Adaptive Optics forVision Science

Nathan Doble

Class Outline• The Basic AO System

• Wavefront Sensors

• Deformable Mirror Technology• Control Loop Theory

• Current AO Systems in Use

• Typical System Performance

• Applications of AO

For a diffraction-limited system (i.e. one free of aberrations),The angular resolution α is given by:

α ≈ 1.22 λ / D

where λ is the wavelength and D is the aperture diameter.

Example: (λ = 550nm)

D = 10m (Keck telescope), α ≈ 0.013 arc secondsD = 8mm (dilated pupil), α ≈ 0.3 arc minutes

For Keck, α ≈ 0.5 arc seconds because of turbulence.For the eye, α ≈ 1 arc minute at best (smaller pupil).

History of Adaptive Optics

• Babcock 1953: suggested basic idea• Military work >> Maui CIS system, 168

actuators (1982)• ESO “Come-ON” system, 19 actuators (1990)• PUEO (1996), Hokupa’a curvature systems• Keck, Altair (Gemini N), NAOS (VLT)• Low cost AO >>> new applications• Eye, FSO Comms, Confocal microscopy

DeformableMirror

DichroicBeam Splitter

Telescope

ScienceCamera

WavefrontReconstructor

ActuatorControl

WavefrontSensor

Generic AO System

Two types of laser guide stars in usetoday: “Rayleigh” and “Sodium”

• Sodium guide stars: exciteatoms in “sodium layer” ataltitude of ~ 95 km

• Rayleigh guide stars:Rayleigh scattering from airmolecules sends light backinto telescope, h ~ 10 km

• Higher altitude of sodiumlayer is closer to samplingthe same turbulence that astar from “infinity” passesthrough Telescope

Turbulence

8-12 km

~ 95 km

Claire Max - CfAO lecture course

Adaptive optics allows telescopesto see through the turbulent atmosphere

Claire Max - CfAO lecture course

(Macintosh et al 1999 and Max et al 2000 in preparation)

Images of Neptune taken with infrared lightwith and without adaptive optics from the Keck telescope

Without AO With AO

R136

AO Off AO On

(Brandl et al, MPE Munich)

(K-band images (2.2µm), 3.6m telescope)

Key Research Issues inAstronomical AO

• Laser guide stars– Increase sky coverage

• Multi-conjugate adaptive optics– Increase field of view

• eXtreme AO (e.g. for planet detection)

• Next generation “overwhelmingly large”telescopes: up to 100m diameter

Claire Max - CfAO lecture course

Free Space Optics

AO needed to correct for effects of transmission medium

Replaces optical fiber for short point to point communications

Needs high temporal bandwidth, dynamic range and has to be

inexpensive Claire Max - CfAO lecture course

• Intracavity laser correction• Extracavity beam shaping• Correction of spherical aberration• Confocal microscopy• Ground-to-space optical communication• Laser materials processing• Submicron optical lithography• ‘Smart’ binoculars• Optical data storage• Optical instrument manufacture and alignment• Industrial inspection• VISION SCIENCE/OPHTHALMOLOGY

Other Applications of AO

Building blocks of AO systems:

• Wavefront Sensor

• Corrective Element

• Control loop

Wavefront Sensing• “Direct” in pupil plane- split pupil up into

subapertures in some way, then use intensity in eachsubaperture to deduce phase of wavefront. Sub-categories:– Slope sensing: Shack-Hartmann, lateral shear interferometer– Curvature sensing

• “Indirect” in focal plane - wavefront properties arededuced from whole-aperture intensity measurementsmade at or near the focal plane. Iterative methods -take a lot of time.– Image sharpening, multidither– Phase diversity

Claire Max - CfAO lecture course

Hartmann-Shack Wavefront Sensor(principle of operation)

Eye

Collimatedinput beam

Laserbeacon

Lensletarray

Hartmann-Shack Lenslet Array

∂W(x,y)∂ x

=D xF

∂ W(x,y)∂ y

=D yF

SLOPES

Liang - JOSA-A 1994

Raw data(CCD)

Wave aberration

Ideal optics JL's optics

contour lines = 0.15 mmDon Miller - Indiana

The Bausch and Lomb Zywave

Curvature wavefront sensing• F. Roddier, Applied Optics, 27, 1223- 1225, 1998

I+ − I−

I+ + I−

∝ ∇2φ − ∂φ∂r r

r δ R

Laplacian (curvature)

