ao system design in vision science - lick observatory · ao system design in vision science donald...

AO System Design

in Vision Science

Donald T. Miller

http://www.opt.indiana.edu/people/faculty/miller.htm

Primary camera architectures

Scanning laser ophthalmoscope (SLO)

Optical coherence tomography (OCT)

Fundus camera (flood illumination)

1. Lateral resolution

2. Axial resolution

3. Temporal resolution

4. Sensitivity

5. Contrast

Camera parameters important

for imaging single cells in the

living human retina

Point Spread Function vs. Pupil Size

1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm

Perfect Eye

Typical Eye

AO

Courtesy A. Roorda

0

5

10

15

20

25

30

0 1 2 3 4 5 6 7 8

Pupil Diameter (mm)

Tra

nsvers

e R

eso

luti

on

(m

)

-100

0

100

200

300

400

500

Dep

th o

f fo

cu

s (

m

)

Tra

nsvers

e r

esolu

tion

(m

)

Pupil diameter (mm)

Depth

of

focus (

m)

wo

2wo

Transverse resolution (solid) and depth of focus (dashed)

as a function of pupil size for an unaberrated eye

l = 0.83 m

A. Roorda, D.T. Miller, J. Christou, “Strategies for High-Resolution Retinal Imaging,”

Chapter 10 (Fig. 10.8) in Adaptive Optics for Vision Science (2006).

Adaptive Optics In Astronomy:

-Proposed in 1953 (Horace Babcock)

-First Implemented in mid-1970s

The laser emerging from the dome of the 120" Shane Telescope at the

Lick Observatory is used for measuring atmospheric aberrations

First Use of a Deformable Mirror In the Eye:

A. W.Dreher, J. F. Bille, R. N. Weinreb, "Active optical

depth resolution improvement of the laser tomographic

scanner," Appl. Opt. 24, 804-808 (1989).

J. Liang, D.R. Williams, and D.T. Miller, “Supernormal vision and high

resolution retinal imaging through adaptive optics,”

J. Opt.Soc. Am. A., 14, 2884-2892 (1997).

First use of wavefront

sensing to correct higher

order aberrations

First demonstration of

retinal imaging and vision

improvement by correcting

higher order aberrations

2006 2008

Additional information on the content of this tutorial can be found in

Donald T. Miller and Austin Roorda, "Adaptive optics in retinal

microscopy and vision,“ chapter in Handbook of Optics, McGraw-Hill,

New York (submitted).

Cartoon suggests adaptive optics for astronomy and

vision science face very different challenges.

<$200K

pupilpatient

Ocular

aberrations

Personnel

Eye

speculum

… not a

patient-friendly

solution.

How do I design an adaptive optics system that is

tailored to the human eye?

increased

lateral resolution

Increased collection

efficiency of reflected light

Permits large pupil

(diffraction & NA)

increased

axial resolution (SLO)

Eye

2. Wavefront

1. Wavefront sensor

Aberrated wavefront

3. Control

system

Laser

beacon

Retina

camera

or

Visual

stimulus

corrector

Outline

1. Wavefront sensor

2. Wavefront corrector

3. Control system

4. Complete AO system

AO’s requirements

to measure, correct, and track

are dictated by the

properties of the ocular aberrations:

1. Spatial distribution of the

ocular aberrations.

3. Temporal distribution of the

ocular aberrations.2. Magnitude of the

ocular aberrations.

4. Field dependence of the

ocular aberrations.(isoplanatism)

Indiana’s flood-illuminated AO retina camera

retina

CCD

S-H WS

Xinetics

mirror

Subject

fiber light

source

Control

computer

Outline

1. Wavefront sensor


3. Control system


“... if an optician wanted to sell me an instrument

which had all these defects, I should think myself quite

justified in blaming his carelessness in the strongest

terms, and giving him back his instrument.”

Hermann

Von Helmholtz(19th century)

Mono aberr s1

J. Porter et al., Adaptive Optics for Vision Science (2006), Figure F.1 p. xviii.

Publication trend for use of wavefront sensors to measure the full wave

aberrations of the human eye (PubMed)

Shack-Hartmann,

spatially resolved refractometer,

crossed-cylinder aberroscope,

laser ray tracing,

scanning slit refractometer,

video keratography,

corneal topography,

phase retrieval,

curvature sensing, and

grating-based techniques

Liang, et al. SHWS

JOSA 1994

Numerous types of objective

wavefront sensors are available

Common path interferometer

Phasing shifting interferometer

Shack-Hartmann sensor

Shearing interferometer

Pyramid sensor

Curvature sensor

Phase diversity

Laser ray tracing

Tscherning aberrometry

Etc.

