-channel exhibits a more complexrelationship than it does in the other two. While the typical gain coefficients associated with the neurologicalcircuitry remains near the kS:kM:kL::100:1000:300 level at the top of the mesotopic region, the “effective values”related to the L–channel begin to fall as the first power of the stimulus in that spectral region. At a level of 300:1below the mesotopic threshold, the contribution of the L–channel signal to the performance of the luminance channel(as well as the Q–chrominance channel) is essentially negligible.

The mesotopic component of the mesopic region in humans is nominally described as beginning with the loss ofcolor constancy. This occurs near 104 cd/m2 corneal exposure with the beginning of the closing of a 8 mm diameteriris, or at 6"102 cd/m2 using a 2mm artificial pupil.

One technical definition of the transition between the mesotopic and scotopic regions in humans is the loss of anyperception of color. This normally occurs near 3"10-3 cd/m2 corneal exposure.

The transition between the mesotopic portion of the mesopic region and the scotopic region can also be definedelectrophysiologically in at least two ways.

A first technical definition is that stimulus level where the signal component in the luminance channel falls belowthe noise component at the location of the stellate cells of the CNS. Below this level, the visual system is internal-noise limited. It can still perform, using spatial integration. However, its performance degrades rapidly.

A second technical definition, would define the transition between the mesotopic and scotopic regions as that


191Neumeyer, C. Wietsma, J. & Spekreijse, H. (1991) Separate processing of “color” and “brightness” ingoldfish. Vision Res. vol. 31, pp 537-549192Fulton, J. (1985) The perception of luminance under various states of adaptation (unpublished)

stimulus level where the noise contribution of the luminance channel is equal to the noise contribution of the stellatecells of the CNS. This constitutes a totally electrophysiological definition. The difference in stimulus level betweenthese two technical conditions is not known.

These technical points are difficult to determine psychophysically and require sophisticated electrophysiologicalinstrumentation.

The neurological (mesotopic) extent of the human mesopic range under these definitions can be as high as 2"105 to 1. Alternately, it could be lower if the CNS noise dominance should occur prior to the loss of the perception of color. It is believed the loss in color perception is defined by a specific net signal to noise ratio in the luminance channel. In man-made systems, this would generally be defined in terms of a ratio of about than 6:1 (peak signal to RMSnoise).

Computation of the noise contributed by the S– and M–channel signals, as well as the noise contributed by thestellate cells of the CNS, is academic at this time. There is no available data to compare with the computations.

Neumeyer, et. al191. made a variety of measurements with goldfish and referenced similar data for honeybees thatrepeatedly suggested a unique range of log1.5:1 (or 30 to 1) in stimulation intensity. They labeled this range theachromatic interval and described it as the difference between the threshold for merely sensing “light” and sensing“color.” The lower limit of this range was described as 1.5 lux for the goldfish. The meaning of this narrowachromatic interval is unclear.

17.2.6.2.3 Caricature of the mesotopic luminance threshold function, T(λ,F)

Figure 17.2.6-4 builds on the baseline developed in [Figure 17.2.1-1] to illustrate the spectral response of the eyeunder mesotopic conditions (conditions where the pupil size is fixed)192. It uses the equations of this chapter andChapter 16. The loss in sensitivity in the long wavelength region of the spectrum is obvious as the stimulus level isdecreased. The curve mesotopic #1 represents a loss in sensitivity of 10:1 relative to the sensitivity normallyobserved at the lower limit of the photopic region. Mesotopic #2 represents a loss of 100:1 compared to the lowerlimit of the photopic region. If the eye is chromatically adapted at the top of the mesotopic region by suppressing theM-channel sensitivity, or if the spectrum of the stimulus is deficient in the M-channel region, the regions labeled theBezold (Bezold-Brucke) Effect and the Purkinje Effect can be observed. See Section 17.2.3.4. The Purkinje Effectis ultimately lost as the sensitivity of the L–channel is lost.


193Weaver, K. (1949) A provisional standard observer for low level photometry. J. Opt. Soc. Am. vol. 39, pg. 278

Figure 17.2.6-4 Caricature of human luminance thresholdresponse under mesotopic conditions (pupil size fixed). Mesotopic levels #1 & #2 are one and two orders lower inthreshold than for the lower edge of the photopiccondition (lower limit of color constancy).

17.2.6.2.4 Comparison with the Mesopicliterature

There is very little literature concerning the incident orperceived spectral characteristics of the Mesopicregion. The CIE formed a panel (TC-1.4) in 1979 toexplore the mesopic regime but it went nowhere. TheCIE formed a panel in 2000 that began its work in2004,CIE TC1-58 with the charter, ‘‘To definemesopic visual performance and related terms. Toinvestigate performance based photometry in theluminance region below approximately 10 cd/m2. Topropose a model for the basis of performance basedmesopic photometry.’’ The work of this group will bediscussed after the following review of earlier work.

Weaver proposed a provisional standard observer in1949193. However, his paper provided very littledocumented support. Since his figure has beenreferenced in later works in modified form, it isimportant to present this curve in its original form andto stress that there are no measured data pointsbetween -4 and 0 log brightness on this curve. Weaverwas asked to construct an interpolated data set to coverthis region for purposes of a British Standard onpaints.

He wrote in 1949: “These tables were based on observational data taken at the photopic and scotopic levels,together with interpolations for intermediate levels carried out by a method which was admittedly arbitrary but wasconsidered reasonable as a first approximation.”

He did not include any original observational data nor did he specify the characteristics of the illumination assumed. Thus, he postulated the two end points of his graph based on scotopic and photopic conditions and drew a reasonablecurve between them. It appears he relied upon the peak wavelengths stipulated in the CIE Luminous EfficiencyStandards. These are 555 nm for the photopic 2° (on-axis) standard adopted previously in 1924 and 507 nm for thescotopic 10° (5° off-axis) standard adopted subsequently in 1951. These are large fields relative to the foveola andto the size of typical objects in a scene. He did not address the other parameters associated with these values.

This work does not support the figure of Weaver. Weaver appears to have selected data points that are not from aconsistent data set. Figure 17.2.6-5 shows the original curve of Weaver along with some additional notation. Weaver’s data is based on an equal energy assumption and used a 2360 Kelvin light source (which was in commonuse as a reference at the time). While his data was collected using a 2.6 degree field, it was “adjusted” to conform tothe CIE Standard. He did not say which standard.

It is important to differentiate between the baselines used in the figure. This work uses the absolute peak associated


194Newhall, S. in (1963) The Science of Color. NY: Optical Society of America pg. 105

Figure 17.2.6-5 Theoretical and putative empirical shift inspectra going from photopic to scotopic vision. The solidcurved line without data points or error bars is fromWeaver, 1949. The horizontal line is based on the peakvalue of T(8, F) and the equal photon flux assumption ofthis model.

with the proposed luminance threshold function, T(λ,F), for scene objects of less than 0.5 degrees. Weaver used thecentroids of the CIE Standards, V(λ) and V’(λ) for large scene objects. It is also important to recognize theconsiderable difference between the relative response of the CIE Standards and actual human vision in the region of400-450 nm. This has been documented by Weaver and by Judd. The difference is discussed elsewhere in thiswork.

Weaver describes the transition between the photopic and scotopic regions as 0.5 foot-lamberts. Newhall194 gives the luminance at the transition between the photopic and scotopic regions as between about 0.01and 0.1 foot-lamberts.


195Ikeda, M. & Shimozono, H. (1981) Mesopic luminous-efficiency functions J Opt Soc Am vol 71(3), pp280-284

Ikeda & Shimozono provided data that is in complete agreement with this work if certain minor changes are made inthe interpretation of their data195. Their spectral filters were nominally 10 nm wide (half width) and they reported an“almost double-peaked shape” for the overall spectrum. If their filters had been 5 nm wide (half width), their datawould have been much clearer. It would have resolved the notches between both the M- and L-channels ( at 572nm) and the S- and M-channels (at 494 nm) more clearly. Resolving these notches makes it clear that neither of thefunctions they used in the following equation were unitary. They used a logarithmic summation of the terms in theluminance equation where the term SR(λ) referred to the “rod” spectrum associated with the scotopic visibilityfunction instead of the more specific spectrum of the combined S- and M-channel photoreceptors. Their term SC(λ)referred to the “cone” spectrum instead of the complete spectrum of the combined S-, M- and L-channels.

Ideda & Shimozono did use a mathematical model of the visual system involving the sum of two logarithmicevaluations of the spectral response. In their case, they employed the logarithm of the overall luminous responserather than the logarithm of the individual spectral responses as proposed here.

Figure 17.2.6-6 reproduces figure 1 of Ikeda & Shimozono to illustrate the variation between subjects taken underas similar conditions as possible. The vertical lines at 437, 532 and 625 nm have been added to show how the datarelates to these wavelengths, in some cases peaking at those wavelengths. The Ikeda & Shimozono data wasacquired using 20 nm FWHA filters. They suggested that one photopic Troland equalled about 2.4 scotopicTrolands using their reference Xenon-arc light. They used a bipartite field approach and the method of adjustment. Five measurements in each of three sessions were used to characterize each data point. Approximately 30 minutesof dark adaptation preceded each data collection session. They represent that the two upper curves acquired at –2-log photopic Trolands, although demonstrably different and with both subjects still perceiving a reddish coloration tothe long wavelength test fields, are characteristic of human scotopic vision. It is not clear how their –2-logphotopic Trolands compares with the commonly accepted start of the scotopic region at 3 x 10–4 cd/m2 viewed with anatural pupil (Table 2.1.1-1). The scotopic region is defined as color perception free.

Figure 1 of Ikeda & Shimozono can be comparedfavorably with the more detailed Figure 17.2.6-7,figure 3 from Hurvich &

Figure 17.2.6-6 Luminous efficiency functions at nineretinal-illuminance levels; two subjects. Top to bottom:–2-log, –1.5-log, –1-log. . . ., 1.5-log, and 2-log photopicTrolands. From Ikeda & Shimozono, 1981.


196Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation J Opt Soc Amvol 43(6), pp 485-494

Jameson of 1953196. Ikeda & Shimozono operated over four log units while Hurevich & Jameson operated over 4.5log units of luminance. The Hurvich & Jameson data are inverted as they show radiant intensity of the stimulusrather than the radiant sensitivity of the retina. This figure is in even better agreement with this work. While a bitmore noisy due to the narrowness of the filters used, the location of the notches near 494 and 572 nm are shownmore clearly and the saturation in the M-channel spectral response at high light levels (near the top of the figure) dueto photoreceptor saturation is beginning to show explicitly. Vertical lines have been added at 437, 532 and 610 mμfor reference.

Hurvich & Jameson provided very detailed descriptions of their apparatus and calibration procedures. Theirspectrally selective filters exhibited wavelength bandwidths “with the entrance and exit slits fixed at 0.2 mmranged from 1.5 mu at 413 mu to 7.6 mu at 680 m. They also offered investigators statistical data on theirmeasurements upon request but did not provide any hints regarding this statistical data. The jaggedness of theirindividual trace suggests more test data would be useful at each measurement wavelength.

“The spectral sensitivity of the fovea of the right eye of each of two practiced observers was measured at 10m intervals from 400 mμ to 700 mμ for the dark-adapted neutral state, and from 405 mμ to 700 mμ for thebright-adapted neutral state (white, 10 mL). Ten complete luminosity functions were obtained for eachobserver for each of the two states of adaptation. The foveally fixated test field was elliptical in form andsubtended 1° X 0.80° at the observer's eye, and the circular surround for the bright-adapted conditionsubtended a visual angle of 37° at the observer's eye. In the dark-adapted neutral condition central fixationwas achieved by the use of a small reflected red fixation dot, and in the bright-adapted state, by fixating thedark elliptical 1° field centrally located in the illuminated surround. The test stimulus appeared within thefixated area and was exposed for 0.045 sec.

The selection of an absolute white adapting stimulus which satisfies the conditions of both perceptual andphysiological neutrality was achieved separately for each observer in a similar series of steps.”


Figure 17.2.6-7 Luminance sensitivity variation from photopic to scotopic regimes. Note the formation of notchesnear 494 and 572 nm as the light level is increased and the broadening of the central peak at high light levels due tophotoreceptor cell saturation. The ordinate scale is correct for the lowest function. The other functions are displacedsuccessively by 0.5 log unit on the ordinate scale. From Hurvich & Jameson, 1953.


197Kurtenbach, A. Meierkord, S. & Kremers, J. (1999) Spectral sensitivities in dichromats and trichromats atmesopic retinal illuminances J Opt Soc Am A vol 16(7), pp 1541-1547

Hurvich & Jameson note the re-evaluation of the CIE Luminosity function under way in 1953 and assert, “Itis amply clear that a considerable body of experimental evidence is now available which contradicts the moretraditional notion that the luminosity function exhibits ‘a notable symmetry’. We are in agreement withThomson who, on the basis of a detailed statistical analysis, concludes that ‘one can say with confidence thatthe spectral sensitivity of the centre of the central fovea cannot be a smooth single-humped function’.”

Thornton has overlaid the data points of Ikeda & Shimonozo for subject HS at scotopic levels with a curve generatedby the sum of three Gaussian functions, with peak frequencies at 450, 530 & 610 nm with excellent empiricalresults. Figure 17.2.6-8 shows the same quality of results can be obtained by overlaying the data points with aspectral response formed of the sum of the logarithmic values of each spectral channel (based on the Helmholtz-Boltzman equation) using the standard wavelength values of this work (effective peaks at 437, 532 & 625 nm. Therelative spectral amplitudes (inside the log) were 25, 1000, 28 ( 1.40, 3.0 & 1.45 outside the log operation) and thecurve was smoothed using “medsmooth” from MathCad, with a smoothing parameter of seven, to accommodate therelatively wide spectral filters of the investigators.. Various other smoothing, interpolation and regression formulascan be used to smooth the underlying functions, but the theoretical function is entirely adequate recognizing thevariations from subject to subject and even session to session for one individual. The large 10 degree visual anglebipartite field also suggests some variation of sensitivity within this large retinal field (the non-uniformity ofMaxwell’s spot as a minimum).

The fit of the theoretical function in the figure to themeasured data can be optimized further by adjustingthe wavelength parameters of the chromophores insteps of one or two nm. However, the variationbetween individuals (both in the average diameter oftheir outer segments and between states of adaptationachieved in different test sessions by the sameindividual) makes this an unproductive approach. Thediameters of the outer segments of the photoreceptorshave been shown to be significant in the Stiles-Crawford Effect (Section 17.3.7) measurements fromindividuals.

Kurtenbach Meierkord & Kremers have provided ananalysis of data collected from trichromats,deuteranopes (red-green colorblind but with fullspectra, including an L-absorber) and protanopes(lacking an L-absorber)197. While the paper is wellcrafted, and employs 4-nm half-bandwidth filters and a6000 Kelvin adapting background, their protocolintroduces problems. Their measurements were madeat intervals much wider than 4-nm. Their empiricalequation for trichromats employs a linear summationbased on six explicit and two implicit free parameters. Their measurements were made at five degrees eccentricity. Their measured data appears to be noise limited at lowmesopic intensities. At high intensities, they report spectral responses for the trichromats exhibiting three peaks at450, 540 and 610 nm.

Figure 17.2.6-8 Overlay of measured data with theoreticalfunction from this theory. Dotted curve from theoreticalcalculation of this work, with peak spectral wavelengthsat 437, 532, & 625 nm. Data from Ikeda & Shimonozo,1981, solid curve from Thornton, 1992.


198Babucke, H. (2008) In German www.dgao-proceedings.de ISSN: 1614-8436199www. lightinglab.fi/CIETC1-58/files/MOVE_Report.pdf dated (2005) ISBN: 951-22-7566-X

Babucke198 has compared his measured mesotopic data with the empirical equations from the MOVE-project andfrom Kurtenbach et al. and the theoretical equation of this work. He found the theoretical equation provides a betterfit as shown in Figure 17.2.6-9. The Kurtenbach et al. data was best fit by eliminating the L-M term (setting theircoefficient fD to zero) from their overall equation.

CIE panel TC1-58 recently released an interim reportwith data in exceptionally good agreement with thiswork. The report is called the MOVE (MesopicOptimisation of Visual Efficiency) report and isavailable on the Internet199. The report provides dataand modeling at an intensity level of 0.1 cd/m2 (0.03foot-lamberts) at an eccentricity of zero degrees. Datawas also collected at 10, 1 & 0.01 cd/m2 foreccentricities of zero and ten degrees and for targets oftwo and 0.3 degrees diameter.

Figure 17.2.6-10 shows the excellent agreementbetween figure 10 of the MOVE report and this work. It specifically shows the peaks in the luminousefficiency spectrum resulting from the short, mediumand long wavelength photoreceptors at 437, 532 and610 nm (indicated by the vertical indicia), with theeffect of the lens absorption impacting the shortwavelength response in the region of 437 nm slightly. The “chromatic model” was developed by the MOVEteam is a simple linear empirical model. The luminance level used is at the transition between the photopic andmesotopic regimes. The amplitude of the long wavelength peak may be reduced marginally at this intensity level,and will begin to drop precipitously as the luminance level is reduced further. This fact is not considered orpredicted by the MOVE chromatic model.

Figure 17.2.6-9 A comparison of theoretical andempirical curve fitting to mesopic measurements. Asnoted, the best fit to the measured data was achievedwithout using the subtractive term in the Kurtenback et al.analysis. From Babucke (personal communication, 2008).


200Trezona, P. (1991) A system of mesopic photometry Color Res Appl vol 16(3), pp 202-216

Trezona has presented an interesting method of defining the mesopic region based on bipartite photometry200. It isbased on the concept that “As long as the spectral luminous efficiency function is unchanged with radiance then aplot of log Eref versus log Etest is a straight line of unit gradient.” If the luminous efficiency should change, a newplot is obtained. It will also be a straight line of unit gradient. Figure 17.2.6-11 shows this relationship and themeasured data points for observer #9. The units are radiometric millitrolands. The10° bipartite matching wasbetween a D65 source and a 588 nm reference light. The performance of the system is defined by the intercept of theV’ locus and the V locus and the value on the vertical axis of the intersection of the transition curve and thereference line drawn equidistant from the two loci. The V locus is traditionally associated with the luminancefunction due to the summation of the three spectral channels of vision. The V’ locus is traditionally associated withthe luminance function due to the rods. However, in this work, it is just as reasonably associated with the luminancefunction at low levels in the absence of the L–channel signal, i.e., the logarithmic summation of the S– and M–channels.

Note the transition from photopic to scotopic vision is accomplished over less that two log units change inillumination. for this subject, the midpoint of the transition occurs at about -0.3 = log radiometric millitrolands.

Figure 17.2.6-10 Recent MOVE data on luminous efficiency. Spectral sensitivity measured directly using contrastthreshold techniques (eccentricity 10o) compared with that generated using a linear chromatic model at 0.1 cd/m2

(0.03 foot-lamberts). The linear model was developed by the MOVE team. Note the linear vertical scale. Themeasured spectral peaks at 437, 532 and 610 nm are quite distinct. From the CIE committee report, MOVE, 2004.


201Trezona, P. (1995) Problems of rod participation in large field colour matching Color Res Appl vol 20(3),pp 206-209

The plot does not suggest any mechanism that could be called rod intrusion into the photopic portion of the response. The two portions of the graph operate at two independent levels of luminous efficiency.

Trezona tried again to describe rod intrusion in a short communication in 1995201. The paper did not reach any majornew conclusions.

17.2.6.3 The full eye at excessive irradiance (Hypertopic region)

While of largely academic interest (and clinically dangerous to explore), the transition between the photopic andhypertopic regions can be described in terms of at least two technical criteria. The first technical definition of that

Figure 17.2.6-11 Plot of logEref versus log Etest. Note the use of D65 illumination. The short diagonal line betweenV and V’, and through 0,0 on these scales, could define the transition between the photopic and scotopic regions. This would define the middle of the mesotopic region. From Trezona, 1991.


202Barlow, H. & Levick, W. (1968) The Purkinje shift in the cat retina. J. Physiol. (London) vol. 196, pp.2P-3P

transition is where the gain of the adaptation amplifiers of at least one of the spectral channels has reached itsminimum value. This corresponds to the initial loss of color constancy at high stimulus levels. Operation abovethis level is frequently reported as resulting in a yellowing of the observed imagery. Such a report would suggest theinitial saturation of the M–channel. A second technical definition is that stimulus level where the conversionefficiency of the outer segments of one of the spectral channels has fallen to its half amplitude value. This level canbe defined in terms of the complete P/D Equation of this work.

17.2.6.4 The full eye with enhanced long wavelength irradiance (Purkinje Effect)

When there are significant changes in the relative amounts of illumination falling on the M- and L-channelchromophores of the eye, the visual system performs in an unexpected manner. This effect has been associated withPurkinje who described it from the behavioral perspective.

The Purkinje Effect is the result of the unique confluence of two static and one dynamic mechanisms associated withvision. The existence of the Effect is a result of the logarithmic nature of the signal summing to form the luminancesignal in the R–channel. Its existence is also dependent on the relative degree of overlap between the longwavelength skirt of the mid wavelength and the short wavelength skirt of the long wavelength absorption spectrums. The reason the effect is so elusive is its time dependency and its operational complexity. The effect is dependent onthe rate of change in sensitivity associated with the dark adaptation amplifier (related to its time constant) beingslower than the rate of change in the illumination during sunset. If the rate of decrease in the mid wavelengthillumination is greater than the rate of increase in sensitivity due to adaptation by the mid wavelength channel, thesensitivity in this channel relative to the long wavelength channel is reduced. The result is a suppression of the midwavelength component of the overall response. This leads to an enhancement in sensitivity at a wavelength betweenthe two nominal absorption bands due to the logarithmic mechanism. the overall

Barlow & Levick have provided electrophysiological data on this effect at the ganglion cell of the cat using broadband illumination sources202. The data suggests the transition from photopic to scotopic response occurs over arange of two log units for their filter set. Figure 17.2.6-12 presents the theoretical basis for the Purkinje BrightnessEffect. When the signals are summed logarithmically, an artifact appears. The artifact is caused by the overlap inthe absorption characteristics of the M- and L-channel chromophores and the relative amplitudes of the signalcomponents in these two channels. When the product of the illumination and the sensitivity of the L-channel ishigher than normal relative to the M-channel, the overall luminosity function exhibits a peak sensitivity near 579 nm. As the product of the illumination and the sensitivity of the L-channel decreases relative to the M-channel, as it doeswith the approach of darkness, the peak in the luminosity function near 579 nm decreases in amplitude. At a certainillumination profile, the luminosity function exhibits peaks of equal amplitude at 532 and 579 nm separated by atrough. At still lower levels of illumination, the absolute peak in the luminosity function is found at 532 nm.


Figure 17.2.6-12 Theoretical foundation for the Purkinje(brightness) Effect. Solid line, kS:kM:kL::50:1000:100.Dashed line, kS:kM:kL::50:1000:10. Dotted line,kS:kM:kL::50:1000:1.

Figure 17.2.6-13 Theoretical foundation for the Bezold-Brucke Effect. Absorption coefficients of the Rhodoninesshown on a relative basis at the bottom of the figure. Luminosity function shown for absorption coefficients ofkS:kM:kL::100:1000:100.

This Effect is asymmetrical with the diurnal change inoutdoor illumination due to the time constants andoperating levels of the adaptation amplifiers. It is alsoa function of the absolute illumination level because ofthe square-law nature of the L-channel transductionprocess. It is most commonly observed with thechange from photopic to mesotopic vision at twilight.

Note that as the overall luminosity function changes,the nominal peak spectral response shifts in anunexpected manner. As the relative sensitivity of theL-channel decreases, the absorption peak near 579 nmdecreases in amplitude relative to the peak near 532nm. When these two peaks are of equal amplitude,there is a trough between them. As a result of thiscondition, the peak wavelength associated with thePurkinje Effect changes in a discontinuous mannerfrom 579 nm to 532 nm. There is never a peak in thespectrum between 532 and 579 nm.

17.2.6.5 The full eye with suppressed mid wavelength amplifier performance (BezoldEffect)

At excessively high levels of illumination, the visual system fails to perform as discussed above. Prior to significantsaturation in the photodetection process, the signal level in the M-channel becomes hard limited by the adaptationamplifier reaching current saturation. As a result of this saturation, the perceived luminosity function exhibits anunusual form due to the logarithmic summation employed in the luminance channel. A similar situation can occurunder differential adaptation in the laboratory, even at normal stimulus levels. As the component due to the M-channel photoreceptors is reduced relative to the other two components, two peaks appear in the overall luminosityfunction as shown in Figure 17.2.6-13. These peakscorrespond to the peaks associated with the Bezold-Brucke peaks in the literature. The short wavelengthpeak occurs near 487 nm and the long wavelengthpeak occurs near 579 nm for the values assumed here,kS:kM:kL::100:1000:100. This set of constants onlyrepresents a 3:1 suppression of the mid wavelengthchannel. Unlike the Purkinje Effect, the Bezold-Brucke Effect is not transient in character.

It is interesting that this effect appears to be importantin the tropical rainforest. Where there is an excess ofmaterial in the scene that reflects in the “green” portionof the spectrum, the absorption function of the humaneye is broadened and the relative sensitivity of the eyeto yellows and aquas is increased disproportionately.

17.2.6.5.1 Background


203Walraven, P. (1961) On the Bezold-Brucke phenomenon J. Opt Soc Am vol. 51, no. 10, pp 1113-1116

The Bezold-Brucke Effect dates from the 1870's. While frequently discussed qualitatively, Walraven is one of thefew that have addressed it more quantitatively203. Walraven provides a brief review of the sparse and widely spacedliterature. Hering claimed in 1880 that the effect could be explained best using his opponent theory. In 1987, Piercefirst attempted a conceptual explanation in terms of the Young-Helmholtz theory. However, the Pierce approachwas criticized by Purdy in 1931 because it was not in accordance with the Abney additive laws. Purdy performedmeasurements increasing from 10 to 1000 Trolands in order of magnitude steps. 10 Trolands corresponds to about 3x 10-1 cd.m2, near the lower edge of the mesotopic region. 1000 Trolands remains within the mesotopic region. Thus, he was not working in the zone of color constancy. It is not clear how Purdy insured the separation ofbrightness perceptions from chrominance perception in measuring the hue shifts he reported.

In 1948, Judd and in 1955, Hurvich & Jameson resurfaced the Hering approach as an explanation. In 1961,Walraven provided a conceptually based mathematical description of the Effect based on hue shifts and using theCIE V(8) curve as an absolute reference. Conceptually, he separated the luminance and chrominance channels ofvision. In addition, he proposed that the contribution of the S–channel to chrominance was 10-12 times greater thanits contribution to luminance. This factor is similar to the 10-16 proposed in this work.

Although Walraven did not include any equations in his paper, he did provide a discontinuous theoretical curvefitting the data of Purdy. The data and curve show no hue shift at 476 and 570 nm and a discontinuity in the regionof 503 to 520 nm (Purdy used 508 nm) when the stimulus was raised from 100 to 1000 Trolands in the mesopicregion. Walraven noted that his results depended on the selection of appropriate “fundamental sensitivity curves,”reliance on the absolute accuracy of the CIE V(8) function, the introduction of a nonlinearity in each spectralchannel, and then a set of arbitrary assumptions concerning the white point. His analysis does revolve around the“interaction” between the integrals associated with the red and green spectral channels and the “interaction” betweenthe integral associated with the blue channel and the integral associated with the sum of the red and green channels. He did not define the color temperature of his conceptual light source or the effect of such a light source on theoperation of the visual system in the mesopic region. The curvatures presented by Walraven between 600 and 650nm appear to be due primarily to the loss in L–channel response associated with the transition from the photopic tothe scotopic operating regions. The discontinuity near 508 nm appears to be due to the merging mechanismemployed within the CNS. These features are not related to the Bezold-Brucke Effect.

To avoid countering the Abney additive law, Walraven concludes that the nonlinearity causing the Bezold-BruckeEffect must reside in the chrominance channel. He notes that any nonlinearity that occurred in each of the spectralchannels would not affect the additivity obtained in the luminance channels. This latter case would only be trueunder small signal conditions, a condition that rules out any significant differential adaptation.

17.2.6.5.2 Analysis

This work takes a quite different view than Walraven of the cause of the Bezold-Brucke Effect. No arbitraryassumptions are made, no linearity laws are imposed, and the same model is used as elsewhere in this work. TheEffect clearly involves large signal conditions (changes involving orders of magnitude within the mesopic region). The Effect is examined with respect to possible causes and mechanisms in the spectral, luminance and chrominancechannels. The fundamental logarithmic conversion of all spectral signals occurring at the pedicle of thephotoreceptor cells appears to be the dominant feature. The subsequent sum of the logarithms of the S–, M– and L–channels gives a signal in the luminance channel (R–channel) that shows distinct peaks that develop as the ratios ofM– to S– signal amplitudes and M– to L–signal amplitudes change. These peaks occur at wavelengths near thosereported for the Bezold-Brucke Effect. A combination of the logarithmic conversion at the pedicles and thesaturation that occurs in the output (distribution) amplifiers of the photoreceptor cells provide the very non-linearitythat Waldren describes.


The situation in the chrominance channels is distinctly different. While the non-linearity introduced by thephotoreceptor cells remains key, the mechanism is different. The differencing of the logarithms of the S– and M–channels and the L– and M–channels does not result in any artifacts in the signals. However, if the amplitude ratioschange, a difference in the slope and null value of the P– and Q–signals as a function of wavelength will result (seeSections 17.3.2.2 & 17.3.2.3). This change in the null point is particularly important because the brain is unaware ofit. The brain has learned that the null value in the decoding of the P– and Q–channel values corresponds to specific“hues (nominally 494 and 572 nm).” However, the shift in absolute signal magnitude at the output of the pediclesresults in a change in the wavelengths at which nulls are encoded in the P– and Q–channels. This is the source ofthe chrominance portion of the “hue change” of the Bezold-Brucke Effect.

As the relative level of the M–channel is reduced relative to the S– and L–channels, the encoded null in theP–channel occurs closer to 532 nm. Similarly, the encoded null in the Q–channel also occurs closer to 532 nm. As aresult, the perceived change in chrominance is the very opposite. A null closer to 532 nm is still decoded asrepresenting the previously learned wavelengths. Thus, a relative reduction in the M–channel will cause a shift inperceived hue away from the M–channel median near 532 nm.

Based on this model and analysis, the Hering school more correctly defines the Bezold-Brucke Effect. The Bezold-Brucke Effect (specifically the null points reported near 571 and 475 nm) is due primarily to the logarithmic signalsummation process in the luminance channel and secondarily to the change in the chrominance channels. Thechanges are associated with a change in the relative signal amplitudes associated with operation in the mesopicregion of vision as well as the color temperature (spectral content) of the radiant energy presented to the eye. Amore precise agreement between the values mentioned here and the values of Purdy will require a much more carefulanalysis of the experimental conditions used by Purdy.

The null observed by Purdy near 507 nm is not associated with the Bezold-Brucke Effect. It is accounted for in thiswork by two mechanisms, the transition within the brain between depending on the P– and Q–signals to define theperceived color of the scene element and the relative insensitivity of both the P– and Q–channel signals to changes inwavelength in this wavelength region.

17.2.6.5.3 A projected Bezold-Brucke Effect near 395 nm

It can be predicted that an additional hue shift can be induced in the region of 395 nm that can be considered anadditional Bezold-Brucke Effect. The Effect could be elicited by a change in the relative signal level in the shortwavelength channel relative to that in the ultraviolet wavelength channel. It could result from a change in balancebetween the short wavelength and ultraviolet sensitivity favoring the short wavelength component. This Effectwould be easily recognized in the aphakic eye and could account for part of Judd’s findings related to the shortwavelength sensitivity of young eyes. For complete young eyes, it would appear as an increased sensitivity in theregion between 400 and 420 nm. If evaluated in the same manner as Purdy, a hue shift would be reported by thesubject.

In the aphakic eye, it should be possible to cause the spectral response function to exhibit three anomalous peaks, at395, 487 and 580 nm, for a short period by suddenly reducing the illumination 10:1 in the mid wavelength regionand by 3:1 in the ultraviolet region relative to a nominal pre-adaptation with a sufficiently broad spectral band source (Nominally 8683 Kelvin). Figure 17.2.6-14 illustrates in caricature the expected results. When combined with theeffect on the O–, P– and Q– channels, hue shift nulls near 385, 476 and 571 nm could be expected.

The peaks in this figure actually reflect the nulls in the O–, P– & Q– channels at about 400 nm, 494 nm and 572–578nm respectively. The last range is due to the uncertainty in the peak wavelength of the L–channel at the currenttime.


Figure 17.2.6-14 (Color ln) The proposed three peaks in the aphakic human spectral sensitivity function underforced conditions. Vertical indicia have been added at 0.342, 0.437, 0.532 and 0.610 microns for reference. Notethe residual presence of the long wavelength absorption characteristic near 0.625 microns.

17.2.6.6 The so-called Purkinje Shifts of the literature

In the recent literature, writers have not always clearly differentiated between the Purkinje Effect and the Bezold-Brucke Effect. Furthermore, they have spoken in terms of a shift in the wavelength of the peak composite spectralabsorption. This has caused a problem. When they speak of the normal Purkinje shift to 580 nm, they consider itnormal for such a shift to be toward longer wavelengths. However, when they speak of the Purkinje shift to about487 nm (actually the appearance of one of the Bezold-Brucke peaks), they speak of it as abnormal. Both of theseEffects are caused by a rise in a local maximum due to logarithmic signal summation and not due to an actual shift inwavelength due to an underlying physical mechanism.

17.2.6.7 The use of the above Effects in precision research

The use of artificial chromatic adaptation offers a unique capability to determine the precise half-amplitudeabsorption parameters of the individual spectral channels. By investigating the above special Effects in detail, theheight and width of the abnormal peaks could be defined. These parameters would support the precise definition ofthe spectral absorption of each chromophore (full width half amplitude, FWHA, values) as found configured in theouter segments.

17.2.7 Luminance threshold & other descriptors related to performance

The subject of minimum luminance differences that can be achieved as a function of average luminance level has notbeen an important one. However, it does provide some important information concerning the noise performance ofthe eye. Traditionally, the overall task has been attacked from three perspectives:


204Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg. 569205Krauskoph, J. & Reeves, A. (1980) Measurement of the effect of photon noise on detection. Vision Res.vol. 20, pp 193-196

+ Measuring the luminance discrimination capability of the eye, using either a bipartite field or two concentric fields,under full illumination using “white light.” These methods appear to provide a general profile of the function but donot appear to give precise information.

+ Measuring the luminance discrimination capability as above using some form of flicker test. As will be discussedin Section 17.3.3, this technique is fraught with difficulties related to temporal processes in the visual system.

+ Measuring the luminance threshold immediately following sustained illuminance at the desired level. Theassumption being that the adaptation mechanism and any other time constants involved have not had time to change.

Wyszecki & Stiles discuss this subject in some detail204. The discussion is couched in terms of rods versus conesinstead of the underlying noise performance of the eye. This alternate approach will be discussed in the followingsections.

17.2.7.1 The Noise and threshold characteristics of the human eye

The evaluation of the limiting performance of the human eye requires close attention to each segment of thephotodetection and the signaling systems of the retina and both the computational and cognitive systems of the brain. Convention would suggest that the eye is noise limited, like most man-made systems at low signal levels. However,personal observation of the psychophysical performance of the eye suggests it is not noise limited. Systemsemploying thresholding techniques need not be noise limited. They may be threshold limited to avoid needlesssignal processing, and in the case of animals--distraction.

Proper analysis of the noise performance of the visual process requires very detailed knowledge of that process. Many previous investigations have assumed very simple models of the signaling channel(s)205. These models did notrecognize the unique nature of the long wavelength channel nor did they recognize the possibility of different noisemechanisms limiting performance in different illumination regimes.

As in any good detection system, it is important to provide signal amplification as early in the system as possible. Otherwise, later signal processing stages may contribute noise to the overall signaling channel of a magnitudeapproaching that of the desired signal. Figure 17.2.7-1 shows a noise model of the visual process developed in thiswork. The details of cortical processing have not been explored in this work. However, it appears that the noisecharacteristics of the cortical circuits are due to a random process rather than a hard threshold.

As will become clear, the noise contribution of elements proximal to the photoreceptor cell is negligible in vision. Two separate noise regimes are of interest in vision: the RMS noise regime associated with low illumination levelsand the noise associated with the circuits of the CNS. Several investigators have shown an interest in the individualnoise events associated with the photodetection process. This is a largely pathological situation of little practicalvalue. It could have some value in determining the precise band gap associated with the first neural amplifier of thephotoreceptor cell.

The eye can be shown to be photon noise limited in the scotopic illumination regime. However, photon noisequickly becomes insignificant as the illumination level increases. It achieves a S/N ratio of at least 50 dB at themesotopic-photopic level transition. Above this level, the noise performance of the eye is of trivial concern. In theabsence of any input illumination, the noise sources of the physiological materials of the eye are the primaryperceived noise source. They are also of trivial practical importance.


206 Baylor, D. Lamb, T. & Yau, K-W. (1979) Responses of retinal rods to single photons. J. Physiol. vol.288, pp. 613-634 207Baylor, D. Nunn, B. & Schnapf, J. (1984) The photocurrent, noise and spectral sensitivity of rods of themonkey, Macaca faxdicularis. J. Physiol. vol. 357, pp. 575-607

Figure 17.2.7-1 The noise model of the visual system. The position of the adaptation amplifier makes the initialnoise source dominant.

There are several potential noise sources in the system related directly to the temperature of the biological tissueinvolved. The first is the noise associated with the liquid crystalline material of the chromophores. The second isthe noise associated with the base region of each of the Activas, serving as adaptation amplifiers, found in thedendritic structure of the photoreceptor. The third potential source is in the base region of the (Summing) Activaalso located within the neuron of the photoreceptor cell. It is important to note two parameters. The operatingtemporal bandwidth of each photoreceptor channel is quite small, typically less than 200 Hertz in animals. Incalculating the amplitude of the noise current at a given point in the system, this low bandwidth is important. Second, the very high amplification of each of the adaptation amplifiers cause the signal current reaching thesumming amplifier from each adaptation amplifier to be significantly higher than the noise current due to thesumming amplifier. The signal current to random noise current at this point is quite high, even under very low lightlevel conditions. This has been amply demonstrated in Figure 2 of Baylor et. al206 who present the generatorwaveform in response to a single photon being absorbed by the chromophore. An individual photon elicits aresponse that is about 18 times the RMS noise level in the case of the toad based on the suction electrode technique. Baylor, et. al. used 520 nm light applied perpendicular to the long axis of the photoreceptor and effectivelyemployed the isotropic absorption characteristic of the photoreceptor that is not employed in vision (In laterexperiments, they converted to end on illumination in order to measure the anisotropic absorption actually employedin vision).

Both the adaptation amplifier and disk stack noisesources can be described as energy threshold devices. They exhibit an energy threshold of about 2.0electron-volts or higher for the adaptation amplifiernoise source. The thermal noise source attempting togenerate free electrons within the base region of theActiva has an RMS energy of between 26 and 27 mVdepending on specimen temperature. The ratio ofnearly 8:1 between these values suggests that very fewnoise electrons are generated by this source. Thesituation is similar in the disk stack. The individual chromophore material has a energy threshold that determines itsspectral characteristics. The threshold associated with the long wavelength absorption is also involved in the noiseprocess. This threshold is near 2.6 electrton-volts for the S-channel, 2.15 electron-volts for the M-channel, and 1.84electron-volts for the L-channel. These values are all much higher than the 26-27 electron-volt thermal energy of thematerials. Although the L-channel is slightly more noisy, the channels also exhibit a ratio of at least 8:1 between thethreshold and the RMS noise source.