Normalderivative at

boundary

More intense Less intense

Claire Max - CfAO lecture course

Wavefront sensor lenslet shapes aredifferent for edge, middle of pupil

• Example: This is whatwavefront tilt (whichproduces imagemotion) looks like on acurvature wavefrontsensor– Constant I on inside– Excess I on right edge– Deficit on left edge

Lenslet array

Claire Max - CfAO lecture course

Curvature sensor signal forastigmatism

Claire Max - CfAO lecture course

Practical implementation ofcurvature sensing

• Use oscillating membrane mirror (2 kHz!) to vibrate rapidlybetween I+ and I- extrafocal positions

• Measure intensity in each subaperture with an “avalanchephotodiode” (only need one per subaperture!)– Detects individual photons, no read noise, QE ~ 60%– Can read out very fast with no noise penalty

More intense Less intense

Claire Max - CfAO lecture course

Advantages and disadvantages ofcurvature sensing

• Advantages:– Lower noise ⇒ can use fainter guide stars than S-H– Fast readout ⇒ can run AO system faster– Can adjust amplitude of membrane mirror excursion as

“seeing” conditions change. Affects sensitivity.– Well matched to bimorph deformable mirror (both solve

Laplace’s equation), so less computation.– Curvature systems appear to be less expensive.

• Disadvantages:– Avalanche photodiodes can fail if too much light falls on

them. They are bulky and expensive. Hard to use a largenumber of them.

Claire Max - CfAO lecture course

Detectors for wavefront sensing

• Shack-Hartmann: usually use CCDs (charge-coupleddevices), sizes up to 128 x 128 pixels– Sensitive to visible light (out to ~ 1 micron)

– Can have high quantum efficiency (up to 85%)

– Practical frame rates limited to a few kHz

– Read noise currently > 3 electrons per pixel per read

– New development: infrared detectors (more noise)

• Curvature: usually use avalanche photodiodes (1 pixel)– Sensitive to visible light

– Slightly lower quantum efficiency than CCDs

– NO NOISE

– Very fast

Claire Max - CfAO lecture course

Building blocks of AO systems:

• Wavefront Sensor

• Corrective Element

• Control loop

Types of Deformable Mirror (DMs)

• Conventional Piezoelectric DMs e.g. Xinetics, Thermotrex

• Bimorph

• Liquid Crystals e.g. Hamamatsu, Sony, Meadowlark

• Bulk micromachined e.g. OKO Technologies, Lucent

MEMS (Microelectromechanical Systems)

• Surface micromachined e.g. BMC, Iris AO

Continuous Faceplate - Xinetics

Claire Max - CfAO lecture course

Continuous face-sheet DM’s:Xinetics product line

Segmented deformable mirrors:

• William Herschel Telescope,UK: ThermoTrex 76element segmented mirror.

• Each square mirror ismounted on 3 piezos, each ofwhich has a strain gauge.

• Strain gauges provideindependent measure ofmovement, are used toreduce hysteresis to below1% (piezo actuators have~10% hysteresis).

Claire Max - CfAO lecture course

Bimorph mirrorsBimorph mirror are made

from a piezoelectric wafersandwiched between onecommon electrode and aseries of individual with anelectrode pattern betweenthe two wafers to controldeformation

Front and back surfaces areelectrically grounded.

When V is applied, one wafercontracts as the otherexpands, inducingcurvature

Claire Max - CfAO lecture course

Bimorph mirrors well matched tocurvature sensing AO systems

• Electrode pattern can beshaped to matchsubapertures in curvaturesensor

• Mirror shape W(x,y) obeysPoisson Equation

Claire Max - CfAO lecture course

Liquid Crystal Spatial Light ModulatorsHamamatsu Meadowlark

Lucent Technologies

d1

d2σ V_+D

• mirror deforms in both directions inresponse to voltage commands (pressurechanges sign with voltage)

• greater mirror deformation: higherelectrostatic pressure can be achievedwith the same voltage as ordinarymembrane mirrors

• more stroke at all spatial frequencies dueto higher electrostatic pressure. Enablescorrection of higher order Zernike modes.