All major commercially-available aberrometers for the eye

measure the wavefront slope*

* The one exception is the OPD-Scan by Nidek (based on the principle of

sequential retinoscopy)

Guang-ming Dai, Wavefront optics for vision correction, Table 4.2 (2008).

Conceptual layout of the Shack-Hartmann wavefront sensor

Video

camera

Eye

Collimated input beam

(l = 800 – 900 nm)

Laser spot

Lenslet array

beamsplittertelescope

Wavefront Sensor Design

Most important

parameters:

CCD array

Lenslet array

F

Aberratedwavefront

•# of lenslets

•Sensitivity

•Dynamic range

•Signal-to-noise

dDxmax

Dxmin

Summary of aberrated wavefront reconstruction

5. Reconstruct

complete aberrated

wavefront ,,,,

1

M

m

mmZcRWrW

4. Calculate

coefficients of

Zernike modescm = V D-1 U T Sl

2. Centroid and determine

displacement (reference) of

Shack-Hartmann spotsrefl

lji

aji

lji

ajiji

al xI

Ix

x ,

,

,,

,

,,,

, D

3. Calculate

local wavefront

slopesf

xs

al

lax

,D

1. Capture raw

Shack-Hartmann

spots


Most important

parameters:

CCD array

Lenslet array

F

Aberratedwavefront

•# of lenslets

•Sensitivity

•Dynamic range

•Signal-to-noise

dDxmax

Dxmin

Maximum number of Zernike modes that can be calculated reliably for a

given number of sampling points.

G. Yoon, “Wavefront sensing and diagnostic uses,“

Chapter 3, Adaptive Optics for Vision Science (2006).

Result:

Maximum lenslets

= Zernike modes to correct

= (N+1)(N+2)/2 - 3,

where N is order #.

Example: Correct up

through 10th order:

Maximum lenslets

= (10+1)(10+2)/2 - 3

= 63

Ideal case:

No other effect,

e.g., noise,

partial occlusion

of edge lenslets,

pathology, dry

eye

, L

, M

M

m

mmZcRW1

,,

AO’s requirements


are dictated by the



ocular aberrations.



ocular aberrations.



-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Zernike Order

Log 1

0 (

Wavef

ron

t V

ari

an

ce)

mic

ron

s^2

Rochester

Indiana

Aberrations in two populations of

70 normal eyes for 7.5 mm pupil

Diffraction limit

l = 0.6 um)

N. Doble & D.T. Miller, “Vision correctors for vision science,“ Chapter 4, Adaptive Optics for Vision Science (2006).

N. Doble, et al., "Requirements for discrete actuator and segmented wavefront correctors for aberration

compensation in two large populations of human eyes," Appl. Opt. 46, 4501-4514 (2007),


Most important

parameters:

= # modes

CCD array

Lenslet array

F

Dxmax

Aberratedwavefront

Dxmin

•# of lenslets

•Sensitivity

•Dynamic range

•Signal-to-noise

≥ 4 pixels

across

2.44lF/d

≥ 4 pix / focal spot

d

4.4pix * 25.8m/pix

= 2.44lF/d

= 1.22l/NA

NA = 0.0083 for

individual lenslet

l = 0.78m

(221; 17 across

6.8 mm pupil)

min = Dxmin / F

<< (25.8m/pix) / 24mm

<< 1.1 mrad

(min << 1.1 mrad;

4.4 pix)

# of pixels = (2.44lF/d) / (pixCCD)

= (2.44*0.78m*24mm/0.4mm)

/ 25.8m

= 4.4 pixels


Most important

parameters:

= # modes

CCD array

Lenslet array

F

Dxmax

Aberratedwavefront

Dxmin

•# of lenslets

•Sensitivity

•Dynamic range

•Signal-to-noise

≥ 4 pixels

across

2.44lF/d


d

= lenslet NA

(221; 17 across

6.8 mm pupil)

max = Dxmax / F

= (d/2) / F

= NA = 0.0083

(min << 1.1 mrad;

