Dual-conjugate adaptive optics for wide-field high-resolution retinal imaging

doi:10.1364/OE.17.004454

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Dual-conjugate adaptive optics for wide-field high-resolution retinal imaging

Jörgen Thaung, Per Knutsson, Zoran Popovic, and Mette Owner-Petersen »View Author Affiliations

Optics Express, Vol. 17, Issue 6, pp. 4454-4467 (2009)
http://dx.doi.org/10.1364/OE.17.004454

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Abstract

We present analysis and preliminary laboratory testing of a real-time dual-conjugate adaptive optics (DCAO) instrument for ophthalmology that will enable wide-field high resolution imaging of the retina in vivo. The setup comprises five retinal guide stars (GS) and two deformable mirrors (DM), one conjugate to the pupil and one conjugate to a plane close to the retina. The DCAO instrument has a closed-loop wavefront sensing wavelength of 834 nm and an imaging wavelength of 575 nm. It incorporates an array of collimator lenses to spatially filter the light from all guide stars using one adjustable iris, and images the Hartmann patterns of multiple reference sources on a single detector. Zemax simulations were performed at 834 nm and 575 nm with the Navarro 99 and the Liou-Brennan eye models. Two correction alternatives were evaluated; conventional single conjugate AO (SCAO, using one GS and a pupil DM) and DCAO (using multiple GS and two DM). Zemax simulations at 575 nm based on the Navarro 99 eye model show that the diameter of the corrected field of view for diffraction-limited imaging (Strehl ≥ 0.8) increases from 1.5 deg with SCAO to 6.5 deg using DCAO. The increase for the less stringent condition of a wavefront error of 1 rad or less (Strehl ≥ 0.37) is from 3 deg with SCAO to approximately 7.4 deg using DCAO. Corresponding results for the Liou-Brennan eye model are 3.1 deg (SCAO) and 8.2 deg (DCAO) for Strehl ≥ 0.8, and 4.8 deg (SCAO) and 9.6 deg (DCAO) for Strehl ≥ 0.37. Potential gain in corrected field of view with DCAO is confirmed both by laboratory experiments on a model eye and by preliminary in vivo imaging of a human eye.

1. Introduction

In his work “Opticks” [1

I. Newton, Opticks, or A treatise of the reflections, refractions, inflections & colours of light (New York, Dover publ. 1952).

] Sir Isaac Newton wrote: “⋯ there would be certain bounds beyond which telescopes could not perform. For the air through which we look upon the stars is in perpetual tremor ⋯”. More than two hundred years later Horace Babcock published his pioneering work on the principles of adaptive optics (AO) [2

H. W. Babcock, “The Possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pacif. 65, 229–236 (1953). [CrossRef]

]. However, AO has only been available to the general research community for the past 15 years or so. Today many telescopes have been equipped with AO systems that compensate for the detrimental effects on imaging caused by the earth’s turbulent atmosphere.

A similar scenario is to be found in ophthalmology. Doctors who want to obtain high-resolution images of the retina instead of the sky are faced with both spatially and temporally changing media that induce aberrations, through which imaging is performed. Ophthalmic AO systems use a technique analogous to the laser guide star technique [3

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 29–31 (1985).

] used by astronomers to create an artificial laser guide star by focusing a thin pencil of light on the retina.

Conventional AO is performed with one point source, or guide star (GS), to probe the aberrated wavefront, and one active component, usually a deformable mirror (DM), to correct the aberrations in the pupil plane for that GS location. It is the prevalent technology in today’s applications [4

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). [CrossRef]

H. Hofer, J. Carroll, J. Neitz, M. Neitz, and D. R. Williams, “Organization of the human trichromatic cone mosaic,” J. Neurosci. 25, 9669–9679 (2005). [CrossRef] [PubMed]

], and will in this paper henceforth be referred to as single-conjugate AO (SCAO). In the case of axially distributed aberrations, as for the eye, field dependant aberrations decorrelate with increasing field angle from the GS. For SCAO this results in a small corrected field of view (FOV) called the isoplanatic patch, originally defined as the region over which the RMS wavefront error is smaller than 1 radian [6

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]

A method to deal with this limitation of SCAO was first proposed by Dicke [7

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys J. 198, 605–615 (1975). [CrossRef]

] and later developed by Beckers [8

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference and Workshop on Very Large Telescopes and their Instrumentation. Garching, Germany: European Southern Observatory (ESO) (1988).