BulkMicromachined MEMSOKO Technologies - G Vdovin

Single membrane - 37 actuators

6 microns of pure defocus

~1.2 microns on correction of higher

order modes

BostonMicroMachines/BostonUniversity MEMS DM

Electrostaticallyactuateddiaphragm

Attachmentpost

Membranemirror

Continuous mirror

Segmented mirrors (piston)

• Fabrication: Siliconmicromachining(structural silicon andsacrificial oxide)

• Actuation:Electrostatic parallelplates

Piecewise Continuous

A rigid, single-crystal-silicon mirror is assembled onto a surface-micromachined parallel-plateactuator. The actuator is elevated 60 microns above the surface of the substrate because ofbending caused by residual stresses in the nickel-polysilicon bimorph flexure.

Iris AO - Segmented piston tip/tilt array

SPECIFICATION XINETICS OKOTECH

BMCMEMS

HAMAMATSULC-SLM

LUCENTTECH

IRISAO

Active area (mm) φ = 75 φ = 15 3.3x3.3 20x20 φ = 10 φ = 7No. of actuators 97 37 12x12 480x480 1024 89

Surface type Continuous Membrane ContinuousPiecewise

Pure Piston Membrane SegmentedPTT

Stroke(wavefront)

± 4 µm ± 0.7 µm ± 2 µm 10's µmsPhase Wrap

±10 µm >15 µm

Response speed 4kHz 0.5kHz 3.5 kHz 13 Hz 250HzOperating voltage 100V 255V 220V 5V 200V 100V% of populationcorrected (Z4 = 0,

6.8mm pupil)75 10 20 100 95 100

Current and Near Future DM Technologies

Requirements of a deformableRequirements of a deformablemirror for vision AOmirror for vision AO

Temporal Bandwidth 1-3Hz closed loop⇒ 30 Hz samplingMirror Stroke(6.8 mm pupil)

10+µm (defocus corrected)6+µm (defocus and astigmatism)

Flatness <30nm rms.Actuator Coupling 10-15%Reflectivity >90% (400-900nm)No. of actuators orsegments across thepupil

13x13 Continuous faceplate11x11 Segmented PTT60x60 Segmented Piston only

Size (diameter) 4-8mm i.e. comparable to pupil size

Brief History of Vision AO

First use of a HS-WFS for the eye was by Liang 1994

In 1997, Liang et al. (JOSA-A) used a 37 channel Xinetics DMoperated open loop with the HS-WFS.

In vivo classification of the three cone classes (Roorda Nature1999)

First active correction of a laser scanning ophthalmoscope (SLO)by Dreher (Appl Opt 1989).

Confocal laser scanning ophthalmoscope with AO (Roorda OptEx 2002)

GROUP TYPE DM WFS PERFORMANCE REFERENCERochester(Williams)

Conventional 97 ch Xinetics

37 ch MEMS

HS

HS

<0.1 µm rms, φ = 6.8 mm

0.17 µm rms, φ = 6.8 mm

Hofer Opt Ex 2001

Doble Opt Let 2002Houston(Roorda)

ConfocalSLO

37 ch Xinetics HS ~0.1µm rms, φ = 7 mm Roorda Opt Ex 2001

Indiana(Miller)

Coherencegated

37 ch Xinetics HS Coming online

Murcia(Artal)

Conventional 37 ch Membrane

LC-SLM

HS

HS

0.12 µm rms, φ = 4.3 mm

0.1 µm rms, φ = 4.7 mm

Fernandez Opt Let2001Martin JOSA-A 1998

Imperial Col(Dainty)

Conventional 37 ch Membraneplus tilt mirrors

HS >0.1µm rms, φ = 4.8 mm Monroe 3rd Int Confon AO for Ind + Med

San Diego(Bartsch)

Conventional 19 ch Membrane HS >0.5 µm P-V, φ = 8 mm Zhu App Opt 1999

LLNL (UCD)(Olivier)

Conventional LC-SLM HS In initial system testing N/A

Chengdu,(Jiang)

Conventional In house 52 chDM

HS 0.18µm rms, φ = ?? Zhang 3rd Int Confon AO for Ind + Med

Paris(Gargasson)

Conventional 13 act. mirror HS φ = 7mm Glanc Sub to Appl.Opt

Vision AO systems - global

Why do we need AO for the eye?SPATIAL Cornea ⇒ anterior surface

⇒ posterior surfaceCrystalline lens

Contribution of each refracting surface to wavefrontaberrations depends on the refractive index differencebetween two optical media.