4.4 pix)

(8.3 mrad,

Dioptersmax for 6.8 mm pupil

= Dmax / pupil radius

2.44 D)

= 0.0083 / (6.8e-6 m / 2)

= 2.44 diopters

-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Zernike Order

Log 1

0 (

Wavef

ron

t V

ari

an

ce)

mic

ron

s^2

Rochester

Indiana



Diffraction limit




Refractive error (diopters)

-10 105-5 0

hyperopiamyopia

Perc

ent of

eyes

0

20

40

60

80

Distribution of refractive error

depends on many factors

including population, age,

education, and cycloplegia.

R. W. Everson, “Age variation in refractive error distributions,” Optom. Weekly, 64, 200-204 (1973).

elderly

(avg 74 yr)peak

0 to +2D

young adult peak

0 to +1D

young adult peak

0 to +1D

13 – 14 yrs cycloplegia most common0 to +1D

12 – 16 yrs cycloplegia most common0 to +1D

6 – 8 yrs cycloplegia vast majority0 to +2D

5 – 7 yrs none vast majority0 to +1D

-12 to +12 Dinfants (30 hrs) cycloplegia range

Reasonable goal:

+/- 5 diopters

covers a large

percentage of

the population


Most important

parameters:

= # modes

CCD array

Lenslet array

F

Dxmax

Aberratedwavefront

Dxmin

•# of lenslets

•Sensitivity

•Dynamic range

•Signal-to-noise

≥ 4 pixels

across

2.44lF/d


d

= NA

(221; 17 across

6.8 mm pupil)

(min << 1.1 mrad;

4.4 pix)

(8.3 mrad; 2.4 diopters)

Noise sources:

photon noise,

CCD read noise

photons/lenslet

astron: ~100 to close

loop

vision: >500,000

high (saturate CCD)

Typical SH sensor parameters for the eye

1. # of lenslets: ~200 (>1/2 million photons/lenslet

for <8 W entering eye.)

2. Lenslet array: lenslet diameter = 400m

(17x17 for 6.8 mm pupil)

focal length = 24mm

3. # pixels across 4 to 14

4. Wavelength 633 to 850 nm

dot core

Eye

2. Wavefront

1. Wavefront sensor

Aberrated wavefront

3. Control

system

Laser

beacon

Retina

camera

or

Visual

stimulus

corrector

Indiana adaptive optics retina camera

17x17 lenslets across 6.8 mm pupil

4.4 pix across each focal spot

2.4 diopter dynamic range

l= 0.78 m SLD beacon

6 W enters eye

Inexpensive areal CCD

1. SHWS wavefront sensor

17x17 SHWS lenslets(0.4 mm spacing)

Sampling geometry of the lensletsat the pupil plane of the eye

6.8 mm

at eye

Outline

1. Wavefront sensor


3. Control system


Various types of wavefront correctors

(Which one is right for my application?)

OKO membrane mirror

Xinetics deformable

mirror

AOptix bimorph

“fast, simple, & robust”

Hamamatsu

LC-SLM

Boston Micromachines

Corp.

Iris AO

Imagine Eyes

Wavefront Corrector Performance

Input from

Eye

actuators

push & pull

on mirror

surface

Most important

parameters:

•Actuator stroke

•Actuator number

•Actuator influence function

•Speed

•Reflectivity

•Diameter

•Cost!

AO’s requirements


are dictated by the



ocular aberrations.



ocular aberrations.



2. Magnitude of the

ocular aberrations.

Indiana

Population

all

no 2nd

order

Rochester

Population

all

no defocus

no 2nd order

N. Doble, et. al, “Requirements for discrete actuator and segmented wavefront correctors for aberration

compensation in two large populations of human eyes,” Applied Optics 46:4501-4514 (2007).

.

(Result: 10-53 m

for 7.5 mm)

(Result: 7-11 m

for 7.5 mm)

Figure. PV wavefront error that encompasses 95% of the population in the Rochester (black

lines) and Indiana (gray lines) populations as a function of pupil diameter.

OKO membrane mirror

Xinetics deformable

mirror

AOptix bimorph

“fast, simple, & robust”

Hamamatsu

LC-SLM

Boston Micromachines

Corp.