]. In astronomy the proposed method, known as multi-conjugate AO (MCAO), uses multiple DM conjugated to separate turbulent layers of the atmosphere and several GS to increase the corrected FOV. In theory, correcting for each turbulent layer could yield diffraction limited performance over the entire FOV. However, as is the case for both the atmosphere and the eye, aberrations do not originate solely from a discrete set of thin layers but from a distributed volume. In this respect, using MCAO with only a few DM (at least two) still allows for significant gain in corrected FOV compared to SCAO. Regarding practical considerations it also reduces the complexity and cost of optomechanics and control system. The technique of MCAO is just emerging. Previous work on experimental MCAO has dealt with laboratory setups for astronomical applications [9–13

I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, and J.-P. Veran, “Design of the dual conjugate adaptive optics test-bed,” in Beyond conventional adaptive optics: a conference devoted to the development of adaptive optics for extremely large telescopes. Venice, Italy: European Southern Observatory (ESO) (2001).

]. Real implementations of MCAO have been achieved at the German Vacuum Tower Telescope (VTT) [14

O. von der Lühe, T. Berkefeld, and D. Soltau, “Multi-conjugate solar adaptive optics at the Vacuum Tower Telescope on Tenerife,” C. R. Physique 6, 1139–1147 (2005) [CrossRef]

] and at the ESO Very Large Telescope (VLT) [15

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J.-L. Lizon, M. Marchesi, S. Oberti, R. Reiss, J. Santos, C. Soenke, S. Tordo, A. Baruffolo, and P. Bagnara, and The CAMCAO Consortium, “On-sky Testing of the Multi-Conjugate Adaptive Optics Demonstrator,” The Messenger , 129, 8–13 (2007)

To date only Bedggood and co-workers have studied the concept of using MCAO for retinal imaging [16

P. A. Bedggood, R. Ashman, G. Smith, and A. B. Metha, “Multiconjugate adaptive optics applied to an anatomically accurate human eye model,” Opt. Express 14, 8019–8030 (2006). [CrossRef] [PubMed]

,17

P. Bedggood, M. Daaboul, R. Ashman, G. Smith, and A. Metha, “Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging,” J. Biomed. Opt. 13, 024008 (2008). [CrossRef] [PubMed]

]. Predictions in [16

] are based on a Zemax model in which the DM are emulated as phase screens embedded in an eye-model. The aim of the present paper is to predict the performance and demonstrate the feasibility of an actual closed loop MCAO setup for wide-field high-resolution retinal imaging. The setup incorporates two active components, a so-called dual-conjugate AO (DCAO) system, with one DM conjugate to the pupil and one DM conjugate to a plane somewhat in front of the retina. We present results from optical simulations of the full setup performed in Zemax that demonstrate the expected superior performance of our DCAO system compared to a conventional SCAO system with regard to the isoplanatic patch size. We also present laboratory experiments on both a model and a real eye confirming predictions from Zemax simulations.

The DCAO setup is not to be confused with a woofer-tweeter arrangement, in which a single wavefront sensor (WFS) is located after a number of DM that are all conjugated to the pupil plane (SCAO). The argument for using DCAO is not to discriminate between higher and lower order aberrations as in a woofer-tweeter arrangement but to enable the correction of field aberrations. This is accomplished by placing the second DM in a separate conjugate plane with a desired amount of GS footprint overlap.

There is a true need for increased resolution in the ophthalmology community, driven by the leading causes of legal blindness in the Western world: age-related macular degeneration (AMD), diabetic retinopathy, and glaucoma. With the increased resolution offered by adaptive optics eye clinicians will be able to investigate currently sub-clinical changes in retinal disease. This will lead to earlier detection and thus earlier treatment. DCAO is our proposal for enabling diffraction limited imaging over a larger FOV.

2. Experimental setup

The basic layout of the system is shown in Fig. 1. It is made up of five sub-units: GS light delivery, wavefront sensing, imaging, flood illumination, and a DCAO corrective unit including the two DM and the Badal focus corrector.

2.1. Retinal guide star formation

The GS light is delivered by a continuous relatively broadband near-infrared light (834±13 nm) from a super-luminescent diode (SLD) (Superlum Ltd, Moscow, Russia). This is fed through a 1:5 fiber splitter to five single mode fibers placed in a custom made fiber holder to obtain an array of point sources. The five separate beams are collimated by a lens before passing through a 5 mm diameter iris (corresponding to 3.3 mm at the eye) with a central block to minimize corneal reflections. The collimated beams pass through a pair of relay lenses and are coupled into the rest of the system by a wedge beamsplitter (WBS).

Part of the light from the GS arm (50%) passes through the WBS and is reflected by a retro-reflector (RR) and used for calibration purposes. The RR is blocked during closed loop operation. The rest of the light is reflected by the WBS and a mirror towards the micromachined membrane deformable mirrors DM1 and DM2 (OKO Technologies, Delft, The Netherlands). DM1 has a 15 mm aperture diameter and 37 actuators, and DM2 has a 40 mm aperture diameter and 79 actuators. The light then passes a Badal focus corrector, used to correct for a subject’s spherical refractive error, to ensure the delivery of well-focused GS spots on the retina. The Badal adjustment is performed to conserve corrective power because the stroke of the DM is limited. The light finally enters the eye via a mirror and through a 50/50 plate beamsplitter (PBS), used to couple imaging flood light illumination into the eye.