Cornea (Anterior > Posterior) > Lens∆n = 0.376 ∆n = 0.05

TEMPORAL AccommodationEye / Head movements

Factors influencing magnitude ofocular aberrations…...

• Pupil Size•Accommodation•Eye ‘instability’•Age•Eye disease

1 mm 2 mm 3 mm 4 mm

5 mm 6 mm 7 mm

Point Spread Function vs. Pupil SizePerfect Eye

pupil images

followed by

psfs for changing pupil size

1 mm 2 mm 3 mm 4 mm

5 mm 6 mm 7 mm

Point Spread Function vs. Pupil SizeTypical Eye

Effect of pupil diameter on the WA

7 mm

3 mm

7 mm

5.8 mm

4.6 mm

(Artal & Navarro, JOSAA, 1994)

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2

Accommodation (diopters)

Seid

el a

berr

atio

n co

effic

ient

(mic

rons

)

ComaAstigmatismSpherical aberration

SC HH PA

Aberrations change with accommodation

4.7mm pupil

⇒ Higher order correction for near viewing not appropriate for distanceviewing and vice versa

HH viewing distant target, 5.8 mm pupil, 550 nm monochromatic light Videos represent wave aberration measurements taken at 25.6 Hz during a 5 second interval.

Short Term Instability Wave Aberration Point Spread Function

Aberrations from the eye is not static. Dynamic range of eye’s wave aberrationsrequires a closed loop bandwidth 1~2 Hz to correct the temporal fluctuation.

Keratoconics suffer from abnormally highamounts of aberration.

Wave Aberration PointspreadFunction Retinal Image

1 deg5.7 mm pupil

Keratoconus

TypicalSubject

The Rochester 2nd generationadaptive optics system

Hot mirror

SLDλ = 820 nm

Lenslet array

CCDHartmann-Shackwavefront sensor

Xinetics Deformablemirror

Hot mirror

SLDλ = 820 nm

Lenslet array

CCDHartmann-Shackwavefront sensor

Xinetics Deformablemirror

CCD

Retinal imageCold mirror

550 nm filter

Kryptonflash lamp

Retinal imaging

System Layout

AO System Parameters

Correction Device 97 channel Xinetics DM, ±4µm wavefront stroke

Imaging Source Krypton flashlamp centered at 550nm, 4msec exposure duration

Science Camera Cooled back-illuminated CCD (Roper Scientific: MicroMAX)512×512, 24µm square pixels, max. frame rate of 3Hz

Wavefront Sensor Hartmann-Shack, 17x17 lenslets, f=24mm, φ = 0.4mm

WFS Source Superluminescent diode at 810nm, 20nm bandwidth

WFS Camera Cooled frame transfer CCD (Roper Scientific: PentaMAX)512×512, 15µm square pixels, max. frame rate of 30Hz

Bandwidth ~1Hz closed loop, 30 Hz sampling, 10th order Zernike correction

RMS after AO <0.1 microns for a 6.8mm pupil.

Important considerationsfor wavefront sensor

design

Corneal Reflection

Cornea > Retina20-20000

3 possible solutions!

• Pinhole

• Use of polarized light

• Off axis entry beam

Removing the corneal reflection

Eye

Collimatedinput beam

Laserbeacon

Lensletarray

PINHOLE

POLARIZEDINPUT BEAM

OFF AXISBEAM

Image Speckle

Rapidly scan beacon across retina (Hofer 1999)( complex )

Let retinal motion decorrelate speckle

(a) Laser, polarized > 500 msec

(b) Laser, unpolarized > 200 msec

(C) SLD, unpolarized > 30-50 msec

Retinal Reflectivity

400 450 500 550 600 650 700 750 800 85010-1

100

101

102

Wavelength in nm

PerifoveaFovea

WFS

SLD chosen wavelength is~800nm. Good reflectivity. Shortcoherence length, minimizesspeckle. Shorter depth of retinapenetrated.

Imaging Wavelength

Chosen to be at 550nm,corresponds to the average peaksensitivity of the L and M conepigment.

How much light can safely enter the eye?