Iris AO

Imagine Eyes

(11 m)

(32 m)

(70 m)

(16 m)

(70 m)

(l)

Peak-to-valley

wavefront correction

available for defocus:

2*stroke = (8 m)

(7? m)

Wavefront Corrector Performance

Input from

Eye

actuators

push & pull

on mirror

surface

Most important

parameters:

•Actuator stroke

•Actuator number

•Actuator influence function

•Speed

•Reflectivity

•Diameter

•Cost!

AO’s requirements


are dictated by the



ocular aberrations.



ocular aberrations.



-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10

Zernike Order

Log 1

0 (

Wavef

ron

t V

ari

an

ce)

mic

ron

s^2

Rochester

Indiana



Diffraction limit

l = 0.6 um)




-5

-4

-3

-2

-1

0

1

2

1 2 3 4 5 6 7 8 9 10

Zernike Order

Lo

g 1

0 o

f W

avefr

on

t V

ari

an

ce (

μm

2)

7.5 mm

6.0 mm

4.5 mm

Diffraction limit

Diffraction limit

l = 0.6 um)

Indiana population:

Log10 of the wavefront

variance after a

conventional refraction

using trial lenses is

plotted as a function of

Zernike order and pupil

size (4.5, 6.0, and 7.5

mm). Diamonds and

corresponding dashed

curves represent the

mean and mean ± two

times the standard

deviation of the

log10(wavefront variance),

respectively, for a 7.5 mm

pupil. Star and open

circle correspond to 4.5

mm and 6.0 mm pupils.

Same Indiana population on previous slide, but

for 3 different pupil sizes.

1. Discrete actuator

deformable mirrors

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 3 5 7 9 11 13 15 17 19 21

No. of Actuators across the Pupil

Str

ehl R

ati

o

All

Zero Z5

ZeroZ4,Z5,Z6

Refraction

Zero Z5

Zero Z4,Z5,Z6

Diff lim result: >14 (Roch), 11-14 (Ind)

Actuators across 7.5 mm pupil

Pre

dic

ted S

trehl ra

tio

Xinetics

37 actuator

BMC

140 actuator

l = 0.6 m

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150


Str

ehl R

ati

o

All

Zero Z5

Zero Z4, Z5, Z6

Refraction

Zero Z5

Zero Z4, Z5, Z6

2. Piston segmented

correctors

Diff lim result: >90 (Roch), 45-85 (Ind)

Pre

dic

ted S

trehl ra

tio

480x480 segments

Meadowlarks

127 segments


l = 0.6 m

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 3 5 7 9 11 13 15 17 19 21


Str

ehl R

ati

o

All

Zero Z5

Zero Z4,Z5,Z6

Refraction

Zero Z5

Zero Z4,Z5,Z6

3. Piston/tip/tilt

segmented

correctorsDiff lim result: 12-19 (Roch), 9-10 (Ind)

Pre

dic

ted S

trehl ra

tio


IrisAO

37 actuator

l = 0.6 m

Elizabeth Daly, Eugenie Dalimier, and Christopher Dainty

in the Applied Optics Group at National University of Ireland, Galway

- 6 mm pupil

-Indiana

Aberration

Study of

100 eyes

Sim

ula

ted r

esid

ual R

MS

err

or

(m

)

Number of modes used for correction

-Includes finite

stroke of

mirrors

AOptix35MIRAO52

BMC140

OKO37

OKO19

(Related publication): T. Farrell, E. Daly, E. Dalimier, and C. Dainty, “Task-based assessment of deformable

mirrors,” Proc. SPIE 6467, 64670F (2007)

Desired parameters for the

wavefront corrector

4 - 8 mm

10-53 m (Rochester)

7-11 m (Indiana)

1-6 Hz fluctuations in the eye

>90% (400-900 nm)

> 14 (Roch), 11-14 (Ind) Discrete actuator

> 90 (Roch), 45-85 (Ind) Piston-only segmented

12-19 (Roch), 9-10 (Ind) Piston/tip/tilt segmented

Temporal Bandwidth

Reflectivity

Physical size

Mirror Stroke(7.5-mm pupil, 95% population)

# of actuators or

segments across 7.5

mm pupil (for 80% Strehl at l = 0.6 m)

OKO37 membrane

OKO19 piezoelectric

AOptix35

MIRAO52

BMC140Specific correctors

evaluated

AO’s requirements


are dictated by the



ocular aberrations.



ocular aberrations.