Combining the two noise sources in the noise model is complicate mathematically because of the internal thresholds. However, the number of noise electrons exceeding the threshold in the combined circuit is quite small. Baylor, et.al207. have measured the rate of occurrance of noise like events at the by capturing all of the current emanating froma single photoreceptor using their suction pipette technique with monkeys. They report a rate of generation of 0.006events per second per photoreceptor (one every three minutes). This rate is measured after the amplification of thenoise signal by the adaptation amplifier. With the experiments being performed in darkness, it can be assumed thatthe adaptation amplifier was operating at a gain of near 3400:1. Subsequent noise sources in the visual system are ofsimilar thermal energy, face similar threshold levels but are not amplified like the above sources. These subsequent


208Rose, A. (1977) Vision: human versus electronic. In Vertebrate Photoreceptors, Barlow, H. & Fatt, P.eds. NY: Academic Press. pp. 1-13

sources can be and have been neglected in the figure.

Baylor, et. al. suggest there is a thresholding process in the signaling channel to account for the very low noise leveland that it might be near the photoreceptors. The above model provides a more detailed description of the actuallocation.

The remainder of the noise model includes several other features of interest. First, the summing channels of thesignal manipulation stage would increase the apparent rate of noise electron generation in each channel. However,the rate would still be quite low. Nevertheless, the parasol ganglion cells of the projection stage do incorporate athreshold and a significant capacitance in their input circuit. This capacitance acts as an integrator ahead of thevoltage threshold that further suppresses the transmission of any noise through the summation channels of thesystem. The differencing channels of the summation stage can cause a significant increase in noise level forconventional thermal noise. However, for the individual noise pulses being discussed here, they act similar to thesumming circuits. There is no threshold in the midget ganglion cells. Therefore, any noise passing through thesecircuits will be passed on to the brain. No analysis of the noise performance of the brain is offered here. However,it is likely that each circuit following the decoding of the projection signals does exhibit a minimum signal threshold. This is especially apparent in the chromatic circuits that cease functioning at ligher illumination levels than theluminance circuits.

A special feature of the L-channel of the visual system should be noted. In order to maintain the excellent noiseperformance of the eye and still detect the lower energy photons in the red end of the spectrum, a compromise wasmade. The energy threshold required to excite the base layer of the adaptation amplifier Activa was maintained atabout 2.0 electron-volts. As a result, the energy of two photons must be accumulated in the chromophore materialbefore the necessary energy level is achieved and excitation of the Activa occurs (coincident with de-excitation ofthe chromophore material). This cannot be described as a two photon process because each photon is absorbedindependently. However, it can be described as a two exciton process in quantum terms since it takes two excitonschanging state within a very short time interval to cause an electron pair in the base material of the adaptationamplifier Activa. In statistical terms, this causes the signal level in the L-channel to decrease faster than theequivalent signal level in the other channels. This is the ultimate reason why the animal eye losses sensitivity in theL-channel before doing so in the other channels.

Although minimal signal amplification is provided further along the signal path, the high signal level due to theadaptation amplifier makes any subsequent noise sources negligible. Based on this situation, the noise performanceof the eye, particularly the human eye, can be calculated based only on the quantum statistics of the incident imageand the quantum efficiency of the optical system of the eye and the Outer Segment of the photoreceptors. This hasbeen done and scenes have been prepared to illustrate the performance of the eye under low light conditions208. It isrelatively easy to demonstrate the eye operates under quantum noise limited conditions because quantum noise isdefined entirely by the illumination level in the image. Under quantum noise limited conditions, the noise levelchanges with the square root of the input illumination level. Under thermal noise limited conditions, the noise levelis independent of the input illumination level.

[xxx rewrite ]The quantum efficiency of the animal visual system, particularly in the chordate and other complex eyes, is nearly100% because of the way the disks are stacked along the optical path followed by the incoming photons. Nearly nophotons, on a percentage basis, reach the RPE or other equivalent surface behind the chromophore material. Thismakes the retina of the animal eye one of the most highly efficient photon detectors known. It is in the same class asthe misnamed “solid state photomultipliers” which are actually quantum mechanical semiconductor absorbers justlike the eye. The retina is about 10 times more efficient a photomultiplier tube based on a photoemissive surface and


50 to 100 times more efficient than a photographic film.

It is not widely known but the “night goggles” worn by the military in this age are still not aseffective in true low light conditions than the famous German naval binoculars of World War II. This is because the product of the collection efficiency of the binoculars times the quantumefficiency of the eye is higher than the similar product of the collection efficiency of the smalleraperture night vision glasses and the quantum efficiency of the photo-emissive surface used in theglasses. The true value of the night vision glasses is in two of their properties. The high signalamplification of the glasses allow a pilot or driver see an image of the scene at a similar brightnesslevel to that of his instrument panel. This allows him to correlate the inputs from the two scenesand perform his mission. They also incorporate a saturation circuit not unlike that of theadaptation amplifier in the eye. The amplifier gain drops precipitously when a very brightillumination source appears in the field of view of the night vision goggles, therreby protecting thesensitivity of the pilots eyes. [xxx rewrite ] This is accomplished by introducing a poorlyregulated power supply into the goggles electronics. This is exactly the same mechanism used tocontrol the sensitivity of the animal eye. However, the electronic circuit has been tailoreddifferently.

17.2.7.1.1 Critical circuit features in low light vision

There seems to be a logical set of design rules at work in the visual system that control its performance at low lightlevels. Individual rules apply to each portion of the visual system. The primary rule is do not process uselessinformation in the form of ordinary data. The question to be answered is how do these rules apply to the three datastreams, luminance, short wave chrominance and long wave chrominance, entering the brain?

The luminance channel has a threshold at the input to the parasol type ganglion cells. This threshold prevents actionpotentials from being generated in the luminance channel if the luminance signal is below a specified level whendelivered to the threshold. If the illumination is so low that, even with the adaptation amplifier operating atmaximum gain, the signal level is below this threshold, no action potential related to luminance is transmitted to thebrain. There is no obvious threshold in the midget ganglion cells associated with the two chrominance channels. These cells produce action potentials under quiescent conditions. However, the time interval between pulses in bothchrominance channels approaches the quiescent pulse interval under very low input signal conditions.

A possible operating scenario is as follows: The photodetection channels are each quantum noise limited inperformance due to the high energy level required for excitation. This level is far above the thermal noise energylevel at biological temperatures. The adaptation amplifiers are similarly immune to noise due to thermal energy atbiological temperatures. This is due to the wide band gap of the material constituting the base region, hydronium. With the high potential amplification of the adaptation amplifier, the signal at the pedicle of each photoreceptor isalways quantum noise limited. There is no noise source farther down any of the three signal chains that is of themagnitude of the amplified and quantum noise limited signal.

The noise performance of the chrominance signals created by the lateral differencing circuits is a function of thespatial integration within the retina. If only two photoreceptors were employed as inputs to a single differencingcircuit, the output signal would be inherently 1.4 times noisier than the individual input signals. However, thisnumber decreases as more photoreceptor signals are averaged in the input structures of the lateral cells. It appears toequal 1.00 in most situations. Lacking a threshold at the input to the midget ganglion cells, at sufficiently lowillumination levels, noisy information will be encoded onto the action potential pulse stream and transmitted to thebrain.

The luminance signal is created by combining the individual photodetection channels associated with the different


209Spillman, L. & Conlon, J. (1972) Photochromatic interval during dark adaptation and as a function ofbackground luminance. Jour. Opt. Soc. Am. Vol. 62, no. 2, pp. 182-185

chromophores at the photoreceptor pedicles. The summation process tends to reduce the noise compared to that inthe noisiest input channel. However, the noisiest channel could be quite noisy. It can be shown that the square-lawsignal associated with the L-channel will be the noisiest channel at a given illumination level. It can also be shownthat both the signal and noise level applied to the adaptation amplifier in this channel falls in amplitude faster thanthe other channels. The result is that this adaptation amplifier reaches maximum gain before the other amplifiers. Under this condition, the low signal and low noise associated with the L-channel has little impact on the combinedluminance signal. The signal and noise level applied to the parasol ganglion cell threshold under low lightconditions is controlled by the sum of the M-channel and S-channel signals.

Under this scenario, three performance conditions must be considered. Two are related to impaired performance. The third is shutdown of the visual system.

(1a) As the illumination level decreases through the mesotopic range, the chrominance discrimination in bothchrominance channels becomes poorer and poorer. The long wavelength discrimination deteriorates faster than theshort wavelength discrimination. (1b) The long wavelength sensitivity in the L-channel spectral range alsodeteriorates as lower level are reached within the mesotopic range.

(2) When the scotopic illumination range is reached, the illuminance channel is still well above the parasol cellthreshold. Although both chrominance channels are still active, they are operating in the null condition. The actionpotentials transmitted to the brain have a pulse to pulse spacing that is near the quiescent spacing except for a smallamount of modulation due to noise. The brain may incorporate a threshold at the output of the chrominance actionpotential decoder. This threshold would suppress any extraneous chrominance patterns due to different noisy signalsarriving relative to different locations in the field of the retina.

(3) When, the luminance signal becomes so low at the input to the parasol ganglion cells, that it does not exceed thethreshold, no action potentials are generated by the cells. No action potential pulses are received at the luminancechannel decoder in the brain. The brain registers a null condition. No image is formed. There is no sensation ofblack. Anything perceived by the brain at this illumination level must come from internal sources.

17.2.7.1.2 A combined achromatic/chromatic threshold performance graph

Spillmann & Conlon have provided two graphs describing the measured threshold performance of the human eyeattempting to separate the achromatic and chromatic thresholds209. This data is in contrast to the many verbaldiscussions concerning the chromatic performance of the eye as it relates to the conventional adaptationcharacteristic. The presentation appears to be in good agreement with the theoretical model presented here. Thefollowing Interpretation of the graph relies heavily on the signaling channels defined in this work. The most criticalassumption is the separation of the signaling path into a summation (luminance) path and a differencing(chrominance) path. Based on this differentiation, the equations for the signal to noise ratio at a given point in thevisual system are seen to be different and can be described. What is not known is the threshold signal to noise ratioof the human eye and the shape of the signal pulse at the output of the photoreceptor cells, the Class D waveform, atthe lowest illumination levels. The data points were collected using a test light source only partially characterized, a1° square created with a tungsten source viewed through a Wratten #61 filter (catalog half-amplitude points 503 &556 nm. by interpolation) and measured with a Crozier-Holway three channel visual discriminometer defined in1939. A 1.5 mm. effective aperture was used in the Maxwellian projection system. The subject experienced a 0.2second test illumination at 6° on the horizontal meridian in the nasal field. The illumination was described as havinga dominant wavelength of 535 nm. When appropriate, a 30° circular surround was provided using a “white light”from a tungsten source. At other times, the eye was pre-exposed to a “white light” from a tungsten source providing


210Tilton, H. (1977) Scotopic luminosity function and color-mixture data J.Opt. Soc. Am. vol. 67, no. 11 pp1494-1501

Figure 17.2.7-2 Combined chromatic and achromaticthresholds for the steady state case showing asymptotesdescribing the three operating ranges, (A), internalthreshold limited, (B), quantum noise limited, and (C)short term dynamic range limited . Open circles,luminance data. Filled circles, chrominance data. Datafrom Spillmann & Conlon (1972)

a 4173 mL. luminance over a subtense of 75° by 90°. Based on the available parameters, it is reasonable to assumethat an insignificant amount of radiation was applied to the S- and L- photoreceptor channel during the test interval. At the lowest levels, the time delay of the P/D equation is probably not important in the data collection. However,the rise time of the Class D waveform may be similar to the 0.2 sec. exposure interval. This condition would resultin a luminance signal pulse that is non rectangular and of less than expected amplitude when perceived by the brain. In the absence of signals from the S- and L- channels, the signal in the chrominance channel would be expected to besimilar temporally to that of the luminance channel. Looking forward to more precise data in the future, this analysiswill focus on the concept.

The results for the steady state case are shown in Figure 17.2.7-2. Looking first at the open circles representing theluminance data, at the lowest radiance levels (only a limited region of the visual spectral range is in use and the termluminance is inappropriate), the threshold appears to be independent of the radiance. It is proposed that thethreshold in this region is due to the internal threshold of the perceptual stage of vision. The theoretical threshold istherefore shown as a horizontal line (A). Above this region, the data points are well represented by a straight linewith a slope of one-half (B). Such a region is indicative of a photodetection system limited by quantum noise at itsinput. At higher radiance levels, the data points can be represented by a straight line with a slope of one (C). In thisregion, and extending to higher levels as the adaptation amplifier begins to lower the overall circuit gain, theperformance of the system appears to be limited by the short term dynamic range of the signaling channel. Althoughthe data points representing the transition from the internal threshold limited case to the photon noise limited case arefew, the gradual transition from one regime to the other suggests that it is also stochastic. The mathematics wouldimply the internal threshold is also a stochastic process.

The distance between the open circles and the closed circles has traditionally been defined as the photochromaticinterval. The term has usually been loosely defined. Sometimes it is presented as a function of spectral wavelengthas measured under a specific set of radiant (more often photometric) intensities. Tilton provided such a definitionduring the 1970's210. However, his work was moreconceptual and based on the standard luminosityfunctions, V(l) and V’(l) that he took to represent actualrather than smoothed spectral data.

The asymptotes drawn in the figure suggest that thecrossover between mesotopic and photopic visionoccurs at a relatively high level relative to the scotopicto mesotopic transition, with the mesotopic regionextending over four orders of magnitude. It appearsthat these are not the optimum asymptotes and thatadditional laboratory data would probably indicate amesotopic to photopic transition one or two orders ofmagnitude further to the left.

Looking at the chromatic data points, a similarsituation is observed at the lowest radiance levels. Thechrominance threshold can be represented by ahorizontal line. The line is at a higher threshold levelfor at least two reasons. First, is the fact that thedifferencing function of the chrominance channelaffects the signal level applied to the perception


211Goldberg, S. Frumkes, T. & Nygaard, R. (1983) Inhibitory influence of unstimulated rods in the humanretina: evidence provided by examining cone flicker. Science, vol. 221, pp. 180-182

process. Second, the amplitude of the signal in the differenceing channel is a function of the wavelength of theirradiance. As shown in Section 17.3.2, the choice of irradiance with a spectral peak near 535 nm. is less thanoptimum from the perspective of chromatic perception. However, its choice was a logical one on the grounds ofminimizing the excitation of the adjacent chromatic channels. In their discussion, Spillmann & Conlon developedthe concept of a “photochromatic interval” to describe the ratio of the achromatic to the chromatic threshold. In theirpaper, this photochromatic interval reached 47 dB (4.7 log units) in the region they describe as below 10-4

millilamberts. It is proposed here that the photochromatic interval is a function of wavelength. Further experimentis needed to confirm and quantify this relationship. For radiances higher than the labeled 100 millilamberts, thechromatic data points appear to follow the achromatic data points quite closely in accordance with the proposedlinear threshold versus radiance relationship caused by short term dynamic range limitations in the signaling channel.

Spillmann & Conlon carefully coached their subjects concerning concentrating on reporting a threshold based ononly color or only brightness. The results of such coaching are extremely difficult to quantify, especially when onlya few data collection runs were made. They also discuss their difficulty in data reduction using a techniquedeveloped by Crawford in 1937. Because of these difficulties, the data points between 0.1 and 100 millilambertswill not be considered from a theoretical perspective here. It is likely that additional experimentation would showthat the horizontal asymptote should be extended to the intersection with the 1:1 asymptote and the dip shown in thedata points, of 10-17 dB, is due to the difficulty a human has in making independent observations in this region.

Goldberg, Frumkes & Nygaard211 performed a set of experiments similar to Spillmann & Conlon, except sevendegrees temporal of fixation. However, they did so under a much less controlled environment, no definition of“green” or “yellow,” etc., and using observers with no psychophysical training, except for one of the principles. One of their curves for green light at a 5 Hz. flicker rate conforms to Spillmann & Conlons luminance curve. Itwould also be described as a luminance response based on Hecht’s papers. They did not present a rigorous theoryon which to base their discussion and did not draw firm conclusions based on their data.

17.2.7.1.3 Discrimination of luminance differences

If one ignores the nature of the threshold for luminance perception in vision, it is possible to simplify the discussionto merely one of the perceivable change in illumination as a function of illumination. Wyszecki & Stiles reproducean early figure from Steinhardt (1936) showing the observed characteristic under these conditions using a “‘white’stimuli and with field sizes larger than the rod-free area.” Unfortunately, the figure does not give data points, onlythe proposed relationship. The relationship does show a saturation value of about 70:1 at high light levels inagreement with this work. It also shows an unexplained deviation in the region of 0.01-0.001 candela per squaremeter just like the data of Spillmann. However, the curve is shown proceeding toward unrealistic ratios at low lightlevels. The curve should become asymptotic to 0.0 at ever lower light levels. With this understanding, the curve(although representing a differential) exhibits the same functional relationships as in the previous figure fromSpillmann.. In the scotopic range, the differential is limited by internal stochastic noise and approaches log Δl/l = 0at the lowest levels. In the mesotopic regime, the adaptation amplifiers are operating at maximum gain and theluminance discrimination function has a slope of 0.5. The differential is limited by stochastic (photon in this case)noise. In the photopic regime, the adaptation amplifiers attempt to control the average signal level applied to thesignal processing stage. As a result, the luminance discrimination function exhibits a very low slope. This slope isapproximately equal numerically to the inverse of the exponent in the transfer characteristic of the adaptationamplifier. At maximum value, the function exhibits a value of about 70:1. In the hypertopic regime, the luminancediscrimination function reflects saturation in the signal manipulation stage. It will eventually return to 0.0 (butprobably not before intense pain is felt by the subject).

17.2.7.2 Thresholds as a function of field position


212Liu, G. Volpe, N. & Galetta, S. (2001) Neuro-Ophthalmology: Diagnosis and Management. NY:Saunders213Aulhorn, E. & Harms, H. (1973) Visual perimetry In Handbook of Sensory Physiology, Jameson, D. &Hurvich, L. ed. Vol. VII, No. 4 NY: Springer-Verlag, pg 118

Liu et al212. have discussed the sensitivity of the eye based on perimetry using a colloquial expression, the “island ofvision.” Figure 17.2.7-3 compares the concept using both a three-dimensional and two-dimensional presentation.

The island of vision clearly shows a peak sensitivity, along the z-axis, that is limited to a very small radius. Thisregion is assumed to be limited to the foveola of the retina.

Aulhorn & Harms have provided provocative data on the threshold performance of the human eye as a function offield position with background illumination as a parameter213. The reference does not describe the size of the testsource and most of their papers are in German. Figure 17.2.7-4 shows their data taken along the zero degreemeridian. Their units of measure are archaic but the results are quite informative. As a result, the meaning of thescales and their discussion must be looked at closely. It is difficult to interpret L/ΔL in their context. It appears thatit is equivalent to Lmin/ΔL since ΔL’s greater than L are present in the data. The use of (Lmax - Lmin)/(Lmin + Lmax), themodulation, would be easier to understand. The fact that the fovea goes from less than average to greater thanaverage sensitivity as a function of background is interesting. The sensitivity appears to vary with field position inboth acuity and vascular system capability.

Note the inversion of the sensitivity function as a function of background illumination. The peak sensitivity isalways at the point of fixation for low background conditions. At very low backgrounds, the peak sensitivity at thefixation point may be as much as one order of magnitude poorer than that of the surrounding retina. Under highbackground conditions, the maximum absolute sensitivity may not be associated with the foveola.

Figure 17.2.7-3 The island of vision (left) based on threshold (static) perimetry and the same information plotted as“kinetic” perimetry.. From Liu et al., 2001.


Figure 17.2.7-4 Profile perimetry along the zero degree meridian for 8 different states of adaptation. Average valuesfor 10 normal subjects. The area or diameter of the test source was not given. Units are in Apostilb (asb). One asbequals 1/π candela/m2. From Aulhorn & Harms, 1973.

17.2.7.3 Defining the quantum efficiency of vision

Many investigators have chased the holy grail, attempting to define the quantum efficiency of the visual process. Unfortunately most of them did not have an adequate model of the process they were trying to evaluate (Section7.2.4).

Most of the investigations focused on psychophysical experiments seeking to define the probability of detection of abrief flash of only a few photons after (putative) complete dark adaptation. These investigations have failed todescribe many features of the visual system that are critically important to the interpretation of these studies. xxxInherent in these studies has been the assumption that the quantum efficiency at threshold was the characteristic


214Levick, W. & Zacks, J. (1970) Responses of cat retinal ganglion cells to brief flashes of light J Physiolvol 206, pp 677-700215Teich, M. Prucnal, P. Vannucci, G. et. al. (1982) Multiplication noise in the human visual system atthreshold: 1. Quantum fluctuations and minimum detectable energy J Opt Soc Am vol 72(4) pp 419-431216Hecht, S. Shlaer, S. & Pirenne, M. (1942) Energy, quanta and vision J Gen Physiol vol 25, pp 819-840217Baylor, D. Lamb, T. & Yau, K.-W. (1979) Responses of retinal rods to single photons J Physiol vol288, pp 613-634

value of the system at all illumination levels. The P/D equation derived in this work clearly shows that response ofthe photoexcitation/de-excitation process does not resemble or employ the photoelectric effect described in detail byEinstein in 1905. The mechanism involves the creation of bound but excited electrons within a liquid crystallineorganic material at a very high absorption and hence a high quantum efficiency. However, the electrostatic fieldswithin the material are not conducive to a rapid transport of these excitons from their point of excitation to theirpoint of de-excitation when only a few excitons are present. As a result, the generation of free charges as a result ofthe excitation of the material by light is smeared out over a period of time. This situation was noted indirectly byLevick & Zacks214 as reported in Teich, et. al215. Levick & Zacks assumed the action potential generation rate at aganglion cell had a direct relationship to the absorption of photons.

Determining the quantum efficiency of any process requires meticulous attention to the details of the experiment andhow the quantum efficiency is defined (Section 7.2.4). As an example, is the loss in efficiency due to a sparse arrayof detectors in a two-dimensional array counted against the efficiency of the detectors or the efficiency of the arraymanufacturing process. This is a particular problem based on the conventional wisdom that the retina containsphotoreceptors that are only active over a part of the illumination regime (the concept of rods and cones). Howmuch of the surface of the retina in a given region is dedicated to photoreceptors active at the target illuminationlevel used in the tests. The position of this work is that there are no achromatic photodetectors described as rods. All of the active area is filled with photoreceptors active at all light levels. The fill factor of this array based on auniform array of adjacent two-micron diameter photoreceptors is very high. This would suggest a very highgeometric efficiency if all of the photoreceptors exhibited equal quantum efficiency for the wavelength of lightinvolved in the test.

A variety of methods of measuring the quantum efficiency of a light stimulated system exist. The most obvious is tocount the charges generated at some point in response to a known number of photons stimulating the transducer. However, at the levels of interest here, that experiment becomes a study in the statistics of quantum mechanicalevents at best. In the case at hand, access to the initial electron stream is not available in the first place. Some of themathematical studies in the literature, such as Teich, et. al., have employed very sophisticated mathematics andwere largely limited by the quality of the data and test protocols used to collect the data.

Hecht, et. al216. and many other investigators have used the charge generation to incident photon approach atthreshold levels except they operated under extreme constraints. They did not control or understand the signalprocessing path between the light generating test set and the response generated by the subject under psychophysicaltest conditions. Even under these constraints, Hecht, et. al. estimated the efficiency of the eye to be in the vicinityof 7 to 20%. More recently, Baylor, et. al. have measured similar values using an electrophysiological approachand the toad217. They concluded the quantum efficiency (photon in to total integrated charge out) is on the order of11% to 17% when measured at the axon of the photoreceptor under near threshold conditions. However, like in theLevick & Zacks activity, the output current waveform did not exhibit a shape suggestive of the input photon flux andit occurred following a significant delay. It must be pointed out that the “rod” evaluated by Baylor, et. al. exhibiteda distinctly M-channel characteristic, not a broadband achromatic sensitivity. They pondered this fact in the paper.

[xxx rewrite based on sec. 7.2.4 ]An alternate method of determining the quantum efficiency of a light related process under operational conditions


involves measuring the threshold contrast change at a given light level and relate that threshold to the RMS variationin the associated steady state light level. This method involves the assumption that the light level used causes thequantum-statistical noise of the light to be the dominant noise in the system. This is easily shown to be trueexperimentally and examples can be found in the research literature. The proof involves showing that the RMSnoise, e. g., the variance associated with the signal is accurately described by the square root of the average photonflux. This method leads to the determination of the quantum efficiency of the initial process at levels significantlyabove the threshold level. The result of this process suggests the quantum efficiency of the visual system is at leastas good as any man-made detection system, and is in the 80-100% range.

As an aside, the fully dark adapted human eye is still able to outperform the best available man-made imagingsystems when employing optical systems of equal performance. These man-made systems, typicallymanufactured using silicon as a substrate, can reach an easily measured 60% quantum efficiency atwavelengths in the 500-1,000 nanometer range. They can also reach this value in the 400-500 nanometerrange if special manufacturing techniques are used (known as back side thinning).

Under carefully controlled conditions, the quantum efficiency of the photodetection process of a singlephotoreceptor cell, PC, approaches 100% (>80% when dark adapted for over 20 minutes) through the use of aunique set of configuration and operating parameters (Section 7.2.4).

Demonstrating the quantum efficiency under specific conditions is a mathematically challenging task. The followingsub-sections will outline the appropriate protocols and conditions while employing a variety of simplifications.


Dealing with light, especially at low incident levels is an inherently statistical process. Light itself is a stochasticprocess, involving random events and necessarily probabilities. Importantly, the spectral channels defined by thespectral absorptions of the individual chromophores do not employ precisely the same mechanisms. The long-wavelength channel operates distinctly differently. To develop these differences, the applicable laws of probabilitytheory are shown in Figure 17.2.8-1. The upper portion of the figure are textbook representations of the applicablelaws of probability theory written for the discrete case, rather than for the distributed function case which involvesintegral calculus.

The additive rule can be simplified by dropping the last term if the events A & B are not mutually exclusive. Asgenerally accepted, there is significant overlap between the spectral absorptions of the individual neural sensoryreceptors. In the general case, the spectra are not mutually exclusive but a specific photon can only excite one or theother of the pair. This introduces the subject of replacement or no replacement in a specific trial in an experimentbut this subtlety will not be introduced here. In the following development, it will be assumed that all photonstreams are monochromatic and occur at the wavelength of the peak sensitivity of one of the neural sensory receptorsof stage 1.

Immediately below the additive rule is an expansion of that rule to three independent but exclusive terms. The rulecan be expanded to four independent terms. In the following discussion, each of the letters A, B, C & D can beassociated with a separate spectral band, UV, S, M & L. However, the mechanisms associated with UV, S & M arethe same. Due to this fact, the UV term will be ignored and A will be associated with the S–channel, B will beassociated with the M –channel and C with the L–channel. Each term will be considered independent. No mutualexclusion will be asserted.

The conditional rule states: the conditional probability that A has occurred relative to the hypothesis that B hasoccurred, is given by the joint probability that both A and B have occurred divided by the probability that B hasoccurred.


The multiplication rule can be looked upon as a modification of the conditional rule by inference.

Bayes’s Theorem is seen to be a rearrangement of the multiplication rule using the two terms on the right.

Finally, the independent event rule shows that the probability of two independent events happening within a giventime period is the product of the probability of each event occurring within the same time period independently.

- - - -

In the visual modality, the stimulation of the individual sensory neuron is a multiple step process. A photon mustinitially create an exciton within the electronic structure of the chromophore, a photo-exciton process. One or moreexcitons within the chromophore must then create a free electron in the electronic structure of the sensory neuronassociated with the chromophore, an exciton-free electron process (that can be considered an acoustic transfer of aquanta of energy between two structures. The result of a photon exciting a molecule of the chromophoric coatingof a disk is the creation of a single exciton. Since the chromophoric material is present as a liquid crystalline state ofmatter, the stimulation of a single molecule is tantamount to the stimulation of the whole liquid crystalline assemblyof molecules to an initial quantum-mechanical level. The stimulation of any molecule of the chromophore in thesame liquid crystalline assembly causes the stimulation of the whole liquid crystalline assembly to a higher quantum-mechanical level (Section xxx).

Each sensory neuron of the visual modality exhibits a minimum quantum-mechanical energy threshold, usually

Figure 17.2.8-1 The laws of probability theory applicable to visual sensing ADD. These laws can be appliedselectively to the operation of the neural sensory receptor channels. See text for their interpretation.


labeled Vγ. Vγ is believed to equal ~2.10 to 2.20 electron-volts based on the work of Sliney (Section 17.2.5.5.2xxx). To excite a sensory neuron, the chromophoric material must be able to transfer an exciton to the neuroncontaining this energy, equivalent to a photon with a wavelength of less than ~590-560 nm respectively nm.

This energy requirement indicates that no single photon of light with a wavelength significantly longer than about590 nm can not excite a visual sensory neuron. However, excitons with the energy of multiple photons can excite avisual sensory neuron. This is the mechanism used in the L–channel sensory channel of vision. The energy of twophotons are summed within the energy band of the L–channel chromophore before that energy is transferred to thesensory neuron, generating a free electron. This process is described as a 2-exciton process to distinguish it from a2-photon process as used in other applications within the light regime. Thus, in the L–channel, centered at either610 or 625 nm (2nd order and 1st order analysis respectively), two photons must be used to create a single exciton thatis capable of exciting the sensory neuron thereby creating a single “photoelectron.” This 2-exciton process hasrepercussions. The slope of the 2 exciton process on a graph of sensory neuron stimulation versus light stimulationintensity is twice as high as that for a S– or M–channels.

It is proposed that all electrolytic neurons of the biological system exhibit threshold values, Vγ, of the samevoltage at normal exothermic biological temperatures (98.6 Fahrenheit, 37 Centigrade). The precise value ofVγ must be confirmed in the laboratory in the near future. Note, this value only affects the cut-in or turn-onof the neuron. It does not indicate a minimum signal amplitude after the neuron is biased into its operatingrange.

- - - -

The conditional rule will be applied to the L–channel where it will be asserted that at low stimulus intensities, twophotons must excite the chromophoric material associated with one disk, or one surface of a disk if the two sides arenot in quantum-mechanical contact within the time constant of the exciton excitation/de-excitation cycle. This timeconstant is typically quite long relative to the arrival of two photons.

- - - -

The noise performance of the human eye is described in Section 17.2.7.1.2 based on the work of Spillmann &Conlon. Their work focused on the M–channel of human vision. They identified a regime where the noiseperformance of the eye was independent of the stimulus intensity (internal noise limited region–as expected in thescotopic region), a region where the slope of the response was unity (photon noise limited--as expected in thephotopic region), and an area of intermediate slope (as expected for the scotopic region). It is proposed that theslope in the photopic region for the L–channel would have a slope of two due to the 2-exciton mechanism.

17.2.7.3.2 Structural configuration of the outer segments

[xxx see Section xxx ]

17.2.7.3.3 Define bleaching in the context of photon absorption at the outer segment

[xxx See Section 7.2.4 ]

17.2.7.4 Defining “bleaching” in the context of the P/D equation

Bleaching of the chromophores of vision has not been a major area of research since the 1960's. At that time, most


218Dartnall, H. (1962) The photobiology of visual processes In Davson, H. ed. The Eye, Volume 2; TheVisual Process. NY: Academic Press pp 323-365219Burns, S. & Elsner, A. (1985) Color matching at high illuminances: the color-match-area effect andphotopigment bleaching J Opt Soc Am A vol 2, pp 698-704220Litt, M. Young, R. & Schaffer (1971) Simple time reaction as a function of luminance for variouswavelengths Percep Psychophysics vol. 10, no. 6, pg 371+. Also in Uttal, W. (1981) pg 487

of the data was analyzed with respect to a simple first order exponential function218. Burns & Elsner wrote on thesubject in 1985219.

As described in detail in Appendix A, the Photoexcitation/De-excitation equation describes the absorption cross-section of the chromophores of vision in terms of the number of potential bound electrons within the ground state ofthe chromophores at a given time.

While individual chromophoric molecules have a very small absorption cross-section when illuminatedaxially, this is not true when they are assembled into the liquid crystalline state. When so assembled into aone molecule thick thin film, the effective absorption cross section is equal to the physical dimension of theliquid crystalline assembly multiplied by the ratio of the unexcited to the total of chromophoric moleculespresent.

As photons are absorbed and some of these bound electrons are transferred to the excited state, this pool of potentialbound electrons is reduced--until the excited electrons can be de-excited and returned to the pool. The degree towhich the pool is depleted is a direct measure of the effective change in absorption cross-section of thechromophores. This reduction in effective absorption cross-section is what is defined in empirical vision research asphysiological bleaching.

Care must be taken to differentiate between physiological bleaching defined above and bleaching due to solvation orother chemical treatment. The Rhodonines only act as the chromophores of vision when they are present in theliquid crystalline state and are supported by an electrical connection providing the de-excitation mechanism required. When the photoreceptors of vision are chemically processed in the laboratory in order to separate them from theretinal substrate or chemically analyze their content, the material is inevitably solvated. In solution, the Rhodonines(like other chemicals of the cyanine family) are essentially transparent. Under these conditions, the Rhodonines areproperly described as bleached by solvation, a form of pathological bleaching.

17.2.7.5 Reaction time as a function of illuminance

[ Old 17.2.8 has moved to 17.2.3 xxx]

The subject of reaction time relative to illuminance will not be explored in detail here. The field involves manyperformance parameters related to the motor system as well as the visual system. To acquire data on other animals,it frequently requires considerable species-specific training. Lit, Young & Shaffer have provided some data onhumans as a function of the color of the stimulus220. Other data is provided in Chapter 12 and Section 17.6.4.

17.3 The Chrominance Characteristic of the human eye

The following material will provide a theoretical foundation for the currently used measures of chromatic visualperformance. Contrary to the conventional wisdom dating from Thomas Young, this section will demonstratethat the human visual system is fundamentally tetrachromatic. The fact that the human retina is tetrachromaticwhile the complete eye is largely trichromatic influenced the development of the theoretical foundation. It wasnecessary to accommodate the tetrachromatic properties of the human visual system in the overall framework.


Simultaneously, it was desirable to provide a link with the available database that was assembled based on thetrichromatic assumption.

Contrary to the baseline assumed by the CIE, and derived from Young, the visual system is not based onadditive color. While the actual chromatic processing in vision is closer to the subtractive color suggested byHering, the subtractive color concept does not provide an adequate baseline either. Chromatic processing inbiological vision is based on a slightly more complex method that can be described most simply as differential colorwhere differential is used in the algebraic sense of a difference between two quantities. A more complete labelwould be multichannel, orthogonal differential color. The system takes the difference in signal intensity betweenpairs of chrominance channels determined by the spectral absorption of the chromophores. It then processes thesedifferences as if they were orthogonal to each other. In interpreting the result, it defines white as the achromaticpoint where the signal value in all of these channels is zero. This interpretation results in a perception of color moresimilar to the opponent theory of color proposed by Hering than the additive approach proposed by Young.

To provide a proper theoretical foundation, it will be necessary to extend a number of current definitions to a higherlevel of specificity and to propose alternate explanations of a number of phenomena (such as color constancy).

The task is complicated by the need to define color with greater precision as well as develop the concepts of colorcontrast more clearly.

A– Based on this work, the definition of color will be clarified considerably. Specifically, it will be shown that color(or a synonym for color) IS a physical property of objects. For clarity, it may be necessary to separate the intrinsiccolor of an object from the “perceived” color of the same object perceived and reported by an individual. Thesemantic difficulty associated with the expression “reported by the individual” will be discussed. Since such a reportis usually given in a specific language, the semantics used depends heavily on the training of the individual involved. As an example, which is truly red, an apple or a plum? If you said apple, which variety of apple is synonymous withred? What is actually needed is a mathematically precise method of specifying an absolute color. This section willprovide such a method for the first time.

B– The problem of defining the color of an object has recently become more significant with the wider use of imagerecording devices that display their record in real time next to the actual object of the recording. This problem is anold one. It was first encountered in the early days of color television development when it was found the perceivedimage of a monitor was different than the perceived image of the actual scene regardless of the linearity of thetelevision channel used. If the reproduced scene had a different luminous intensity than the initial scene, the humanobserver saw a differently colored image on the monitor. The industry determined it was more important to presenta pleasing picture to the audience viewing the monitor than it was to maintain “color constancy” between the sceneand the image.

C– This problem of reproducing an accurate or a pleasing rendition of a scene is shared in the graphics industry ingeneral. The limitations of the common 4-color subtractive color process used in printing is well known. It is soserious in the current day that Pantone is now promoting a 6-color subtractive printing process (the Hexachromeprocess) as more compatible with the requirements of the printer’s customers.

D– The problem of rendering a chromaticity diagram of acceptable precision is the same as that in rendering highquality printing. Pending the development of a rendering of the New Chromaticity Diagram for Research using amore precise subtractive color process, the Diagram proposed by this work will be presented in additive color on amonitor with the most important colors specified by the number assigned according to the Munsell renotationsystem.

When discussing color monitors and their use in psychophysical research, it is important to notethat monitors differ significantly in their spectral characteristics. Sproson has addressed this


221Sproson, W. (1983) Colour Science in Television and Display Systems. Bristol: Adam Hilger Ltd. pp 25-115222Graham, C. et. al. (1965) Vision and Visual Perception. NY: John Wiley & Sons pg 452223Byrne, A. & Hilbert, D. (2003) Color Realism and color science Behavior Brain Sci vol. 26, no. 1, pp 3-64. Continues in vol. 26, pp 52-63 (2003)

224Byrne, A. & Hilbert, D. (07 May 2004) Continuing commentary on “Color Realism and Color Science"http://web.mit.edu/abyrne/www/colorrealismrevisited.html

problem obliquely when discussing color television221. He emphasizes that the European (PAL)and United States (NTSC) systems do not call for the use of the same ideal phosphors, and that theactual systems offered by manufacturers in these two areas use different phosphors. Although hehas called for world wide standardization, this is unlikely to occur. Non television monitors oftenuse different phosphors as well. It is important that a researcher be much more specific about thechromatic content of his test stimuli. Giving a brand name for the overall monitor does notdescribe the characteristics of the cathode ray tube enclosed.

E– Providing clear definitions regarding color contrast is more difficult than for color itself because of the impact ofboth spatial and temporal factors. Graham & Brown have provided several definitions to clarify this problem.222 “Simultaneous color contrast involves a change in the hue, saturation and brightness of a test light owing to theinfluence of a nearby inducing color.” “Color adaptation is manifested by changes in hue, saturation, and brightnessthat occur during exposure to a given light; these changes may influence the perceived color of a succeeding light.” However, even these definitions do not separate brightness variations from color variations. This additionalseparation will be observed here. They also focus on the concepts of hue and saturation that are not intrinsic to thevisual system as discussed below.

It should become evident that the current debate in philosophical circles is complicated by their reliance upon aninadequate model of the biological (and particularly the human) visual system as well as its interaction with thephysical world223. It appears this community continues to rely primarily upon the additive assumption concerningthe sensing of spectral light in the determination of color (although they also struggle with the Hering model whichis incomplete), has relied upon an incorrect proposition related to the peak spectral wavelengths of absorption by thephotoreceptors of the biological eye (particularly the long wavelength photoreceptor), and has not interpreted thecolor constancy effect properly. This leaves them at a great disadvantage when attempting to ascertain the truth withregard to almost any aspect of color. However, these problems do not discourage the debate among dedicatedphilosophers from continuing224. These discussions make interesting reading except for a fact noted by one of theirown, “Teller sees only a tedious squabble about words.” This work will show that the physical color provided bythe real world can be traced through the neural system until it results in the generation of three analog signalamplitudes that represent any color perceived by the organism. How the organism describes this perception toanother organism is primarily a question of semantics.

The three analog values representing the perception of color related to an element of the scene can be stored in thevolume of three small neurons. This is why the source of this register has not been found within the billions ofneurons within the CNS. If the saliency map within a brain can be located, it will then be possible to locate theneurons storing the perceived color of any currently imaged scene element. It does not appear likely that thesaliency map stores perceived color information in long term memory with any degree of precision.