Wavelength Exposure Max Perm Exposure

0.4 - 0.7 18x10-6 to 10 sec 0.0006927 t3/4 joules

0.0006927 t3/4 10 2 (λ - 0.7) joules0.7 - 1.05 18x10-6 to 103 sec

ANSI, American National Standard for the Safe Use of Lasers, ANSI Z136.1-1993,(Laser Institute of America, Orlando, FL, 1993).

Eg 1: What is the maximum power"safely" allowed for a 1/4 secexposure?

Ans: 1 mW for λ < 0.7µm1.4 mW for λ = 0.78 µm

Eg 2: How far below the MPE is a typical Hartmann sensor for the eye?(10 µ Watts, 200 msec, λ = 0.63 µ m)

Ans: Energy of HS = 2 µjoulesMPE= 207 µjoules

Configuration of 97 channel DM

Clear aperture77.4 mm (7.24 mm)

Pupil size for AO6.8 mm

Pupil size for retinal imaging6 mm

PMN Actuators7 mm (0.672 mm) spacing4 µm stroke

Configuration of 221 lenslet array and 97 channel DM

Clear aperture77.4 mm (7.24 mm)

Pupil size for AO6.8 mm

Pupil size for retinal imaging6 mm

Actuators7 mm (0.672 mm) spacing4 µm stroke

Lenslets (221 of 17×17)0.4 mm (0.384 mm) spacing24 mm focal length

Hartmann-Shack spot array

Hartmann spot on CCD Centroid boxes

Wavefront sensing --- Centroid algorithm

Local tiltedwave front lenslet

Focalplane

∆kθk

f

skx =∆xf

∆y =

∂ϕ (x, y)∂yk

∫∫dxdy

k∫∫

=

P(j∑

i∑ i. j)yij

P(i, j)j∑

i∑

∆x =

∂ϕ(x, y)∂x

k∫∫

dxdyk∫∫

=

P(j=1

j= J

∑i=1

i= I

∑ i.j) xij

P(i, j)j=1

j= J

∑i=1

i= I

∑

sky =∆yf

Local slope

Spot centroid

Real spotcentroid

Ideal spotcentroid

Initialcentroid box

Lastcentroid box

Wavefront sensing --- Centroid iteration algorithm

Shrinkingcentroid box

Advantage: reducing noise effect and improving the precision for centroid

estimatedcentroid

realcentroid

realcentroid

estimatedcentroid

Shrinkingcentroid box

Wavefront Control – Reconstruction of the wavefront todetermine the actuator commands

Wavefront correcting----Direct slope control algorithm

Slope vectorResidual

WavefrontReconstruction

Voltage vectorZ+ E+

Slope vector Voltage vectorD+

Direct Slope Control – Using wavefront slope as controlobjective.

Benefit of direct slope control algorithm

• Fast

• Without wavefront reconstruction error

• Tolerance to small misalignment betweenwavefront sensor and DM

Direct slope control algorithm

Flow chart to generate influence function matrix

Flatten DM

Add V1to Actuator i

Actuator i=1

Average 10 frames wavefront slope data in Si1

Add V2 to Actuator i

Average 10 frames wavefront slope data in Si2

Si=(Si2- Si1 )/(V2-V1)

i>97No

i=i+1

YesD=[S1, S2, ……, Si, ……S97]442x97

End

Start

D =

s(1,1)x s(2,1)x L s(N ,1) xs(1, 2)x s(2,1)x L s(N ,2) x

M M M M

s(1,M) x s(2,M) x L s(N,M)xs(1,1) y s(2,1)y L s(N ,1) ys(1,2)y s(2,2)y L s(N ,2) y

M M M M

s(1,M) y s(2,M) y L s(N,M)y

2M ×N

M: total number of lenslets (221)N: total number of actuators (97)

Direct slope control algorithm

S =

s1xs2xM

sM x

s1ys2 yM

sM y

V =

V1V2M

VN

V = D+Svoltage forupdata actuators slope influence function slope from WFS

M: total number of lenslets (221)N: total number of actuators (97)

D =

s(1,1)x s(2,1)x L s(N ,1) xs(1, 2)x s(2,1)x L s(N ,2) x

M M M M

s(1,M) x s(2,M) x L s(N,M)xs(1,1) y s(2,1)y L s(N ,1) ys(1,2)y s(2,2)y L s(N ,2) y