Conventional fundus image

Optic disc

Fovea

1 degree

isoplanatic patch

size

Example: 40 deg fundus image

would require collection of p40/2)2 = 1,257

one-degree AO images.

Eye

2. Wavefront

1. Wavefront sensor

Aberrated wavefront

3. Control

system

Laser

beacon

Retina

camera

or

Visual

stimulus

corrector


2. Xinetics wavefront corrector

37 actuators fill 6.8 mm pupil

4 m stroke

Predicted Strehl = 0.2-0.4 (7.5 mm)


4.4 pix across each focal spot

2.4 diopter dynamic range


6 W enters eye



Xinetics:- 37 elements, - 4 µm stroke

37 Xinetics actuators(1.12 mm spacing)


Sampling geometry of the actuators and lensletsat the pupil plane of the eye

6.8 mm

at eye

Pupil size for

retinal imaging(6 mm)

Deformable mirrors used in the AO woofer-tweeter system

Actuator

geometry

AOptix Bimorph:-35 actuators + guard ring + front face electrode, -16 µm stroke available for defocus,- used for lower order aberrations

BMC MEMS: - 140 elements (12x12),-3.7 µm stroke, -used for higher order aberrations

12x12 36 total

AOptix Bimorph:- 36 elements, - 15 µm stroke

BMC MEMS: - 140 elements (12x12),- 3.7 µm stroke

12x12 BMC actuators

36 AOptix actuators

20x20 SHWS lenslets


6 mm

at eye

Outline

1. Wavefront sensor


3. Control system


AO system has distinct spatial and temporal

control characteristics

focular(x,y)

Spatial

control,

fcorrect(x,y)

focular(x,y)

-fcorrect(x,y)

1.

focular(t)

Temporal

control,

fcorrect(t-t)

focular(t)

-G fcorrect(t-t)

2.

Direct slope

reconstruction

method:

Sl = Fl,a Ma

Measured

sensor

slopes

(2l,1)

Response

matrix for the

mirror-sensor

system

(2l, a)

Mirror

Voltages

(a,1)

1. Spatial control of the adaptive optics system

F -1 typically does not exist

as F needs to be singular.

Problem:

Solution: Determine pseudo-inverse,

F *, using for example

singular value decomposition.

Direct slope

reconstruction

method:


Sl = Fl,a Ma

Measured

sensor

slopes

(2l,1)

Response

matrix for the

mirror-sensor

system

(2l, a)

Mirror

Voltages

(a,1)

Singular value decomposition

Fl,a = U D V T

Least squares inverse

Fl,a* = V D-1 U T

Direct slope

reconstruction

method:


Sl = Fl,a Ma

Measured

sensor

slopes

(2l,1)

Response

matrix for the

mirror-sensor

system

(2l, a)

Mirror

Voltages

(a,1)

Ma = V D-1 U T Sl

Fl,a*, least squares

solution to inverse

Ḿa = Fl,a* (Sl - Sl) - Ma

remove mean slope and piston

Fl,a

Response matrix for

the mirror-sensor

system (m,n)

Least squares

solution to inverseFl,a*

Actu

ato

r #

(2 x total lenslets)

Actu

ato

r #

Note: axes should be flipped

AO system has distinct spatial and temporal

control characteristics

focular(x,y)

Spatial

control,

fcorrect(x,y)

focular(x,y)

-fcorrect(x,y)

1.

focular(t)

Temporal

control,

fcorrect(t-t)

focular(t)

-G fcorrect(t-t)

2.

How fast does my AO need to go?

AO’s requirements


are dictated by the



ocular aberrations.



ocular aberrations.



Temporal fluctuations in the eye’s PSF(viewing distant target, 6.8mm pupil, 780nm monochromatic light)

Video represents wave

aberration measurements

taken at 21 Hz

during a 4 second interval.

Figure. Temporal traces of the total rms wave-front error and Zernike terms: defocus,

astigmatism, coma, and spherical aberration for one subject when accommodating on a target

at 2 D. A trace of the total rms wave-front error for an artificial eye is also shown.

Result:

Fluctuations are found

in all of the eye’s

aberrations, not just

defocus.