The philosophical community does not have the information required to discuss color constancy with any degree ofprecision. The tone of their discussions suggest they are only talking about the first order perception of color whileoperating within the photopic region of vision. They appear to overlook the second order changes in color


225McCamy, C. (1993) The Primary hue circle. Color Res. & Appl., vol. 18, no. 1, pp. 3-10226MacAdam, D. (1985) The physical basis of color specification, in Color Measurement: Theme &Variation, NY: Springer-Verlag, pp 1-25.

introduced when an object is viewed using one source of light and then viewed using a second light source ofsignificantly different spectral distribution, even within the photopic region. When comparing daylight toincandescent light, they do not recognize the significantly different perception related to the loss of signal underincandescent illumination related to the 400–437 nm region of the spectrum.

17.3.1 Historical background & the definition of color

The literature of the chrominance characteristics of human vision is so extensive as to be described as humongous. However, it is frequently contradictory, contains large amounts of anecdotal and unsubstantiated general material,and lacks a strong scientific base. The literature also exhibits two other prominent characteristics.

It is the most prominent example in science of reliance upon semantics in the absence of atheoretically based numerically oriented description of a phenomena or system.

It is fundamentally in error since it does not recognize the inherent tetrachromatic capabilityof the human visual system.

McCamy characterized the situation with regard to one system of color descriptors as: “Unfortunately, the fiveprinciple hues of the Munsell hue circle do not relate in any way to any previous theory of color vision nor to theapplication of trichromacy to color reproduction.225” This is because every scientific epoch in vision has assumed adifferent number of critical pigments or lights. The first began with Young using three. Then Hering focused onfour (or six). Munsell then introduced the idea of five. It will become clear later that Munsell’s choice wasfortuitous in an unusual aspect.

As McCamy points out, the problem is further complicated by a lack of precise definition of the word color. Thereare a variety of specialized definitions of color, most of which are found in the creative and graphic arts, not thesciences. MacAdam recently addressed this problem just within the scientific community226. Section 17.3.1.4.1 andthe glossary of this work provides eight specialized definitions of the term color. This work will focus on color asthe perception reported by the human in response to an external electromagnetic stimulus. This perception can beassociated with a perceptual space that is closely correlated with the electrical signals in the S-Plane of the retina.

Another complication is the frequently heard assertion that the human eye can discriminate as many as severalmillion colors from each other. These types of statements are semantically sloppy. The human eye has no absolutechromatic sensitivity. It operates on chromatic (and luminous) differences. In most color oriented laboratoryexperiments, the eye is used as a null detector or to arrange a set of samples in a orderly sequence. The eye is notable to estimate the chromatic difference between two samples unless it views them simultaneously.

As an example, show a subject two shades of red in a time sequence separated by three seconds. Then ask him/her to tell you which one was closer to green and specifically how much closer togreen it was (in terms of resolvable steps).

As a second example, ask a subject to view three similar color samples in time sequence, two ofwhich are metameres. After two or three seconds, ask the subject to tell you which two of thethree were metameres and how they differed chromatically from the third sample. Then ask thesubject about the difference between the metameres.

It matters little in the above experiments whether the subject knows in advance what questions hewill be asked. It also matters little what the ambient light conditions are. The subject is hardpressed to assign an absolute color to any color sample.

In everyday usage, a subject is limited in absolute color discrimination to about twenty colors. The basic colorstypically consist of the number of named radials in the Munsell Color Space consisting of about six clearly differentcolors and the colors intermediate between these colors. Beyond this dozen colors, the ability of two subjects toprovide the same names to samples presented in a double blind experiment becomes very small.


227Birren, F. (1966) Color: a survey in words and pictures. New Hyde Park, NY: University Books, Inc. pg.145228Fehrman, K. & Fehrman, C. (2000) Color: the secret influence. NY: Prentice-Hall229Venkataraman, K. (1977) The anaylytical chemistry of synthetic dyes. NY: John Wiley & Sons.230Werner, J. (1998) Aging through the eyes of Monet. Chapter 1 in Backhaus, W. Kliegl, R. & Werner, J. Color Vision: perspectives from different disciplines. Berlin: W. de Gruyter pp 24-26 & 35-38231Silvestrini, N. & Fischer, E. (2003) Color order systems in art and sciencehttp://www.colorsystem.com/index.htm

To achieve, maximum discrimination (under controlled lighting conditions to assure repeatability) sample pairsshould be of finite size (to be determined) and uniform surface reflectance. They should also be in juxtapositionwith each other with the part line falling on the fovea and possibly be limited to part lines falling on the foveola.

Although authors frequently describe either the C.I.E. and the Munsell systems of color notation as predating andleading to the other, they are inherently different. They indicate the significant problem of interpreting empiricaldata in the absence of an adequate theoretical model.

The description of the human color capability based on a circle is a very ancient methodology. Birren provides aninteresting summary of some of the variants encountered over time227. One of these, due to John Ruskin, equates thecolor circle with the twelve signs of the zodiac. The color names John used are, if nothing else, lovely. Morerecently, Fehrman & Fehrman have re-visited this ground from a current artistic and architectural perspective228.

The inadequacy of the C.I.E system has been summarized very succinctly by Venkataraman; “the CIE system doesnot provide a satisfactory specification of color for two reasons: (a) the variability of chromaticity coordinates withcolorant concentration, and (b) the non-uniformity of the color space with respect to visual perception.”229

This work will correct the above problems. It will provide a definition of the word color as it applies to a number ofsituations. It will also provide a theoretical foundation for both the Munsell Color System and, to the extentpossible, the C.I.E Chromaticity System.

----The development of our understanding of color as a science has occurred during a series of epochs. These beganwith the early “philosophical” scientists, was followed by the empirical “physicists” and has recently culminatedwith the efforts of the psychophysicists.

17.3.1.1 Early philosophical models; Young, Maxwell, Hering & Kries

Thomas Young is generally credited with being first to concentrate his efforts on the science of color in 1802-03. However, Newton preceded Young by at least 130 years.

Newton included a color wheel in his 1666 Opticks that was later also developed by Hering and perfected byMunsell.

Young’s steps were quite tentative. Young espoused a three node color space that was initially described by thecolors red, green and blue. A year later he wrote in terms of red, green and violet without giving a clear reason forthe change. Maxwell followed Young by a half a century and stayed with the red, green & violet triad. Late in the19th Century, Hering espoused his system based on a quadrate consisting of two pairs of colors. His color pairs werered & green and blue & yellow. Kries introduced a different mathematical arrangement based on Hering230. In thered-green pairing, he specified perceived red as resulting from stimulation of both the S– and L– spectral channels. In is blue-yellow pairing, he specified yellow as resulting from stimulation of both the M– and L– spectralchannels.These writers based there choices primarily on their own observations. Any further justification waslargely philosophical (in the current usage of the word). Silvestrini and Fischer have provided an extensive historyof the various theories of color (59 by their count) from Young’s time forward231.

Each of the color spaces described by the above investigators can be rationalized with the more fundamental colorspace of this work. The key is to recognize that perception involves color differencing in an orthogonal color space. In this interpretation, white is represented by a null condition in each of two color difference channels. Based on the


proposed fundamental color space, both the Hering and the Kries color spaces involve color differences in thepresence of a specific spectral bias. While the Young and the Maxwell conceptions of perceived color can beunderstood, as due to the summation of spectral signals involved, the underlying situation is quite different.

The descriptive words of Werner regarding Monet’s visual condition and artistic accomplishments late in lifeare very useful (pp 35-38). However, the words lack scientific credence based on our current knowledge ofthe visual process and the additional capabilities of the aphakic eye to see colors (in the 342 nm to 400 nmregion) not otherwise seen or named by humans and to impact the perception of colors in the 400 nm to 437nm region) See subsequent sections below.

As a preview, Figure 17.3.1-1 shows how the theoretical model of this work provides a foundation for bothNewton’s original color wheel and the Young equilateral color space. While Young’s color space was equilateral,based on his reading of the laws of colored light summation in object space, it is easily transformed to a right trianglein perceptual space and overlaid on the New Perceptual Chromaticity Diagram. The diagram assumes equal photonflux per unit wavelength for all stimuli and a fully dark adapted eye (or equivalent). While this triangletransformation can be considered conformal, it is not rectilinear. The result is a “white” that appears near thehypotenuse of the triangle shown by the dashed line at 45 degrees. With the transformation, the white point is at40% of the length of the two legs of the triangle from the right angle. Newton’s color wheel was perceptual incharacter and merely needs to be rotated 135 degrees to overlay the New Perceptual Chromaticity Diagram as shownby the dashed circle. The circle is annotated with labels corresponding to Munsell’s color space.

The triangular overlay demonstrates the broad area of color space (the magenta’s) not addressed adequately byYoung’s color space. This is the region that cannot be matched to additive combinations of three narrow bandprimaries of red, green and blue in photometry (colorimetry). Such matching requires a green component be addedto the test sample to bring it within the confines of the right triangle. Newton’s color space, as definitized byMunsell, includes all of the color space of human vision.


232Long, J. (2011) The New Munsell Student Color Set: 3rd Edition NY: Bloomsbury Academic ISBN-13:9781609011567

None of these early investigators were aware of the ultraviolet sensitive spectral channel of the human retina. Theytypically ignored the color space represented by spectral wavelengths shorter than 437 nm.

17.3.1.2 Early empirical model of Munsell and the C.I.E.

In the early 20th Century, two efforts were made to quantify the color space. Munsell provided a largelyphilosophical color space, based on his work as an artist, but one quantified so that he could use it to specify thecolors needed to prepare different paints232. He offered no theoretical foundation for his choice of a five node systembased on red, yellow, green, blue and purple.

The C.I.E took a different approach based largely on the blossoming needs of industry to quantify what people couldsee within the color space. While basing their approach on the trichromatic hypothesis of Young-Maxwell,quantifying their results with a precision of about five nm, and presenting their color space using cartesiancoordinates, the C.I.E. approach lacks any theoretical foundation. Fairman, et. al. have provided a recent narrative

Figure 17.3.1-1 A foundation for both Newton’s and Young’s conception of color space. Only simple transformsare required to overlay them onto the New Perceptual Chromaticity Diagram


233Fairman, H. Brill, M. & Hemmendinger, H. (1997) How the CIE 1931 color-matching functions werederived from Wright-Guild data. Color Res. Appl. vol. 22, no. 1, pp 11-23234Indow, T. & Aoki, N. (1983) Multidimensional mapping of 178 Munsell colors. Color Res. & Appl., vol8, pp. 145-152235Fehrman, K. & Fehrman, C. (2000) Op. Cit. pp. 202-203236Guth, S. (1991) Model of color vision and light adaptation J. Opt. Soc. Am. A. vol. 8, no. 6, pp 976-993237Boker, S. (1995) The representation of color metrics and mappings in perceptual color space. www.nd.edu/~sboker/ColorVision2/ColorVision2.html

describing the development of the C.I.E color-matching functions233. Their conclusions were two. First, theprocedure followed was logical based on the formulating principles adopted. Second, they concluded “We haveshown that likely none of these formulating principles would be adopted if the system were formulated from a freshstart today.”

Neither Munsell or the investigators associated with the C.I.E. were aware of the ultraviolet sensitive spectralchannel of the human retina.

17.3.1.2.1 The Munsell perspective

McCamy has provided a good review of the background of the Munsell Color System, including the left-handednessof the Munsell system notation. He also provides a proposed modification to the Renotated Munsell Color Systemof 1967. Unfortunately, his paper does not contain any substantive theoretical model supporting his proposal norspecific wavelengths for the variety of colors he deals with. Although he bemoaned the lack of a theoreticalfoundation in the work of others as noted above, his new proposal remains based on semantics and empirical data. While the problem he desires to correct is well known, the more rigorous statistical approach of Indow & Aoki234 ismore appropriate but remains based on empirical data, not a theoretical base. Lacking a theoretical base, it is uselessto discuss which of the Munsell labels blue-violet, blue, and violet-blue better describe the semantic blue describedby McCamy. Fehrman & Fehrman have provided a detailed list of Munsell’s conception of the original space235.

Guth has introduced a largely conceptual model of the visual system (not related to physiology) and raised severalproblems with the Munsell Color Space236. These concerns are at a very precise level. Similar concerns have alsosurfaced in the development of this work. However, Guth continues to assume a color space based on radials that donot change hue with radius.

Boker237 has introduced a level of mathematical theory not commonly found elsewhere in the visual sciences. Heoutlines the steps required to show that what he calls the perceptual color space is in fact continuous from amathematical perspective. This condition is satisfied if the coefficients of the terms in the functions defining thecolor space are continuous and well behaved. This condition is necessary if the color space is to be amenable toroutine mathematical description. Unfortunately, Boker’s approach cannot be used to demonstrate his thesis that thecolor space has a metric (is in some mathematical sense continuous) without knowledge of the underlyingmathematical functions that describe that color space. His lack of an adequate theoretical model of the visualsystem is indicated by the empty section of his paper labeled “Neurophysical models.” Using the models of thiswork, equations will be presented below that demonstrate that the visual color space does exhibit a “metric” sincethe functions creating that space are mathematically well behaved both individually and as a group. In fact, the colorspace conforms to the so-called local Euclidean metric. This is the type of color space sought by the C.I.E. inmoving toward, but not achieving, a uniform color scale in their more recent Chromaticity Diagrams.

Relying on the literature, Boker describes the nature of the signaling transforms present in the visual system as atruly tangled mapping which is both many-to-one and simultaneously one-to-many. This work attempts to providesignificant clarification in this area. It shows that the “many-to-one and simultaneously one-to-many situations hedescribes are in fact entirely determinate. One must merely use a different transformation to obtain an orderlymapping through the system. The question of mapping entails several levels of encoding, some of which arereversible and some are not. It concludes the system only involves feedforward signal processing at the signal pathlevel and that the fundamental many-to-one nature of the system is the result of a simple integration over the spectralinterval of each photoreceptor cell. For purposes of signal projection, an additional many-to-one encoding scheme isused that is completely and unambiguously reversible within the cortex if required.

The redefinition of the Munsell Color Circle by McCamy relies upon a mixture of the color names commonlyassociated with both additive and subtractive color mixing without defining these colors scientifically. This isunfortunate, because these names are associated with spectral characteristics that are not mutually exclusive. This


238Kuehni, R. (2002) Color: what could it be? SPIE Proc vol 4421 pp 642-645239Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg 509240Sproson, W. (1983) Colour Science in Television and Display Systems. Bristol: Adam Hilger Ltd. pg152

work will replace the term cyan (a name associated with a broad spectral band in printing) with aqua (defined asassociated with a narrow spectral band centered on 494 nm) when discussing a hue circle to avoid this problem. Asimilar problem is associated with the term yellow which is used widely in applications involving both additive andsubtractive color. It would be best if this term could be divided into two semantically acceptable terms where yellowwas defined as referring to a narrow spectral region centered on 572 nm. In this case, an alternate term, like canary,would define a color with a broader spectral absorption described below that was still centered near 572 nm. Unfortunately, the Y in yellow is used as part of the description of the CMYK, subtractive, color system of printing. This application oriented designation is not likely to change within the popular press in the foreseeable future. Within the process color community, the alternative label, CMCK is frequently encountered. The letters stand for“Cyan,” “Magenta,” “Canary,” and “Black” respectively. Canary, not yellow, is used to label the broadband spectralpigment.

The New Chromaticity Diagram for Research presented in this Section should accomplish three goals. It shouldalleviate, and/or quantify, the concerns of McCamy over the accuracy of the renotated Munsell Color System. Itshould also provide the theory required to precisely define the mathematical characteristics of the radials of theMunsell Color System (and if desired both the McCamy suggested modifications to that system and the C.I.E. (1976)Chromaticity Diagram ). It also provides a method of determining how well the available empirical Munsell data hasbeen matched to a quasi-theoretical framework ala Indow & Aoki and how close the C.I.E. (1976) Diagram hascome to an undistorted Euclidean color space. This work does not support the embarrassment expressed byMcCamy concerning the location of semantic labels on the chromatic planes of the Munsell Color System. It doesprovide a theoretical framework with which to judge the assertions by both Judd and Nickerson and by the ISCC-NBS regarding the semantic labels (in English) to be assigned to the radials of Munsell.

The 2-dimensional color space of the New Chromaticity Diagram, in agreement with the Munsell book of Colors, ISNOT circular. It is both rectangular and rectalinear. The axes are orthogonal. Any use of a color circle is merely alimited representation, for pedagogical purposes, of the rectilinear color space in circular coordinates.

Kuehni asserted in 2002, “A Euclidian uniform psychological or psychophysical color space appears to beimpossible238.” While he did not provide a detailed proof of this assertion, it is clear that he was not considering anadequate physiological model of the visual system. He does note the need to define the term uniform precisely. “Here, uniform has the meaning of equal relative increments in unique hue and in blackness/whiteness based ondefined starting and end points.” He did not include saturation. He discounts the Munsell Color Space as not beinga meaningful psychological space as its chromatic axes are not defined. Sections 17.3.4 & 17.3.5 provide aresolution to this shortcoming. He concludes his limited discussion as follows. “Much fundamental work needs tobe done.”

The color space developed by Munsell relied upon the concept that the sensation of hue did not change withsaturation. As a result, the color space exhibited cylindrical symmetry about the white point. Wyszecki & Stilesnote that this symmetry is not perfect and the observed hue rotated with illuminance239. By overlaying the MunsellColor Space on the New Chromaticity Diagram for Research, an additional complication is recognized. Theskewing recognized by Wyszecki & Stiles is not uniform with hue angle. They made the empirically based observation that there was no skew associated with the 10Y radial and a second radial between 5P and 7.5P. Basedstrictly on theoretical considerations, only the 10PB, 10Y, 5R and 5BG radials should be straight lines in the NewChromaticity Space. Stated differently, there is no skew associated with the Hering axes of the Munsell Space, onlyfor off-axis radials. The skewing is due to the fact that the underlying color space is rectilinear (based on P and Qvalues) and not radially symmetrical. When expressing the New Chromaticity Diagram for Research using a radialcoordinate system, hue is not constant along a given radial. Sproson has plotted the radials of the Munsell ColorSpace on the CIE UCS (u’, v’) color space to illustrate the curvatures between the two240. Unfortunately, the 1976modification of the 1960 CIE UCS space is still not orthogonal. It would be useful to see the same data, as well asthe UCS coordinates plotted on the New Chromaticity Diagram for Research. .

17.3.1.2.2 Hue and Saturation are not intrinsic

A number of systems have been defined to illustrate the chromatic properties of vision based on a cylindrical


241Bird, G. & Jones, R. (1965) estimation of the spectral response functions of the human cone pigments JOpt Soc Am vol 55(12), pp 1686-1691

coordinate system. However, there is no indication that the visual system can process the transcendental functionsrequired to support a cylindrical (or spherical) coordinate system. While presenting chromatic information in arho,theta format is useful pedagogically, this presentation mode can not be related to the mechanisms of vision. Thevisual system employs a cartesian coordinate system. The quantities actually utilized in the visual systemcorrespond to rho tan theta and rho cotan theta.

17.3.1.3 The C.I.E. (1931 & 1964) concept of color space is invalid for research

A brief description of the C.I.E color spaces surfaces some of the critical factors underlying their representations.

1. Grassman hypothesized a set of "matches,” not mathematical equations.

2. During the 1920-30's, the community interpreted Grassman's matches as algebraic laws applicable to light inobject space. The CIE 1931 and 1964 chromaticity diagrams were based on the assumed additivity law and appliedto a stimulus-based model in object space. Because of inconsistencies in this approach (RGB had to be replaced byXYZ), a "Standard Observer" was defined that was consistent with the XYZ system.

3. A well known problem in applying the stimulus-based approach was the failures of a real human observer tomatch colors in a bipartite color matching experiment in accordance with the standard observer.

4. Beginning in the 1960's, the CIE addressed the problem of developing a perception-based framework. The CIELab & Luv spaces were perception-based and their equations involved differences instead of Grassman's additions(see equations for L*a*b* & L*u*v*in the attachment).

5. The latest L*a*b* color space is approaching and very near my theoretical Chromaticity Diagram for Research (ascited earlier) if the a* and b* axes are rotated about 20 degrees. The L*a*b* space is also in agreement withMunsell's Color Space and compatible with Hering's axes in color space.

Grassman's Matches apply in additive form to the stimulus-based CIE 1931 & 1964 Chromaticity Space and theartificial "standard observer." Luminosity is always an additive process. Chromaticity is always a subtractiveprocess. Chromaticity also involves two orthogonal axes (three for any wavelengths shorter than 437 nm) andvectorial subtraction. Grassman's Matches in subtractive form apply to the perception-based L*u*v* and L*a*b*uniform color spaces and the human or "real observer" (along with Herings's hypothesis, Munsell's empirical ColorSpace, and my theoretical Color Space). Bipartite color matching conforms to the subtractive form of Grassman'sMatches as easily demonstrated using these latter Color Spaces.

- - - - -

The C.I.E developed a color space based largely on the blossoming needs of industry to quantify what people couldsee within the color space. The result was a first order, application oriented, description of color vision. Theirapproach was based on the trichromatic hypothesis of Young-Maxwell. However, the approach lacked any rigoroustheoretical foundation. It is a description of color in object space and does not claim to represent the humanperception of color. It is not compatible with the larger context of tetrachromatic vision relevant to the researchenvironment.

A critical problem with the C.I.E. concept of color space is its intrinsic assumption that the human visual system islinear and a linear transform can be created between the perceived response functions, R(λ), G(λ) & B(λ) and theC.I.E. object space functions x(λ), y(λ) & z(λ)241. Unfortunately, this assumption is known to be, and isdemonstrably, false, thus undermining the entire C.I.E. color space concept. This is a major problem in the study ofvision. Using linear matrix algebra to convert between the parameters of object space and perceptual spacespecified by the C.I.E. is not viable. Bird & Jones discuss the fact that at least three different methods exist forrepresenting the fundamental response functions. They also discuss the fact that if the response functions are notlinear representations of the C.I.E. 1931 color mixture functions, “it is not possible to define the correspondingprimaries on the C.I.E.-1931 chromaticity diagram.”

The Perception-based Chromaticity Diagram of this work and the Object-space Chromaticity Diagram of the C.I.E


242Rubin, M. & Walls, G. (1969) Fundamentals of visual science. Springfield, IL: Charles C. Thomas, pp.251-268243Miller, K. (1985) Call to the colors. Photonics Spectra, February, pp. 75-82

are not contradictory. They are complementary. The research oriented Perceptual Chromaticity Diagram providesmore details that can be applied to the object oriented C.I.E. Chromaticity Diagram. The perceptual diagram isparticularly useful in illuminating the spatial non-linearities of the C.I.E. Chromaticity Diagram (Section 17.3.5.3).

It is also important to note the C.I.E concept of color space relies on a single zone model. It assumes the signalsfrom the various photoreceptors are linearly summed to provide the brightness signal and that other groupings ofsignals are linearly summed to provide the chrominance signal(s). These assumptions are demonstrably false basedon electrophysiological measurements made as early as the 1950's by Svaetichin and by Tomita (Section 17.3.1.4). The human visual system involves a multi-zone architecture that is incompatible with the C.I.E. concept ofcolor.

17.3.1.3.1 Analyses by other investigators

[xxx need to rewrite showing that one cannot match a purple with red green and blue ]Rubin & Walls242 provide a good review of the development of the CIE Chromaticity Diagram. A morecomprehensive review including the 1976 modifications can be found in Miller243. Unfortunately Miller published ina trade journal not widely indexed. The progression from the 1924 diagram to the 1931, and then the 1960 whichwas “rapidly” replaced by the 1976 version, indicates the problems with the underlying concept (Section 17.2.xxx).

Basically, the diagram is derived from two linear equations:

C = xR + yG + zB where C is the “total color” and x, y & z are in percent

x + y + z = 100

The terms R, G, & B are assumed to be real functions representing the spectral absorption of the individualphotosensitive channels of animal (in this case human) vision. Real is used here in the mathematical sense. Thecoefficients of these terms are assumed to be positive. Based on these two equation, both of which are linear, thedescription of a color is specified by plotting x and y with z known implicitly from the second equation. It isconventional to plot x and y along orthogonal axes in a Euclidean space. As pointed out by Rubin & Walls; “If threedistinct primaries (red, blue, and green) are carefully chosen and standardized, all colors can be denoted ascontaining a certain proportion (i.e. percentage) of each of the primaries in the mixture.” They go on: “If we takeonly the colors in the spectrum, all the colors which correspond to the monochromatic radiations in this spectrum canbe plotted on a curved line called the ‘spectrum locus’. The end points of this curve are joined by a straight linecalled the ‘purple line’.” They then proceeded to define how these primaries are chosen. Their two paragraphs arequoted in their entirety below.

“By far the most satisfactory method of colorimetry [to date] is one which is actually a process oftricolorimetry but employs an imaginary tricolorimeter, three imaginary primary lights, and animaginary observer. This is the modus operandi of the CIE system of color specification. The rawdatum required is simply the spectroradiometric curve of the sample--drawn automatically ‘whileyou wait’ by such an instrument as General Electric’s recording photoelectric spectrophotometer. From this curve, three others are derived, each of which shows for each wavelength the amount ofone CIE primary light required to help afford a tricolorimetric match for the sample’s energy atthat wavelength. The integrals of these three curves are thus the total amounts of the three CIEprimaries which, mixed, would form an equivalent stimulus. The CIE primaries themselves arehypothetical lights whose colors are supersaturated--made so quite simply with pencil and papersince they represent perfectly legitimate ‘homogeneous linear transformations’ of the real color-mixture data of a group of real human observers. The average of these real observers constitutesthe hypothetical CIE ‘standard observer,’ mixing the hypothetical primaries in a nonexistentinstrument to make a visual match for the sample.

Any way you slice it, the colorimetrist has a nerve if he claims he is measuring anything about thesample he is ‘specifying’!”

The last sentence is quite compelling from recognized leaders in the field.


244Comm. on Colorimetry, ibid, pg 242-245245Hunt, R. (1991) Measuring colour, 2nd ed. NY: Ellis Horwood, pg. 56246Comm. on Colorimetry of Optical Society of America (1963) The Science of Color. Washington, DC:Optical Society of America pg. 265247Comm. on Colorimetry, ibid, pg 264-267

These are only a few of the comments by many authors calling for a new Chromaticity Diagram for scientificpurposes. It is granted that the 1931 Diagram is widely used in commerce where precision and correctness takes aback seat to consistency and stability. Furthermore, adding pigments in the commercial world is an inherently linearprocess. However, science should not be trapped into a situation where the locus of the spectral wavelengths arearbitrarily and erroneously specified as in the 1931 Diagram. For an interesting defense of the current standard, seethe Science of Color244.

Hunt added the observation245 that “It is also very important to remember that chromaticity diagrams are maps ofrelationships between colour stimuli, not between colour perceptions.” This statement appears too strong and a bitbizarre since these diagrams have all relied upon psychophysical data which by definition involves perceptions. However, Hunt’s position can be accepted to the extent the data was collected using the visual system as a nulldetector (a small signal technique).

17.3.1.3.2 Analyses based on this work

In visual research, a basic difficulty is that the CIE “color-mixture data of a group of real human observers” wasassumed to involve linear visual processes. Furthermore, the G light was specified as the Photopic LuminosityCurve adopted by the CIE in 1924. Because of these assumptions, the pencil and paper transformations invariablyrequired a secondary peak in the response of the red receptor; this secondary peak is 35% as high as the longwavelength peak and is located near 0.45:246. More seriously, this secondary peak is in the negative direction. Nospectrographic recording has ever shown such a negative peak in the absorption characteristic of the longwavelength visual channel of any animal. Such a negative peak is not explainable theoretically.

The linear assumption simply cannot be supported under large signal conditions. Normal daylight vision involveslarge signal conditions. The color constancy phenomenon of vision is specifically designed to eliminate anymisleading color shifts under large signal conditions. Vision is fundamentally logarithmic and involves a variety of highly nonlinear process. The scientists247 developing the adopted 1931 standard implicitly recognized the non-linearity involved. To avoid them, they presented the Tristimulus Computation Data with values ranging from 1 to100,000, i.e., their methodology collapsed if they encountered values less than 1.0. Such values would involvenegative logarithms. The same restriction was encountered in Chapter 13 when developing the equations relating tothe non-algebraic addition encountered in animal vision.

In addition, defining the G light of the CIE tristimulus concept, which naturally becomes associated with the mid-wavelength spectral channel, as identical to the photopic luminosity function is not supportable. If true, thisassumption would preclude the observation of brightness changes associated with the long wavelength or shortwavelength spectral channel. While the Boynton school has attempted to eliminate the short wavelength spectralchannel from the perceived luminance response, the difficulty with even this thesis will be analyzed in Section17.3.1.5.

It is also worth noting the color mixture data developed for humans in the 1950’s by the National TelevisionStandards Committee (NTSC) for color television. It showed clearly that humans did not require equal luminositiesin each “color channel” of a color reproduction system for the human to experience a white sensation. Theequations adopted involved about 15% for B and R with the remainder in the G light. These are similar to thepercentages presented in Chapter 13 under Photopic conditions. Based on these studies, it is clear that themethodology, used by the C.I.E. is quite suspect. Equal weighting of the terms in the equation, x + y + z = 100 isnot appropriate.

An even more basic difficulty is the assumption that the visual system is based on the principle of “additive color” inobject space. This thesis is strongly objected to by the Hering school. By totally separating the discussion of theluminance and chrominance capabilities of vision, a more realistic model of vision can be obtained. This model willdemonstrate that, while the luminance aspects of vision rely upon additive processes, the chromatic aspects relyupon a spectral differencing technique.

Another significant problem with the diagram is its treatment of “white” as a function of color temperature. Thediagram is usually displayed as having a band of “white” that parallels the “Planckian radiator line.” This display


248Fehrman, K. & Fehrman, C. (2000) Color; the Secret Influence. Upper Saddle River, NJ: Prentice-Hall,figure C-7249Nassau, K. ed. (1998) Color for science, art and technology. NY: Elsevier250Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 825-830251Krauskopf, J. Williams, D. & Heeley, D. (1982) Cardinal Directions of color space. Vision Res. vol. 22,pp 1123-1131

gives an erroneous impression and raises a question about how widely Hunt’s statement is observed. Depending onhow it is observed, the conventional figure gives the impression that either the color stimuli along this band remainswhite continually, or the perceived color along this band remains white continually. However, neither of thesesituations is tenable. It is difficult to believe, the “color stimuli” can remain white over such a range of contentbased on additive color principles. The perceived color across the face of the chart varies considerably as a functionof color temperature. At a color temperature near 6500 Kelvin, the “white” zone is an elliptical area near x=0.32,y=0.32 and the area near x=0.42, y=0.45 is yellowish-orange. At 2856 Kelvin, the situation is reversed, the first areais greenish-blue and the second area is “white.” This is apparently the reason the CIE never sanctioned a colorizedCIE Chromaticity Diagram. The perceived colors are not stable when referred to the coordinate system in this figure.

As presented, the white band of the CIE Diagram is more accurately defined as an envelope that contains theinstantaneous area perceived as “white” without properly representing the instantaneous perception of color in thisarea. A more realistic representation of the correlated color temperature of a source is presented in Fehrman &Fehrman and credited to Bright Ideas248. The presentation in color plate 4 & 5 of Nassau249, and credited to Minolta,are believed to more properly represent both the 1931 Chromaticity Diagram and the 1976 u,v diagram. However, itis important to note that these figures are reproduced using a very limited capability 4-color subtractive color systemas used in commercial printing.

The list of theoretical difficulties with the C.I.E. (1931) Chromaticity Diagram can continue ad nauseum. The mostserious objection is that it does not represent the actual color performance of any real individual. The StandardObserver is an entirely artificial object. The revised (1976) Diagram attempted to at least linearize the color space itattempted to represent. The success of this process can be gauged from [Figure 17.3.3-10] below. This figureshows the axes of the theoretical color space developed in this work to the color space of the C.I.E (1960) UniformColor Space based on the work of Farnsworth. A goal of any new chart should be a rectilinear chromaticitypresentation and/or a Spectrum Locus that display equal wavelength increments in equal distance increments. Insuch a chart, it would be possible to properly illustrate the actual spectral response of the eye in a proportionalmanner. Showing clearly its total gamut would also be possible, although the printing process might fail toreproduce it completely. It would also be possible either to eliminate or give more meaning to the Purple Line.

Until a new CIE Chromaticity Diagram is adopted, any researcher should use great caution when invoking the 1931through 1976 Diagrams as a foundation for, as a tool in or as corroboration of his work.

17.3.1.3.3 The C.I.E. color space is nonconformal

The C.I.E. 1931 color space has been known to be nonconformal for a very long time. Farnsworth first provided aquantitative discussion of this subject. A wide variety of studies have been made over the years attempting to definevarious empirical formulas to define the human color space250. These empirical studies resulted in the arbitrarychanges in the CIE color space of 1960, and then in 1976. The change between the 1960 and the 1976 Diagramswas an arbitrary change in the v* scale of 1.5:1. It is unfortunate that the CIE chose to call the new color spaces as“Uniform Color Spaces.” These spaces remain nonconformal as reported in the general literature.

Krauskopf, Williams & Heeley have attempted to define the cardinal directions of color space using psychophysicalmeasurements plotted on the nonconformal C.I.E. (1931) Chromaticity Diagram251. As demonstrated in Section3.5.3, the obvious problem was there assumption that tangents generated in a local area of the Diagram could beextended as straight lines to their intersection with the spectral locus. These intersection are occasionally definedusing the term copunctal points. Their terminology employed reddish, greenish, bluish and yellowish instead ofmore precise terms. Their discussion summarizes the limited utility of their proposed axes.

17.3.1.3.4 The interpretation of the C.I.E (x,y) Chromaticity Diagram

The C.I.E. Chromaticity Diagram (x,y) is known to be highly distorted in its presentation (See Section 17.3.5.3). It


252Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and500 nm. Vision res. vol. 15, pp. 16-171253Brindley, G. (1955) The color of light of very long wavelength J. Physiol. vol. 130, pp. 35-44 and laterwritings.254Kelly, K. (1963) Lines of constant correlated color temperature based on MacAdam’s (u,v) uniformchromaticity transformation of the CIE diagram J. Opt. Soc. Am. vol. 53, pp 999-255Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons, pp. 133- 146 & 224-228

also exhibits characteristics that are hard to define. The “purple line” is one of these characteristics. It has notheoretical foundation and merely connects two arbitrary points on the spectral locus as calculated in r,g and hencex,y space. These points are usually taken as 380 and 700 nm. The spectral locus is also based on less than a strongtheoretical foundation. There is a triangular sector bounded by “a white” point and the two end points of the spectrallocus. This area is frequently labeled the area of non-spectral colors for non-obvious reasons. The underlyingreason relates to the methodology of “one-wavelength colorimetry.” This methodology is based on the principle ofadditive color and says that any color should be obtainable by mixing a white light with a second monochromaticlight. It is obviously impossible to achieve this result along radials from the white point that do not intersect thespectral locus. Thus colors in this region are labeled non-spectral even though they are easily obtained by merelymixing two spectral lights.

Smith & Pokorny discuss a variety of other problems with the above diagram252. Some of these have been discussedelsewhere in this document.

A very important point is that the C.I.E. Chromaticity Diagram relates to “matches” made in object space undernominal but undefined or poorly defined conditions. As an example, the viewer should be fixated on the center of abipartite field of unspecified diameter. Furthrmore, for similar matches to be achieved by two different observers,both observers must be pre-adapted to the same unspecified illumination prior to the matching.

To avoid the effects of color constancy due to adaptation, it is necessary that an individual match be made during ashort time interval.

Long ago, a spectral locus was calculated for the C.I.E. (1931) Chromaticity Diagram. This locus is generally shownas a single valued function in x,y coordinates. However, Brindley has shown that this is not the case in the spectralregion beyond 645.2 nm253. Beyond this value the function is dual valued. This fact is recognized in the 1964Supplement to the original diagram.

As a result of this work, figures have been drawn illustrating the nonconformality of the CIE (1931) ChromaticityDiagram. See Sections 17.3.5 for a detailed discussion and Section 18.1.5 with regard to an application. Similaranalyses are available showing the nonconformality of the the CIE 1960 and 1976 Chromaticity Diagrams.

17.3.1.3.5 An interpretation of the Planckian Locus on the CIE Diagram

In 1963, Kelly computed a Planckian Locus for application to the C.I.E. (1931) Chromaticity Diagram254. Hecontinued the assumption that the Chromaticity Diagram applied to object space and that all of the coefficients in thedefining equations related to vision were constant. The discussion in Wyszecki and Stiles provides the backgroundfor these highly abstract and empirical calculations255.

The formulation of Kelly was based on fixed coefficients and additive color processing. It exhibits a minimalcorrelation with actual vision. The results of the calculations are not compatible with any change in the gain of theadaptation amplifiers of the photoreceptor cells that normally result in the phenomena of color constancy. As aresult, the description of the Planckian Locus on the CIE Chromaticity Diagram is limited to an object space that isobserved by a man-made colorimeter employing constant gain coefficients in its signal processing circuits. It doesnot represent any perception of color by any biological visual system.

A human observer viewing a scene illuminated by a Planckian radiator does not perceive any change in the scene aslong as the illumination level is compatible with the photopic illumination range of the eyes (all adaptationamplifiers are within their operating range). Under these conditions, the gain of the individual spectral sensingchannels change gain inversely with the magnitude of the stimulus. To the extent the adaptation amplifiers are ableto maintain constant signal levels at the pedicles of the photoreceptor cells, the white point of a scene does notchange as a function of color temperature and the Planckian Locus is perceived as a single white point located atP=0, Q = 0 in the coordinates of the New Chromaticity Diagram or approximately x = 0.33 and y = 0.33 in the CIE


256Wyszecki, G & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 166-167257Svaetichin, G. (1953) The cone action potential Acta Physiol Scand vol 29, Suppl 106, pp 565-600258Tomita, T. (1965) Electrophysiological study of the mechanisms subserving color coding in the fishretina In Cold Spring Harbor Symposia on Quantitative Biology, Volume XXX. Long Island, NY: ColdSpring Harbor Laboratory pp 559-566259Tomita, T. Kaneko, A.Murakami, M. Pautler, E. (1967) Spectral response curves of single cones in thecarp Vision Res vol 7(7), pp 519-31

Chromaticity Diagram.

It is only when the illumination intensity falls below the level needed to maintain photopic operation that theperceived Planckian Locus begins to move. This can occur in two different ways. In the first, the light level can bereduced while maintaining a fixed color temperature. Under this condition, the perceived white point will varydepending on which spectral channel first deviates from maintaining a nominal signal amplitude at its pedicle. Describing the result of this event is complex because of the possibility that the long-wavelength spectral channelmay go into square-law operation independent of the actual adaptation amplifier performances (another characteristicof the mesotopic illumination range). In the second case, the light intensity can be maintained constant in someradiometric sense while only the color temperature of that source is reduced. This condition is also complex sincehow the radiometric intensity is to be maintained is not obvious.

Artists have adopted different approaches to illustrating the Planckian Locus on a colorized CIE ChromaticityDiagram based on the assumption of constant coefficients and Kelly’s calculations. The most common approach hasbeen to show the “white area of the diagram as including the majority of the Planckian Locus between 2400 and10,000 Kelvin. This has resulted in a hot dog shaped white area. However, this is in conflict with reality. The“white” area remains a nearly circular ellipse with a ratio of less than 1.5:1 between major and minor axes regardlessof color temperature. When viewed by a man-made colorimeter, the center of the white area would move along thePlanckian Locus. When viewed by a human, the white point would remain fixed until the photopic range of the eyesis no longer maintained. There is no problem in representing the white point in the perceived color space of the NewChromaticity Diagram. It remains fixed at P = 0, Q = 0 while the perceivable range of color space moves in towardthe white point at reduced color temperatures or reduced incident intensity.