M M M M

s(1,M) y s(2,M) y L s(N,M)y

2M ×N

TEMPORAL

CHARACTERISTICS

Sampling period T(33ms):

VExposure Readout Centroid

Voltage Updata mirror

Timing sequence in AO system

Time delay τ=2TV

2TT 3T 4T

Exposure Readout Centroid

Voltage Updata mirror

Time

1 − e−Ts

Tse−τs C(s) 1

Eye aberration DMResidualaberration

y(s)r(s)e(s)

1 − e−Ts

Tse−τs

Eye aberration Residual aberration

y(s)

r(s)e(s) kcs

Feedback control: V((n)T)= V((n-1)T)+0.3Voltage((n)T)

C(s)=kc/s

-

-

+

+

+

Sensornoise

n(s)

+

Sensornoise

n(s)

AO system with transfer function model

From this model, the bandwidth is 0.9Hz@ 20Hz sampling rate, and 1.1Hz @30Hz sampling rate.

100.01

0.1

1

10

100

0.1 1

Static compensation

Dynamiccompensation

Average wavefront power spectrum

System performance---Dynamic compensation

Rat

io c

lose

d-lo

op p

ower

/ op

en-lo

op p

ower

model

data

0.01

0.1

1

10

0.1 1 100.01

0.1

1

10

0.1 1 10Temporal frequency (Hz) Temporal frequency (Hz)

Wavefront disturbance rejection

Model: 0.9Hz, Experimental data: 0.85Hz

6 subjects, 20Hz frame rate

00.10.20.30.40.50.60.70.80.91

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Frame number

Rm

s wav

efro

nt er

ror

(6.8

mm

pup

il)mydriacyl, 67msec exposure, 30% gain, no binning with CCD, 8 Hz frame rate

Evolution of the correction - Pupil and PSF planes

GYY, 6.8 mm pupil, 550 nm

AO Retinal Imaging at a Microscopic Spatial Scale

Courtesy Austin Roorda

Cone classing experiments

Courtesy Austin Roorda, Heidi Hofer

JC, 1.25 deg temporal

%L = 66 ± 4

JW, 1 deg temporal

%L = 80

BS, 1.25 deg nasal

%L = 94 ± 3

MD, 1.25 deg nasal

%L = 60 ± 3

AP, 1.25 deg nasal

%L = 51 ± 3

YY, 1 deg nasal-superior

%L = 51 ± 5

1

1.5

2

2.5

3

3.5

0 4 8 12 16 20 24 28 32V

isual

ben

efit

Spatial frequency (c/deg)

5.7 mm pupil

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Mod

ulat

ion

tran

sfer

Spatial frequency (c/deg)

all monochromatic aberrations corrected

only defocus and astigmatism corrected

Visual Benefit of correctinghigher order aberrations

Mean of 109 subjects

5.7 mm pupil

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4

Visual Benefit

Num

ber o

f Sub

ject

s Keratoconics

16 c/deg5.7 mm pupil

Keratoconics could especially benefitfrom correcting higher order aberrations

Conventional refraction Adaptive optics

The Rush Rhees tower viewed from half a mile away in broadband light with a large (6.8mm) pupil.

Improvement in average Strehl RatioImprovement in average Strehl Ratiowith dynamic AO correctionwith dynamic AO correction

0

0.1

0.2

0.3

0.4

0.5

No AOcorrection

Staticcorrection

Dynamiccorrection

6 subjects6 mm pupil size

550 nm

Stre

hl R

atio

Heidi Hofer

Increase in the power at the coneIncrease in the power at the conespatial frequenciesspatial frequencies

2

11.11.21.31.41.51.61.71.81.9

Spatial Frequency (c/deg)10 20 30 40 50 60 70 80 90 100 110 1200

Rat

io o

f Im

age P

ower

cones

Heidi Hofer

Ratio for a dynamic to static correction

• 512 X 480 pixels• 30 frames per second (uncompressed digital video)• 660 nm wavelength• 37-channel Xinetics deformable mirror• Shack-Hartmann wavefront sensor• Continuous zoom from 1 X 1 to 2.5 X 2.5 deg field

AOSLO Schematic

Axial Sectioning Capability

Vision AO system for UCDavis Medical Center

Laboratory systemdeveloped at LLNL, inconsultation withUniversity of Rochester,for use at UC DavisMedical Center for clinicalinvestigation of the limitsof human visual acuity