Fig. 1. Sketch of experimental system layout. Only marginal rays of the axial star are shown. SLD, superluminescent diode; WBS, wedge beamsplitter; RR, retro reflector; DM1, deformable mirror 1; DM2, deformable mirror 2; FT, fixation target; CLA, collimating lens array; CCD, wavefront sensor camera. P, pupil plane; R, retinal image plane. P’ denotes a split pupil plane and R’ a collapsed retinal image plane of the five different GS.

Fig. 2. Fundus photograph with an inset of the actual FOV and GS positions. Retinal center-to-center separation of peripheral GS from central GS is 3.1 deg (880 μm).

The four peripheral incoming GS beams are separated from the central GS by a visual angle of 3.1 deg, corresponding to a retinal separation of approximately 880 μm in the eye models used in the simulations. The beacons on the retina are arranged in a cross (Fig. 2) with a spot size (full width at half maximum, FWHM) of approximately 1.2 arcmin (5 μm). Retinal GS separation was based on investigations of the isoplanatic patch size from the Zemax modeling and is in agreement with [16

]. Total power entering the eye depended on the configuration but was always kept below 20 μW per GS. This is around ten times below recommended safety levels for a 20 minute exposure or around eight times below recommended safety levels for a 60 minute exposure.

2.2. Wavefront sensing

Reflected light from the retina travels back through the optical media of the eye and emerges through the pupil as five aberrated wavefronts, one from each GS (Fig. 3, left). They pass through the Badal focus corrector and the two DM (Fig. 3, right). DM1 is located in a plane conjugate to the pupil of the eye and will perform identical corrections for all field-points. DM2 is conjugated to a plane approximately 3 mm in front of the retina. DM2 will be able to perform different corrections on the 5 GS at this location (Fig. 3, bottom right) and thus compensate for different aberrations in the 5 field-points (anisoplanatic aberrations). The location of DM2 was chosen to provide adequate correction over the desired field (the macula) and to avoid extra relay optics.

Light then continues through the WBS, a relay lens and a cold mirror, before passing through a collimating lens array (CLA) containing one lens for each GS. The CLA enables the placement of a single spatial filter at a plane conjugate to the retina. Spatial filtering is performed to reduce unwanted light from parasitic source reflections and scattered light from the retina (Fig. 4). The light is collimated by a lens and sampled by a single Shack-Hartmann wavefront sensor, consisting of a lenslet array (pitch 200 μm, focal length 6.3 mm, Northrop Grumman’s Adaptive Optics Associates, Cambridge, MA, USA) allowing for ~12 lenslets across the 6 mm exit pupil of the eye, and a monochromatic CCD camera (Retiga EXi Fast 1394, QImaging, Surrey, BC, Canada). In addition to separating the Hartmann patterns as in [13

A. V. Goncharov, J. C. Dainty, S. Esposito, and A. Puglisi, “Laboratory MCAO test-bed for developing wavefront sensing concepts,” Opt. Express 13, 5580–5590 (2005). [CrossRef] [PubMed]

] this arrangement makes it possible to filter the light from all five GS using one focusing lens and one pinhole.

2.3. Retinal imaging

When the instrument is to be used in imaging mode, light from a flash delivery system will illuminate the retina via a 50/50 plate beamsplitter located just in front of the eye. The retina is illuminated with a 1-millisecond 120 μJ flash from a Xenon flash lamp, filtered by a 575±10 nm wavelength bandpass filter (FF01-575/15-25, Semrock, Rochester, NY, USA) and a small central block in a corneal plane. The size of the block was determined empirically to minimize corneal reflections without significantly reducing cone response, as contrast of cones in the retinal image will be highest if the illuminating light comes in on axis [18

W.S. Stiles and B.H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. B. 112, 428–450 (1933). [CrossRef]

]. The flash pupil diameter entering the eye is around 3 mm, and a field stop limits the illuminated field to 7 × 7 deg on the retina. Light returning through the system will be diverted by the cold mirror in front of the wavefront sensor and relayed through a pair of matched photographic objectives (50 mm f/1.8D AF Nikkor, Nikon Corporation, Tokyo, Japan), chosen to minimize non-common path errors, to a monochromatic CCD science camera used for retinal imaging (Pike F-421B, Allied Vision Technologies GmbH, Stadtroda, Germany). An adjustable iris between the two photographic objectives limits the pupil size and corresponds to a diameter of 6 mm at the eye.