17.3.1.3.6 The interpretation of the C.I.E (a*,b*) or CIELAB Chromaticity Diagram

Nassau has also provided color plate 6 attempting to provide a visualization of the CIELAB Diagram overlayed witha Munsell Color Space, also credited to Minolta Corporation. Here again, the limitations of the 4-color subtractivecolor process used in commercial printing must be emphasized. Furthermore, the artist is attempting to show thecolor rendition at a much higher luminosity than he shows the central null area. The caption makes it clear that theCIELAB nomenclature is meant to be a scaled version of the Munsell renotated Color Space. What is not shown isthe fact that the Munsell Color Space is not circular. The Munsell space is distinctly non-circular and the neutralpoint is not at the geometric center of Munsell space. The CIELAB presentation appears to remain an approximationto accommodate the empirically derived mathematical approximations used rather than represent any theoreticaldescription or empirical measurements. The actual, and relatively bazaar, forms of the CIELAB and CIELUV colorspaces are shown in detail in Wyszecki & Stiles256. The last line of the caption of each of these presentations isinteresting if not confusing.

17.3.1.4 The early electrophysiological measurements; Svaetichin and Tomita

Beginning in the early 1950's, Svaetichin began exploring the retina using electrical probes257. He was followedclosely by Tomita in the 1960's258,259. They were the first to record electrical signals from the retina with respect tothe spectral wavelength of the excitation source. They published a variety of their results but were unable to providea complete interpretation of them. Such an interpretation required a theoretical model that was more sophisticatedthan those available based on either Young-Maxwell or Hering, or the single zone model adopted by the C.I.E..

17.3.1.5 More recent psychophysical models

17.3.1.5.1 Recent psychophysical model of McLeod & Boynton

During the latter part of the 20th Century, a new set of color spaces were presented based loosely on a trichromatichypothesis with respect to photoreceptors but the Hering hypothesis with regard to color perception. These spaces


260MacLeod, D. & Boynton, R. (1979) Chromaticity diagram showing cone excitation by stimuli of equalluminance. J. Opt. Soc. Am. vol. 69, no. 8, pp 1183-1186261Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and500 nm. Vision Res. vol. 15, pp 161-171262Tansley, B. & Glushko, R. (1978) Spectral sensitivity of long-wavelength-sensitive photoreceptors indichromats determined by elimination of border percepts. Vision Res. vol. 18, pp 699-706263Tansley, B. & Boynton, R. (1978) Chromatic border perception: the role of red- and green-sensitivecones. Vision Res. vol. 18, pp 683-697264Drum, B. (1983) Short-wavelength cones contribute to achromatic sensitivity. Vision Res. vol. 23, no.12, pp 1433-1439265Derrington, A. Krauskopf, J. & Lennie, P. (1984) Chromatic mechanisms in lateral geniculate nucleus ofmacaque. J. Physiol. Vol. 357, pp 241-265

were based primarily on psychophysical measurements and presented in a totally uncalibrated context. MacLeod &Boynton recognized the nonconformality of the C.I.E. Chromaticity Diagram and sought a better color space260. They proposed a new projection space, that remained based on additive color principles, by postulating “nocontribution to luminance by B cones.” Their claim was that this projection “directly represents the excitation ofeach cone type without the use of oblique coordinates.” It exhibited the unusual feature that a bright blue light didnot exhibit any luminance because of the definition, luminance = R + G.

Their postulate that B cones do not participate in perceived luminance is a strange one. They reference Smith &Pokorny as the first source of this position261. However, fig. 3 of that paper clearly shows the shoulder near 437 nmthat represents the contribution of the blue spectral channel to the formation of what is clearly a photopic luminousresponse. Smith & Pokorny do not address directly the subject of B cone participation in the overall luminousresponse. Their second source is two papers by Tansley et. al. in 1978. Tansley & Glushko stipulate that theycarefully selected protanopes missing a red cone and deutranopes missing a green cone262. Yet, their photopicluminous efficiency functions for these individuals matched each other as well as that of a normal trichromat. Tansley & Boynton make a more defendable observation with regard to the dependence of matching colors acrossthe transition line of a bipartite field under minimally distinct border (MDB) conditions263. They conclude that “theB cones make little or no contribution to the perception of borders at the MDB point.” This appears to have more todo with the bandpass of the P-channel ( as noted in the NTSC, see Section 17.3.3.2.8 xxx) than it does with theparticipation of the S-channel in the luminous efficiency function. Neither of these papers offered any model of thevisual system they were attempting to evaluate.

In 1983, Drum re-examined the subject of S–channel signals contributing to the “achromatic sensitivity function.”264 His graphics show a considerable contribution from the short wavelength photoreceptors in the luminous efficiencyfunction, reminiscent of the Judd discussions of the 1950's. Even while using 3400 K light and an equal energyassumption, he concluded that the premise that b-cones did not contribute to the luminosity function should be re-considered.

MacLeod & Boynton stress the lack of conformality in their figure without using the term. They perform elaboratecalculation that relate back to the underlying C.I.E. dataset to describe distances that are apparently equal in theirfigure. They note the variation in threshold with position in their figure. No experimental verification of their colorspace was provided in their paper.

All of the scales used in the M-B color space were relative scales. However, they did plot a spectral locus on thegraph with absolute wavelengths shown. The vertical, b, scale was defined as b = B/(R + G). The horizontal scalewas defined by R + G = 1. These scales do not relate to any electrical or physiological model of the visual system.

17.3.1.5.2 The DKL model of Derrington, et. al. based on electrophysiology

Derrington, Krauskopf & Lennie have made measurements at the LGN of a group of macaque monkeys265. Theirbasic assumption was that the signals they recorded at that location were linearly related to the intensity of thestimuli provided. The so-called DKL color space was an outgrowth of the McLeod-Boynton approach. They used aspherical coordinate system that was largely conceptual. Their detailing of this system appears ambiguous. Theyclaim they the luminance scale reflected the contribution of all three spectral channels proportionally. However, theylater speak of luminance cells that responded only to the sum of the R and G components of the stimulus. They saidthe two axes in the chrominance plane intersected at the white point. However, they did not indicate the significanceof negative values of B along the constant R & G axis. Most of their discussion involve measurements on cellsexhibiting a difference signal, i. e, R-G or B-(R&G) or their negatives. They did not define the mathematical


266Derrington, A. & Lennie, P. (1984) Spatial and temporal contrast sensitivities of neurons in lateralgeniculate nucleus of macaque. J. Physiol. vol. 357, pp. 219-240267Chatterjee, S. & Callaway, E. (2002) S cone contributions to the magnocellular visual pathway inmacaque monkey Neuron vol. 35, pp 1135-1146268Chatterjee, S. & Callaway, E. (2003) Parallel colour-opponent pathways to primary visual cortex Naturevol. 426, pp 668-671269Walkey, H. Barbur, J. Harlow, J. & Makous, W. (2001) Measurements of chromatic sensitivity in themesopic range Color Res. Appl. suppl vol 26,pp S36-S42

relationship expressed by R&G. However, it is defined in a preceding companion paper266. The symbology R&G isused to describe “some combined signal from red-sensitive (R) and green-sensitive (G) cones.” They also assumedthat the frequency of the action potentials represented a vector that was directly proportional to the modulation of thesignal at the point of measurement. This vector could be resolved into a component related to the modulation ofeach of the three classes of cones (assumed vector addition).

Based on their analysis, they offered two estimates of the wavelengths associated with two specific colors Thesewavelengths were determined using an approach similar to Krauskopf, Williams & Heeley discussed above. As willbe seen below, the two estimates offered by DKL differed from the values proposed here by only a few nanometers. This was primarily due to their assumption that the C.I.E. 1931 Chromaticity Diagram was conformal (See [Figure17.3.5-8]).

No unit vectors were defined for the DKL color space. The axes were only defined conceptually.

17.3.1.5.3 The Chatterjee & Callaway data based on electrophysiology

Chatterjee & Callaway have recently reviewed the participation of S-channel photoreceptors in macaquemonkeys267,268. Their experiments were based on a tri-color monitor as a light source. Although they performedextensive calibrations to maintain stability within their experimental data, they did not describe the effective colortemperature of their monitor. Modern monitors have a typical color temperature exceeding 5000 K. Sperling &Harwerth have shown that the spectral performance of macaque monkeys and humans is virtually identical (Section12.2.2). Chatterjee & Callaway showed the S–channel photoreceptors contributed 9% to the overall photopicspectral response of their subjects. This value was based on the additive assumption concerning the contribution ofindividual spectral channels to the total response rather than the more appropriate logarithmic assumption used inthis work. Their value was determined from electrophysiological response as a function of contrast based onnormally adapted and spectrally adapted eyes. In either case, it is clear that the S–channel photoreceptors play asignificant role in the photopic luminosity function of mammalian eyes.

17.3.1.6 Recent measurements in the mesotopic region

Walkey, et. al. have recently presented some measurements269. Unfortunately, they used photometric units todetermine stimulation levels on a tricolor monitor. It would have been preferred if they had calculated the amount ofstimulation on a spectral channel of vision basis. They originally determined their data points in CIE (1931) x, yspace and then transformed them to CIE (1976) u’,v’ space. Most of their work was within a relatively narrow chromatic range of the CIE color space. Their data appears to highlight two conditions, the continuednonconformality of the CIE scotopic color space and the greater loss of chromatic performance of the eye along thered-green axis. They noted on page S41; “The nonuniformity of the u’, v’ color space is well known, . . .” Theyalso noted that the asymmetry in their ellipses varies with stimulation level. The cause of this will be developedtheoretically in Section 17.3.3.6.

17.3.1.7 Continuing difficulties in empirical experiment design

17.3.1.7.1 The persistent introduction of pigment triangles and tetrahedrons

Many investigators have attempted to represent the color space of the trichromat, and more recently the tetrachromat,using equilateral geometric figures. As discussed in Section 16.1.3, these color spaces are highly nonconformal. Their value is limited almost entirely to introductory level pedagogy. They are unable to represent the full


270Goldsmith, T. (1990) Optimization, constraint, and history in the evolution of eyes. Quart. Rev. Biol. vol.65, no. 3, pp 281-322271Neumeyer, C. & Arnold, K. (1989) Tetrachromatic colour vision in goldfish and turtle. XXX pp 617-631272Davson, H. ed. (1962) The Eye, Volume 2: The Visual Process. NY: Academic Press, opposite pg 234

Figure 17.3.1-2 The appearance of 10 degree fieldsarranged for metameric matches with differentcombinations of spectral lights. A 2 degree circle hasbeen superimposed on each field. See the higher qualityplate referenced. The outer parts of the field give aperfect match, but the central part, “Maxwell’s spot,”does not. The effect varies considerably in differentobservers. The numbers at the sides give the wavelengthsin nm mixed in each half of the matching field. From aplate in Davson, 1962 redrawn from an original by Stiles.

perceptual range of color. Goldsmith used these forms in a recent review270. In an unusual twist, he used the termsS, M & L as relative terms in his figure 23. The lower left of his triangles are both marked S but they refer todifferent wavelengths in the blue or ultraviolet. Neumeyer and others have generally used the terms UV, S, M & Las absolute terms271. Since these color spaces are nonconformal, they have little utility in research. The variousinconsistent figures in the literature attempting to plot the spectral locus within such a space illustrates thedifficulties involved.

17.3.1.7.2 A critical problem with CIE conforming color measurements

The CIE has settled on the use of 10 degree and 2 degree fields for the collection of visual data over a period ofyears. When collecting data using the smaller field, it is quite common to use a bipartite field of this size surroundedby a larger field, typically of degrees. The bipartite field is frequently split by a horizontal line. Figure 17.3.1-2shows that this is an inherently poor choice. The figure is reproduced from a plate in Davson based on an original byW. S. Stiles272. The original plate should be viewed to better interpret the following remarks.

In each panel of the figure, the field is quite uniform, indicating an excellent match during chromatic discriminationstudies, except for the central region along the line of fixation. In these studies, the results become quite differentwhen the area within the 2 degree field surrounding the line of fixation is studied. There is a small area of about 1.2degrees that is representative of the foveola of the retina. However, in the transition between this area and thesurround, the measurements show two lips. These lips exhibit a smooth variation in chromatic discriminationcapability with distance from the point of fixation, due to averaging of the signal illuminated by the test source.

Measurements within the 1.2 degree area representing the foveola are relatively uniform, except for a sharp divisionbetween the upper and lower lips. This division appears to be due to the method of chromatic discrimination withinthe higher neural centers of the brain. The area above and below the horizontal meridian are processed by separateregions of the brain and then merged. It appears the merging is not done well. In practice, the visual system doesnot rely upon chromatic discrimination in this region. The system is known to be largely insensitive tospatially fine changes in color within this area. Itappears to rely upon the average value of thesurrounding colored region to define the perceivedcolor of material within the area of the foveola.

17.3.1.8 A new conformal color space basedon electrophysiology is required

There is an obvious need for a truly conformal colorspace adequate for research purposes. Such a spacewould replace the earlier attempts at such a spacediscussed above. It would necessarily be atetrachromatic color space to accommodate the genericvisual system. Finally, it would recognize theelectrophysiological architecture of the visual system. This architecture is based on multiple signalingchannels employing differences in scalar voltages. Itwould not be based on the concept of additive color. Such a color space is presented in Section 17.3.3.

17.3.2 The chromatic discriminationfunction, C(8,F)

17.3.2.1 Background

There is good wavelength discrimination data for the


273Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 570-274MacAdam, D. (1942) Visual sensitivities to color differences in daylight J. Opt. Soc. Am. vol. 32, no. 5,pp 247-273275McCree, K. (1960) Colour confusion and voluntary fixation Opta Acta, vol. 7, pp 281 and 317-323. Also in Crone R. (1999) A history of color Boston, MA: Kluwer Academic Publishers pg. 197

human eye in the literature. Wyszecki & Stiles273 provide a good review as of 1982, although individual cited papersmust be examined on questions of experimental procedures. Of particular importance was the energy distribution ofthe illumination source used, the band edge characteristics of the filters used, and the statistical variation in therecorded data. As Wyszecki & Stiles noted, “Wavelength discrimination depends on the luminance level, surround,field size, portion of the retina used...as well as the technique of observation (strict fixation or scanning).” As theynoted using the data of Willmer & Wright, under strict conditions of fixation, the wavelength discrimination wasgreatly reduced. In fact, based on this work, it should disappear in the absence of temporal changes in the sceneassociated with presenting the test imagery. Willmer & Wright’s data shows a better sensitivity in the 532 nm. to625 nm. region than at shorter wavelengths under fixation conditions. However, this work would suggest that part oftheir increased sensitivity may be due to the flicker rate used in their experiments. The square-law response of the L-channel appears to contribute to this change in sensitivity.

The data from Wright & Pitt (1934) for a two degree diameter bifurcated field is very similar to the 1958 data ofBedford & Wyszecki except in the 400-430 nm. Region where it appears Wright & Pitt were probablyinstrumentation limited. Whereas Wright & Pitt reported data at 70 Trolands, Bedford & Wyszecki reported for 100,500, & 2000 Trolands while using different and smaller field sizes. The variation in discrimination capability withrespect to illumination level does not appear systematic in the latter data, probably because of limited repetition ofthe experiments and no statistical averaging. MacAdam has provided very precise data274.

McCree has provided data at 0.85 and 150 Trolands275.

No significant discussion of the theoretical wavelength discrimination capability for human, or animal, vision couldbe found in the literature. The only discussion was based on a mathematical calculation based on a “line model” ofthe visual detection process. The recent experimental data of Griswold & Stark concerning aphakic human eyes inthe ultraviolet is relevant and reviewed in Section 17.2.5. It strongly suggests the short wavelength limits on thechromatic discrimination function is due largely to the absorption of the lens.

17.3.2.2 Theoretical capability

As in the case of the new Chromaticity Diagram, it is expedient to consider the signaling situation at the input to themidget ganglion cells. This allows deferral of discussion about the signaling characteristics between the ganglioncells and higher cognitive centers, e.g. using the pulse techniques associated with projection neurons. The nominalsituation is shown in Figure 17.3.2-1 for any chordate, including humans. While the spectral absorption band of theUV–channel is truncated in the humans, and other large chordates, by the absorption of the lens (see Section 2.4.2),there is data showing the UV–channel photoreceptors are functional in these retinas. Data was reviewed in Section17.2.5 that supports the conclusion that this is true even in adult humans.


Figure 17.3.2-1 The signal flow schematic used for calculating the chromatic discrimination function of humanvision (and other chordate vision). The details of spatial encoding are ignored in this figure. Photoreceptor cells infoveola (also) connect directly to individual bipolar and parasol ganglion cells projecting directly to the Pretectum. While the UV–spectral channel is truncated in large chordates, it still plays a significant role in chromatic vision.

Because of limited data to aid in determining whether the relevant lateral cells are associated with the Inner or OuterPlexiform Layers, only the designation lateral cells will be used. Each transducer element (Trans) contains theappropriate chromophore. Each element labeled G may be either a photoreceptor cell or a combination of aphotoreceptor cell and a bipolar cell. During the discussion of chromaticity, the only condition on these amplifiersare that they exhibit a stable gain condition during experimental procedures. This requirement is compatible with thesmall signal tests anticipated. It is also compatible with the operation of the adaptation amplifiers within thephotopic operating region. It is desired to determine the nature of the signal applied to each channel represented by amidget ganglion cell (MG). What is at the moment unspecified is the order of subtraction in the lateral cells(triangular symbols) and the difference in gain between the lateral cell inputs, if any.

17.3.2.2.1 Simplified calculation of the amplitude portion of the C(8,F)

To simplify the mathematical manipulations required in this discussion, this section will ignore the contribution ofthe UV–channel photoreceptors. The methodology can be expanded by the reader if desired. The contribution ofthe UV–channel will be considered in the overall performance provided by the chromatic threshold function.

Assuming the lateral cells have a linear transfer characteristic, the output of each cell as a function of the amplitudeof the inputs should be a straight diagonal line. The major question is whether, the input presented to the lateral cells


Figure 17.3.2-2 (a)The transfer function between thelogarithm of the input illumination and the output of thelateral cells of the chrominance channels. (b) Thederivative of the of the transfer function. Solid line; shortwavelength chrominance channel. Dotted line; longwavelength channel assuming linearity. Dashed line; longwavelength channel assuming L-channel follows a square-law relationship.

is a current directly associated with the signal current or a voltage representing the logarithm of the signal current. Both assumptions were examined in the development of the following scenario. It was found that only thelogarithmic assumption conformed to the measured data. Thus the input to the lateral cells will be taken as thevoltage at the output node of the amplifiers, typically the pedicle of the photoreceptor cells.

The signals at the output of the lateral amplifiers is then given by:

C = ±(ln A - ln B) and G = ±(ln D - ln E)

where A, B, D & E may have different peak amplitudes.

The sensitivity to each of these channels to variations in the input is generally found by taking the derivative of thesignal C or G and comparing it to some threshold value, either a fixed threshold level or possibly a statistical noiselevel. This is a trivial step until the actual input as a function of wavelength is specified. Under the specifiedconditions of stable small signal gain, the input as a function of spectral wavelength for each channel is described bya gain term multiplied by the absorption characteristic of the individual chromophoric transducer. Considering all ofthe gain terms to be equal to a constant for the moment and setting that constant to unity, Figure 17.3.2-2 (a) and(b) show the resulting output signals and their derivatives using the parameters of the Standardized Human Eyefound in this work. These curves are shown on the assumption of a constant photon flux per unit spectral bandwidthacross the spectrum and recognize the square-law characteristic of the L-channel. They also make the assumptionthat C is given by the form A - B, or the S-channel minus the M-channel signal. In the second case, G is given bythe form D - E, or the M-channel minus the square of the L-channel signal.

The solid line in (a) represents the transfercharacteristic at the output (C) of the short wavelengthdifferencing circuit. Note the change in the characterof the function at the extremes. The function ismonotonic. This differencing circuit providesexcellent performance between 400 and about 560 nm.with a nominal midpoint at 486 nm. It provides nosensitivity to wavelengths outside of this range. Thedotted line represents s similar fictitious situation for along wavelength differencing circuit wherein the L-channel transducer was linear. It is also monotonicand provides excellent but unrealizable performance. The dashed line represents the output (G) of the longwavelength differencing circuit for the real situationwith the L-channel de-excitation process creating asquare-law type signal. The linearity of the outputsignal is not as good as for the short wavelength case. In addition, the curve is not monotonic, showing areversal in slope beyond 655 nm. However, it isadequate within the region it is normally used as seenbelow.

Yang, et. al. have provided data for the goldfish thatclosely tracks the theoretical short wavelength


276 Yang, X-L. Tauchi, M & Kaneko, A. (1983) Convergence of signals from red-sensitive and green-sensitive cones onto L-type external horizontal cells of the goldfish retina. Vision Res. vol. 23, no. 4, pp.371-380277Trezona, P. (1976) Aspects of peripheral colour vision, in Modern Problems in Ophthalmology, Streiff,E. ed. vol 27, pp 52-70

discrimination function presented in (a)276

Pane (b) of the figure presents the derivatives of the functions in (a). The solid line represents the short wavelengthcircuit and the dashed line represents the actual long wavelength circuit. The dotted line is shown only for referenceand assumes a linear L-channel response to photoexcitation. The solid line actually presents a better fit to the datapoints of Trezona (for observer PMG labeled Y(588 nm)) than does her proposed best fit277. Similarly, thetheoretical dotted line fits her data for B(468nm) quite well after factoring in the absorption of the lens atwavelengths shorter than 400 nm.

17.3.2.2.2 Calculation of the complete chromatic threshold function

If the merging of the information from the individual chrominance channels is as suggested in the previousparagraph is correct, the theoretical composite chrominance amplitude function becomes quite similar to that shownin [Figure 17.3.2-2], a nearly straight line with a constant slope across most of the visual spectrum from the 400 nmlimit due to the lens out to about 600 nm.. The derivative of such a line is a constant. This derivative would definethe change in composite chrominance signal amplitude as a function of wavelength interval.

Investigations supporting this work have generally described the dominant noise (or threshold) factor in the visualsystem under photopic conditions to reside in the stellate cells of the CNS. If this is correct, the theoreticalcomposite chrominance threshold would be related to the absolute amplitude of these thresholds in the individualchrominance channels. If these threshold were equal, the theoretical composite chrominance threshold functionwould then be a constant signal amplitude as a function of wavelength interval divided by a constant threshold value. Under these conditions, the theoretical function would be essentially a constant truncated by the overall absorptionenvelope of the visual system.

[Figure 17.3.2-2(a)] suggests that the performance of the human visual system need not employ the UV–channelphotoreceptors of its retina. Alternately, [Figure 17.3.3-2 ] suggests that it may. The few documented reportsavailable for both normal and aphakic humans suggest they perceive a very de-saturated color when exposed tonarrowband light at 400 nm. These observations would indicate the O–channel is fully functional and controllingthe perceived chrominance in humans. The perceived color is labeled lilac in this work. The consequences of thisfinding will be explored in Section 17.3.3.2.

17.3.2.2.3 Apparent equal participation of the spectral channels in forming C(8,F)

While the form of the luminance threshold function, T( λ,F), suggests the dominance of the M–channel in theperception of luminance, this does not appear to be the case with respect to the perception of chrominance. As aresult, the question raised in the theoretical formulation of the luminance threshold function can also be addressedhere. The amplitude of the chrominance threshold function across the visual spectral band appears nearly constant(truncated primarily by the absorption associated with the lens and the long wavelength skirt of the L–channelspectrum). This suggests that the contributions of the individual spectral channels to the chrominance thresholdfunction are nearly equal. If true, this would suggest that the density of the spectrally selective photoreceptors werenearly uniform in the retina of Chordata throughout their lifetime.

17.3.2.2.4 C(λ,F) under mesotopic conditions

The chromatic threshold function is a clear example of a function defined in terms of signalto noise ratios at apoint(s) within the CNS. The noise threshold within the CNS remains essentially constant. Similarly, the signalamplitude is also held constant within the photopic operating range. However, the signal and the resultant signal tonoise ratio begin to fall as the system enters the mesotopic operating region. Because of this, the chromaticthreshold function, frequently expressed in terms of a just noticable spectral difference (JND) as a function ofwavelength, begins to take on a more complex shape than within the photopic region.

While the function generally shows a reduced JND across the spectrum as a function of light level, the effect is morepronounced in the Q–channel region of the spectrum because of the square-law character of the L–channel signal


278Uttal, W. (1981) A taxonomy of visual processes. Hillsdale, NJ: Lawrence Erlbaum Associates, pg 422

and the resultant Q–channel signal. The evaluation of the function is also compounded by the fact that the intrinsicsignal to noise ratio of the signal due to quantum fluctuations in the photon flux must also be considered. Because ofthe complexity of the mathematical manipulations involved, the complete function will not be evaluated here. Instead, data from the literature will be presented as the baseline.

17.3.2.3 Comparison with the literature

Figure 17.3.2-3 presents a comparison of the theoretical and measured chromatic threshold function under photopicconditions. In this case, the noise level is dominated by the noise of the stellate cells of the CNS. Frame (a) isdrawn on the assumption that the higher cognitive center eventually receiving the two chromatic difference signalsfrom the midget ganglion cells is able to select the channel that gives the best spectral wavelength discriminationsignal. Thus, at wavelengths shorter than a nominal 500 nm., the short wavelength difference signal will be used. At longer wavelengths, the long wavelength difference signal will be relied upon. The resulting wavelengthdiscrimination function is calculated using the input from only three photoreceptors, one chromophoricphotoreceptor of each type.

Figure 17.3.2-3(b) presents the wavelength discrimination function from data of Bedford and Wyszecki, forobserver G.W. The presentation is a bit complex because of the test conditions used. Several variables were variedat one time. The solid curve represents a horizontally bifurcated visual field of one degree and a nominalillumination level of 100 Trolands. The dashed curve represents two 2.0 minute diameter visual fields with centersseparated by 24 minutes of angle. The test fields are illuminated at a nominal 500 Trolands. The dash-dot curve isfor two 1.5 minute fields separated by 40 minutes and illuminated at 2,000 Trolands. The horizontal scales of (a)and (b) are different. The “projected wavelength diff.” scale in (a) is completely arbitrary and is added only to aid inthe comparison. The scale value of 6 was aligned with the transition point near 625 nm. The scale raises manyquestions which deserve experimental attention. It would be useful to determine the relationship between theminimum detectable color difference and the associated signal to threshold ratio within the cognitive center. Datafrom several investigators over a more limited spectral range is summarized in Uttal278. The empirical law of hisfigure does not conform to the actual situation in the region of 400 to 450 nm.


279Wyszecki & Stiles, op. cit, pg. 665280Pg. 308281Hurvich, L. & Jameson, D. (1955) Some quantitative aspects of an opponent-colors theory. J. Opt. Soc.Am. vol. 45, pg.602

Figure 17.3.2-3 The proposed wavelength discriminationfunction for human vision and relevant supporting data. (a) The theoretical function. (b) Measured datadescribing the same function based on a three light levelsand visual field sizes. See text. From Bedford &Wyszecki (1958)

The agreement between the proposed theoreticalwavelength discrimination function and the measureddata is remarkable. The agreement is exceptional evenwithout taking into account the quality of the filtersused in the laboratory experiments or otherexperimental considerations discussed earlier (such asthe large spacing between the test fields at highluminance levels). It should be noted that the primarycompeting model in this area, the Stiles line elementmodel279, does not indicate any minor maximum in theregion of 440-460 nm. at all. There have been anumber of “line element” models. They all involve anumber of assumptions and approximations notsupported by the actual measured data.

The line element model of Stiles and the related testdata of both MacAdam280 and Wyszecki & Fiedler allhave presented a series of discrimination ellipses thatare similar and point generally to the actual peakchromophoric absorption wavelengths proposed in thiswork, 437,532 and 625 nm. The discriminationsensitivity figures are ellipses because the coordinatesystem used was not a conformal one. When plottedon the various C.I.E. chromaticity diagrams, theygenerate graceful arcs terminating at the abovewavelengths. The basic data needs to be re-plotted in aconformal space such as the proposed NewChromaticity Diagram for Research. See Section17.3.3.

The transfer functions between the logarithm of theinput illumination and the output of the lateral cells ofthe chrominance channels, shown in [Figure 17.3.2-2(a) can be compared with the valence functionsdefined by Hurvich & Jameson281, and frequentlyreproduced. While they are conceptually similar, they are quite different in detail.

The valence functions of Hurvich & Jameson are entirely postulated based on heuristic assumptions drawn frompsychophysical experiments, and relate to the Hering school. Furthermore, their experimental design did not call for“double blind” procedures. In fact, they used data based on their personal visual performance. The failure to usedouble blind procedures has been a frequent expedient and common problem in visual research. They were theleading and outspoken exponents of the Hering Theory in their time. This apparently shaped how they interpretedand presented their data.

At the extremes in wavelength, their functions appear to go to zero because of a loss in brightness sensitivity not aloss in chromatic response. It appears their valence functions are related to the product of chromatic sensitivity andbrightness sensitivity. Between the extremes, their valence functions are biphasic or even triphasic. Theirchromatic valence versus wavelength function for the short wavelength difference, labeled blue-yellow, isappropriately positioned but trails off inappropriately at the extremes and appears mis-assigned with respect to theproposed source. Their long wavelength difference function also appears poorly positioned and shows a reversalbelow 530 nm. which is not found in the actual situation (See Section 17.3.2.4). The first order nature of theirproposition does not predict the necessary deviations in these functions. These deviations are necessary to providethe appropriate derivatives that are actually employed in the wavelength discrimination process.


282Lewis, P. (1955) A theoretical interpretation of spectral Sensitivity curves at long wavelengths J Physiolvol 130, pp 45-52

Figure 17.3.2-4 Observations of hue reversal in the deepred. From Stiles & Burch, 1955.

A surprising fact is that the theoretical long wavelength differential is in excellent agreement with the measured data. The slope of the putative long wavelength function based on the square-law characteristic of the L-channel predicts aperceived hue reversal for wavelengths beyond 655 nm. This is almost exactly what is reported by Stiles & Burch asshown in Figure 17.3.2-4.

The figure is taken from Wyszecki & Stiles, page 425. They have made slight changes in the interpretationthat should be reviewed. The data points labeledBrindley Isochromes are actual data for a four degreefield. The curves are from the C.I.E. (1964) large-fieldchromaticity coordinates for a ten degree field. Thedata appears to show, and the curves do show bydefinition, a crossover point at precisely 645.2 nm. However, the curves are abstract in that they werecomputed in the tristimulus context. The r10 (λ) valuewas not zero at this wavelength, only omitted as aconvenience. Furthermore the C.I.E. curves do nottrack the points of Brindley, especially beyond 700 nm.

The difference between a predicted cross-overwavelength for hue reversal of 655 nm. and theStandardized value of 645.2 nm. is not large, 1.5%. This is undoubtedly smaller than the experimental errorin any individual data acquisition cycle. However, it istroubling. A preliminary perturbation analysis wasperformed on the model. It was found that the relativeamplitudes of the perceived illumination and the specific ½ amplitude wavelengths of the chromophore did notsignificantly effect the predicted crossover at 655 nm. However, it was found that the color temperature of the inputradiation played a major role. As the color temperature was reduced below the equal flux condition, the cross-overwavelength and the amplitude of the hue reversal both decreased. There was no hue reversal at the equal energycondition, and of course, no cross-over. These results suggest one of two things. There may have been absorptivematerials in the optical path, either biological or man-made, that were not characterized or controlled. The optics ofthe eye are generally not color selective in this spectral range. Alternately, the color temperature of the luminanceviewed by the test subject and used to acquire the data, standardized in the C.I.E. (1964) large-field chromaticitycoordinates for a ten degree field, was not adequately controlled. It was apparently over-rich in the shorterwavelengths. This could have been due to a number of conditions in the test set, including the use of coated opticsthat were optimized for shorter wavelengths. It is important that any revised standard quantify the intensity andcolor spectrum of the radiation used to collect the data. The exact adaptation state of the subject should also bespecified.

All of the data presently available in the literature regarding wavelength discrimination, and particularly that citedabove must be considered exploratory in terms of experiment design. This is because each experiment had at leastthree independent variables that were not effectively separated and/or controlled. These include, the illuminationlevel, the precise illumination color temperature, the illumination duration, the fixation level, spatial integrationwithin the retina and spatial sharpening within the retina, particularly affecting small scenes. Consideration of thesefactors would normally result in the smoothing of the theoretical function. This smoothed result would generallyresult in even better agreement with the data.

Figure 17.3.2-5 shows a different graphic of the fold back of perceived color in human vision developed byLewis282. He notes, in agreement with the above prediction of this work, “This leads to an interesting predictionabout changes of hue in the far red. If two visual pigments, with different values of λ0, have equal gradients at somewavelength in the red their gradients should diverge again at still longer wavelengths, the pigment with its maximumfurther towards the red having the steeper gradient. In other words, if the ratio of 'red' to 'green' sensation rises withincreasing wavelength to an apparently constant value, that value must be a maximum, and the ratio should begin todecrease again at sufficiently long wavelengths. This prediction has been strikingly confirmed by the observations ofBrindley (1955).” Lewis uses 526.3 nm (1/19,000 cm–1)as λ0 in his calculations. It is proposed he could have used


1/18798 cm–1 just as well, giving 532 nm for his λ0.

.

Wyszecki & Stiles indicated there were significantsignatures in the data of Wright & Pitt and Bedford andWyszecki. Table 17.3.2-1 summarizes their remarksand compares them to those suggested by this work.

TABLE 17.3.2-1Spectral Signatures in Wavelength Discrimination

Wyszecki & Stiles This TheoryRelative maxima ~460 nm. 485

~530 500 & 546 combined

625 (inflection point at L-channel peak)

Relative minima ~440 413~490 485~590 574

The maxima and minima are obviously related to the orientation of the graph. The designations by Wyszecki &Stiles appear to be more influenced by the work of Wright & Pitt than by that of Bedford & Wyszecki. Wright &Pitt were probably limited by their instrumentation in the short wave region. Whereas the former work shows amaxima at ~460 nm., the latter work would suggest a lower number in line with the theoretical value. Thesuggested value of ~530 nm. appears to correlate well with a smoothed curve based on the theoretical 500 & 546 nm. The theoretical feature at 500 nm. may not be as sharp as shown in the figure. It represents the transition point usedby the higher computational center. At shorter wavelengths, maximum discrimination capability is achieved usingthe S- minus M- difference. At longer wavelengths, the M- minus L2- difference is more precise. The inflectionpoint near 625 nm. was not mentioned but it appears in the data of Bedford & Wyszecki.

The suggested relative minimum at 440 is clearly closer to the theoretical value in Bedford & Wyszecki. The 490nm. minimum is in good agreement with the proposed theoretical value of 485 nm. The suggested minimum near590 nm. Is clearly closer to the proposed theoretical value of 574 nm. in Bedford & Wyszecki.

Although less than obvious, the impact of the individual chromophoric channels can be seen in the proposed

Figure 17.3.2-5 Plot of equivalent wavelengths-wavelengths giving the same colour sensation in the farred. The circles are experimental values obtained byBrindley (1955) and the crosses are theoretical valuescalculated as described in the paper by Lewis. FromLewis, 1955.


283Thomson, L. (1949) Intensity discrimination of the central fovea measured with small fields. J. Physiol.(London) vol. 108, pp. 78-91284Romney, A. (2005) personal communication.285Trezona, P. (1987) Individual observer data for the 1955 Stiles-Burch 2O pilot investigation J Opt Soc AmA vol 4, pp 769-782286Neumeyer, C. (1984) On spectral sensitivity in the goldfish. Vision Res. vol. 24, pp 1223-1231

Figure 17.3.2-6 Wavelength discrimination as a functionof wavelength. Blue lines; a composite of the theoreticaldiscrimination functions of vision without any allowancefor averaging between signal paths. Red lines;empirically measured discrimination functions fromTrezona. Figure prepared by Romney, 2005.

wavelength discrimination function. They are represented by the relatively flat areas between 413 & 485 nm.,between 485 & 546 nm., and the inflection point at 625 nm.

Wyszecki & Stiles introduce the subject of fixation during experiments to determine the wavelength discriminationfunction. They show an early discrimination curve attributed to Willmer & Wright (1945). The curve shows verypoor discrimination in the 420-520 nm. region compared to the 520-620 nm. region. Their explanation that this isdue to the essentially tritanopic nature of the fovea under small field viewing conditions seems inadequate. Thediscrimination was quite good in the 520-620 nm. region. A different explanation can be drawn from the fact thatthe refractive Wright colorimeter at Imperial College used a 2848 Kelvin light source as a standard. Such a standardhas very little energy in the shorter wavelengths of the visual spectrum283.

Hurevich & Jameson collected considerable data (1° field and 37° white surround) using similar techniques. Thatwork has been reported widely and summarized frequently (Wyszecki & Stiles, pp 454-458). Romney284 hasprepared a composite of the data presented in Trezona285 and the theoretical curves of this work. The Trezona data(based on a 2° field) is reproduced in Figure 17.3.2-6. The averaged crossovers of Trezona and the theoreticalcrossovers are quite similar. at 487.8/494 nm and 579.7/572 nm respectively, and well within experimental error atthis time. Boynton reproduced a curve from Wright (1946) that shows the short wavelength crossover at 494 nm. He also explained the protocol (such as the 10° field) used in obtaining the Wright data. The major disparity in theseexperimental works appears associated with the measured red line in the vicinity of 500 nm (which also appears inWright). It probably results from the linear assumption of signal addition commonly found in the early literature.

Neumeyer has collected information on the spectralsensitivity of goldfish286. There is considerableagreement between figure 4 of her 1984 paper and thetheoretical waveform of [Figure 17.3.2-3] if a fewpoints are noted. She used an inverted ordinate andtruncated the measurements at 400 and 725 nm. Aquestion can also be raised concerning themeasurements at 725 nm with respect to the actualintensity of the test source at this wavelength. Thesensitivity between 510 and 560 nm is difficult toresolve with filters of 8-14 nm width (as in the case ofsimilar data for humans from Bedford & Wyszecki). Within these considerations, her peaks at 470 nm, 530-540, and 660 nm are comparable. As seen in theanalysis of this work, these peaks are due to adifference between the response of the individualchromophores and have no direct relationship to thespectral peaks of the underlying chromophores at 437,532 & 625 nm (or as listed in that paper, 450, 530 &625 nm).

17.3.2.3.1 Discrimination versus fixation

If one separates the question of field size fromillumination intensity and from the degree of fixation in the experiments of Willmer & Wright, a more appropriateexplanation is available. Recall that the degree of fixation we are discussing here is related to the control of the so-called tremor of the eye, not the gross motions associated with tracking or scanning. This work has reviewed thedata in the literature that confirms that the visual mechanism in animals requires a change in signal level at thephotoreceptor for detection. More precisely, a change is required that is adequate to exceed the discriminationthreshold in the higher cognitive centers. The change may be generated temporally or spatially through relativemotion between the line of sight of the photoreceptor and the object field. Because of the square-law nature of the


Figure 17.3.2-7 Measured and predicted values of thewavelength discrimination function in humans. The lowerfigure shows the predicted function for six differentillumination levels at a color temperature of 7053 Kelvin. The upper figure is for two illumination intensities. Thecolor temperature of the source was not given. FromMcCree (1960).

L-channel response, the changes in response applied to the long wavelength discrimination circuits are larger thanthose applied to the short wavelength discrimination circuits for the same degree of temporal or spatial change. Normally, the tremor of the eye is approximately one pixel in amplitude. This amplitude is large enough to cause anadequate signal for most scenes. However, as the scene detail is reduced, the tremor is not adequate and the signalsgenerated fail to exceed the threshold level required by the brain. The experiments of Willmer & Wright wereperformed in the 1940's and used “strict fixation,” a less than precise term. However, the degree of fixation waslarge enough to cause the average wavelength discrimination capability in the short wavelength region to fall to 50nm. while the long wavelength average remained below 5 nm. Clearly, these experiments had nothing to do with atritanopic condition in the fovea.