H. Hofer, et. al, "Dynamics of the eye’s wave aberration," JOSA 18, 497-506 (2001).

Time (s)

Ab

err

ati

on

Mag

nit

ud

e (

m

)

model eye

total

defocus

astigmatism

coma

spherical

aberration

4.7 mm pupil

Figure. Comparison of the power spectrum of the fluctuations in the total rms wave-front error

for an artificial eye and for a human subject with paralyzed accommodation. Aberrations were

computed for a 4.7-mm pupil size.

Result (not shown):

Fluctuations in higher-order

aberrations share similar spectra and

bandwidth, dropping at f-4/3, (4dB/octave).

All spectra have

measurable

power out to ~5-6 Hz.

Frequency (Hz)

Avera

ge P

ow

er

4.7 mm pupil


Total rms

for subject

Total rms

for model eye

Figure. Time-averaged Strehl ratio versus bandwidth for a perfect adaptive optics system,

calculated for a 5.8-mm pupil for paralyzed accommodation and for natural

accommodation on a far target.

Result: A closed-loop bandwidth of an ideal AO system of

1-2 Hz can correct ocular aberrations well enough to achieve Strehl > 0.8.

Static correction Static correction


Bandwidth (Hz) Bandwidth (Hz)

Str

eh

l R

ati

o

Str

eh

l R

ati

o

Best

refraction

Best

refraction




All spectra have

measurable

power out to ~5-

6 Hz.

Frequency (Hz)

Avera

ge P

ow

er

4.7 mm pupil


Total rms

for subject

Total rms

for model eye

Result (not shown):




2

L. Diaz-Santana, et. al, "Benefit of higher closed–loop bandwidths in ocular adaptive optics," Opt. Express

11, 2597-2605 (2003)

Method: AO system with a 240 Hz sampling rate and 0 to 25 Hz closed-loop

bandwidth.

Result: Aberration power spectra show same slope as in Hofer et. al paper,

but extended up to 30 Hz.

Frequency (Hz) Time (s)A

ve

rag

e P

ow

er

Ab

err

ati

on

Ma

gn

itu

de

(

m)

f-4/3

Result: Increase in the closed-loop bandwidth above 2Hz may offer a marginal

benefit in corrected Strehl for real AO systems.

Hofer’s

diff limited

prediction

for ideal AO.

noticeable

variability

L. Diaz-Santana, et. al, "Benefit of higher closed–loop bandwidths in

ocular adaptive optics," Opt. Express 11, 2597-2605 (2003)

Bandwidth (Hz)

Str

eh

l R

ati

o




All spectra have

measurable

power out to ~5-

6 Hz.

Frequency (Hz)

Avera

ge P

ow

er

4.7 mm pupil


Total rms

for subject

Total rms

for model eye

Result (not shown):




2

0.001

0.01

0.1

1

10

100

1000

10000

0.01 0.1 1 10

Frequency (Hz)

Po

we

r S

pe

ctr

a

No Correction

10% Gain

30% Gain

50% Gain

Unstable (30% Gain)

Temporal power spectra of the wavefront disturbance

without and with dynamic correction

Frequency (Hz)

Pow

er

spectr

a

0.1 1 10

0.01

0.1

1

10

Pow

er

reje

ction m

agnitude

Temporal frequency (Hz)

power spectra with AOPower rejection

magnitude power spectra w/o AO=

0.55

Schematic of a closed-loop AO system

Residual,

R(s)

+-

Aberrations,

X(s)

Mirror,

M(s)

Hopenloop(s)

s=i2pfHOL(s) = M(s)

R(s)

Goal: find Hcloseloop(s)

HCL(s) = R(s)

X(s)

R(s) = X(s) – M(s)

R(s) = X(s) – HOL(s) R(s)

M(s) = HOL(s) R(s)= ?