• Demonstrates high-accuracy, small, inexpensive Liquid CrystalSpatial Light Modulator wavefront corrector technology

THE END

The Whole Eye is Better than the Sum of Its Parts

Cornea Internal Optics Whole Eye

Artal, Guirao, Berrio, and Williams, Journal of Vision,1, 2001

0

0.5

1

1.5

2

2.5

3

3.5

4R

MS

wav

efro

nt er

ror (

µm)

Z20 Z 2

-2 Z22 Z 3

-1 Z31 Z 3

-3 Z33 Z4

0 Z42 Z 4

-2 Z44 Z 4

-4 Z51 Z 5

-1Z53 Z 5

-3 Z55 Z 5

-5

80%

2.7%10%

1.8%0.9%

0.9%0.7%

1.6%

0

0.1

0.2

0.3

0.4

0.5

Z 2-2 Z2

2 Z 3-1 Z3

1 Z 3-3 Z3

3 Z40 Z4

2 Z 4-2 Z4

4 Z 4-4 Z5

1 Z 5-1 Z5

3 Z 5-3 Z5

5 Z 5-5

Mean of 109 subjects5.7 mm pupil

Population Statistics of the Eye’s Wave Aberration(Zernike Analysis)

DefocusAstigmatism

Coma SphericalAberration Porter - JOSAA 2001

Inter-subject variability in MTF(Castejón-Mochón et al., Vision Res., 2002)

MTF

Perfect Eye

Planar wavefront

Spherical wavefront

Aberrated Eye

Aberrated wavefront

Wavefront Errors of the Eye:

Ordinary AO vs. MCAO: Computer Simulation

J band (1.2µm) , 1’ FOV Ø, “Gemini like” MCAO, stars magnified 10xClaire Max - CfAO lecture course

1.2µm Claire Max - CfAO lecture course

Wavefront Stroke - 5.7mm Pupil

Optimized Defocus Optimized defocus and corrected astigmatism (0.25D)

Data from Jason Porter, U of R

.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 More

P-V in microns

.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

P-V in microns

Wavefront Stroke - Wavefront Stroke - 6.8mm Pupil6.8mm Pupil

Populat ion_PV_Stroke

0

1009594

75

54

28

0

10

20

30

40

50

60

70

80

0 4 8 12 16 20 24 28 32

PV (microns)

Zeroed defocus

Data: Hauwei Zhao, U of Indiana 70 subjects - left eye shown

Populat ion_PV_Stroke

0

10010010091

81

43

0

10

20

30

40

50

60

70

80

0 4 8 12 16 20 24 28 32

PV (microns)

Zeroed defocus andastigmatism

Influence functions for XineticsDM

• Push on four actuators, measure deflectionwith an optical interferometer

Claire Max - CfAO lecture course

Shack-Hartmann wavefrontsensor concept - measure

subaperture tiltsf

CCD CCD

Claire Max - CfAO lecture course

Raw data(CCD)

Wave aberration

Eye lid wide open Normal position

Simulation of curvature sensorresponse

Wavefront: pure tilt Curvature sensor signal

G. ChananClaire Max - CfAO lecture course

Measurement error fromcurvature sensing

• Error of a single set of measurements is determined byphoton statistics, since detector has no noise:

where d = subaperture diameter and Nph is no. of photons persubaperture per sample period

• Error propagation when the wavefront is reconstructednumerically using a computer scales poorly with no. ofsubapertures N:– (Error)curvature ∝ N, whereas (Error)Shack-Hartmann ∝ log N

σcs2 = π 2 1

Nph

d

r0

2

Claire Max - CfAO lecture course

Wavefront Sensing - Laser Beacon

� Superluminescent diode (SLD) : 810nm wavelength, 20nmspectral spread

� Coherence properties : 30 micron, less speckle in wavefrontsensor spots

� SLD power: ~ 5µW

� Suppliers – Volga, Superlum, (Anritsu?) etc

Towards low cost AOsystems for clinicalresearch settings

Retinal Imaging with BMCRetinal Imaging with BMCMEMSMEMS

Without AO With MEMS AO

6 registered images for each caseFOV ~ 0.250 , 75µm on the retina