As seen elsewhere in this work, if the degree of artificial spatial fixation had been 100%, the only wavelengthdiscrimination capability of the human eye would have been due to temporal transients. The word “null” at the topof the y-axis in the figure is to denote a meaningless value for the wavelength discrimination capability at zeroangular motion of the line of sight with respect to the object, e.g. zero tremor or 100% tremor compensation in thetest equipment. Before reaching the null condition, both the short wavelength and long wavelength discriminationcapability will approach 100 nm., their nominal maximum condition due to the width of their differencing range. The short wavelength discrimination capability willapproach this limit faster than will the long wavelengthcapability due to its inherent square-law capability asindicated earlier. The curves labeled 1, 2 & 3 illustratethese conditions.

17.3.2.3.2 Discrimination versusIllumination

The gross characteristics of the wavelengthdiscrimination performance of the human eye can bepredicted based exclusively on the model. Assumingthat the theoretical discrimination function of Figure17.3.2-3 represents the photopic performance of theeye, the performance under mesotopic and scotopicconditions can be estimated. Figure 17.3.2-7 containsmeasured wavelength discrimination function at twoillumination levels and a predicted wavelengthdiscrimination function as a function of illumination. The upper half of the figure is from McCree. Thelower half of the picture shows the predictedperformance of the eye based on this work.

At lower light levels, only a straight line segment isused. Initially, as the illumination level is reduced, theadaptation amplifier gain in each photodetectionchannel will attempt to rise in order to maintain arelatively constant signal amplitude at the input to thedifferencing circuits. As long as this signal level canbe maintained in each channel, the function willresemble the theoretical curve, 5. As the illuminationis reduced farther, the performance capabilityassociated with the long wavelength discriminationcapability will fall faster than its short wave equivalentdue to the square-law nature of the L-channel, 4. Thisperformance can be associated with the mesotopicrange of vision and will continue up through 3. As theillumination level is still farther reduced, the signallevel in the L-channel becomes too low for effectiveoperation and the Scotopic region is reached, 2. In thisregion, the long wavelength discrimination condition isnull and the short wavelength discrimination capabilityis quite low if not null. At this illumination level,vision is essentially achromatic. At lower light levels,both channels are at null, 1, and vision ismonochromatic.


287Wyszecki, G. & Stiles, W. (1982) Color Science. 2nd. Ed. NY: John Wiley & Sons. pg. 422288Vos, J. & Walraven, P. (1972) An analytical description of the line element in the zone fulctuation modelof colour vision. Vision Res. vol. 12, pp. 1327-1365289Weale, R. (1960) The eye and its function. London: Hatton Press. Pg. 127290Walraven, P. (1962) On the mechanisms of colour vision. Soesterberg, Netherlands: Thesis, Institute forPerception pg. 63

Figure 17.3.2-8 Wavelength discrimination functions forvarious tests field sizes. From Weale, 1960.

Purdy has provided data related to this figure that has been interpreted by Wyszecki & Stiles287. They interpret thedata for a three degree field split field with intensities of 100 Td and 1000 Td, to be a Bezold-Brucke hue shift withchanges in retinal illuminance. Based on the model, this should be interpreted as a change in hue sensitivitybetween these two levels. Because of the large change in illumination intensity, part of this sensitivity shift may bedue to a change in the adaptation level of the chromatic photodetection channels also. By subtracting these twofunctions, a hue shift can be defined. However, this shift is not due to a change in mechanism leading to a hue shift,only to a change in sensitivity. Vos and Walraven have also provided calculated wavelength discriminationfunctions for three different illumination levels based on a line element (geometric) model of the visual process288.

17.3.2.3.3 Discrimination versus spatial integration

The order of spatial integration appears to vary with location within the retina. Only a few data were found in theliterature describing the effect of spatial integration on chromatic discrimination. Most only reflected differences asa function of circular test field size (presumably in the region of the fixation point). Figure 17.3.2-8, from Weale289

shows the data of Forshaw for one degree, 27 minute, and 14 minute field diameters. These field sizes areconsiderably above the size of individual pixels in the field. They suggest a significant discontinuity in the 460 nm.region for very small field sizes. Nothing has appeared in the development of the model to account for thisdiscontinuity. A similar discontinuity, involving tritanopes, has been discussed by Walraven290.

17.3.2.3.4 Color discrimination in cases ofanomalous color vision

The data of Section 16.3.4.5.5 suggests that thesimplified analysis of color discrimination based onlyon the P– and Q–channels may not tell the completestory for human vision. Wright noted that in theabsence of proper operation of the P–channel, thesubjects still showed “very keen wavelengthdiscrimination in the far violet.” That data stronglysuggests that the O–channel plays a significant role inhuman color discrimination in the 400-437 nm region. If true, the curve in [Figure 17.3.2-6] is the result ofmerging all three chrominance channels with theO–channel dominating below 437 nm, the P–channeldominating from 437 to 532 nm and the Q–channel dominating at wavelengths beyond 532 nm.

17.3.2.3.5 Discrimination versus other independent variables

On first review of Figure 17.3.2-3, it is surprising to see the wavelength discrimination of the human eye becomesbetter at lower illumination levels. Further review shows that this is only because of the difference in test image sizeused. The immensely larger test field size used at the 100 Troland level impacts the interpretation of the results. Itis reasonable to assume this is due to spatial integration among the illuminated photoreceptors. It may also be thatthe narrow gap between the two halves of the test field provide additional signal enhancement involving spatialdifferencing. Such differencing may be designed to “sharpen” the edge response of the channels due to thescanning motion of the photoreceptors, in response to tremor, and their finite size.

If more extensive data were available regarding wavelength discrimination as a function of illumination that was notpolluted by variations in test field size, it would be possible to select an appropriate illumination level and perform aseries of tests involving only the size of the test field, or only the spacing of the test and reference fields. The


information gained could provide significant information concerning the role of spatial signal enhancement inwavelength discrimination performance.

17.3.2.4 Comparison of the C(λ,F), T( λ,F) and V(λ) functions

Figure 17.3.2-9 compares the photopic Chrominance discrimination and the luminance discrimination functionsplotted with respect to wavelength and normalized to a common value. Both the empirical luminosity function, CIEStandard V(λ), and the theoretical luminance threshold function, T(λ,F), are shown. The critical feature to note isthe much flatter and broader character of the measured chrominance discrimination function. It closely matches theproposed chrominance threshold function, C(λ,F) for F near 100 Trolands. The horizontal dash-dot line is thetheoretical chrominance threshold function without incorporating any loss in sensitivity at the edges of the spectralband of the S– or L–spectral channels. It is the derivative of the chrominance discrimination function of [Figure17.3.3-2]. The chrominance discrimination function remains nearly two orders of magnitude higher at 437 nm thanthe empirical luminous efficiency function, and about one order higher than the theoretical luminance thresholdfunction. The situation is similar, but not as prominent near 625 nm. This difference highlights the uniquelyseparate signal processing paths proposed in the fundamental block diagrams of the visual system presented inSection 17.1.4. It also confirms that the gain coefficients used to compute the performance descriptor of theluminance channel, T(λ,F), are different from the coefficients used to define the performance descriptor of thecomposite chrominance channel, C(8,F).

No data is currently available for the change in the theoretical chrominance threshold function, C(8,F), as a functionif the intensity level.

17.3.2.5 Features of the new function

Besides providing a road map for the identification of features in future wavelength discrimination experiments, theproposed wavelength discrimination function places a clear limit on the capability of the human eye to discriminatecolors. There is a very well defined zero in this capability at wavelengths below 380 nm. There is also a longwavelength limit. Further analysis and/or experiment may be needed to determine if it is at 655 (the point of polarityreversal) or 696 nm. It is also clear that wavelength discrimination degrades in an orderly manner with illuminationlevel. It degrades more rapidly in the long wavelength portion of the spectrum. The degradation continues in boththe long and short wavelength channels until it has a magnitude on the order of 100 nm. as limited by the maximumamplitude excursions of the differencing circuits, as a function of wavelength. At still lower illumination levels, nowavelength discrimination is reported by the animal. Whether the cessation of color discrimination is related to theanalog circuitry of the retina or the circuitry related to higher computational centers is unresolved.


Figure 17.3.2-9 Comparison of the chromatic and luminous discrimination functions. Solid line, Bedford &Wyszecki, 1958. Long dashed line, CIE (1924) visibility function, i. e., a negotiated Standard based on anunrealizable (ficticious) Standard Observer. Short dashed line, theoretical luminous threshold sensitivity function ofthis work in the absence of filtering. Dash-dot line, the theoretical composite chrominance threshold function assuggested by this work (ignoring truncation due to the absorption spectrum of the visual system).

The function could easily be expanded to include the effect of spatial integration with image field size if more datawere available.

17.3.3 Definition of a “New” Chromaticity Diagram

This section will employ a variety of color graphics to illustrate the concepts involved in anew chromaticity diagram. However, it must be noted that neither the available printingtechniques nor the available trichromatic monitors are able faithfully to reproduce the colorsassociated with the different wavelengths of light. (See Section 17.3.3.3.8). The human visualsystem has a color palette broader than any of these systems.

Currently the hue, saturation and luminance palettes of computer programs have notevolved to an industry standard. As they are currently, these palettes are designed to onlyencompass the three primaries defined in terms of additive color by the conventionalwisdom. They are unable to address the perceived fully saturated color capabilities of thehuman eye at 415 nm (saturated purple), the limit of short wavelength vision near 395 nm and the nominal limit of long wavelength vision near 655 nm.

Because of these limitations, the actual color related to a given wavelength of light is bestdetermined by observing the atomic spectral lines of radiating gases. Only approximatecolors can be presented using any other techniques. When observing such a line, recall thatthe human visual system is not able to memorize a specific color. It is designed to perceiveinstantaneous differences in color over small spatial distances.

The recognition that the human visual system, along with that of most other chordates (if not all animals), istetrachromatic requires development of a New Chromaticity Diagram for Research. The new Diagram must bebased on real color-mixture data using the proper transformations (which are not homogeneous or linear). Such adiagram can be based on a variety of foundations; biophysical, electrophysical, psychophysical or other.


While Griswold & Stark have shown that the aphakic human eye is tetrachromatic, there are still questionsconcerning whether the O–chrominance channel is fully functional. While Stark has described his color sensationsin part of the 300-400 nm region, the description is not comprehensive. He has remarked that he perceives a bluefading to white-blue as the wavelength becomes shorter. This would be expected based on this theory. The questionremains: what does he perceive at wavelengths significantly shorter than 395 nm. A distinct color may be perceivedin that region. If so, its perception is shared only between aphakic humans and the other animals sensitive to thisspectral region.

The results of this work suggest that an electophysical color space can be defined that is compatible with recentlydefined psychophysical color spaces. This type of color space will be taken as the baseline. As shown in [Figure17.1.4-1], all three of the chrominance channels associated with a tetrachromat (O–, P– and Q– ) must be representedin the new color space. To accommodate the tetrachromatic nature of the visual process, it is necessary to define athree dimensional color space for the new Diagram. To maintain conformality in this space, it will be based on aright parallelepiped. Several simplified variants of the complete New Chromaticity Diagram will be defined forpedagogical purposes. The basic form of these diagrams was developed in Section 16.1.3.

In this Section, appreciating that only the chromatic channels of the visual process are being considered is important. It is postulated that the luminance channel is entirely separate from the chrominance channels. Avoiding thinking interms of a total visual experience where the luminance and chrominance information is mixed may be difficult forsome readers (as in the conceptual foundation of the current C.I.E. Chromaticity Diagram). Possible presentationscombining both the luminance and chrominance descriptors will be discussed in Section 17.4.

It is also important to differentiate between the various illumination levels, defined here as the hypertopic, photopic,mesotopic and scotopic levels. It is shown that when defining a more fundamental chromaticity diagram, thediagram depends on the above illumination levels. This is true for all long wave trichromats and all tetrachromats. The hypertopic and photopic diagrams are stable with illumination. The scotopic diagram is also stable but different. Recognizing the dynamic nature of the New Chromaticity Diagram for Research at the Mesotopic Level isimportant.


Recalling that the charge, or current, at the input to the adaptation amplifier of each photoreceptor cell is a linearfunction of the input photon flux to the respective channels is important. An exception is the L-channel where thecharge is related to the square of the input photon flux. In both of these situations, there is also a potential non-linearity due to saturation in the level of excitons in the disks. This potential situation is of little consequence atillumination levels at least as high as the photopic range.

At photopic and hypertopic illumination levels, the adaptation amplifiers in the photoreceptors operate at less thanmaximum gain. Their actual gain is controlled by the avalanche breakdown phenomena. The result is a largeamount of negative internal feedback in each individual photodetection channel. This results in a constant (average)output current level at the pedicles of all photodetection channels, at least in a given region of the retina, over a verywide range of photon flux intensities. The resulting overall gain is determined individually for each photodetectionchannel. The instantaneous dynamic range of each channel remains on the order of 100:1. This phenomenonessentially eliminates the difference in the output characteristic of the L-channel, as compared with the otherchannels, within the hypertopic and photopic illumination ranges. When the illumination level falls into themesotopic range, the charge or current delivered to the input of the adaptation amplifiers is so small that avalanchebreakdown is still significant. However, the effect of negative feedback is no longer a significant factor. Under thiscondition, all of the adaptation amplifiers are operating at full gain and the square-law characteristic of the L-channelis faithfully reproduced at the pedicle in that channel.

Recalling that the signals represented symbolically by the letters UV, S, M, and L are scalar amplitudes of thecurrent at the pedicles of the photoreceptors is important. These scalar values are obtained by the integration of theproduct of the incident flux and the spectral absorption associated with each photodetection channel, both as afunction of wavelength. The same scalar value can be obtained in a given channel by employing either amonochromatic light source or a broader band light source of lower peak intensity. Before the invention of the laser,using a relatively wide spectral bandwidth test signal in psychophysics was normal. The cost of an incandescentsource was less. It will be seen that these wider bandwidth test sources can introduce several problems into goodexperiment design with which investigators must deal. One of the problems is that the P and Q signals are generallynot independent. They are obtained by taking the difference between the UV, S, M and/or L channel signalsresulting from test sources that excite more than one channel at a time. It is quite possible, and probable, that aninvestigator can obtain different, even diametrically opposite, results from his experiments depending on the energydistribution within the specific spectral bandwidth of his test source(s).

The signal paths through the visual system of the retina are directly coupled. This condition makes themathematical description of each stage difficult. It is possible to represent each processing stage in multiple waysdepending on what properties are associated with the previous and following stages. This would be an almostintractable problem if the signal paths were all interconnected on a current basis. However, as shown earlier, thecurrent at the output of each photoreceptor is passed through a diode. The resulting voltage across the diode is thevoltage of the pedicle with respect to the surrounding inter-neural matrix (INM). It is this voltage that is sensed bylater stages using a high impedance connection. The impedance of this connection is sufficiently high that even alarge number of parallel connections do not change either the signal or resting potential component of the totalvoltage. The signal voltage at each pedicle is proportional to the natural logarithm of the current through the diode.

17.3.3.1 Conceptual framework for the new chromaticity diagrams

At the current time, defining four distinct types of chromaticity diagrams is important. The first would be a completediagram suitable for describing tetrachromatic vision. This is the default diagram that can be used to describe thecolor vision of any animal. A simpler diagram is only appropriate if it is shown that the animal lacks one or more ofthe four chromophores of vision. The second would be a diagram suitable for describing the short wavelengthtrichromat (as typically associated with Arthropoda). Members of Arthropoda are generally believed to lack the L-channel chromophore. However, this has not been proved conclusively. Most of the experimental work in this areahas been psychophysical in nature. The third would be a diagram describing the long wavelength trichromat (astypified by the human and other large animals based on the conventional wisdom). This diagram would beappropriate if the O-chrominance channel has completely atrophied. The final form would represent the largeanimals, including humans, who exhibit tetrachromatic vision that is significantly blocked in the ultraviolet by theabsorption of its own lens.

Before proceeding, it is important to stress this work does not support the so-called “colorequation” defined as the linear vectorial sum of three spectral colors, R, G & B. Neither does itsupport the belief that the color performance of the visual system is derived from a factoring (insome unknown manner) of this equation. This work relies upon the architecture of the visual


291Boynton, R. Op. Cit. Pp. 128-144292Dow, B. (1991) Colour Vision, in The Neural Basis of Visual Function, Leventhal, A. ed. as volume 4 ofVision and Vision Dysfunction, Cronly-Dillon, J. general ed. Boca Raton, FL: CRC Press. Pg. 318

system to define the equations relative to the color signaling performance of that system. Theseequations are not directly related to the perception of luminance by the system.


Several investigating teams have attempted to define a chromaticity diagram compatible with tetrachromatic vision. These have generally employed an equilateral tetrahedron and made the assumption that the color information issummed linearly in the visual process. These approaches have not progressed to the point of providing absolutescales to the figures or concerning themselves with conformality in the color space. See Section 16.1.3.1-2. Noattempts were found in the literature to extend the C.I.E. Chromaticity Diagram into the ultraviolet.

Boynton291 has written on attempts to rationalize a chromaticity diagram based on his psychophysical background. Unfortunately, the work is all based on the principle of additivity, an interpretation of the color equation in linearspace, and a trilateral graphic presentation. In some cases, he has suggested portions of his work are onlyappropriate for pedagogical purposes.

Dow292 addressed the psychophysics of vision and suggested that the luminance component of vision is based on thesummation of photoreceptor signals while the chrominance component uses signal subtraction. He lists the 12possible subtractive permutations of signals from three photoreceptor types. This is followed by a brief discussion ofthe ambiguities still present in the Hering model of the visual system. No conclusions were drawn but manyreferences were provided.

Adopting the foundation developed in this work, the new chromaticity diagram should be independent of theluminance of the signal. The luminance should be treated exclusively in the Luminance Response Diagram. Toaccommodate tetrachromatic animals, the chromaticity diagram should include three orthogonal axes. The peakwavelengths associated with the absorption of each chromophore of vision should be located along these axes. Thescale along each axis relates to the difference signal created from the signal amplitudes of the respectivechromophore channels. Since the visual system involves a number of non-linearities, defining the specific locationin the visual system represented by the new chromaticity diagram is also necessary. The temptation is to define it atthe output of the perceptual system. This location is represented by the response of the animal to interrogationabout what he thinks he sees. The response is frequently hindered by the perceived luminance information.

17.3.3.1.2 The morphological location supporting the New Diagram

[Figure 17.2.5-12] has provided the overall signal processing architecture of the tetrachromatic visual system. Itshows clearly that the chrominance signals are formed in Stage 2. Signals associated with each chrominance signalare available in analog form at the output of the differencing amplifiers (generally labeled horizontal cells). Encodedversions of these signals are available in pulse form at the output of the ganglion cells of Stage 3. Recoveredversions of these signals are found at the output of the stellate cells of Stage 3.

Two questions need to be answered. First, where can the desired signals be most easily measured by electricalprobe? Second, where is the quality of the signals best? Many investigators would prefer to probe for pulse signalsprimarily because they do not understand the role of analog signals in the retina. These investigators prefer to probethe outputs of the ganglion cells. However, they do not know the encoding algorithms used to convert the analogsignals into those pulse signals. Therefore their data is at best exploratory. Svaetichin and Tomita probed for analogsignals in the retina and defined what became known as the S-plane. This plane is essentially the location of theaxons of the horizontal and bipolar cells (probably the area now known as the inner plexiform layer). They recordedboth chrominance (difference) and luminance (summation) types of signals at this location. While not preciselydefined in their day, this is the earliest physical location that these types of signals exist within the visual system. The S-plane will be taken as the physical location associated with the New Diagram. It is important to note that theperformance of the visual system at the S-plane is subject to differential adaptation. This adaptation may be inducedby the normal operation of the photoreceptor cells. It is also important to note that the psychophysical responses ofsubjects may differ from the electrophysical data associated with this plane due to nonlinearities and asymmetries inthe subsequent signal processing. However, these deviations seem small and associated primarily with temporalmechanisms that introduce transient effects.


293Science of Color (1963) Jones, L., chairman of the committee NY: Optical Society of America pp. 34-83including color plates

17.3.3.1.3 Development of fundamental chrominance signals

The signals produced at the S-plane have been developed in detail in Chapter 16. Only the symbolic forms of theseequations will be used in this section. The chrominance signals were shown to be given by one of two sets ofequations depending on the operational status of the adaptation amplifiers in the L photodetection channels. Forhypertopic and photopic conditions, they are given in symbolic form as:

O = LnUV - LnS Eq. 17.3.3-5

P = LnS - LnM Eq. 17.3.3-6

Q = LnL - LnM Eq. 17.3.3-7

Under the less favorable mesotopic conditions, the last equation changes to:

Q =LnL2 - LnM Eq. 17.3.3-8

Whereas the symbols S, M & L represent integrated values corresponding to actual currents in the axons of thephotoreceptors, the logarithms of these terms represent the voltages measured at the pedicles of the respectivephotoreceptor cells in the retina.

Look first at equations 5, 6 & 7. As shown in [Section 16.3.4] the values of O, P and Q are nearly linear functionsof spectral wavelength. However, they are also functions of the irradiance level. As the radiation level is reduced,the signals approach the threshold level of the circuits associated with the stellate cells monotonically. As thisoccurs, the perception of color is lost gradually beginning with the colors nearest the null axes of 494 and 572 nm. Eventually all sensation of chromaticity in the scene is lost. Now look at equation 8. Because of the squareassociated with the L signal, the voltage associated with this channel decreases even faster than those associatedwith the other channels. This causes an additional loss in the perception of the reds. In practice, the subjecttypically sees the saturation of all colors decreasing as the radiation level falls. While he fails to perceive lowsaturation colors first, he retains some chromatic perception of high saturation colors near 437 and 532 nm even afterthe loss of all perception of the reds. Finally, the observer becomes achromatic. This condition is encounteredalthough all of the photoreceptors are still operating at maximum sensitivity and gain. This process was illustrated in[Figure 17.1.1-2].

17.3.3.2 Defining the tetrachromatic chromaticity diagram

The Science of Color293, written by the Committee of Colorimetry of the Optical Society of America, presents adiscussion of the complex parameters involved in the perception of color (without any recognition of thetetrachromatic sensitivity of the human eyes). The discussion struggles to separate the chromatic parameters fromthe luminance parameters while attempting to continue to use the common semantics of the English language. Theirconceptual discussion centers on the use of cylindrical coordinates. The term hue is used to define the color of thescene on their chromaticity diagram and the term saturation is used to describe the intensity of that color relative towhite. The form of the above equations does not involve trigonometric functions. No substantive report could befound in the electrophysiological literature where neurons performed transcendental calculations. Although usinganalogies to hue and saturation in art and pedagogy may be convenient, it is best to avoid cylindrical and sphericalcoordinates in research. The mathematical analogies to the actual process rely upon the simple logarithmic functionspresented above.

[Figure 11.6.4-2] presented the architecture of the visual system related to signal formation in the retina. Thisfigure shows a distinct separation of the signaling paths into three chrominance channels (O–, P– and Q–) and oneluminance channel (R–). Each of these channels generates a scalar signal based on the scalar potentials at thepedicles of the photoreceptor cells. It is most likely that the brain uses the actual values of O, P & Q recovered fromStage 3 (signal projection) to perceive the chromatic characteristics of the individual locations in a scene. It woulddo this by comparing these values, stored in a saliency map, to a “lookup table.”


294Tan, K. (1971) Vision in the ultraviolet, PhD Thesis, Utrecht, available in Univ. of Missouri Library, calQP481.T16

Figure 17.3.3-1 (Color ) The foundation for thechromaticity diagram of tetrachromatic vision. W marksthe location of “white” in the diagram. W’ shows thelocation of “white” for a long wavelength trichromat. W”shows the location of “white” for a short wavelengthtrichromat.

The scalar values of O, P & Q are essentially independent of each other. How they are presented graphically islargely a matter of preference if certain conditions are observed. The goal would be a simple presentation that iseasily interpreted, uses absolute scales and is conformal. Conformality insures proper portrayal of relationshipsbetween the quantities. The easiest way to achieve these goals is to employ a three-dimensional color spaceconformally transferred onto a Cartesian coordinate system. Since it has been shown that O, P & Q are nearly linearwith respect to wavelength, it is intriguing to attempt to use a spectral locus conformally transformed onto such aCartesian system. Section 16.1.3.3 has shown that this can be done through the introduction of only two arbitraryfeatures. These are the wavelengths at which the spectral locus is folded. These points have been chosen tocoincide with the nominal peak absorption of the two chromophores, Rhodonine(7) and Rhodonine(9). Thesechromophores have peak absorption wavelengths of 532 nm and 437 nm respectively. The only availablejustification for these choices is found in Section 17.3.2. It is shown there that a transfer occurs within the brainbetween relying on the P-channel value and the Q-channel value to determine the “color” of the scene element. Thistransfer occurs at a wavelength very close to 532 nm for one of the transitions. It will be assumed similarexperiments in the future will confirm a similar transition between the O– and P–channels at a wavelength near 437nm. The only data relevant to this choice appears to be from Tan294. It is quite exploratory in character. Futurelaboratory work may optimize the above choices. Based on these choices, Figure 17.3.3-1 illustrates the resultingtotally conformal three-dimensional color space.

Note that the spectral locus is continuous. Theorientation with 300 nm at the extreme upper cornerwas chosen arbitrarily. This choice gives a NewChromaticity Diagram that is compatible with much ofthe recent psychophysical literature.

Note that there is a null in each of the threechrominance equations. The location of this null inobject space is a function of the state of adaptation ofthe eye. When transferring the chrominance equationsto this color space under dark adapted conditions, thenull in the equation for Q occurs at 572 nm. The nullin the equation for P occurs at 494 nm and that for Ooccurs near 395 nm. These values are shown by thelong dashed lines.

When O = P = Q = 0, there are no chrominance signalsto transfer from the retina to the brain. However, thereis still luminance information being transferred. Theabove equation defines the “white point,” W. Basedon the above determinations, the “white point” for atetrachromat occurs at the intersection of 395, 494 and572 nm using the folded spectrum locus as a scale. Note that this point is not described by the sum of anysignals. It is described by the condition where thethree difference equations are all equal to zero. Thiscolor space differs fundamentally from theconventional assumption of additive color. Additivecolor assumes that white is described by the sum of theintensities associated with a group of spectral terms.

Since O, P & Q are nearly linearly related to wavelength and all are equal to zero at the intersection W, consideringthis point a displaced zero within the conformal space is convenient. As a result, any color can be uniquelydescribed in terms of its O, P & Q coordinate values.

17.3.3.2.1 What colors does a tetrachromat perceive?

There has long been a question concerning what do bees, and other animals sensitive to the ultraviolet spectrum,perceive when viewing ultraviolet light. Recently it has been shown that the aphakic human perceives ultravioletlight. The precisely measured spectral efficiency functions of Tan and of Griswold & Stark show that the human


295Wolbarsht, M. (1976) The function of intraocular color filters. Fed. Proc. vol. 35, no. 1, pp 44-50296Stark, W. & Tan, K. (1982) Ultraviolet light: photosensitivity and other effects on the visual system,Photochem. Photobiol. vol. 36, pp 371-380297Tan, K. (1971) Op. Cit.

luminance channel is described precisely by the proposed spectral efficiency of this work. The congruence of thepredicted and independently measured composite spectral response is strong support for the validity of the model. However, a question remains to be answered. Is the third chrominance channel (the O-channel) of tetrachromaticvision fully functional in the human? This section will show the answer is Yes!

The English language has a profusion of words to describe colors dominated by radiation at very short wavelengths,less than 437 nm. This condition might suggest active mechanisms associated with short wavelength vision that arenot well understood. The model of this work would suggest that the human retina can perceive colors in the regionof 300 nm to 437 nm. To do this, the O–channel must be functional. The model also suggests a null in the O-channel response near 395 nm. It would exhibit the same characteristics as the nulls in the P- and Q-channels. If theabove is true, the question focuses on what colors does the aphakic eye see in the region of 395 to 437 nm and in theregion of 300 to 395 nm?

Tan, Stark & Tan, Griswold & Stark, Chen & Stark and Stark (in a personal communication) have described whatthe aphakic perceives in these regions. Some of these papers either relied on the conventional wisdom or did notcontrol all of the pertinent variables.

Tan presented a PhD dissertation in 1971. The work investigated both the spectral efficiency function and colormatching focused on the ultraviolet capability of aphakic humans. He used lights at 444.4, 526.3 and 645.2 nm assources of comparison. The discussion of his work that is most widely available is by Wolbarsht295. Much of thebroader discussion in Wolbarsht is not supported by this work. There is also some discussion of it in a review byStark & Tan (apparently written largely by Stark)296. Unfortunately, these two papers provide differing versions ofthe same figure from Tan297. Although both are labeled chromaticity diagrams, they are based on graphs ofanomaloscope readings (note the negative values along both scales in these figures). Both graphs show a bendingand intersection of a locus with itself. This feature suggests the inadequacy of the anomaloscope configuration used. The configuration only allowed matches using mixtures of blue, green and red lights. Wolbarsht noted that “If thelens is removed, the sensitivity in the ultraviolet will be such as to produce color confusion. Monochromatic lightwithin the ultraviolet spectrum appears to be matched by something other than blue.” He noted in his caption tofigure 9 that “it would be necessary to substitute a wavelength in the ultraviolet for the blue at 444.4 nm in theanomaloscope to make a real match. An aphakic individual cannot match ultraviolet light shorter than 340 nm withany visible wavelength between 400 and 700 nm.”

Stark & Tan summarized their work through 1982 in the above review. Unfortunately, their descriptions are heavilyflavored by several apriori assumptions. They encountered difficulty relying on the trichromatic assumption. Theyalso had difficulty in settling on the precise mechanisms supporting absorption in the ultraviolet. After noting apeak in the ultraviolet absorption of the aphakic eye near 350 nm, they attributed it to the “cis-peak of rhodopsin.”This was presumably the putative achromatic rod chromophore. They also assume the spectral characteristics of theshort wavelength chromophore extend into the ultraviolet farther than previously assumed. They also assume thetotal ultraviolet sensitivity to be the summation of the β-peaks in the response of the S, M and L channels. This isbased on their assumption that the β-peak in the absorption of retinoids in dilute solution is significant in vision. Finally, they interpreted their findings using a unique chromaticity diagram as discussed above.

The Stark school was ambivalent concerning the nature of the ultraviolet absorption as late as 1994. In Stark,Wagner & Gillespie, the absorption in humans is presumed to involve a summation of β-peaks associated with the S,M and L chromophores. However, they confirmed Tan’s earlier findings. They said “data for sensitivity mediatedby the short-, and perhaps the long-, wavelength cones suggest UV sensitivities beyond those expected from thecone rhodopsin’s cis peak. . . . ” In Chen & Stark, the ultraviolet absorption in goldfish is attributed to a distinctultraviolet photoreceptor (referred to as a “cone”). These ideas suggest a convergence toward the model of thiswork.

Tan developed part of a color space based on the above assumptions, use of a 58 minute diameter stimulus andbipartite color matching. It is noteworthy that he used 494 nm and 582.5 nm as normalizing wavelengths in theseexperiments. These are the null wavelengths of the P– and Q– chrominance channels proposed in this work. Thefigure of Tan reproduced in Stark & Tan is the result of a complex de-convolution using a technique first used byWright. It should not be accepted as factual without understanding the mathematics involved.


298Gaydon, A. (1938) Colour sensations produced by ultraviolet light Proc Physiol Soc (London) vol 50, pp714-720299http://www.bbc.co.uk/iplayer/episode/b00rqgh4/Richard_Hammonds_Invisible_Worlds_Out_of_Sight/300Derrington, A. Krauskopf, J. & Lennie, P. (1984) Op. Cit.301Abramov, I. & Gordon, J. (1994) Color appearance: on seeing red–or yellow, or green, or blue Ann RevPsychol vol 45, pp 451-485

Stark & Tan contributed the following. “For aphakic observers, monochromatic UV looks violet or blue, thoughsomewhat whitish (unsaturated). These stimuli trace a loop extending into the color triangle near the blue-violet(400-450 nm) portion of the triangle’s perimeter.” If this statement is reworded to suggest saturation decreases asthe wavelength approaches 400 nm, it would be precisely as expected by this theory. This appears to be the casebased on subsequent discussion with one of their subjects (twenty years later).

A question remains about what color is perceived on the short wavelength side of the null point near 395-400 nm. Gaydon298 stated that the color appeared blue, not violet, as quoted on page 116 of Wyszecki & Stiles. Until thequestion of what color is perceived for narrowband stimuli between 300- and 395 nm under photopic conditions isanswered more definitively( See [Figure 17.1.4-1]), the perceived color of light at 342 nm will be defined as Monet(in honor of the famous painter who became aphakic while still painting). Purple will be reserved for a spectralcolor near 410 nm (on the long wavelength side of the null at 395 nm).

In April, 2008, I encountered a subject exhibiting at least partial UV vision due to a malformed lens at birth. Shereported ultraviolet light generated either a lilac or pinkish-purple due to UV light.

Richard Hammond presented a TV program over the BBC on 23 March, 2010 involving a man with hisbiological lenses removed who discusses his resulting UV vision299. The program should be available in theUSA on the Discovery Channel in the near future. He claimed that after the operation he started to see brightpurplish and blue light emitting from scanners used to scan currency notes. He also said that rainbows hadfar more color in them now than he had seen before. This is completely expected. No information wasprovided on the types of replacement lenses he was using. He did not demonstrate his ability to see atwavelengths shorter than 400 nm.

In summary, the human visual system is fundamentally tetrachromatic. In the absence of the lens, the luminancechannel of the system exhibits a spectral sensitivity that is considerable between 300 and 700 nm. The systemexhibits three fully functional chrominance channels. These channels broaden the Hering concept to include threeopponent color axes,

+ the aqua-red axis passing through 494 nm, + the yellow-violet axis passing through 572 nm and + an axis passing through 395 nm (lilac) whose other terminus is not labeled at this time.

Derrington, Krauskopf & Lennie determined axes very close to two of the above three axes in 1984300. Theyspecified one axis as 492 ± 3 nm and the second axis as 558 ± 4 nm. In referring to the Derrington et al. material,the psychologists Abramov & Gordon301 introduce the color name “teal” to describe 492 nm. Similarly, they usedthe color name “chartreuse” when describing 558 nm. They describe the complement of teal as “cherry” and thecomplement of chartreuse as violet. These designations are compatible with this work although it may be useful toconsider a different name for a color at 572 nm which would be more yellow than 558 nm.

For purposes of discussion, the aphakic eye perceives a color near 300 nm that will be labeled hyacinth and a colorat 342 nm that will be labeled Monet. A very unsaturated color is perceived at 395 nm (a null point) that will belabeled lilac. For the aphakic human eye, white is an indication of a null in all three chrominance channels.

The experiments of Tan on aphakic humans are worthy of repetition using a source wavelength near 300 nm ifanomaloscope matches are to be obtained for monochromatic lights in the region of 300 to 395 nm.

The ultraviolet photoreceptors and signaling channel of normal humans are active, although significantly blocked bythe absorption of the lens. A source of radiation near 400 nm must be used if precise anomaloscope matches are tobe obtained for humans when they are presented with monochromatic radiation in the region of 400 to 450 nms.

[xxx too much duplication regarding the term and physiology of “aphakic” here and in 17.1 and 17.2 to 17.4.


17.3.3.2.2 What colors does a human perceive?

Based on the knowledge that the human visual system is fundamentally tetrachromatic, defining what a humanperceives in detail is possible.

A human uses four quantum-sensitive spectral channels with peak sensitivities at 342, 437, 532and 625 nm. Theoretically, it can determine the mean wavelength of any stimulus between 300and 655 nm. Practically, it can determine the mean wavelength of any stimulus within this rangelimited primarily by the absorption of its own lens, the color temperature of the radiation sourceand the reflectance of the scene in object space. This restricts its chromatic discrimination range to395 nm to 655 nm under suitable photopic illumination conditions.

The theoretical color discrimination range of the human visual system is shown in Figure 17.3.3-2. In this figure,the mean wavelength of the radiation from a scene element is computed as an integral. It is the integral of theproduct of the spectral properties of the radiant source, the reflectance of the scene element and the absorption of theindividual chromophore to that irradiation. Thus, a given scene element may stimulate more than one chromaticchannel if the reflectance of the element is sufficiently broad. As a result, the scene may be represented inchrominance space by a point that is not on the spectral locus.

For scene elements with a mean wavelength shorter than 437 nm, the location in human chrominance space is determined by signals acquired by both the UV-- and the S-- spectralchannels. These signals will be reported via the O--chrominance channel as shown by thesolid line in the figure.

Without a functional O--channel, the data in the 400-437 nm region would be reported viathe P--channel. There would be no transition in signal processing between the O-- and P--channels.


Figure 17.3.3-2 Theoretical composite human color discrimination function under high contrast photopic conditions. The individual discrimination functions are aligned to show their individual ranges and their composite range (solidline portion of each function). Cross over between functions occurs at 437 and 532 nm. Scene elements with amean spectral wavelength of less than 437 nm are reported by the O-channel. Scene elements with a mean spectralwavelength of between 437 and 532 nm are reported via the P-channel. Scene elements with a mean spectralwavelength of greater than 532 nm are reported via the Q-channel. See text.

Whether the UV-channel participates in signal generation is highly dependent on the color temperature and hencethe spectral content (on a quantum flux basis) of the radiant source. Both the UV– and S–channels are excited bysignals in the 395 to 437 nm range. Figure 17.3.3-3 illustrates the significance of the color temperature of thesource and the limitation introduced by the absorption of the lens. The excitation is relative to the input to the neuralportion of the photoreceptor cells (before the adaptation amplifiers). While the adaptation amplifiers cancompensate for the reduced excitation if it is part of the background, such compensation reduces the extent of thephotopic operating range of the visual system significantly. This compensation will adversely affect the incrementalsignal gain relative to the other spectral channels. The overall effect is to reduce the apparent contrast in this region.


Figure 17.3.3-3 Effect of source color temperature on the color discrimination capability of the human eye. Thethree curves were normalized with respect to 700 nm. The precipitous drop in excitation near 400 nm is due to theabsorption of the human lens. Note the substantial reduction in excitation of the photoreceptor cells in thewavelength region between 395 and 437 nm using 2856 Kelvin illumination, (illuminant A).

It can be concluded that the ultraviolet spectral channel of human vision is important in perceiving colors in thespectral range of 395 nm to 437 nm. The ultraviolet channel is crucial to the fidelity of the perception process whenthe source of illumination is of adequate color temperature. If the source temperature is not adequate, perception ofpurples, indigos and blues near 437 nm will be hampered.

17.3.3.2.3 A simplified three-dimensional framework for true trichromats

While a three dimensional Cartesian coordinate system is easy to visualize, working with it on paper is difficult. Figure 17.3.3-4 illustrates a simplified coordinate system that remains conformal. Its derivation is discussed inSection 16.1.3.3. The figure is obtained by splitting the figure along the vertical axis and rotating the UV-S-Msurface around that axis until it is in the same plane of the S-M-L surface. The coordinate space on either side of thevertical axis remains conformal. However, the two sides are not connected conformally and certain colors cannot berepresented properly. The criteria for the perception of “white” remains the same. The values of O, P and Q mustall be equal to zero. For a short wavelength trichromat, a complete chromatic space can be created based on the lefthalf of the figure. This assumes the Q–channel is absent or dysfunctional. For a true long wavelength trichromat, asimilar chromatic space can be created based on the right half of the figure. Here, it is assumed the O–channel is


Figure 17.3.3-4 (Color) A simplified foundation for athree- dimensional color space. Each side of the figureremains conformal. However the two sides are notconnected conformally. The human visual space can be represented by the space to the right of the 395 nm line.

absent or dysfunctional.

Recently, it has been determined that the human visualsystem is tetrachromatic at the S-plane of the retina andthe O-channel is fully functional. However, theexcitation of the O-channel is very limited by theabsorption of the lens at wavelengths between 310 and395 nm. Furthermore, very few artificial light sourcesemit radiation in the 300 to 310-nm region. As aresult, the total figure can be used to represent normalhuman vision by ignoring the region between 300 and395 nm. Under conditions where sufficient ultravioletirradiance reaches the retina, the entire figure can beused to define human color vision. However, suchhigh levels of ultraviolet irradiance could be medicallydamaging to phakic eyes.