1

1+ HOL(s)


Residual,

R(s)

+-

Zero-order

holdCompensator

Readout &

Computational

delay

SHWS

exposure

Aberrations,

X(s)

Mirror,

M(s)Hexp(s)Hdelay(s)Hcomp(s)Hzoh(s) = HOL(s)

1-e-sT

sTe-st

1-e-sT

G1-e-sT

sT, s=i2pf

1

122

2

T = 50 mst = 118 msGain = 0.31T = 100 ms2

Timing diagram of Indiana’s AO system

apply & hold

voltage on

corrector

1

T2

(integrate)

2

(integrate)

3

(integrate)

= 100 ms

10 Hz, 0.3 Gain

= 50 ms

SHWS

exposure

1

T1

(integrate)

2

(integrate)

3

(integrate)

= 50 ms

Readout1

t1

(delay)

2

(delay)

3

(delay)

= 68 ms

Reconstruct1

t2

(delay)

2

(delay)

3

(delay)


Residual,

R(s)

+-

Zero-order

holdCompensator

Readout &

Computational

delay

SHWS

exposure

Aberrations,

X(s)

Mirror,


Error

transfer

function

= HCL(s) =R(s)

X(s) 1 + HOL(s)

1=

Power

rejection

curve

=

1-e-sT

sTe-st

1-e-sT

G1-e-sT

sT, s=i2pf

1

122

2

T = 50 mst = 118 msGain = 0.31T = 100 ms2

0.1 1 10

0.01

0.1

1

10P

ow

er

reje

ctio

n m

ag

nitu

de


Predicted and measured power rejection magnitude

of the Indiana AO retina camera

0.5

10 Hz

T1 = 50 ms

t = 118 ms

T2 = 100 ms

Gain = 0.3

0.1 1 10

0.01

0.1

1

10P

ow

er

reje

ctio

n m

ag

nitu

de


Predicted and measured power rejection magnitude

of the Indiana AO retina camera

2.00.5

10 Hz

T1 = 50 ms

t = 118 ms

T2 = 100 ms

Gain = 0.3

50 Hz

T1 = 20 ms

t = 40 ms

T2 = 20 ms

Gain = 0.3


Residual,

R(s)

+-

Zero-order

holdCompensator

Readout &

Computational

delay

SHWS

exposure

Aberrations,

X(s)

Mirror,


Error

transfer

function

= HCL(s) =R(s)

X(s) 1 + HOL(s)

1=

Power

rejection

curve

=

1-e-sT

sTe-st

1-e-sT

G1-e-sT

sT, s=i2pf

1

122

2

T = 50 mst = 118 msGain = 0.31T = 100 ms2

Outline

1. Wavefront sensor


3. Control system


Eye

2. Wavefront

1. Wavefront sensor

Aberrated wavefront

3. Control

system

Laser

beacon

Retina

camera

or

Visual

stimulus

corrector




4 m stroke


3. Control system

Zonal reconstructor

(direct slope)

0.5 Hz cutoff frequency


~4 pix across each focal spot


6 W enters eye



Xinetics:- 37 elements, - 4 µm stroke

37 Xinetics actuators(1.12 mm spacing)



6.8 mm

at eye

Pupil size for

retinal imaging(6 mm)

Dynamic correction in one subject’s eye

as revealed by sensor-measured PSF

Before correction:

After correction:

1.6 m RMS

0.16 m RMS

6.8 mm pupil

10% Gain

21 Hz

l= 0.78 m

27 frames

to converge

80 frame video


as revealed by sensor-measured PSF

Before correction:

After correction:

1.6 m RMS

0.16 m RMS

6.8 mm pupil

30% Gain

21 Hz

l= 0.78 m

6 frames

to converge

80 frame video

Time (frames)


as revealed by measured total RMSW

ave

fro

nt

err

or

(m

)

10% Gain

30% Gain

20% Gain

3.8 sec0 sec

Eye

2. Wavefront

1. Wavefront sensor

Aberrated wavefront

3. Control

system

Laser

beacon

Retina

camera

or

Visual

stimulus

corrector




4 m stroke


3. Control system

Zonal reconstructor

(direct slope)

0.5 Hz cutoff frequency


~4 pix across each focal spot


6 W enters eye



Video rate: 10 fps

2° FOV

1° ecc.

6.0 mm pupil

AO correcting

at 15 Hz

Turning on the AO during a 10 Hz

video of the cone mosaic

3

3.5

Cone images in one subject’s eye

50 m

No AO correction AO correction

1° field of view; 1.25° eccentricity

Summary

1. Wavefront sensor- Type: Shack-Hartmann is used exclusively.

- Performance: Lenslet #, sensitivity, dynamic

range, and noise.

2. Wavefront corrector- Type: Many types are used.

- Performance: Actuator #, stroke, and influence function.

3. Control system-Type: Direct slope reconstruction

-Performance: Spatial and temporal properties


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