As noted below, the line connecting 437 and 532 nm isthe spectral line and not a Hering axis. The chromaticspace between the 437-532 nm line and the 395 nmline is not represented correctly in previouschromaticity diagrams. It is out of the plane of thetypical x,y chromaticity diagram. The region centeredon 415 nm is labeled purple in this work. The regionof 420-425 nm is labeled indigo. A mixture of eitherof these colors and a spectral yellow or red cannot be represented in this figure.

17.3.3.3 A New Chromaticity Diagram for human vision

As discussed in Section 17.3.3.2.2, the human cannot be defined as a trichromat for research purposes. Humans aretetrachromats suffering from a physiological blockage of light in the region of 310 to 395 nm. However, his/her UVsensitivity is significant in determining the chromatic perception of the overall system. Therefore, humans are bestdescribed as blocked tetrachromats.

For clarity, this section refers to the perceptual space of the human visual system as represented at the S-plane of theretina under dark adapted conditions. It should be noted, there is no direct relationship between any component ofthe chrominance space and the perceived illumination of the scene. This perceptual quality is determined completelyindependently in the R-channel of the system. This is one area where the C.I.E. Diagram, which defines theamplitude of the M-channel signal as equivalent to the perceived brightness of the scene illumination. Thechromatic signal channels do not relate to luminance intensity in any simple direct way. In this presentation and inreality, the signal information in the luminance and chrominance channels are calculated completely independentlyfrom the information presented by the photodetection channels. See Section 17.1.4.

Creating a two-dimensional color space for human vision similar to that described above is possible. Thisopportunity arises from two conditions. The first is the frequent relative lack of irradiance from a scene in the 395 to437-nm region. The second is the relative unimportance of mixtures of two or more lights where one light contains asignificant number of quanta in the 395 to 437-nm region. Under these conditions (typical of artificial illumination),the utility of the UV– and O– channels are limited. It is also indicative of why artists and museums attempt toachieve a higher color temperature illumination in their exhibition spaces. Movie theaters also use higher colortemperature sources so that purples can be reproduces more effectively.

17.3.3.3.1 A chromaticity diagram under optimal illumination

Consider the three-dimensional color space of a tetrachromat as a hollow cardboard box instead of a solid cube. For convenience, assume that the Q axis only extends to 655 nm. Cut the box in a plane containing the 395 nm lineand parallel to the S-M-L plane. Now unfold the four panels that are perpendicular to the S-M-L plane to form onlyone plane. Figure 17.3.3-5 shows two variants of the resulting two-dimensional color space.


Figure 17.3.3-5 A complete color space for blocked tetrachromats (including humans). Left; the proposed spacewith locations described by wavelengths. Right; the proposed space with locations described by named colors. Thethird Hering chromatic axis, passing through 395 nm (Lilac) is defined as the null value of the O-channel. It circlesthe figure. This representation shows all three pseudo-white points individually.

The curved lines in the figure are to indicate the identity between the two points at the ends of each arc. The scalefor the O-channel is shown along a radial. It applies equally to both the horizontal and vertical representations of theO-channel.

Both variants illustrate the three pseudo-white points that represent the individual conditions where two out of thethree chromatic signals have null values. W’ represents the white of conventional wisdom. This is a location alongthe two conventional Hering chromatic axes represented mathematically by P = Q = 0.00. W” represents the similarcondition where O = P = 0.00. W”’ represents the condition where O = Q = 0.00. W” and W”’ are each shown attwo locations representing the same axes for different values of the unspecified third parameter. The frames alsoillustrate a collection of unique colors to be defined below.

This diagram provides the answer to the question, what color does a bee see in place of white? White! In this conceptual chromaticity diagram, white is perceived as the absence of signals in allavailable chrominance channels.

While not totally conformal, this figure is conformal within each area delineated by fold lines. Under conditions ofartificial illumination, the values of the O–signal approach zero in each of the four foldout panels. Therefore, theperceived chromaticity diagram of the human under normal artificial illumination can be appropriately representedby the space within the rectangle bounded by 437, 532 and 655 nm.

Under higher color temperature illumination or when using monochromatic sources in the laboratory, the presence ofsignals in the O–channel must be anticipated. Trimodal stimuli can only be interpreted in terms of the three-dimensional color space. However, because of the selection criteria used in the brain, many bimodal stimuli can beadequately represented in the above two-dimensional representation.

The presence of signals in both the O– and Q–channels will elicit the perception of colors represented within theareas of the top and bottom foldouts. One interesting color is located at 655 nm and 415 nm. It is labeled mauve inthis figure. While magenta is defined as a mixture of blue and red, mauve is a mixture of purple and red. It can beconsidered a “super magenta.” The definition agrees with that of the American Heritage Dictionary and is amongthose used to describe the same area in the Munsell Color Space.

The presence of signals in both the O– and P–channels will elicit the perception of colors represented within theareas of the left and right foldouts. These colors are perceptually less distinct and will remain unnamed at this time. These spaces include combinations of colors, such as bluish-purple mixed with green, that are not found along the


spectral locus. These are bimodal spectra. Bluish-purple mixed with green is distinctly different from the spectralcolor labeled aqua.

Reproducing all of the colors perceived by the human under ideal illumination is virtually impossible. Neitherprinted media nor monitors are designed to faithfully or consistently reproduce such a range. The use ofconventional trichromatic monitors in psychophysical experiments is a major impediment to research in colorvision.

Important colors will be defined explicitly as to spectral content in Section 17.3.4.

17.3.3.3.2 A chromaticity diagram under incandescent illumination

As noted in the equations of Chapter 16, the value of the O–signal approaches zero under two conditions. First,when there is low chromatic saturation in the UV– and S– portions of the object spectrum. Second, when the sourceradiance levels in both of these channels are low. Thus, for incandescent illumination, the value of the O–signal isusually insignificant and location W’ represents the actual perceived white. This point indicates the absence ofchromatic signals in all of the chrominance channels. If the actual perceived white in a scene exhibits a bluish orpurplish tinge, it is because the value of the O–signal is not identical to zero.

Under conditions of normal artificial illumination (color temperatures below 3600 Kelvin), the values of theO–signal are negligible in each of the four foldout panels. Therefore, the perceived chromaticity diagram of thehuman under normal artificial illumination can be appropriately represented by the space within the rectanglebounded by 437, 532 and 655 nm. Since the signal in the O-chrominance channel is negligible, the selection rulesused in the brain will always favor the chromatic discrimination function presented by the P-channel. Under thiscondition, the limit of color discrimination at short wavelengths is due to the limit in the P-channel discriminationfunction (nominally at 400 nm).

17.3.3.3.3 Fundamental, primary and cardinal axes in perceptual space

The complete equations for P and Q (Section 16.3.4) allow a chromaticity diagram to be constructed that employslinear scales in these two quantities. Using P and Q as the fundamental axes insures that the graph remainsconformal with the dataset. [Figure 16.3.4-1] shows the nearly linear relationship between the value of P and Q andtheir respective wavelength regions. Therefore, a choice can be made between preparing the diagram based on usinglinear scales based on the scalar values of P and Q or on the associated wavelengths. Convenience is served bymaking the scales on the primary axes linear with wavelength and presenting a secondary set of scales for P and Q. The scales expressed in absolute wavelength will be considered the primary axes of this work. This approachintroduces a slight distortion in the P and Q scales. Where maximum precision is required, and when the abovefigure has been confirmed by precise laboratory measurement, the actual P and Q secondary scale values corresponding to the primary scales can be plotted exactly.

These primary axes do not pass through any of the white points of the three-dimensional color space appropriate fordisplaying the color perception of the human. It is useful to define such a set of axes to maintain compatibility withthe experimental, particularly the psychophysical, community. These axes can be defined as the cardinal axes andare best defined as parallel to the primary axes. When defined in this way, there are actually three cardinal axes asshown in [Figure 17.3.3-4 & 17.3.3-5]. The axes passing through the wavelengths of 494 nm and 572 nm are theclassic axes of Hering. The third axis, passing through 395 nm, is a newly defined Hering axis compatible with theblocked tetrachromatic color space of the human.

17.3.3.3.4 Hue and saturation are not fundamental parameters

While many investigators have adopted polar coordinates in the display of their data, and polar coordinates play auseful role in pedagogy and the arts, the fundamental parameters associated with color vision are not polar incharacter. As discussed in [Section 17.3.3], a true perception of “white” involves the absence of signals in all of theoperational chrominance channels. This condition requires that O = P = Q = 0.00 in the general tetrachromat and inthe human (a blocked tetrachromat). This point can be rigorously defined in a three-dimensional color space, a colorcube. If desired, polar coordinates can be used to describe a color relative to this white point. However, the angles(preferably measured relative to the Cardinal axes) and lengths of the vectors do not have any intrinsic relationshipto the visual process.

A true perceptual white cannot be rigorously defined by a single point in a two-dimensional color space. The point P= Q = 0.00 can be considered a true white point if no significant signal exists in the O-chrominance channel. Thiscondition is often achieved in the psychophysics laboratory by employing a light source of limited color temperature.


However, this condition seriously limits the perception of colors in the blue and purple region of the color space.

Under the above conditions, the use of polar coordinates based on a “white point” within the S-M-L plane must bedefined as a secondary set of parameters. Here again, polar coordinates can be used to describe a color relative tothis white point. However, the angles (preferably measured relative to the Cardinal axes) and lengths of the vectorsdo not have any intrinsic relationship to the visual process.

17.3.3.3.5 The New (hypertopic & photopic) Chromaticity Diagram for Research

A New Chromaticity Diagram for Research can be prepared using absolute scales in a rectilinear two-dimensionalgraph space with minimum compromise. However, several caveats must be attached to the figure.

First, the color space only applies to blocked tetrachromats (primarily chordates with ocular globes > 20 mm indiameter).

Second, the color space is primarily used for stimuli with half-amplitude full spectral widths greater than 50 nm. Ifmulti-modal, each mode of the stimuli will meet the above criteria.

Third, when narrower band stimuli are used in the short wavelength regions, the impact of the O-chrominancechannel must be recognized.

Fourth, if a color temperature of less than 3600 Kelvin is provided by the ultimate source, filters of any spectralwidth can be used with this diagram.

These caveats are designed to surface the fact that the perceived colors in the spectral region of 400 to 437 nm willdiffer depending on the test circumstance. They depend on the color temperature of the light source and theselection rules used by the brain. The second and fourth caveats insure that the subject will not perceive saturatedpurples at test wavelengths below 437 nm. In the absence of these two caveats, the subject may perceive saturatedpurples correctly.

With these caveats, the resulting complete graph of perceived color by humans is shown in Figure 17.3.3-6. Thenominal color shown within each circular segment representing the maximum saturation color perceived at thecoordinate value of the center of the segment. This method of presentation of the human color gamut does notrequire the introduction of a “purple line” and there are no “non-spectral colors.” Saturated magenta, for instance, isa bimodal color obtained by mixing 437 nm. radiation and 655 nm. radiation.

Note the word perceived in the above paragraph. This is a Diagram of the response of the human eye in perceptualspace, not the nominal stimulus applied to the eye in object space as used to define the CIE Chromaticity Diagram. As presented, it is applicable to the nominal eye under dark adapted conditions. This state of adaptation is presumedto be the same as that achieved when viewing an equal quanta per unit wavelength source, e. g., a “daylight” sourcewith a color temperature of 7053 Kelvin for the normal human eye.

Using this presentation format, the wavelength scales are linear and the field of the graph is conformal. A uniquecolor can be defined precisely and unequivocally using only two wavelength numbers. Furthermore, the result ofadding two lights of known spectral distribution can be determined using simple arithmetic and geometry.

White is always perceived at one point, the point where the value of both P and Q are zero. A perception of purewhite can be obtained by mixing only two monochromatic spectral wavelengths, 494 and 570 nm in object spaceunder dark (and presumably equal flux) adaptation. A perception of white can also be obtained by mixing any twolights where the integrated product of the spectral characteristics of the individual lights and the photodetectionchannels of the eye result in a chrominance channel response given by P = Q = 0. Adjusting the spectral content oftwo lights to meet the above condition is essentially impossible without an adequate model of the eye. The C.I.E.Chromaticity Diagrams are misleading in this area because of their lack of conformality. Therefore, theconventional practice is to use three lights and vary their relative intensity levels until the condition P = Q = 0 isobtained empirically.

The above procedure is the key to the perception of white under nominal variations in the weighted average spectralcontent of the nominal scene. The individual adaptation amplifiers of each photoreceptor in the eye share a commonmetabolic energy source. This source has a common source impedance for all of the photoreceptors in a givenregion of the retina. Therefore, the amplifier gain of these individual photoreceptors tend to respond as a group inorder to maintain a constant signal level at their output terminals. The result is the well-known fact that after a short


interval, the individual exposed to such atypical scene irradiance will not perceive it as atypical. This is thephenomenon of color constancy. It will be developed further in Section 17.3.6.


Figure 17.3.3-6 [Color] A physiology-based Chromaticity Diagram for Humans applicable to the Hypertopic andPhotopic regions. The colors shown are only for discussion purposes. Monitors and “North American” process colorprinting cannot reproduce the correct colors for wavelengths below 447nm. At least some “European” process colorprinting can reproduce the purples between 400 & 430 nm but at the expense of the blues between 440- & 470 nm. The figure is conformal and shows the limits of chromatic discrimination in the O, P and Q chrominance channels. This theoretical figure is based on a uniform photon flux per unit bandwidth source. A blackbody at a colortemperature of 7053 Kelvin is the closest equivalent. Such a source is equivalent to nominal daylight and is verysimilar to a D65 source. In the region beyond 655 nm, the perceived color of an object is no longer monotonic. Theperception of color in the region between 400 and 437 nm is restricted when using normal incandescent illumination. The purples will appear as blues.


In brief, if the scene in object space exhibits an excess of radiation in one region of the spectrum, assume red for themoment, the adaptation amplifiers associated with the L-channel will reduce their gain parameter automatically. This is due to the higher current attempting to pass through them in the presence of the internal feedback mechanism. The result is the phenomena of color constancy in perceptual space. The integrated product of the spectralcharacteristics of the scene in object space and the gain characteristic of the individual photodetection channels willremain essentially constant in the face of slow variations in the average spectral content of the scene. The perceivedvalue for white in perceptual space remains at the point P = Q = 0. However, the actual coordinates of the samepoint reflected into object space may be quite different from this value. This is due to changes in adaptation by thephotoreceptor cells.

In object space, the white point is always described by a specific set of coordinates. However, defining thesecoordinates precisely under clinical conditions is difficult. The clinician will normally define a circular area(typically elliptical on a C.I.E. Diagram) including the white point as the locus of white. This circular locus canmove about as the spectral content of the object space radiation changes. The fact that the white locus remains asmall ellipse while it moves about, due to changes in color temperature of the source, is not illustrated correctly inthe normal C.I.E. Chromaticity Diagram presentation.

The edges shown at 400 nm and at 655 nm are drawn to describe the limit of color discrimination as a function ofwavelength for the P and Q channels. The area beyond 655 nm is perceived as a slightly less saturated Red than theregion near 655 nm. This phenomenon is discussed elsewhere in this work.

The colors shown in [Figure 17.3.3-7 xxx ]can be specified much more precisely mathematically than they can beillustrated in printed pictures. Colors, with their nominal English names, are defined by their P and Q values asshown in Table 17.3.3-1


302Livingstone, M. & Hubel, D. (1984) Anatomy and Physiology of a color system in the primate visualcortex J Neurosci vol 4(1), pp 309-356303Pridmore, R. (1999) Unique and binary hues as functions of luminance and illuminant color temperature,and relations with invariant hues Vision Res vol 39, pp 3892-3908

TABLE 17.3.3-1Mathematical Definition of Principal Colors in the

New Chromaticity Diagram for Researchfor the Hypertopic & Photopic Condition

Color name P value Q value Radial Comment CoordinatesRel to H. Red @ Saturation

Red, Hering 0 Ln[1 + Lx/K] 0 494,655

Violet Ln[1 + S/K] 0 90 437,572

Aqua 0 --Ln[1 + M/K] 180 494,532

Green --Ln[1 + M/K] = --Ln[1 + M/K] 225 Values are negative and equal 532,532

Yellow --Ln[(1 + M/K] 0 270 532,572

Orange --Ln[1 + M/K] Ln[1 + Lx/K] --- L2 must be greater than M see defin [1 + M/K]

Magenta Ln[1 + S/K] Ln[1 + Lx/K] 45 Angle for small L, where Lx. S see defin

Cyan Ln[1 + S/K] --Ln[1 + M/K] 135 Angle for S = M see defin

* The bold numbers correspond to the single wavelength commonly associated with this color.

The first point to note is that the three “primaries,” red, green and blue, are not equally spaced in angle around thewhite point. This asymmetry has lead to the definition of “Hering” color pairs. Using the above definition, HeringRed is complementary to Aqua (not green) and Violet is complementary to Yellow. The terms black and white playno formal role in this New Chromaticity Diagram for Research. White, in the context of chromaticity is a nullcondition. It can represent any point along the black-white continuum.

The second point to note is that the power, x, associated with the L-signal is equal to 1.0 within the photopic rangedue to the adaptation process related to the L-spectral channel. The value of x is 2.0 within the mesotopic range (SeeSection 17.3.3.6).

Livingstone & Hubel made a particularly significant comment concerning their experiments involving color in1984302. “In typical experiments the object viewed is a small test spot of light on a dark or diffusely lit whitebackground. The results can be deeply counterintuitive—that monochromatic light seen as “blue” added in the rightamount to monochromatic light that we call “yellow” produces the sensation of “white,” a sensation also evoked bylight containing all wavelengths; that cyan (blue-green) plus red similarly produces white; that red plus green givesyellow.” These are exactly the results predicted by this theory and illustrated by the New physiologically-basedChromaticity Diagram. Their use of the term counterintuitive appears based more on their prior training than ontheir observations.

Pridmore has recently completed an extensive set of experiments expanding on those of Purdy (1937). The labels ofsome of the features of the spectra are different. However, the result confirm many of the wavelengths defined in theabove table to at least +/–5 nm and some to an accuracy better than +/–2 nm303. His reported effect of colortemperature on perceived wavelengths is quite interesting (pg 3903). It shows the performance loss when the photonflux in the short wavelength region is reduces disproportionately. Unfortunately, his “extended spectrum” is entirely


304Pridmore, R. (1993) Extension of dominant wavelength scale to the full hue cycle and evidence offundamental color symmetry Color Res Appl vol 18(1), pp 47-57

empirical and based largely on freehand graphic curve drawing304.

17.3.3.4 Limitations on the presentation of the New Chromaticity Diagram

The presentation of the New Chromaticity Diagram for Research in full color is difficult. The art of colorreproduction (as opposed to the creation of original art) does not employ a continuous pallette of colors. The brainrelies upon the computational powers of the retina to develop sets of parametric values, O, P and Q that it perceivesas specific colors. For primarily economic reasons, both the printing and display industries have settled on the use ofthree fixed chromaticity colors near the edges of the human color space that can be mixed by adjusting theirintensities. The mixing is accomplished within a pixel size that is below the resolution capability of the observingsystem. The result can be a very satisfactory rendition of the original object for colors within this color gamut. However, such systems cannot reproduce, or present “colors” outside the selected color gamut. Such systems cannotcreate an O–, P– or Q– value exceeding that of the selected pigment or phosphor.

To adequately reproduce the New Chromaticity Diagram for Research, it is important that the three pigments orphosphors be carefully chosen. Ideally they should be located on the spectral locus. The mean wavelength of themiddle component should be located near 532 nm. The mean wavelength of the long wavelength component shouldbe at or beyond 655 nm. The mean wavelength of the short wavelength component should be as near 400 nm aspossible. This is necessary to adequately stimulate the O–channel and reproduce the purples properly. If thiscomponent has a mean wavelength near 437 nm, colors found in the 400-437 nm region of actual human vision willnot be reproduced.

17.3.3.4.1 Broad versus narrow irradiances in the laboratory

Because of the significant overlap in the absorption spectra of the Rhodonines when configured for vision, thespectral width of the irradiance used to probe the color space of vision is important. The mean wavelength of theirradiance is always the critical parameter. However, the deviation about the mean has a significant impact on theexcitation of the spectrally adjacent absorbers. As a result, using narrowband irradiance sources when attempting toqualify the New Chromaticity Diagram for Research is important. A bandwidth of less than 5 nm is expected at thistime. These same specifications apply when one is using two separate sources simultaneously to reproduceirradiances applicable to the interior of either the 2-D or 3-D color space.

17.3.3.4.2 Capability of displays

Before making a comparison of chromaticity diagrams, discussing the capability of the various display methods usedto present them and the performance of the eye observing the diagrams is important.

All conventional display systems are based on the linear processing of either active sources (lights) or passivematerials (pigments). The interplay of active sources is described mathematically by addition. The similar interplayof passive materials removes spectral content from the original illumination. The resultant change in illumination isbest described by subtraction.

The various display methods are invariably based on linear summation of chromatic information. In fact, since it is atransmission and reproduction medium, color television has taken great pains to maintain a linear relationshipbetween the reproduced image and the source image. To insure this feature, a term known as gamma in the graphicarts is used. Gamma is the exponent of the transfer coefficient between the output and input signals. The gamma istypically not 1.0 in cathode ray tubes and additional circuitry is needed to compensate for this fact. Thephotographic arts industry is also an image reproduction medium. However, it both suffers from and frequently usesto its advantage variations in the gamma on a spectral channel by channel basis.

The animal (and human) eye is not based on linear addition of chromatic information. In fact, it is much morecomplicated. It involves a variable gain mechanism in each spectral channel and exponential addition (andsubtraction) of signals from each spectral channel.

With the arrival of computer-supported publishing, both desktop and commercial, this subject has taken on greaterinterest and reached a higher level of understanding among the graphic arts community. Appreciation of thedifference between additive color systems, as used in light generating systems such as computer displays andtelevision monitors, and subtractive color systems, such as inks, paints and tinted materials, has become more


common. Each of these display methods has a proscribed range of color rendition, known as a gamut, determined bythe phosphors or other light source used in additive systems, or the family of pigments used in subtractive systems. The gamut of the human eye is wider than the gamut of either of these systems. Usually, this is based on acommercial decision. There is no reason an additive or subtractive system cannot exceed the gamut of the humaneye. Many additive systems do, particularly in the ultraviolet region, but the human is unable to perceive this fact.

The subtractive color system used to print most books, called process color, has a gamut that is significantly smallerthan the gamut of the human eye. Therefore, printing a Chromaticity Diagram representative of the capability of thehuman eye using process color is not possible. An alternative printing technique uses what is called “spot color.” This system uses more specific inks for each color or group of colors but is more expensive commercially. Thecapability of most additive systems, including common computer monitors, is somewhat better in this respect butstill not adequate for research purposes.

For research in vision, the color gamut should extend from the short wavelength limit of human color discrimination,at 400 nm, to the long wavelength limit that is less precisely defined but is near 655 nm. This range excludes theperceived color reversal range beyond 655 nm. The source should be capable of generating narrow band intensitiesof constant flux per unit bandwidth. The only method of achieving this gamut currently is with a multi-channelnarrow bandwidth colorimeter incorporating a 7053 K source. A black body source at this temperature that is notencumbered by a spectrally limiting envelope or optical system provides a uniform illuminant within +/-5.7% overthe human visual spectrum. Table 1.3.3.4 provides quality factors for other common illuminants.

There is little correlation between the names and RGB values assigned to colors used in personalcomputer displays, and the color capability of the human eye. This is true for both Macintosh andWindows based systems. As illustrated below, the RGB computer values (now represented bymultiple versions of what is described as sRGB encoding) are based on a three dimensionalorthogonal color space, not the two dimensional color difference space of the neural system. Investigators are cautioned to avoid the introduction of uncontrolled variables in the use of suchdisplays in psychophysical experiments. Windows has recognized that the terms dark green andlight green are not appropriate. Dark and light are better reserved for discussions of intensitylevel. Microsoft has chosen to describe a fully saturated “green”, hexadecimal code 00FF00, aslime. This name is commonly associated with a color close to the Hering axis terminus at 572 nm. However, this location differs significantly from the corner of human color space near 532 nm.

17.3.3.4.3 Remaining functional complications

The possibility of cross-coupling of signal information within the retina before the chromatic signals are createdmust be addressed. There are two major possibilities, involving several possible configurations, with differentconsequences.

Spatial filtering in the process of chrominance signal formation

Many locations in the literature suggest cross-coupling between the output of horizontal cells and the pedicles of thephotoreceptors. The output of the horizontal cells is usually associated with the outer plexiform layer. Since thiscoupling would feed color difference signals back to a spectrally pure output of a photoreceptor cell, it wouldconstitute external feedback relative to that spectral channel. If the arborization of the horizontal cell was extensive,this mechanism would also introduce chromatic cross coupling between distant points in the field of view. Theresult would be that the perceived colors would be highly complex functions of the color of the surrounding scene. The perceived colors could even be functions of variations in the surround if the arborization of the horizontal cellsintroduced spatial filtering techniques to emphasize, or de-emphasize, certain spatial frequencies.

Spatial processing between luminance channels

There is also the possibility that the lateral neurons associated with the inner plexiform layer, frequently groupedunder the name amercine cells, might introduce spatial cross-coupling between the luminance channel signals fromthe bipolar cells. This would be the case if the lateral cells of the inner plexiform layer introduced the results of theirprocessing back into the dendrites of the bipolar cells in the inner nuclear layer. Depending on arborization of theamercine cells, spatial filtering of the luminance information relative to the surround would result.

Spatial processing between chrominance channels

The possibility that amercine cells may manipulate the chrominance signals must be considered. They would obtain


305Zworykin, V. & Morton, G. (1954) Television, 2nd ed. NY: John Wiley & Sons.

signals from the pedicles of either horizontal cells or intermediary bipolar cells. Again depending on arborization level, the output of these cells could be of endless variety. They could reflectcenter surround relationships or sensing of spatial patterns of a specific chromaticity.

There can be little doubt that cross-coupling does occur between the luminance and chrominance signal paths. Theliterature is replete with many examples of the sensitivity of the psychophysical experiments in this area to both thecolor of the surround and the spatial extent of the test image and/or the surround. However, two points areimportant. Many of the observed cross-couplings are unimportant in the real world. No clear examples of externalfeedback of horizontal cells to the pedicles of photoreceptor cells have been recorded electrophysiologically. Furthermore, no requirement for such feedback exists in the proposed system.

Bandlimiting of chromatic information

The literature also includes a considerable amount of data on this subject compiled by the National TelevisionStandards Committee, NTSC, in the 1950's. This data was compiled for two reasons. There was a need to determinethe least amount of data required to be transmitted to satisfy the needs of the observer and to minimize thecomplexity of the electronic hardware involved. The latter were particularly important when combined with themandate that the new color television system produce a color signal that could be received without distortion on ablack and white receiver of the day. The resulting dot-sequential-color system took advantage of the limitation onthe performance of the human eye to the greatest possible extent.

Two primary conclusions were developed by the NTSC305. The human eye could not determine the color of finedetail in a scene and the perception of color by the eye was bandwidth limited, particularly along the (S–), (L–)diagonal in a polar coordinate chromaticity diagram. A major criterion for the adoption of any axes was that thesystem could reproduce the skin tones of a Caucasian with maximum fidelity using the camera tubes and the displaymonitor phosphors available then. The system adopted, and is currently used around the world, transmitted thechrominance information in an asymmetrical bandwidth-limited channel separate from the luminance information. Two chrominance subchannels were defined within this channel. One channel transmitted a signal representing theinformation along a diagonal axis drawn generally through the white point and a point of high green saturation. Thesecond channel transmitted a signal representing a diagonal through white and perpendicular to the above diagonal. The signal representing the diagonal including S and L (the Q channel of that system) was bandlimited moreseverely than the other (I) channel (400 kilocycles and 1.3 megacycles respectively in the NTSC system). Theresulting NTSC axes are shown in [Figure 17.3.3-8].

Additional discussions of the temporal bandlimiting features of the chromaticity channels will be found in Section17.6.3.

17.3.3.5 Auxiliary Constructs applied to the New Chromaticity Diagram

The orthogonal feature of the new Chromaticity Diagram for Research lends itself to many extensions. Theseextensions allow other data to be coordinated with the Diagram in order to make additional predictions andinterpretations. The Diagram is a representation of the perceived color performance of the human eye as representedby the signals occurring in the plane of the lateral cell axons. It is possible to compare the object scene with thisDiagram and make judgements about the operation of the photodetection and matrixing elements distal to thisposition. The obvious features that can be studied are:

+ the performance of these elements as a function of illumination level,

+ the performance of these elements as a function of the color temperature of the illuminance of the observed scene

+ both the gross and individual adaptation levels of the photodetection channels.

Additional constructs include:

+ the pulse intervals of the action potentials related to the chrominance channels

17.3.3.5.1 Theoretically achievable chromatic discrimination capability


Figure 17.3.3-7 [Color] Illustration of extended newChromaticity Diagram to show ideal and theoreticallyachievable chromatic discrimination capability undernominal conditions. Discrimination capability loci shownexpanded 10:1

In Figure 17.3.3-7, a new Chromaticity Diagram withan auxiliary construct is shown. This combinationdisplays the ability of the human eye to discriminatehue under nominal conditions. An auxiliary set ofaxes has been aligned with the original axes. Both atheoretically ideal and the measured discriminationfunctions of [Figure 17.3.2-7] are shown. The twowaveforms have been bisected to accommodate theconformal transformation used in the new ChromaticityDiagram. The y-axis of the auxiliary constructsspecifies the hue discrimination capability, d.c., of theeye as it would be represented by a line parallel to thespectrum locus at that wavelength. Thus in the idealsituation, the d.c. would be a constant value of about 2nm. This would be represented by a series of doubleended arrows parallel to each axis and two nm. inlength (The arrows are shown expanded 10:1 forclarity). At any location within the normal color space,the individual would be able to discriminate with anaccuracy of 2 nm. parallel to either of the two spectrumloci. If the capability of the observer is taken as anRMS function, it is possible to combine these twovalues probabilistically. The result is a d.c. of 2 nm. indiameter at that point. This is the conceptualfoundation for what are generally known as MacAdamellipses, because of their appearance in theconventional C.I.E. color space.

Looking at the achievable theoretical wavelengthfunctions, it is seen that the achievable d.c. is not the same throughout color space. At a wavelength of 440 nm., theachievable d.c. is about 5 nm. This is shown as a double arrow parallel to the spectrum locus near 440 nm. On the y-axis. At 580 nm., the achievable value is about 2 nm. A double arrow is shown near 580 nm., as above. At theintersection of the 440 and 580 nm. lines in color space, the achievable d.c. is an ellipse with a vertical axis of 5 nm. and a horizontal axis of 2 nm. as shown. By repeating this procedure, the theoretical discrimination capability of theeye can be specified throughout the new Chromaticity Diagram for any set of assumed nominal conditions.

17.3.3.5.2 Achievable discrimination capability versus test field RESERVED

17.3.3.5.3 Achievable discrimination capability in color deficient subjects

It is quite possible to use the New Chromaticity Diagram to evaluate color deficient individuals, particularly thosesuffering from poor blue-yellow discrimination capability. There is a small difficulty in using the Diagram toevaluate those with a red-green deficiency caused by the conformal mapping used to bend the axes at 532 nm. Theirdiscrimination capability along the red-green axis should extend “around the corner” on this Diagram. It would bebetter to use a slightly different diagram as will be developed in the next Chapter on abnormal vision.

17.3.3.5.4 Action potentials of the optic nerve vs illumination spectrum

Figure 17.3.3-8 provides the New Chromaticity Diagram extended to indicate the pulse interval and frequency of theaction potentials produced by the midget ganglion cells of the chrominance channels in human. Both a frequencyand a interpulse interval scale are shown along each axis for convenience. The exact location of W is not known atthis time. However, the figure shows the best available estimate based on the neutral points reported by colordeficient individuals. Protanomalous and deuteranomalous individuals report a neutral point at or near 494 nm. Similarly, tritanomalous and tetartanomalous individuals report a neutral point at or near 572 nm. Thus, W is shownas 570,494 on this spectrum locus. There is data (See Section 16.7.1) indicating that the nominal frequency of thecontinuous streams of pulses generated by ganglion cells in complete darkness is typically 30 pulses per second. This value will be taken as the nominal pulse rate for midget ganglion cells under null conditions. The arrowsindicate the direction of increasing values based on available data from the NTSC committee, see Zworykin &


306Zworykin, V. & Morton, G. (1954) Television, 2nd ed. NY: John Wiley & Sons. pp. 817-825

Figure 17.3.3-8 [Color] New Chromaticity Diagramextended to show the interpulse interval of the actionpotentials of the chrominance channels, P and Q as afunction of median spectral wavelength.

Morton306. They did not discuss action potentials within the eye. They did indicate that humans were slower toperceive the colors exciting the short wavelength and long wavelength channels of vision. Therefore, as discussed inChapter 14 and in Section 17.6, the tentative conclusion is drawn that the pulse frequency increases as the medianspectral color in the P-channel approaches 532 nm. A tentative conclusion is also drawn that the pulse frequencyincreases as the median spectral color in the Q-channel approaches 532 nm. as well. Additional experiments will berequired to determine the minimum and maximum frequency (pulse intervals) encountered in actual subjects.

17.3.3.5.5 Definition of Hue and Saturation

There has long been an interest in defining a colorsystem based on radial coordinates that described theperformance of the eye. It has been difficult becauseof the impact of color temperature on the perceivedcolors. Using the New Chromaticity Diagram forResearch, this problem of definition is avoided. Furthermore, by transforming the coordinates of theNew Diagram back to the old diagram and a specificcolor temperature, mathematically definable lines ofconstant hue and saturation can be plotted on the olddiagram. Before performing such transformations, it isimportant to define hue and saturation precisely.

In the past, hue has generally been defined in terms ofa radial angle relative to an arbitrary referencedirection, generally using an artistic rendition of a“color wheel” but occasionally using the C.I.E. 1931(x,y) Chromaticity Diagram. The definition based onthe (x,y) diagram is different when transferred to theC.I.E. (u,v) Chromaticity Diagrams.

The definition of saturation has been even moredifficult. One generally used definition defines the saturation scale as a linear scale from a specific “white” point onthe (x,y) diagram to the spectral locus or purple line. Such a representation involves two problems. The saturationscale is of variable length as a function of hue. In addition, the saturation scale loses credibility in the region near500 nm. because of the recognized distortion of the chromatic scale in this region. This distortion was one of themain reasons the (u,v) diagram was adopted.

The availability of the two chrominance channel scalar values, P & Q, provides the opportunity to define saturation(and hue) more formally. Particularly in the case of P, these functions have well defined extreme values as shown inFigures 17.3.2-2. They exhibit distinct threshold levels as shown in 17.3.2-3. They also change in amplitude withrespect to the illumination parameter in a monotonic manner as shown in Figure 17.3.3-2. Based on these facts, thefundamental definition of saturation involves the magnitude of the P and Q signals in relation to a threshold value. Although it is possible the relationship could involve a difference, it is more likely to be represented by a ratio. Making this basic assumption, the mathematical definition of saturation for a specific perceived color is given by theratio of the absolute value of P or Q to a fixed threshold value. The maximum value of these ratios is set by themaximum value of the scalar values of P and Q.

The above mathematical definition is completely compatible with Eq. 17.3.3-11 & 12 and their special cases to beexamined below. It is immediately seen that the maximum saturation achievable at a given location in the spectralspace of the New Chromaticity Diagram is given by two values, |P|/Thresh. and |Q|/Thresh. at that location. Withinthe hypertopic and photopic illumination regimes, these values are independent of the illumination level. Thesaturation level is essentially proportional to the rectilinear distances between the white point and the specificspectral location. Within the mesotopic regime, the P and Q values at a given spectral location decrease withillumination. As the P and Q values reach threshold level at a given spectral location, chromatic vision is lost at thatlocation. Upon reaching scotopic levels, the saturation level falls below the threshold level at all spectral locationsand only achromatic vision is possible.

As indicated in Section 17.3.3.2, P & Q are not independent of each other for negative values. The M–channel


Figure 17.3.3-9 [Color] Hue and Saturation coordinatesapplied to the New Chromaticity Diagram. The squarebox surrounding the white point and passing through 456,532 and 608 nm. describes the highest absolute saturationthat can be obtained for an arbitrary hue. The rectanglepassing through 418, 532 and 646 nm. describes the locusof twice the absolute saturation that is only achievable forwavelengths shorter than 456 nm. and greater than 608nm.

input dominates both signals. In addition, after recovery of the P and Q signals in the brain, there appears to be aselection process where the more positive of P and Q is used to define the saturation level. This selection processavoids conflict in the perception of hue and also limits the maximum perceived saturation in the region between 494and 570 nm. As in Section 17.3.3.2, the assumption will be made that this transition wavelength occurs at the centerof the M-channel absorption spectrum, 532 nm. Because of this selection process, the absolute saturation level in theregion between 494 and 570 nm. is never as high as in the regions of 400 nm. and 655 nm. The resultant map ofabsolute saturation level in P,Q space is the same as the map adopted for the New Chromaticity Diagram, arectangular area which is asymmetrical with respect to the white point. Within this space is an additional squarecentered on white that defines a constant absolute saturation contour determined by a monochromatic sourcetraversing the visual spectrum. This absolute level is equal to the maximum absolute saturation value achievable inthe region of 532 nm. A second set of values corresponding to an absolute mathematical saturation of twice theunity value occur at wavelengths of 418 and 646 nm. for a monochromatic source. The highest achievable value ofabsolute mathematical saturation is between 2.2 and 2.5 based on this derivation.

The definition of hue is much simpler using the New Diagram. The logical zero angle reference is the positive Qaxis. This radial leads directly to a mathematically definable “red” that contains no “blue” or “green,” P = 0. Similarly, a mathematically definable “blue” that contains no “red” or green” is definable at the extreme positivevalue of P, Q = 0. Finally, a mathematically definable “green” that contains no blue or red is found at the extremevalue of the radial at 225 degrees where P = Q. Note carefully that these three mathematically defined primaries arenot equally spaced in angle. Figure 17.3.3-9 defines a the mathematical hue and absolute saturation spaceaccording to the above rationale. At wavelengths shorter than 400 nm., the saturation value remains constant at thelevel corresponding to 400 nm. At wavelengths beyond 655 nm., the saturation decreases slightly in consort with thehue reversal.

The space within the unity saturation square provides a mathematically defined and traceable “square” color wheelthat is believed to be distortion free when based on the values of P and Q (See Section 17.3.3.5.1). It appears thatthis space covers most of the hue and saturation space used in normal practice, both artistic and commercial. Ifnecessary a slightly rectangular and off-axis color wheel can be used based on the nominal maximum absorptionpoint of the three chromophores, 437, 532, and 625 nm. This rectangle extends to a maximum absolute saturation ofabout 1.5 in P and Q. This degree of asymmetry issimilar to that used in NTSC color television.

The derivation of a conventional artistic andcommercially useful color wheel from the abovemathematical color space would be desirable. However, there are three problems.

+As shown above the mathematical hue and saturationspace is not symmetrical about the white point forabsolute saturation values greater than unity.

+The details regarding the selection process involvingthe P and Q functions in the region between 494 and570 nm. is not known precisely.

+The two functions are not related by an equation ofthe form x2 + y2 = z2.

Because of these problems, there is no simple way totransform the rectangular mathematical hue andsaturation space into a conventional circular colorwheel with the primaries separated by 120 degrees anda saturation vector of constant maximum value. Byadopting a color wheel with the primaries spaced by 90and 135 degrees, and adopting a relative saturationscale, a color wheel results that is only mildlydistorted.

17.3.3.6 Perception and display of colorspaces


307MacAdam, D. (1942) Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. Vol. 32, pg.247308Farnsworth, D. (1944) The Farnsworth rectilinear uniform chromaticity scale diagram No 38. Memorandum Report # 44-1 New London CT: Med. Res. Lab. U.S. Submarine Base or Wyszecki & Stiles,2nd Ed. pg. 311309Rodieck, R. (1998) The first steps in seeing. Sutherland, MA: Sinauer Associates pg. 352310Greenstein, V. Zaidi, Q, Hood, D. Spehar, B. Cideciyan, A. & Jacobson, S. (1996) The enhanced S conesyndrome: An analysis of receptoral and post-receptoral changes. Vision Res. Vol. 36, pp. 3711-3722311Tansley, B. & Boynton, R. (1978) Chromatic border perception: the role of red- and green-sensitivecones. Vision Res. vol. 18, pp 683-697

17.3.3.6.1 Comparing the new diagram with MacAdam, Farnsworth, etc.

D. L. MacAdam307 performed some meticulous experiments during the 1940's in an attempt to define the colordiscrimination capability of the human eye on a point by point basis in color space. He used the C.I.E. 1931Chromaticity Diagram as a framework for his data. The resulting maps of sensitivity ellipses have been a subject ofconsiderable discussion ever since. What has never been noted in the literature to the authors knowledge is theproclivity of the ellipses to point to the true peak spectral wavelengths of the visual chromophores, 437, 532 and 625nm. Of course this phenomena is easier to recognize in hindsight.

Farnsworth308 attempted to re-present the data of MacAdam using a color space topology that caused all of theellipses to approximate circles. The results are quite enlightening. Although his border continued to consist of aspectrum line derived from the same fundamentals as the C.I.E. (1931) Chromaticity Diagram, the results bear astriking resemblance to the orthogonal coordinates of the new Chromaticity Diagram presented above. Figure17.3.3-10 presents the data of Farnsworth with the two orthogonal axes of the new Diagram as an overlay.

Recently, a diagram similar to that of Farnsworth but based on a modified Hering foundation has become popular. Italso appears in the same orientation as the new diagram proposed here. However, it maintains the old spectral locusand purple line. Rodieck has provided a textbook version of this diagram but it does not incorporate any scales309. Greenstein, Zaidi, et. al310. have provided papers describing the derivation of this “S-cone system.” Associated withRodieck’s version are some unique diagrams suggesting that the L and M chromophoric channels are notindependent. The reproduction quality of that figure is quite limited due to the use of process color in the printing. The purples are not shown properly. See Section17.3.3.6.2.

MacAdam presented his data based on illuminant C as defined in the 1930's. This illuminant is located at x=0.315,y=0.315 on the C.I.E Diagram and approximates an equal energy source. An illuminant more closely approximatingan equal flux source, a Planckian radiator near 8000 Kelvin would be at x=0.295, y=0.303. A new rectilinearcoordinate system, compatible with this theory, can be overlaid on the data of Farnsworth. The white point at P = Q= 0, approximately (494, 570) in nm., can be overlaid on the equal flux point at x=0.295, y=0.303 and the axesrotated about this point to obtain a reasonable match. A reasonable match is primarily for artistic and pedagogicalpurposes since the spectrum line and the purple line are derived from a set of conceptual principles that are nottraceable to the absorption characteristics of the animal eye.

Lacking new experimental data, the orientation of the overlay axes was chosen to conform approximately to theC.I.E. spectrum line and to include all of MacAdam’s data within the new spectral envelope.

As indicated above, no discussion is appropriate concerning the exact location of the “Spectrum Line” in theseearlier diagrams since it is derived under less than ideal assumptions. However, it does exhibit a relatively linearscale between 530 and 620 nm. If the scale in the area of 530 to 570 was brought into alignment with the proposedaxes, the ellipses could still be circular within the 10-20% error estimated for the data in Wyszecki & Stiles. Littledata was taken by MacAdam in the far blue region of the spectrum because of instrumentation and subjectperformance difficulties. Therefore, the effect on the ellipses of adjusting the topology and linearizing the scalebetween 532 and 400 nm. can not be stated. A new re-presentation of the raw data is needed to answer this question.

Tansley & Boynton have provided an unusual variant of the C.I.E. (1960) UCS grid311. It uses a non orthogonalcoordinate system with y plotted on a scale that appears to be double logarithmic.


Figure 17.3.3-10 A re-plot of MacAdam ellipses compared to the new Chromaticity Diagram. MacAdam ellipsesare plotted on a rectilinear coordinate system by Farnsworth, (1944). Note the x and y coordinate values of theC.I.E. Chromaticity Diagram shown as curved lines. The data is overlaid on the rectilinear coordinate system of thenew Chromaticity Diagram.

Wyszecki & Stiles critiqued Farnsworth by pointing out the data points of Farnsworth were not as circular as thecircles drawn over them suggested. This should have been expected. Farnsworth was performing an empiricalmanipulation of data of un-quantified precision. Stiles had previously analyzed methods of bringing his line elementmodel of color discrimination into agreement with the data of MacAdam. Neither of these investigators employedan orthogonal chromaticity space as used in the New Chromaticity Diagram. Using the new Diagram and theextended scales of minimum wavelength discrimination capability of Section 17.3.3.3.2, it is clear that the raw datagenerating “MacAdam ellipses” should be ellipses even in an orthogonal color space. This is true without anymanipulations of the data relative to tristimulus values or space. It is true for the theoretical case using equal photon


312Zworykin & Morton, Op. Cit. pp. 762-813 &912-915313Adobe Illustrator 8.0: User Guide (1998) San Jose, CA: Adobe Systems Incorporated pp. 157-159314Ready, K. & Warner, J. (1996) Hybrid HTML Design. Indianapolis, IN: New Rider Publishing pp.279-285315Backhaus, W. Kliegl, R. & Werner, J. (1998) Color Vision: Perspectives from different disciplinesBerlin: W. de Gruyter, pg 11. The same background spectrum was used in many figures of this work.

flux illumination and it is certainly true at the color temperature of the luminance used by Bedford & Wyszecki. The ellipses will be even more elliptical at lower color temperatures.

17.3.3.6.2 Difficulty in documentation and display

An important subject is seldom addressed in the vision research literature but is important in the graphic arts. Thegamut of colors perceived by the human is larger than that provided in a typical computer monitor or televisiondisplay device. The visual gamut is considerably larger than that available in conventional color printing using whatis known as “process color.” This situation makes it difficult to display the chromatic capability of the eye usingconventional graphics. Zworykin & Morton have discussed this subject in some detail and provided compositeChromaticity Diagrams of the capabilities of various systems along with the technical performance characteristics ofpractical television display devices312. Adobe Systems Incorporated313 also discusses this subject in connection withtheir graphic arts software program, “Illustrator.” Ready & Warner314 discuss the situation from the context of thedesk top computer. Their figure on page 283 shows the difficulty of reproducing a color image, from a monitor, onpaper using process color. They also suggest alternate “special names” for some colors to provide a moreunderstandable correlation between computer colors and graphic arts colors. These context specific names probablyonly confuse the issues raised in TABLE 17.3.3-1.

Another problem in displaying an appropriate human color gamut is the difference between the inks commonly usedin “North America” and “Europe.” A comparison of the widely reproduced spectra of Dowling illustrates theproblem. In Gouras (printed to North American process color standards), the spectrum does not represent the regionbetween 400-430 nm well. While it should appear purple, that region appears blue like the region from 440 to 460nm. However, in the same figure printed in Backhaus, et. al.(printed to European process color standards), thespectrum reproduces the 400-430 nm region as a saturated purple315. However, the region 440-460 does notreproduce as a saturated blue. It is distinctly purplish. While it appears the two authors used separation negativesfrom the same source , the difference appears to be due to the use of a different magenta ink in the two color printingprocesses.

A more detailed explanation of this problem appears as question 236 on the website, www.askpantone.com.

The two main CMYK standards are SWOP and Euroscale. SWOP is an acronym that stands forStandard for Web Offset Publication, and is the North American standard. Euroscale, as the nameimplies, is used primarily in Europe. There is an actual shading difference in the Cyan andMagenta inks between SWOP and Euroscale, such that if the same set of CMYK values are usedin the two standards, you would likely achieve two different results. Further, Euroscale inks aregenerally printed at a higher density than SWOP inks.

The difference in process color reproductions can be understood most clearly in the tetrachromatic context of[Figure 17.3.3-1] of Section 17.3.3.2. While the cyan and yellow inks have the same, or similar, spectraldistributions in the two systems, the magenta is significantly different. The North American magenta has onespectral peak in the red and the second between 440 and 460 nm in the blue. The reproducible color gamut is in theplane defined by 437, 532 and 655 nm. Positive values cannot be generated in the O-channel of vision by this dyeset. Hence, a purple, in the range of 400-430 nm cannot be reproduced by this system. The European magenta (atleast that used to print Backhaus, et. al., has one spectral peak in the red and the second between 400 and 430 nm inthe purple. The reproducible color gamut is now in a plane defined by a point between 400 & 430 nm, and 532 and655 nm. While positive values can be generated in the O-channel of vision by this dye set, a high positive valuecannot be generated in the P-channel. Hence, a blue, in the range of 440-460 nm cannot be reproduced by thissystem. The area expected to represent a saturated blue will appear as an unsaturated blend of purple and aqua

The conclusion from reviewing the above material are several.

The field is confusing because of the evolution of many systems for describing the chromaticcapability of various presentation mediums and visual systems.


Both of the widely used additive and subtractive color systems, are based on the linear summationof individual colored lights or pigments. They both attempt to achieve control of both brightness,hue and saturation simultaneously. They both suffer significant limitations in the reproduction ofthe visual spectrum.

The additive systems have been more successful in this regard when using only three lights, red,green and blue (RGB). The subtractive systems have generally found it unsatisfactory to use onlythree pigments. A four pigment system is usually employed based on cyan, magenta, yellow(canary is preferred) and black (CMYK). Even this four color system of subtractive color is quitelimiting and the highest quality graphic arts material is manufactured using spot color, i.e., specialdyes with greater spectral purity and saturation range than that in commercial process colorreproduction.

There can be significant differences in process color printing when magenta inks of differentspectral characteristics are used to reproduce visual spectra.

It is only possible to display the entire human visual color gamut using monitors and printedgraphics by incuring higher than normal costs. The printed graphic must employ specially tailoreddyes in what is known as “spot color” in the trade. Alternately, the new system known as“hexachrome™” printing, introduced by Pantone, can be used. It remains deficient in renderingpurple when using SWOP inks.

Because of the above difficulties, it is important to provide a numerical value for the peak wavelength of theabsorption or transmission spectrum of the light or pigment, as a minimum, when discussing the spectral elements ofvision. Where possible, both the peak wavelength and some indication of the dispersion from that peak is desirable.

One should be particularly aware of the poor performance of the CMYK system with regard to high saturationyellow and blue.

One should also be aware that the specification of a numerical value for a color in computer code only specifies therelative intensity of the electrical signal applied to the presentation device, it does not necessarily relate to the actualcolor produced. The color produced depends on the specific phosphor, filter or other transducer used in the displaydevice.

17.3.3.6.3 Typical achievable color spaces

As developed previously in this section, the maximum perceptible color gamut in animal vision is basically aconformal rectangle when presented in P, Q color space. The perceptible color gamut may be more limited at certainstimulus levels due to a variety of individual limiting mechanisms.

Although one is free to draw various triangles on the New Chromaticity Diagram by drawing lines connectingvarious colors along the periphery of the P,Q color space, such as red, green and blue, the perceptible colors ofvision are not confined to the interior of such constructions. The human is able to perceive a distinct color for everycombination of P and Q where P and Q may have positive or negative values. Using the wavelength scales, the totalcolor space perceptible to humans is a rectangle enclosed by 400 nm to 530 nm. on the vertical scale and 530 tobeyond 655 nm. on the horizontal scale.

When examining the capability of broad spectral band sources to create perceivable colors, it is necessary tocompute the P and/or Q values (p,q) caused by each source. This procedure is similar to the calculation of x,y valuesfor the C.I.E. diagram. However, no imaginary absorption spectrums are used. The actual absorption spectrums ofthe animal chromophores are used. The calculations do involve the difference in logarithms where the logarithmarguments are integrals of products with respect to wavelength. If desired, the fundamental (p,q) values can betransformed directly into spectral values consisting of two wavelengths, one less and one more than 532 nm.

As the model shows, the computation of a pair of P and a Q values involves the subtraction of pairs of valuesdirectly related to the spectral values at the pedicles of photoreceptor cells. While the auxiliary wavelength scales ofthe New Chromaticity Diagram show that any given color can be perceived based on stimulation by only twoindividual sources of appropriate mean wavelength, this is not the most convenient method. The general method isto use three sources, whose mean wavelengths are located near the corners of the New Chromaticity Diagram. Bymodulating the intensity of these three sources, any color included within the rectangle defined by these threesources can be perceived.


Figure 17.3.3-11 Realizable human color space usingkinescope and printing techniques. The white wedgeshows colors not well represented in “North American”process color. Some “European” process color uses amagenta containing a deeper purple instead of a blue. Inthis case, the purples are reproduced better at the expenseof the blues (440-470 nm).

In the case of active sources used to create trichromatic display devices, the spectrums of the individual sources isreasonably narrow and does not overlay more than one chromophoric absorption spectrum of vision. and thecentroid of their radiant spectrum as a function of wavelength can be taken as their location on the NewChromaticity Diagram. Using these simplifying assumptions, the perceivable color gamut created by a typicaltrichromatic cathode ray display is also shown in Figure 17.3.3-11 .

In the case of the process color method of color printing, the procedure is basically the same. The achievable colorgamut is also shown in Figure 17.3.3-11.

17.3.3.7 The New Chromaticity Diagramfor Research at Mesotopic levels

The performance of the visual system is distinctlydifferent in the mesotopic region than it is in thephotopic or scotopic regions. The individual spectralchannels of the visual system are not operating inunison and color constancy, among other phenomena,is lost. However, human perception can still bedescribed using a modified form of the NewChromaticity Diagram for Research.

17.3.3.7.1 Mesopic versus mesotopic vision

There is a terminology problem in this area similar tothe one involving achromatopia and achromatopsia. Inboth cases, the shorter form is descriptive of a clinicalcondition known as a syndrome. In the case ofachromatopia, it includes several independent diseases,one of which is a specifically defined condition calledachromatopsia. The same situation applies here. Mesopia is the common term for a clinicallyrecognized condition (syndrome), namely poor visualperformance in the presence of limited lightstimulation. The most obvious phenomenon occurringwithin the mesopic range is the operation of the iris. While not defined as closely with respect to themesopic range as the next condition, the top of themesopic range is generally associated with the irisbeginning to open and allow more total flux to reachthe retina (See Section 2.4.3.1). The top of themesopic range is generally considered to occur near10+1 cd/m2 (See Section 2.1.1.1). Measurements in thisfield have a very large statistical range (nominally 3:1or more between investigators).

A second condition (disease) occurring within this syndrome is mesotopia. Mesotopia is defined as a neurologicalcondition wherein at least one of the adaptation mechanisms associated with the individual spectral photoreceptorchannels has reached full amplifier gain and can no longer compensate for the quantum-mechanical nonlinearityassociated with the phototransduction mechanism of the chromophore-neuron interface. Mesotopia is therefore morespecifically defined than mesopia. It is closely related to the failure of the phenomenon of color constancy. It canarise in the presence of very high average illumination levels if the spectral content of the illumination is highlyconstrained with respect to one or more spectral channels. Twilight typically represents such a condition whereinthe S–spectral channel is typically operating in the mesotopic condition while the L– and M–channels are not. Asthe M–channel enters the mesotopic condition, the Purkinje Peak appears in the perceived luminance of the scene(but not in the actual luminance of the stimulus). This peak is a result of the logarithmic signal processing withinthe neural system.

17.3.3.7.2 Equations of mesotopic vision

Equations 17.3.3-6 & 17.3.3-8, can be expanded to introduce the additional quiescent component, K, as was done inSection 17.3.3.2.3. The complete form of P and Q, under both mesotopic and scotopic conditions, can be written as


P = Ln(K+S) - Ln(K+M) = Ln[(K+S)/(K+M)] or Ln[(1+S/K)/(1+M/K)] Eq. 17.3.3-16

Q=Ln(K+L 2) - Ln(K+M) = Ln[(K+L2)/(K+M)] or Ln[(1+L2/K)/(1+M/K)] Eq. 17.3.3-17

The formulations on the right show that the P and Q channels perform differently. There is now a square term in theQ channel signal. Both signals are dependent on the ratios of the S-, M- and L2 signals to K. For large values ofthese ratios, the P and Q signals become dominated by a second set of ratios, those of S to M and L2 to M. As theselater ratios become small, the P and Q signals approach zero. This is similar to the photopic condition. However,there is another condition. As the signal levels decrease, the first set of ratios becomes small relative to 1, both thenumerator and denominator of each logarithm approaches 1. P and Q approach zero regardless of the ratio of S to Mand L2 to M. This situation describes the scotopic condition.

The manner in which P and Q approach zero is slightly different at low signal levels. Looking initially at thecondition where S, M and L2 are much larger than K, the equations become:

P = Ln [S/M] --Mesotopic condition, K is small Eq. 17.3.3-18

Q = Ln[L2/M] --Mesotopic condition, K is small Eq. 17.3.3-19

For positive values of P and Q, if the signal level begins to decrease, the Q signal decreases faster than the P signal. This is the primary explanation for the loss in saturation of long wavelength scene elements relative to that of shortwavelength scene elements.

For negative values of P and Q and low signal values, the situation is the same as for the photopic condition:

P = Q = -Ln[1 + M/K] --Mesotopic condition, M<K Eq. 17.3.3-20

Recognizing that the chromatic performance of the long wave trichromat degrades asymmetrically as theillumination level falls, as predicted by equations 17.3.3-16 & -17, it is useful to explore this effect on the NewChromaticity Diagram. The fundamental change is due to the nature of the equation for the Q channel signal. Sincethis region is characterized by the adaptation amplifiers beginning to operate at maximum gain and the variableinternal negative feedback reaching a minimum, the square-law aspect of the L-channel signal is now clearlyrepresented along the horizontal axis of the New Chromaticity Diagram. As the light level falls, the perception ofcolor is lost at ever shorter wavelengths.

Equations 17.3.3-16 & -17 also illustrate a second feature of the visual system. As the light level falls, the values ofboth P & Q approach zero regardless of the spectral content of the light in object space. Thus, less and less chrominance information is transmitted to the brain. Any scene in object space appears less and less saturated. Thisis the situation in the mesotopic region of vision. When the values of P & Q both fall below the threshold for the channels, the visual system is left with only luminance information. This is the case in the scotopic region.

17.3.3.7.3 The New Chromaticity Diagram under reduced stimulus conditions

To simplify the discussion, it will be assumed that the stimulus is a 7053 K blackbody source and the physiologicaloptical system is achromatic. This will insure that the photon flux as a function of wavelength is uniform at theretina.

It is difficult to illustrate both the loss in chromatic range and the loss in saturation in a single plane of the NewChromaticity Diagram. The signal level available at the pedicle of the L–channel photoreceptors falls rapidly withlight level in the mesotopic range. This fall causes the signal level in the Q–channel to become skewed toward thegreen. However, the M–channel signal is also falling. The result is that the Q–channel signal begins to decrease inabsolute amplitude toward zero (the condition of achromatic operation within the Q–channel). The samecircumstances occur in the P–channel. However, both the S– and M–channels are linear with respect to stimulation. Therefore, the decrease in P–channel signal amplitude remains symmetrical as the light level is decreased and the netsignal converges on the achromatic point. Figure 17.3.3-12 describes the loss in performance of both the P– andQ–channels as the light level is reduced. In this figure, the P– and Q–channel scales are primary. Let the largest boxbe drawn for a stimulus level corresponding to the top of the mesotopic region (and the pupil size fixed). This box isapproximately that available using a conventional (North American) tricolor monitor. At the top of the mesotopicregion, the wavelength scales represent the actual wavelengths of the stimuli. A circle inscribed within the largestbox would represent a Munsell Chroma of about 24. The individual boxes are caricatures meant to represent a


316Walkey, H. Barbur, J. Harlow, J. & Makous, W. (2001) Op. Cit.

Figure 17.3.3-12 (Color) New Chromaticity Diagram atmesotopic levels. The series of decreasing box sizes areillustrative of the more rapid loss in red-greenperformance as the light level is reduced. Each box ismeant to represent a change in stimulus level of 1.5@k:1from the adjacent box. Below a certain box size, thevisual system discards all chromatic information and reverts to achromatic operation.

change of 1.5"k:1 in logarithmic stimulus level compared to the adjacent boxes (where k can have any value). Theindividual boxes would represent different mesotopic brightness levels in a complete luminance-chrominance colorspace (See Section 17.4). At these lower stimulus values, the wavelengths corresponding to the sides of the boxesrepresent the perceived wavelengths of the light rather than the impressed wavelengths due to the tricolor monitor. The vertical and horizontal dimensions of each box define the maximum saturation level that can be achieved withinthe P– and Q– chrominance channels as a function of stimulus level. The lower the stimulus level, the smaller andnarrower the box. The perceived chroma circles of Munsell become highly elliptical due to the precipitous loss insignal in the L–channel. This predicted condition is compatible with the results of Walkey, et. al. (even though theywere measuring perceptions using the nonconformal CIE object spaces)316.

Young has confirmed the change in perceived responsewith reduced stimulus level in the field of visualastronomy (Section 17.3.8.1.7). He notes, “Amoderate yellow like Munsell 5Y 7/7 appears moderateolive if its reflectance is reduced 5 or 10 times, to 5Y3/7.” He is speaking here using the conventional(relative) Munsell Color Scale. Using the newAbsolute Munsell Color Scale defined in the abovereferenced section of this work, the second set ofvalues given would be precisely 5Y 2/7 for a reductionof 10:1 in reflectance, or the product of reflectance andirradiance.

Reference may also be made to the performance of thechrominance channels individually as represented bythe deutranope and tetartanope of Section 18.1.5. These may aid in understanding the independentoperation of the P– and Q–channels with light level.

17.3.3.7.4 Curvature of some loci in theNew Chromaticity Diagram

The above figure illustrates the loss in color constancyencountered under mesotopic conditions. Thediagonals of the boxes change angle with stimuluslevel. Equally obviously, MacAdam circles (in thisperceptual color space) become ellipses. It can beinferred from these conditions that color rendition ispoor under mesotopic conditions.

If a loci is defined representing the corners of theboxes, the resulting “radials” are curved. Thecurvature of these radials represents a change in bothsaturation and color as a function of stimulus level. These curvatures suggest a significant problem in theMunsell Color Space. It suggests that the Munsellradials are not perceived as of constant “value” as the light level is reduced.

The square-law nature of the quantum-mechanical mechanism associated with phototransduction in the L–spectralchannel has a significant impact on color rendition in the mesotopic region.

17.3.3.8 Features of the New Diagram[xxx overlaps with 17.3.4.2 ]

The new Chromaticity Diagram for Research is fundamentally different from the engineering and commerciallyoriented C.I.E. Diagrams. This new diagram describes “perception space.” The C.I.E. Diagrams describe “objectspace” (although psychophysicists frequently use them to interpret their perceptual results). The relationshipbetween these two presentations is dynamic due to the time constants of the adaptation amplifiers associated witheach chromatic channel. The formulation of the new chromaticity diagram presents a number of attractive features:


Major Features;

+ The formulation of this chart does not require the use of Tristimulus values or other mathematical devicesof any kind. The so-called real primary stimuli given by R,G,B and the imaginary primary stimuli given byX,Y,Z are not used. The coordinates of the presentation are directly in the wavelengths of the appliedstimulus.

+ There are no “non-spectral” colors.

+ The presentation does not require any auxiliary lines, such as a Purple Line, or construction lines tospecify a color as a “complementary wavelength.” All colors occupy individual and unique locations on thechart. The old Purple Line is replaced by two lines defining the actual limits of human color discrimination. The concept of an alychne, a line of zero luminance and defined as the line at y=0.0 in the conventionalchromaticity diagram, is not used. Luminance is not present explicitly or implicitly in the New Diagram. Itis orthogonal to the new color space. See Section 17.4.

+ The presentation clearly delineates the limits of color discrimination in human vision.

+ The coordinates of a given color may be described in terms of rectilinear values, associated directly withthe dominant (or mean) wavelengths of the constituent lights, or in terms of circular coordinates based onthe point defined as white. The white point is an intrinsic point that does not change with sourceillumination color temperature if sufficient adaptation time is provided. For circular coordinates, thesaturation is indicated by the length of the radius line from W and the hue can be indicated by the anglefrom the horizontal line to the right of W or by using any other initial angle.

+ The presentation is completely independent of the Brightness perceived by the animal.

+ The saturation level is defined in mathematically verifiable terms. Contours of constant saturation can bedrawn explicitly.

Other features include;

+ White is uniquely defined as the point W in normal “long wave” trichromats like humans. This point can be takenas 0,0 in circular coordinates to describe the hue and saturation of a unique individual color or the location of thecentroid of a complex color.

-As the eye ages, the lens system loses transmission in the short wavelength spectrum. This effect isautomatically compensated by the adaptation amplifiers. The subject always perceives white as whiteregardless of his age.

-When exposed to chromatic illumination for an extended period, the subject will still report “white”objects in object space as occurring at the W point in this diagram. The “white” object may appear asdistinctly colored to a photoelectric spectrophotometer.

+ Certain colors can be given explicit names that are mathematically and uniquely defined in terms of the NewChromaticity Diagram for Research under Photopic conditions;

Unique Aqua is defined as a monochromatic illuminant with a spectral wavelength of 494 nm. It can beapproximated under broad band conditions by an illuminant with a mean spectral wavelength of 494 nm.and no spectral content at wavelengths longer than 570 nm. (P =0, Q is negative)

Unique Yellow is defined as a monochromatic illuminant with a spectral wavelength of 570 nm. It can beapproximated under broad band conditions by an illuminant with a mean spectral wavelength of 570 nm.and no spectral content at wavelengths shorter than 494 nm. (Q=0, P is negative)

Unique Green is defined as a monochromatic illuminant with a spectral wavelength of 532 nm. It can beapproximated under broad band conditions by an illuminant with a mean spectral wavelength of 532 nm.and no spectral content at wavelengths shorter than 494 nm. or longer than 570 nm. (P is negative, Q isnegative, and P=Q)

Unique Red is defined as a monochromatic illuminant with a spectral wavelength of 655 nm. It can be


approximated at maximum saturation under broad band conditions by an illuminant with a mean spectralwavelength of 655 nm. and no spectral content at wavelengths shorter than 570 nm. (P=0, Q is positive)

Unique Purple is defined as a monochromatic illuminant with a spectral wavelength of 400 nm. It can beapproximated at maximum saturation under broad band conditions by an illuminant with a mean spectralwavelength of 400 nm. and no spectral content at wavelengths longer than 494 nm. (P is positive, Q=0) This definition only applies if the visual system is truly trichromatic and not that of a blocked tetrachromat.

Similar definitions can be given for each of these unique colors under saturated conditions by defining the radialpassing between them and “white.” This is easiest in circular coordinates with the red radial defines as zero angle.

Under unsaturated conditions, the colors leading to these unique colors (but not the unique colors) can be describedin terms of the length of the radial leading to the unique color. The length of the radial is an indication of thesaturation level.

+ Under lower than photopic conditions, the same unique colors exist. However, they may not be perceivablebecause of the low average signal magnitudes in the P and Q chrominance channels. The perception of all colorsapproach zero saturation as the illumination conditions approach the scotopic value, i. e., the values of P & Qapproach zero.

+ In absolute darkness, the brain receives a full set of null signals from the ganglion cells of the retina;- The null signals generated by the midget ganglion cells corresponds to a continuous pulse train of nominalpulse interval due to the bias condition of the cells.- The null signals generated by the parasol ganglion cells correspond to an absence of pulses at their outputdue to the bias condition of the cells.

+White is uniquely presented to the brain as a null signal in all (both) chromatic difference channels in the presenceof any luminance signals.

+ In the presence of a scene with a spectral intensity other than that represented by an 8,000 K source, the adaptationamplifiers in the photoreceptor cells adjust their gain automatically in order to present a nominal signal level in thechromatic channels at the input to the midget ganglion cells centered around the coordinate point, W. This appearsto be an open circuit adjustment, no feedback to the photoreceptor cells is required, because of the high degree ofinternal feedback found in the collector circuit of the adaptation amplifiers.

+ The automatic adjustment performed by the adaptation amplifiers makes calculation of an alternate “white point”for sources of other color temperature than nominal inappropriate, and meaningless.

- If desired, auxiliary constructs can be used associated with the two spectral axes to indicate theconversion of the radiation from a given spectral source into its perceived values on the newDiagram. It should be noted that the transfer functions are time dependent due to the time constantassociated with the adaptation amplifiers in each chromophoric channel.

+ Following full adaptation (and while remaining within the photopic region), the perception of white is independentof the color temperature of the illumination source. As in the case of the Purple Line and alychne, there is noPlanckian Locus in the New Chromaticity Diagram for Research.

17.3.3.8.1 An important feature of chromaticity diagrams

[ need ln terms in P equation ??]An important point shared with the C.I.E. Chromaticity Diagram relates to the underlying mathematics. The form ofthe expression defining each axis is important. For the short wavelength axis, P = S- minus M-. But the S- signal isthe product of the gain of the S-channel amplifiers multiplied by the integral of the spectral luminance exciting the S-photoreceptor and the absorption coefficient of that photoreceptor. Thus P is the scalar difference between twointegral terms. The chromatic character of the initial illuminance is lost in the integration process. The value of P isnot uniquely defined in terms of the spectrum used to compute it. In essence, a chromaticity diagram is only precisewhen dealing with monochromatic specular lights. As the spectral width of each light broadens, the precision of thechromaticity diagram presentation becomes less precise. If the spectral distribution of a light becomes significantlydifferent than a smooth curve typified by either the Fermi-Dirac or the Gaussian function, the presentation on thechromaticity diagram becomes even less precise. Finally, a spectral distribution that excites the S- and M- channelequally in the steady state will generate a null condition and the brain will interpret this light as a monochromaticlight of 494 nm. wavelength. A similar analysis applies to the Q chromatic channel.


317Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate visualcortex. J. Neurosci. vol. 4, no. 1, pp 309-356, pg. 348.

Figure 17.3.3-13 (Color) An extended New ChromaticityDiagram and an arbitrary source spectrum.

The above situation prevents the use of simple auxiliary axes on the New Chromaticity Diagram to present thespectral distribution of the light presented to the eye. It is possible to use such axes if they are subdivided further tosegregate the illumination received by each chromophoric detection channel. This segregation insures that the lightis considered as part of the appropriate integral. Figure 17.3.3-13 provides a conceptual view of this extendeddiagram (for the vertical axis only). The line at 475 nm. Is the approximate point of equal absorption between thetwo spectrums. Such auxiliary axes cannot be applied to the C.I.E. Diagram at all since it is not an orthogonalpresentation. However, the underlying mathematical concepts and resulting limitations on presentation precision doapply.

The mathematics described above and associated withthe signal processing in the chrominance channels ofvision provide a general explanation for the specialchromatic effects described by Land and incorporatedin his Retinex Theory of color vison. See Section17.8.4 for further discussion of these phenomena.

It also explains a “counterintuitive” observation ofLivingstone & Hubel317. In experiments using a smalltest source displayed against a dark or diffusely litbackground, they observed “that monochromatic lightseen as ‘blue’ added in the right amount tomonochromatic light that we call ‘yellow’ produces thesensation of ‘white,’ a sensation also evoked by lightcontaining all wavelengths; that cyan (blue-green) plusred similarly produces white; that red plus green givesyellow.” These statements may appearcounterintuitive to someone trained using the C.I.E.(1931) Chromaticity Diagram but they are simplyobvious based on the New Chromaticity Diagram forResearch. Although using color names that are poorlydefined in the paper, they correspond conceptually tothe four orthogonal colors of the Hering Theory whenplotted on the New Diagram and shown in the Figures of the following sections.

17.3.3.8.2 Display device overlays

[XXX The art in the following figure is inadequate for the purpose intended and will be reconfigured.]

Figure 17.3.3-14 provides an estimated capability of two classes of display devices in terms of the NewChromaticity Diagram, those using active (emitting) sources and those using passive (absorptive) techniques. As inthe case of the C.I.E. Chromaticity Diagram, it is seen that neither of these classes of devices can provide acompletely adequate reproduction of the chromatic capability of the human eye using only three spectral channels.

The active source display can provide the broadest representation of the visual color space. However, the use ofonly three phosphors in a kinescope selected to provide maximum brightness as well as good spectral separationfrequently limits the performance in the extreme short and long wavelength regions. An active display superior toany current kinescope display can be, and has been, provided using three individual laser light sources at 400 nm,532 nm and 650 nm. Such a machine has been in commercial use for many years as both a television projector and akinescope recorder.

In the New Chromaticity Diagram for Research, the available color gamut for active sources is defined by the areaenclosed by asymptotes drawn perpendicular to the axes at the centroidal wavelength of the individual light sources. The area is normally rectangular.

The passive display device based on subtractive (process) color, typically ink on paper, has been severely limited inits ability to reproduce the visual color space. This capability is so limited that a fourth color, black, is usually usedto improve the color rendition leading to the nomenclature CMYK or four color printing. The printer frequently


adjusts the specific cutoff wavelengths of his inks to improve performance in a specific area when a customer insists. However, to achieve better performance, the printer will introduce spot color when necessary. Spot color involvesadding an additional step in the printing process using a narrow spectral band, and frequently highly reflective, ink..

In recent commercial printing, a new six color subtractive process has been introduced to attempt to compete inquality with the additive color representations available in the marketplace.

Any printed representation of the New Chromaticity Diagram for Research, which is meant to describe theperformance of the human eye will be found wanting unless spot color or a six color process is employed.


Figure 17.3.3-14 (Color) XXX A comparison of additive and subtractive (process) color “sets” with the capabilitiesof the long wavelength trichromats normal color space. The additive color set can reproduce any color within thetriangle formed by connecting the centroids of the R,G & B emission sources. The subtractive color set exists in twoforms. C, Y & M filters can be used to create a projected color image. The achievable range is shown by the passband of the three filters. The deepest blue achievable is that shown for the filter itself. Similarly, the deepest red isthat of the magenta filter. C,Y & M inks can also be used in printing. To avoid a series of problems, the inks areusually restricted to narrower spectral ranges as indicated by the dashed box. They reproduce a narrower processcolor pallet by varying the percentage of pigment covering the surface. The result is dependent on the colortemperature of the illuminant and the reflectivity of the paper used.


Figure 17.3.3-15 (Color) Alternate axes applied to theNew Chromaticity Diagram. Solid axes are the “Hering”set. I and Q axes are the “NTSC” set.

17.3.3.8.3 Auxiliary axes

There are two special sets of auxiliary axes that can be applied to the New Chromaticity Diagram using W as theauxiliary reference point. They are illustrated in Figure 17.3.3-15. (See Section 17.4.1.1 for similar extensions inthree dimensional space.)

A set of “Hering” axes can be defined using axes parallel to the axes of the spectrum locus. In this case, the “blue-yellow” axis is a vertical line at 570 nm. The “red-green” axis is a horizontal line at 494 nm.

A set of “NTSC” axes can be defined using axes at anangle to the axes of the spectrum locus. These axesare used because of the difference in bandwidthrequired to transmit an adequate representation of ascene using television techniques. The “I” and “Q”axes of this system are rotated 33 degrees counterclockwise from the “Hering” axes. The Q axis istransmitted using only about one quarter of thebandwidth of the I axis.

Whereas the nominal zero angle of the NTSC axeswere chosen to represent a Caucasian skin tone, a moretheoretically defendable zero angle for the newChromaticity diagram corresponds to an angle with itsapex at “white” and measured from the displacedhorizontal axis at a wavelength of 494 nm.


Figure 17.3.3-16 (Color) A 2-D Chromaticity Diagramfor Short Wave Trichromats. See text for details.

17.3.3.9 A Chromaticity Diagram for Short Wave Trichromats

Section 17.3.3.1 developed a theoretical structure appropriate for describing the color space of all animals. Theremainder of Section 17.3.3 has concentrated on long wavelength trichromats, in particular humans. Figure 17.3.3-16 presents a 2-dimensional color space for short wavelength trichromats for completeness. Although the human hasno way of knowing what a short wavelength trichromat animal (many if not all arthropods) perceives as the color ofan object, that performance can be portrayed in chromaticity space. In this figure, that portion of the color spaceshared with long wavelength trichromats is shown as humans perceive it. However, no data could be founddescribing the null wavelengths of the O- and P-channels of arthropod vision. The values of 388 and486 qualify as “WAG’s (wild ass guesses) in somecommunities. The intersection of the axes drawnthrough these two null wavelengths would describe the“white” point of such a visual system. It is assumedthat the sharing of the S-channel signals between the O= LnS - LnUV and the P = LnS - LnM chrominancechannels, would result in the same shape to thePrimary Axes as for long wavelength trichromats. Thecolor perceived at the intersection of the 486 axis withthe spectral locus is shown as “greenish-blue,” and is alow saturation color similar in concept to the aqua ofhuman vision. The color perceived at the intersectionof the 388 axis with the spectral locus is shown as“bluish-triangle,” a low saturation color similar inconcept to the aqua or yellow of a long wavelengthtrichromat. As the wavelength of excitation is reducedbelow 388 nm, the animal would perceive a moresaturated “triangle.”

Proceeding up along the 486 axis, the animal wouldinitially experience a sensation similar to aqua, passthrough ‘white’ and then approach the complement ofaqua shown here as a large “square.”

If the animal were exposed to 580 nm light plus a lightof decreasing wavelength, the animal would perceive ayellow light passing through a low saturation colorshown as “small circle” and proceed to a moresaturated sensation labeled here as a large “circle.”

17.3.3.9 A chromaticity diagram for optically blocked tetrachromats

The previous material in this section has assumed that the human visual system can be described as that of a longwavelength trichromat. This has been in spite of the known sensitivity of the human retina to ultraviolet light. Thehuman retina, even in maturity, exhibits an ultraviolet sensitivity equivalent to its sensitivity in the blue and greenregions of the spectrum. If the signals from such ultraviolet photoreceptors participate in the formation of a thirdchrominance signal (even if significantly blocked), this must be considered. The response of such an O-channelmust be considered when determining what colors a person perceives.

It would still be useful to have a two-dimensional color space for human vision on the assumption that the UVphotoreceptors and the O-chrominance channels were fully functional. Such a color space would correctly accountfor the entire spectrum of the human eye. The color space would begin near 395 nm (the limit set by the absorptionof the lens). It would end near 655 nm (but be expandable to at least 1000 nm when required). This can be done aslong as the exciting irradiance is of narrow spectral bandwidth (typically 10 nm, FWHM). It is accomplished by notfolding the spectral locus at 437 nm. The resulting graph is shown in Figure 17.3.3-17. The region at wavelengthsgreater than 437 nm is completely conformal when the exciting radiation has negligible energy at less than 437 nm. Thus it is useful for nearly all laboratory experiments and practical applications where the color temperature of thesource is less than 3000 Kelvin. The area above the 437 nm line is a one dimensional color space that cannot beproperly shown in this coordinate system. The graphs of [Figures 17.3.3-1 or 17. 3.3-2] must be used to properlydisplay the chromatic performance of a blocked tetrachromat on flat paper.


Figure 17.3.3-17 (Color) A more simplified foundationfor a human oriented color space. The human is assumedto be a blocked tetrachromat with a functioning O-chrominance channel. Under this condition, the figure isonly conformal at wavelengths longer than 437 nm.

CHAPTER 17 CONTINUES WITH SECTION17.3.4 IN PART 1b OF THE CHAPTER AT

www.neuronresearch.net/vision/pdf/17Performance1b.pdf


TABLE OF CONTENTS 4/30/17

17 Performance descriptors of Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

17.1.1 Baseline human visual system required to understand this chapter . . . . . . . . . . . . . . . . . . 217.1.1.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217.1.1.2 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

17.1.1.2.1 Regions of the radiometric and illumination environment . . . . . . . . 417.1.1.2.2 The baseline schematic of the visual system . . . . . . . . . . . . . . . . . . 517.1.1.2.3 The baseline for operations leading to perception and cognition . . . 517.1.1.2.4 Past difficulties in performing experiments . . . . . . . . . . . . . . . . . . . 517.1.1.2.4 Separation of the CIE functions from the threshold functions of this

work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717.1.1.3 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.1.1.4 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

17.1.1.4.1 Closed loop feedback in the motor-neural circuits of vision . . . . . . 917.1.1.4.2 Other feedback within the signal processing circuits of vision . . . 1017.1.1.4.3 Application of various mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 10

17.1.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.1.2.1 Photometric units are archaic in research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

17.1.2.1.1 Limitation on the Troland, an archaic unit of photometry . . . . . . . 1417.1.2.1.2 Available commercial photometers lack precision . . . . . . . . . . . . . 1417.1.2.1.3 Precision requires photon-flux based radiometric units . . . . . . . . . 15

17.1.2.2 The precise definition of “color” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.1.2.2.1 Expanding the definition of colorimetry . . . . . . . . . . . . . . . . . . . . . 16

17.1.2.3 Metameres, initial conceptual definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1617.1.2.4 The “expanded exponential sinusoid” SCREWED UP ART . . . . . . . . . . . . . 1917.1.2.5 Nomenclature associated with the composite ERG and LERG . . . . . . . . . . . . 2017.1.2.6 Concepts relating to optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

17.1.2.6.1 Spatial characteristics of the physiological optics and retina . . . . . 2217.1.2.6.2 Computing the limiting optical performance of the visual system . 23

17.1.2.7 Concepts involving resolution and bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . 2317.1.2.7.1 Temporal bandwidth of the signal generated by the P/D process . . 2417.1.2.7.2 Temporal bandwidth of the generator waveform . . . . . . . . . . . . . 2417.1.2.7.3 Temporal bandwidth of signal resulting from signal summation . . 2417.1.2.7.4 Temporal bandwidth of signal due to signal differencing . . . . . . . 2417.1.2.7.5 Temporal bandwidth of the spatial signal from the foveola . . . . . . 2517.1.2.7.6 Temporal bandwidth of the channel supporting signaling . . . . . . . 26

17.1.2.8 Cartography requires conformality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2617.1.2.9 Conceptual loading of the signaling channels . . . . . . . . . . . . . . . . . . . . . . . . . 27

17.1.3 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2817.1.4 The simplified block diagrams used to define the descriptors of vision . . . . . . . . . . . . . . 30

17.1.4.1 The key role of adaptation in the visual process . . . . . . . . . . . . . . . . . . . . . . . 3017.1.4.2 The signaling matrix applicable to luminance and chrominance descriptors . . 3117.1.4.3 The block diagram applicable to temporal descriptors . . . . . . . . . . . . . . . . . . 3217.1.4.4 The block diagram applicable to oculomotor performance descriptors . . . . . . 35

17.1.5 Problems with “black,” univariance, “silent substitution” and arbitrary normalization . . 3617.1.5.1 The phenomenology of “black” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3617.1.5.2 The Univariance Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3717.1.5.3 The silent substitution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3817.1.5.4 Problems leading to expansion of the CIE functions, V(l) and V’(l) . . . . . . . 3917.1.5.5 Problems associated with arbitrary renormalization . . . . . . . . . . . . . . . . . . . . 42

17.1.6 Problems with center-surround experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4317.1.7 Historical composite descriptors of vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

17.1.7.1 The CIE Standard Observer and other (largely archaic) descriptors . . . . . . . . 4617.1.7.2 The use of empirically based standards and templates . . . . . . . . . . . . . . . . . . 46

17.1.8 “Rod intrusion” as a concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4717.1.9 Particularizing the photometry and colorimetry of vision . . . . . . . . . . . . . . . . . . . . . . . . . 50


17.1.9.1 Stimulus matching methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5117.1.9.2 Problems with luminance descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5317.1.9.3 Problems with chrominance descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5317.1.9.4 Threshold performance descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5417.1.9.5 Internal calibration of the human visual system . . . . . . . . . . . . . . . . . . . . . . . 55

17.1.10 Other individual descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5517.1.10.1 Frequency Domain Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

17.1.10.1.1 Specific definitions related to contrast functions versus frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

17.1.10.1.2 Attempts to differentiate between temporal and spatial contrast . 5717.1.10.1.3 Lack of attempts to differentiate between chromatic and temporal or

spatial contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5817.1.10.1.4 Temporal Frequency Domain Descriptors . . . . . . . . . . . . . . . . . . 5917.1.10.1.5 Spatial Frequency Domain Descriptors . . . . . . . . . . . . . . . . . . . . 6017.1.10.1.6 Chromatic Frequency Domain Descriptors . . . . . . . . . . . . . . . . . 61

17.1.10.2 Parametric properties clarified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6117.1.10.3 Anomalies and Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

17.2 The Luminance Characteristic of the human eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6217.2.1 Determination of the luminosity related functions of the visual system . . . . . . . . . . . . . . 65

17.2.1.1 Historical determination of the luminosity function . . . . . . . . . . . . . . . . . . . . 6517.2.1.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

17.2.1.2.1 Energy related matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6717.2.1.2.2 Noise related matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

17.2.1.3 Operational considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6817.2.1.3.1 The relationship between dark, light and chromatic adaptation . . . 6917.2.1.3.2 A chromatic spectrum for reference . . . . . . . . . . . . . . . . . . . . . . . . 6917.2.1.3.3 Chromatic filters for laboratory use . . . . . . . . . . . . . . . . . . . . . . . . 7017.2.1.3.4 A light source for laboratory use . . . . . . . . . . . . . . . . . . . . . . . . . . 7117.2.1.3.5 The systemic variation in retinal sensitivity with spatial position . 7117.2.1.3.6 The systemic variable related to ageing . . . . . . . . . . . . . . . . . . . . . 73

17.2.2 The relationship between brightness and luminance in vision . . . . . . . . . . . . . . . . . . . . . 7317.2.2.1 The perceived intensity of sound versus its actual intensity . . . . . . . . . . . . . . 7417.2.2.2 The perceived intensity of light versus its actual intensity . . . . . . . . . . . . . . . 7517.2.2.3 Analysis of the brightness/luminance relationship . . . . . . . . . . . . . . . . . . . . . 8117.2.2.4 Compression factors found in other sensory modalities . . . . . . . . . . . . . . . . . 82

17.2.3 The luminance threshold (AKA luminous efficiency function) of the human eye . . . . . . 8317.2.3.1 The tetrachromatic spectral sensitivity of the human retina . . . . . . . . . . . . . . 84

17.2.3.1.1 Effect of aging on ultraviolet vision . . . . . . . . . . . . . . . . . . . . . . . . 8817.2.3.2 The spectral characteristics of the physiological optics of the human eye . . . 89

17.2.3.2.1 The primary in-band spectral absorption of the physiological optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

17.2.3.2.2 The spectral absorption of the macular area . . . . . . . . . . . . . . . . . . 9217.2.3.3 The tetrachromatic spectral sensitivity of the complete human eye . . . . . . . . 92

17.2.3.3.1 The spectral sensitivity of the complete human eye (except inmacular) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

17.2.3.3.2 The spectral absorption of the complete human eye in the macular. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

17.2.3.3.3 The measurement of the reflectance of the retina through thephysiological optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

17.2.3.4 Comparison with the ultraviolet research literature . . . . . . . . . . . . . . . . . . . . . 9417.2.3.5 Comparison with the photopic research literature . . . . . . . . . . . . . . . . . . . . . . 95

17.2.3.5.1 The photopic research literature–normal broadband . . . . . . . . . . . 9517.2.3.5.2 The photopic research literature–infrared . . . . . . . . . . . . . . . . . . . 10917.2.3.5.3 The photopic research literature–chromatic adaptation (A MAJOR

PROBLEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11117.2.3.5.4 The photopic research literature–Difference spectra . . . . . . . . . . 11417.2.3.5.5 The photopic research literature–Foveal . . . . . . . . . . . . . . . . . . . 117

17.2.3.6 Interpretation of the photopic standards literature . . . . . . . . . . . . . . . . . . . . 11717.2.3.6.1 State of the Photopic Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . 11717.2.3.6.2 Individual factors not addressed in the CIE Standard . . . . . . . . . 11817.2.3.6.3 Light versus dark adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12317.2.3.6.4 Calculation of the neural component of the CIE luminous efficiency

function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124


17.2.3.6.5 Extended remarks on the familiar C.I.E. Luminosity Standards . . 13017.2.3.6.6 Obtaining the familiar C.I.E. Luminosity Function by smoothing

T(8,F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13317.2.3.7 Comparison with the photopic standards literature . . . . . . . . . . . . . . . . . . . . 134

17.2.3.7.1 State of the theoretical description . . . . . . . . . . . . . . . . . . . . . . . . 13517.2.3.7.2 Comparison of the theory and empirical data . . . . . . . . . . . . . . . . 135

17.2.4 Resolving the difference between spectra of the chromophores and other spectra . . . . . 13817.2.4.1 Comparing the long pulse versus flicker photometry . . . . . . . . . . . . . . . . . . 13817.2.4.2 Reviewing other the measurements based on long pulse photometry . . . . . . 140

17.2.5 Predicted versus measured spectra and color-matching functions . . . . . . . . . . . . . . . . . 14017.2.5.1 Interpretation of the Thornton work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14617.2.5.2 Reviewing the measurements supporting “cone-fundamentals” . . . . . . . . . . 14817.2.5.3 Rationalizing “cone-fundamentals” and p-parameters with other spectral

parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15217.2.5.3.1 The design and interpretation of spectral sensitivity experiments

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15217.2.5.3.2 Background from the literature . . . . . . . . . . . . . . . . . . . . . . . . . . 15317.2.4.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15617.2.4.5.4 Graphic comparison of spectral characteristics . . . . . . . . . . . . . . 157

17.2.6 The performance of the eye under unusual illumination conditions . . . . . . . . . . . . . . . . 16217.2.6.1 The full eye at very reduced irradiance (Scotopic region) . . . . . . . . . . . . . . . 162

17.2.6.1.1 Comparison with the scotopic research literature . . . . . . . . . . . . . 16217.2.6.1.2 Comparison with the scotopic standards literature . . . . . . . . . . . 163

17.2.6.2 The full eye under transition conditions (Mesopic and Mesotopic regions) . 16417.2.6.2.1 The physiological mechanisms associated with the mesopic region.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16517.2.6.2.2 Brief summary of the neurological phenomonology and mechanisms

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16517.2.6.2.3 Caricature of the mesotopic luminance threshold function, T(l,F)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16717.2.6.2.4 Comparison with the Mesopic literature . . . . . . . . . . . . . . . . . . . 167

17.2.6.3 The full eye at excessive irradiance (Hypertopic region) . . . . . . . . . . . . . . . 17417.2.6.4 The full eye with enhanced long wavelength irradiance (Purkinje Effect) . . 17517.2.6.5 The full eye with suppressed mid wavelength amplifier performance (Bezold

Effect) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17617.2.6.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17617.2.6.5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17717.2.6.5.3 A projected Bezold-Brucke Effect near 395 nm . . . . . . . . . . . . . . 178

17.2.6.6 The so-called Purkinje Shifts of the literature . . . . . . . . . . . . . . . . . . . . . . . . 17917.2.6.7 The use of the above Effects in precision research . . . . . . . . . . . . . . . . . . . . 179

17.2.7 Luminance threshold & other descriptors related to performance . . . . . . . . . . . . . . . . . 17917.2.7.1 The Noise and threshold characteristics of the human eye . . . . . . . . . . . . . . 180

17.2.7.1.1 Critical circuit features in low light vision . . . . . . . . . . . . . . . . . . 18317.2.7.1.2 A combined achromatic/chromatic threshold performance graph

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18417.2.7.1.3 Discrimination of luminance differences . . . . . . . . . . . . . . . . . . . 186

17.2.7.2 Thresholds as a function of field position . . . . . . . . . . . . . . . . . . . . . . . . . . . 18717.2.7.3 Defining the quantum efficiency of vision . . . . . . . . . . . . . . . . . . . . . . . . . . 189

17.2.7.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19017.2.7.3.2 Structural configuration of the outer segments . . . . . . . . . . . . . . . 19317.2.7.3.3 Define bleaching in the context of photon absorption at the outer

segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19317.2.7.4 Defining “bleaching” in the context of the P/D equation . . . . . . . . . . . . . . . 19317.2.7.5 Reaction time as a function of illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . 193

17.3 The Chrominance Characteristic of the human eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19417.3.1 Historical background & the definition of color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

17.3.1.1 Early philosophical models; Young, Maxwell, Hering & Kries . . . . . . . . . . 19717.3.1.2 Early empirical model of Munsell and the C.I.E. . . . . . . . . . . . . . . . . . . . . . 199

17.3.1.2.1 The Munsell perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20017.3.1.2.2 Hue and Saturation are not intrinsic . . . . . . . . . . . . . . . . . . . . . . . 201

17.3.1.3 The C.I.E. (1931 & 1964) concept of color space is invalid for research . . . 202


17.3.1.3.1 Analyses by other investigators . . . . . . . . . . . . . . . . . . . . . . . . . . 20317.3.1.3.2 Analyses based on this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20417.3.1.3.3 The C.I.E. color space is nonconformal . . . . . . . . . . . . . . . . . . . . 20517.3.1.3.4 The interpretation of the C.I.E (x,y) Chromaticity Diagram . . . . 20517.3.1.3.5 An interpretation of the Planckian Locus on the CIE Diagram . . 20617.3.1.3.6 The interpretation of the C.I.E (a*,b*) or CIELAB Chromaticity

Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20717.3.1.4 The early electrophysiological measurements; Svaetichin and Tomita . . . . . 20717.3.1.5 More recent psychophysical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

17.3.1.5.1 Recent psychophysical model of McLeod & Boynton . . . . . . . . . 20717.3.1.5.2 The DKL model of Derrington, et. al. based on electrophysiology

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20817.3.1.5.3 The Chatterjee & Callaway data based on electrophysiology . . . 209

17.3.1.6 Recent measurements in the mesotopic region . . . . . . . . . . . . . . . . . . . . . . . 20917.3.1.7 Continuing difficulties in empirical experiment design . . . . . . . . . . . . . . . . . 209

17.3.1.7.1 The persistent introduction of pigment triangles and tetrahedrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

17.3.1.7.2 A critical problem with CIE conforming color measurements . . . . . . . . . . . . . . . . . 21017.3.1.8 A new conformal color space based on electrophysiology is required . . . . . 210

17.3.2 The chromatic discrimination function, C(8,F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21017.3.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21017.3.2.2 Theoretical capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

17.3.2.2.1 Simplified calculation of the amplitude portion of the C(8,F) . . . 21217.3.2.2.2 Calculation of the complete chromatic threshold function . . . . . . 21317.3.2.2.3 Apparent equal participation of the spectral channels in forming

C(8,F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21417.3.2.2.4 C(l,F) under mesotopic conditions . . . . . . . . . . . . . . . . . . . . . . . . 214

17.3.2.3 Comparison with the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21417.3.2.3.1 Discrimination versus fixation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21917.3.2.3.2 Discrimination versus Illumination . . . . . . . . . . . . . . . . . . . . . . . 22017.3.2.3.3 Discrimination versus spatial integration . . . . . . . . . . . . . . . . . . . 22117.3.2.3.4 Color discrimination in cases of anomalous color vision . . . . . . . 22117.3.2.3.5 Discrimination versus other independent variables . . . . . . . . . . . 221

17.3.2.4 Comparison of the C(l,F), T( l,F) and V(l) functions . . . . . . . . . . . . . . . . . . . 22117.3.2.5 Features of the new function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

17.3.3 Definition of a “New” Chromaticity Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22317.3.3.1 Conceptual framework for the new chromaticity diagrams . . . . . . . . . . . . . . 225

17.3.3.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22617.3.3.1.2 The morphological location supporting the New Diagram . . . . . . 22617.3.3.1.3 Development of fundamental chrominance signals . . . . . . . . . . . 227

17.3.3.2 Defining the tetrachromatic chromaticity diagram . . . . . . . . . . . . . . . . . . . . 22717.3.3.2.1 What colors does a tetrachromat perceive? . . . . . . . . . . . . . . . . . 22817.3.3.2.2 What colors does a human perceive? . . . . . . . . . . . . . . . . . . . . . . 23017.3.3.2.3 A simplified three-dimensional framework for true trichromats . 233

17.3.3.3 A New Chromaticity Diagram for human vision . . . . . . . . . . . . . . . . . . . . . . 23417.3.3.3.1 A chromaticity diagram under optimal illumination . . . . . . . . . . . 23417.3.3.3.2 A chromaticity diagram under incandescent illumination . . . . . . 23617.3.3.3.3 Fundamental, primary and cardinal axes . . . . . . . . . . . . . . . . . . . 23617.3.3.3.4 Hue and saturation are not fundamental parameters . . . . . . . . . . . 23617.3.3.3.5 The New (hypertopic & photopic) Chromaticity Diagram for

Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23717.3.3.4 Limitations on the presentation of the New Chromaticity Diagram . . . . . . . 241

17.3.3.4.1 Broad versus narrow irradiances in the laboratory . . . . . . . . . . . . 24117.3.3.4.2 Capability of displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24117.3.3.4.3 Remaining functional complications . . . . . . . . . . . . . . . . . . . . . . 242

17.3.3.5 Auxiliary Constructs applied to the New Chromaticity Diagram . . . . . . . . . 24317.3.3.5.1 Theoretically achievable chromatic discrimination capability . . . 24317.3.3.5.2 Achievable discrimination capability versus test field RESERVED

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24417.3.3.5.3 Achievable discrimination capability in color deficient subjects . 24417.3.3.5.4 Action potentials of the optic nerve vs illumination spectrum . . . 24417.3.3.5.5 Definition of Hue and Saturation . . . . . . . . . . . . . . . . . . . . . . . . . 245

17.3.3.6 Perception and display of color spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246


17.3.3.6.1 Comparing the new diagram with MacAdam, Farnsworth, etc. . . 24617.3.3.6.2 Difficulty in documentation and display . . . . . . . . . . . . . . . . . . . 24817.3.3.6.3 Typical achievable color spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 250

17.3.3.7 The New Chromaticity Diagram for Research at Mesotopic levels . . . . . . . . 25117.3.3.7.1 Mesopic versus mesotopic vision . . . . . . . . . . . . . . . . . . . . . . . . . 25117.3.3.7.2 Equations of mesotopic vision . . . . . . . . . . . . . . . . . . . . . . . . . . . 25117.3.3.7.3 The New Chromaticity Diagram under reduced stimulus conditions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25217.3.3.7.4 Curvature of some loci in the New Chromaticity Diagram . . . . . 253

17.3.3.8 Features of the New Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25317.3.3.8.1 An important feature of chromaticity diagrams . . . . . . . . . . . . . . 25517.3.3.8.2 Display device overlays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25617.3.3.8.3 Auxiliary axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

17.3.3.9 A Chromaticity Diagram for Short Wave Trichromats . . . . . . . . . . . . . . . . . 259CHAPTER 17 CONTINUES WITH SECTION 17.3.4 IN PART 1b OF THE CHAPTER . . . . . . . . . . 260


Chapter 17 EquationsSome complex equations are inserts and are not shown explicitly here

“The Expanded Exponential Sinusoid” Eq. 17.1.1-a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19“Alternate Expanded Expon.Sinusoid” Eq. 17.1.1-b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19“Extended Exponential” Eq. 17.1.1-c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20“Vector form of R(t) and constructs” Eq. 17.1.2-1 . . . . . . . . . . . . . . . 27

C = xR + yG + zB Eq. 17.2.1-1 . . . . . . . . . . . . . . . . . . . . . . 67R = lnC = ln xL2 + ln yM + ln zS Eq. 17.2.3-2 . . . . . . . . . . . . . . . . . . . . . 125R = lnC = ln xL + ln yM + ln zS Eq. 17.2.3.-3 . . . . . . . . . . . . . . . . . . . . . 125R =LnC = [Ln(KL x L) + Ln(KM x M) + Ln(KS x S)]/Const. Eq. 17.2.3-4 . . . . . . . . . . . . . . . . . . . . . 126O = LnUV - LnS Eq. 17.3.3-5 . . . . . . . . . . . . . . . . . . . . . 227P = LnS - LnM Eq. 17.3.3-6 . . . . . . . . . . . . . . . . . . . . . 227Q = LnL - LnM Eq. 17.3.3-7 . . . . . . . . . . . . . . . . . . . . . 227Q =LnL2 - LnM Eq. 17.3.3-8 . . . . . . . . . . . . . . . . . . . . . 227P = Ln(K+S) - Ln(K+M) = Ln[(K+S)/(K+M)] or Ln[(1+S/K)/(1+M/K)] Eq. 17.3.3-16 . . . . . . . . . . . . . 251Q=Ln(K+L 2) - Ln(K+M) = Ln[(K+L2)/(K+M)] or Ln[(1+L2/K)/(1+M/K)] Eq. 17.3.3-17 . . . . . . . . . . . . . 251P = Ln [S/M] --Mesotopic condition, K is small Eq. 17.3.3-18 . . . . . . . . . . . . . . . . . . . . 252Q = Ln[L2/M] --Mesotopic condition, K is small Eq. 17.3.3-19 . . . . . . . . . . . . . . . . . . . . 252


Chapter 17 Figures 4/30/17

Figure 17.1.1-2 Top level schematic of the visual system of Chordata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 17.1.1-3 An overall descriptor of the illumination range of the eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 17.1.2-1 Test configuration for metameric matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 17.1.2-2 Concept of optimizing the performance of an imaging system . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 17.1.2-3 Concept of the temporal spectrum utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 17.1.4-1 The luminance, chrominance and appearance channels of the eye . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 17.1.4-2 The large signal circuit diagram of the fundamental signal paths . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 17.1.4-3 Overall Servomechanism of the human visual system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 17.1.5-1 A photopic operating visibility function, Vo(l), for the rhesus monkey . . . . . . . . . . . . . . . . . . . . . 40Figure 17.1.5-2 Operational visibility functions shown on the same graph for HS . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 17.1.9-1 Three major matching geometries of photometry & colorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 17.2.1-1 (Color ln) The tetrachromatic luminous efficiency function of human vision . . . . . . . . . . . . . . . 64Figure 17.2.1-2 Variation of increment threshold in traverses through the dark-adapted foveal and parafoveal area

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 17.2.2-1 The perceived audio loudness as a function of sound intensity in humans ADD . . . . . . . . . . . . . 74Figure 17.2.2-2 Proposed template for the perceived visual brightness as a function of luminance intensity in

humans ADD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Figure 17.2.2-3 Relationship between lightness-scale value V and luminance factor Y . . . . . . . . . . . . . . . . . . . . . 77Figure 17.2.2-4 The human visual response based on the Munsell Color Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 17.2.2-5 Brightness functions for various levels of adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Figure 17.2.2-6 The theoretical performance of the visual modality with adaptation as a parameter . . . . . . . . . . . 83Figure 17.2.3-1 (Color ln) Comparison of aphakic vision and the theoretical model . . . . . . . . . . . . . . . . . . . . . . . 85Figure 17.2.3-2 Heterchromatic brightness sensitivity change per decade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Figure 17.2.3-3 CR Light transmission through the physiological optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure 17.2.3-4 “Equation for optical density of physiological optics” Eq. 17.2.3.1 . . . . . . . . . . . . . . . . . . . . . . 90Figure 17.2.3-5 The equivalent optical density of the physiological optics of the eye . . . . . . . . . . . . . . . . . . . . . . 90Figure 17.2.3-6 (Color ln)The theoretical absorption of the macular. Compare with the empirical data . . . . . . . 92Figure 17.2.3-7 (Color ln) Calculated tetrachromatic spectral sensitivity of the normal human eye compared with

the best data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 17.2.3-8 A comparison of aphakic and phakic eyes based on Griswold & Stark. . . . . . . . . . . . . . . . . . . . . 94Figure 17.2.3-9 Early spectral sensitivity curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 17.2.3-10 Comparison of theoretical and empirical spectral sensitivity functions (luminous efficiency

functions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Figure 17.2.3-11 Incremental threshold spectral sensitivity of two normal human subjects . . . . . . . . . . . . . . . . . . 98Figure 17.2.3-12 Visual sensitivity of the rhesus monkey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 17.2.3-13 A human spectral response confirming all of the curves and shoulders predicted by the theoretical

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 17.2.3-14 High precision spectral data for SG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Figure 17.2.3-15 Increment-threshold spectral sensitivity for rhesus monkeys . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Figure 17.2.3-16 Increment-threshold data for Rhesus monkeys corrected for color temperature . . . . . . . . . . . . 106Figure 17.2.3-17 Comparison of luminous efficiency functions for absolute threshold and for heterochromatic

brightness matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Figure 17.2.3-18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Figure 17.2.3-19 The predicted dark adapted photopic luminosity function in the infra-red . . . . . . . . . . . . . . . . 110Figure 17.2.3-20 Wald figure 4 with overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Figure 17.2.3-21 The spectrum of the “blue monochromat” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 17.2.3-22 Comparison of difference spectra with the CIE Photopic Luminosity Standard . . . . . . . . . . . . 114Figure 17.2.3-23 Annotated Stockman et al. data compared to the proposed theoretical peaks . . . . . . . . . . . . . . 116Figure 17.2.3-24 The signal flow schematic used for calculating the luminance function . . . . . . . . . . . . . . . . . . 120Figure 17.2.3-25 Equations for the spectral absorption of the physiological optics of the eye. . . . . . . . . . . . . . . 122Figure 17.2.3-26 The summing circuit at the output terminals of four photoreceptor cells. . . . . . . . . . . . . . . . . . 124Figure 17.2.3-27 The theoretical photopic luminosity function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 17.2.3-28 Comparing a theoretical human spectral sensitivity function and its smoothed counterpart . . . 133Figure 17.2.3-29 Comparison of the theoretical and empirical Photopic Luminosity Functions. . . . . . . . . . . . . . 138Figure 17.2.4-1 Comparing spectral sensitivity based on 1o 10 ms test flashes and flicker photometry . . . . . . . . 139Figure 17.2.5-1 Three-color matching functions for a fixed power “standard light.” . . . . . . . . . . . . . . . . . . . . . . 143Figure 17.2.5-2 Tabular comparison of peak absorption wavelengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Figure 17.2.5-3 Absorption spectra based on power measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145


Figure 17.2.5-4 Comparison of measured and theoretical spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Figure 17.2.5-6 The effects of flicker frequency on the observed spectral sensitivity curves in humans . . . . . . . 154Figure 17.2.5-7 The luminosity function and partially isolated spectral responses of the human eye . . . . . . . . . . 155Figure 17.2.5-8 A comparison of various spectra claimed to represent human vision . . . . . . . . . . . . . . . . . . . . . 158Figure 17.2.5-9 Predicted long wavelength peak versus flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Figure 17.2.5-10 The flicker frequency versus peak spectral wavelength relationship . . . . . . . . . . . . . . . . . . . . . 161Figure 17.2.6-1 The difference spectrum recorded psychophysically in the human retina . . . . . . . . . . . . . . . . . . 163Figure 17.2.6-2 Comparison of the theoretical and other scotopic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Figure 17.2.6-3 ERG data showing the change in spectral sensitivity with stimulus level . . . . . . . . . . . . . . . . . . 165Figure 17.2.6-4 Caricature of human luminance threshold response under mesotopic conditions . . . . . . . . . . . . 167Figure 17.2.6-5 Theoretical and putative empirical shift in spectra going from photopic to scotopic vision. . . . 168Figure 17.2.6-6 Luminous efficiency functions at nine retinal-illuminance levels; two subjects . . . . . . . . . . . . . 169Figure 17.2.6-7 Luminance sensitivity variation from photopic to scotopic regimes . . . . . . . . . . . . . . . . . . . . . . 171Figure 17.2.6-8 Overlay of measured data with theoretical function from this theory . . . . . . . . . . . . . . . . . . . . . 172Figure 17.2.6-9 A comparison of theoretical and empirical curve fitting to mesopic measurements . . . . . . . . . . 172Figure 17.2.6-10 Recent MOVE data on luminous efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Figure 17.2.6-11 Plot of logEref versus log Etest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174Figure 17.2.6-12 Theoretical foundation for the Purkinje (brightness) Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Figure 17.2.6-13 Theoretical foundation for the Bezold-Brucke Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176Figure 17.2.7-1 The noise model of the visual system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Figure 17.2.7-2 Combined chromatic and achromatic thresholds for the steady state . . . . . . . . . . . . . . . . . . . . . 185Figure 17.2.7-3 The island of vision (left) based on threshold (static) perimetry . . . . . . . . . . . . . . . . . . . . . . . . . 187Figure 17.2.7-4 Profile perimetry along the zero degree meridian for 8 different states of adaptation . . . . . . . . . 188Figure 17.2.8-1 The laws of probability theory applicable to visual sensing ADD . . . . . . . . . . . . . . . . . . . . . . . . 191Figure 17.3.1-1 A foundation for both Newton’s and Young’s conception of color space . . . . . . . . . . . . . . . . . . 199Figure 17.3.1-2 The appearance of 10 degree fields arranged for metameric matches with different combinations of

spectral lights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210Figure 17.3.2-1 The signal flow schematic used for calculating the chromatic discrimination function of human

vision (and other chordate vision) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212Figure 17.3.2-2 (a)The transfer function between the logarithm of the input illumination and the output of the lateral

cells of the chrominance channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Figure 17.3.2-3 The proposed wavelength discrimination function for human vision . . . . . . . . . . . . . . . . . . . . . 216Figure 17.3.2-4 Observations of hue reversal in the deep red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Figure 17.3.2-5 Plot of equivalent wavelengths-wavelengths giving the same colour sensation . . . . . . . . . . . . . 217Figure 17.3.2-6 Wavelength discrimination as a function of wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Figure 17.3.2-7 Measured and predicted values of the wavelength discrimination function . . . . . . . . . . . . . . . . 220Figure 17.3.2-8 Wavelength discrimination functions for various tests field sizes. . . . . . . . . . . . . . . . . . . . . . . . 221Figure 17.3.2-9 Comparison of the chromatic and luminous discrimination functions . . . . . . . . . . . . . . . . . . . . . 222Figure 17.3.3-1 (Color ) The foundation for the chromaticity diagram of tetrachromatic vision . . . . . . . . . . . . . 228Figure 17.3.3-2 Theoretical composite human color discrimination function under high contrast photopic conditions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232Figure 17.3.3-3 Effect of source color temperature on the color discrimination capability of the human eye . . . 233Figure 17.3.3-4 (Color) A simplified foundation for a three- dimensional color space . . . . . . . . . . . . . . . . . . . . 233Figure 17.3.3-5 A complete color space for blocked tetrachromats (including humans) . . . . . . . . . . . . . . . . . . . 235Figure 17.3.3-6 [Color] A physiology-based Chromaticity Diagram for Humans applicable to the Hypertopic and

Photopic regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238Figure 17.3.3-7 [Color] Illustration of extended new Chromaticity Diagram to show ideal and theoretically

achievable chromatic discrimination capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Figure 17.3.3-8 [Color] New Chromaticity Diagram extended to show the interpulse interval of the action potentials

of the chrominance channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Figure 17.3.3-9 [Color] Hue and Saturation coordinates applied to the New Chromaticity Diagram . . . . . . . . . 246Figure 17.3.3-10 A re-plot of MacAdam ellipses compared to the new Chromaticity Diagram. . . . . . . . . . . . . . 248Figure 17.3.3-11 Realizable human color space using kinescope and printing techniques . . . . . . . . . . . . . . . . . . 250Figure 17.3.3-12 (Color) New Chromaticity Diagram at mesotopic levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Figure 17.3.3-13 (Color) An extended New Chromaticity Diagram and an arbitrary source spectrum. . . . . . . . . 255Figure 17.3.3-14 (Color) XXX A comparison of additive and subtractive (process) color “sets” . . . . . . . . . . . . 257Figure 17.3.3-15 (Color) Alternate axes applied to the New Chromaticity Diagram . . . . . . . . . . . . . . . . . . . . . . 257Figure 17.3.3-16 (Color) A 2-D Chromaticity Diagram for Short Wave Trichromats . . . . . . . . . . . . . . . . . . . . . 259Figure 17.3.3-17 (Color) A more simplified foundation for a human oriented color space . . . . . . . . . . . . . . . . . 259


(Active) SUBJECT INDEX (using advanced indexing option)

2-exciton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111, 1922-photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145, 1923D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24195% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126action potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153, 183, 184, 189, 207Activa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 111, 123, 124, 153, 181, 182adaptation . . 2, 5, 8, 10, 11, 13, 15, 19, 20, 24-26, 28-32, 37, 38, 40, 41, 43, 45, 47-50, 59-61, 64, 65, 69, 73-76, 78,

80-83, 86, 96, 98, 107-109, 111-118, 120, 123-127, 129, 130, 134, 135, 137, 138, 149-153, 155-158, 162, 166, 167, 169, 170, 172, 175-185, 187-189, 195, 200, 206, 207, 212, 217, 220, 225-228,

232, 237-240, 243, 251-255adaptation amplifier . . . . . 5, 10, 11, 24, 26, 28, 38, 69, 74, 75, 82, 111, 112, 125, 175, 176, 181-185, 187, 207, 220,

225alarm mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 28, 30, 31, 45, 61, 69, 120, 121, 180-183analytical mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57arborization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242, 243attention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13, 58, 79, 80, 157, 180, 189, 215axoplasm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125a-wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21band gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67, 68, 180, 183Black Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 13, 71, 121, 128, 136, 242bleaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12, 30, 31, 41, 112, 163, 193BOLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240broadband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 19, 24, 47, 58, 66, 78, 95, 141, 142, 152, 190, 201b-wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21, 22C.I.E. . . 1, 13, 14, 26, 37, 39, 46, 53, 54, 62, 65, 66, 71, 83, 84, 97, 107, 115, 118, 128-138, 162-164, 197, 199-209,

216, 217, 224, 226, 234, 237, 239, 244, 245, 247, 248, 250, 253, 255, 256calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13, 55, 78, 80, 105, 106, 165, 170Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96, 113cerebellum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 35CIE . . . 1, 7, 8, 13, 15, 17, 39, 41, 42, 46, 47, 53, 77, 78, 105, 106, 108, 114, 117-119, 121, 124, 129, 130, 132, 133,

141, 143, 146, 148, 149, 163, 165, 167, 168, 171-173, 177, 194, 197, 199, 201-207, 209, 210, 221,222, 237, 252

CIE 1960 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206CIE UCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201CIELAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46, 207CIELUV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46, 207cis- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84, 229colliculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9color-rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38, 73, 106, 134, 220, 232computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 127, 167, 204, 250computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43, 62, 100, 133, 180, 218, 222, 241cone fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108, 109, 114, 116, 149, 162confirmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60, 106continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58, 240critical color flicker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159critical flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116, 158, 159, 161cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62, 193cut-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75, 192dark adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 20, 31, 47, 49, 69, 76, 123, 129, 153, 162, 169, 175, 184, 189data base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 128, 135database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83, 95, 133, 194decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125, 159, 184DG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165


diencephalon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61, 124, 126, 127, 225disparity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48, 118, 219Duplex Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 23dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . 4, 10, 11, 36, 54, 55, 74, 120, 128, 129, 135, 162, 165, 185, 186, 225EOG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80, 81ERG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 21, 112, 165evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, 209, 249expanded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 40, 53, 143, 164, 191, 212, 223, 244, 251external feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 242, 243feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 9, 10, 41, 57, 75, 81, 121, 123, 124, 225, 238, 242, 243, 252, 255feedforward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200flicker frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28, 29, 51, 52, 108, 116, 154, 156-161Fourier transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22free running . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 67, 68, 70, 113, 133, 136, 138, 164, 171, 255genetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Grassman’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16, 37, 38half-amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70, 97, 105, 106, 111, 116, 147, 179, 185, 237hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111homogeneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89, 224hydronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183illusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15internal feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121, 123, 225, 238, 255inverting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10lateral geniculate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104, 208light adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31, 48, 49, 69, 108, 109, 200lips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210long term memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196lookup table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227LOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 140Maxwell’s Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 52, 59, 171, 210mesotopic . . 5, 11, 14, 28, 30, 36, 38, 41, 43, 44, 53-55, 58, 65, 69, 100, 120, 123, 125, 127, 164-167, 172-174, 176,

177, 181, 184, 185, 187, 207, 209, 214, 220, 224, 225, 227, 240, 245, 251-253metamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16midbrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 23, 57, 153, 157, 159, 184, 188, 209narrow band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 66, 67, 112, 116, 141, 142, 150, 157, 198, 242noise . 2, 6, 7, 11, 21, 23, 28, 31, 36, 37, 41, 54, 55, 67, 68, 73, 95, 119-121, 129, 135, 152, 162, 165-167, 172, 180-

185, 187, 189, 190, 192, 213, 214P/D equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175, 185, 189, 193pain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 28, 187parametric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61, 241parietal lobe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Pauli exclusion principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102percept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87perceptual space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135, 162, 166, 196, 198, 202, 234, 236-239perigeniculate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4perigeniculate nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4perimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187, 188poditic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10POS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 35Pretectum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 26, 35, 120, 212probabilistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28, 29protocol . . . 19, 52, 58, 71, 87, 101, 104, 106, 111, 112, 116, 119, 127, 140, 149, 150, 153, 154, 156-158, 165, 172,

219pulvinar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4quantum-mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142, 192, 251, 253reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 49, 64, 131, 142, 148, 195, 198resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123rod intrusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47-49, 147, 148, 174saliency map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 196, 227


segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255servo loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35servomechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 35signal-to-noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152signal-to-noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152spectral colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141, 205, 225, 237square law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 37, 38, 43, 68, 69, 86square-law . . . . . . 15, 44, 142, 145, 150-152, 162, 166, 176, 184, 207, 211, 213, 214, 216, 219, 220, 225, 252, 253sRGB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242stage 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 152stage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 40, 121, 157, 190stage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31, 32, 37, 40, 157, 159, 226stage 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37, 40, 50, 52, 58, 62, 106, 139, 157, 159, 161, 226, 227stage 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37, 153, 157, 159stage 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40stage B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Standard Observer . . . . . . . . . . . . . . . . . 1, 17, 39, 40, 46, 53, 118, 129, 130, 133, 141, 146, 167, 168, 202, 205, 222stellate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32, 106, 166, 167, 214, 226, 227Stiles-Crawford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89, 165, 172stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46, 141, 168, 208, 225superior colliculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9synapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124syndrome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 28, 247, 251tetrahedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226thalamic reticular nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4thalamus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4threshold . . . 5, 7, 8, 23, 28, 29, 31, 40-43, 46, 49, 54-56, 58, 59, 63, 67, 68, 71, 72, 80, 83, 86, 95, 98, 104, 106-108,

111, 116-119, 121, 124, 133, 135, 139, 140, 153, 155-157, 162, 166-168, 173, 179-190, 192, 208,212-215, 219, 221, 222, 227, 245, 252

topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21, 124, 247transcendental functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201transduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32, 47, 54, 106, 176translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65, 86trans- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29tremor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 24, 25, 27, 56, 57, 60, 219-221verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81, 83, 208visual cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70, 127, 209, 240, 256vitamin A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46, 144vitamin A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144xxx . . . . 73, 77, 78, 81, 82, 95, 104, 106, 110, 143, 147, 148, 154, 155, 158, 159, 163, 189, 192, 193, 203, 207, 208,

210, 239, 257[xxx . . 1, 1, 41, 48, 50, 65, 68, 78, 79, 81, 87, 116, 122, 130, 140, 142, 146, 153, 158, 165, 183, 190, 193, 203, 230,

253, 256

(Inactive) DEFINITIONS INDEX (Use individual marks)Principle of UnivarianceRetinal illuminanceTransport delay

net photoreceptor

ELECTROCHEMISTRY OF THE NEURON17.1.1 Baseline human visual system required to understand this...

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Transcript of ELECTROCHEMISTRY OF THE NEURON17.1.1 Baseline human visual system required to understand this...