The retinal image camera CCD has a format of 2048 × 2048 pixels, with a pixel size of 7.4 μm, corresponding to an area of 15.2 × 15.2 mm². This corresponds to a retinal FOV of 6.7 × 6.7 deg² (approximately 1.95 × 1.95 mm² according to the eye models used in the simulations). The FWHM of the Airy disk in the retinal image plane at 575 nm is 15 μm and hence the image is sampled according to the Nyquist-Shannon sampling theorem (two pixels per FWHM).

Fig. 3. Side view of GS light paths through the optics of the eye (left). Only the blue (center) rays from the central GS are used in SCAO correction. Also shown are the GS footprints on DM1 (top right) and DM2 (bottom right).

Fig. 4. Layout of the multiobject wavefront sensor with spatial filtering with one adjustable iris (left). This arrangement makes it possible to use a single camera to image the Hartmann patterns of multiple reference sources. Simulated image of Hartmann spot arrangement on the wavefront sensor camera (right).

For in vivo retinal imaging the pupil of the subject’s emmetropic right eye was dilated with 0.5% Tropicamide before imaging. The experiment on a human retina conformed to the tenets of the Declaration of Helsinki and written informed consent was obtained.

2.4. Adaptive optics control loop

Under the assumption that the DM can be described as a linear superposition of the actuator influence functions, the DM actuator commands can be calculated by matrix multiplication:

c = G^{+} s

(1)

where c is an n × 1 vector of DM actuator commands, G is the m × n interaction matrix (G ⁺ is the pseudoinverse of G) and s is an m × 1 vector of measured wavefront slopes. The total number of Hartmann spots in the wavefront sensor image is m/2 and the total number of DM channels is n. The interaction matrix G is constructed by poking individual DM actuators in sequence, starting with the first actuator on DM1 and ending with the last actuator on DM2, i.e., s = Gc. In order to improve the linearity of the system we estimate the partial derivatives by poking each actuator with a positive and a negative unit poke applied with respect to a chosen DM bias voltage and calculating an average response

\partial s_{i} / \partial c_{j} = [s_{i} (c_{j +}) - s_{i} (c_{j -})] / [(c_{j +}) - (c_{j -})]

(2)

where s_i (c _j+) and s_i (c _j-) are signals obtained with the positive and negative unit voltages, respectively [13

A. V. Goncharov, J. C. Dainty, S. Esposito, and A. Puglisi, “Laboratory MCAO test-bed for developing wavefront sensing concepts,” Opt. Express 13, 5580–5590 (2005). [CrossRef] [PubMed]

The interaction matrix G is over-determined and the inverse cannot be computed by ordinary matrix inversion. The reconstructor matrix G ⁺ is instead calculated using singular value decomposition (SVD) since

G = {UΛV}^{T}

(3)

where U is an m × m unitary matrix, Λ is an m × n diagonal matrix with nonzero diagonal elements and all other elements equal to zero, and V ^T is the transpose of V, an n × n unitary matrix. The non-zero diagonal elements λ_i of Λ are the singular values of G. The pseudoinverse of G can now be computed as

G^{+} = {VΛ}^{+} U^{T}

(4)

which is also the least squares solution to Eq. (1). The diagonal values of Λ are set to λ_i ^-1, or zero if λ_i is less than a defined threshold value. Non-zero singular values correspond to correctable modes of the system and removing modes with very small singular values will reduce noise sensitivity.

For each temporal sample in the control loop, incremental signals are obtained according to Eq. (1). In order to increase stability, these are multiplied with a gain g ∈ [0,1] before they are added to the integrated mirror commands. Software for control of one or two DM and one to five GS was developed, implemented, and tested by Landell [19

D. Landell, Implementation and optimization of a multi conjugate adaptive optics software system for vision research (Güteborg, Chalmers University of Technology 2005).

3. Simulation results

An optical model of the full setup comprising realistic implementation of all optical components was established in Zemax. Two eye models, the Navarro 99 eye [20

I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A 16, 1881–1891 (1999). [CrossRef]

] and the Liou-Brennan eye [21

H.-L. Liou and N.A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1694 (1997). [CrossRef]

], were alternatively used to simulate the eye’s optics. A centered physical pupil diameter of 5.6 mm was chosen for both eye models. The DM were modeled as Zernike polynomial sag surfaces in reasonable accordance with the number of actuators, DM1 correcting up to fourth order Zernike terms (12 terms, excluding piston, tip, and tilt), and DM2 correcting up to fifth order Zernike terms (18 terms, excluding piston, tip, and tilt). Closed loop performance of the system was emulated using the optimization routine in Zemax with the mirror Zernike coefficients as variables. In accordance with the format of the lenslet array a pupil sampling of 10 × 10 points was used to optimize the DM surfaces. Although the procedure is not as described in the AO control loop above (section 2.4) it is believed to adequately simulate expected performance. SCAO was modeled by controlling the pupil DM with the axial GS, and DCAO was modeled by controlling both DM with all five GS. All angular measures in the following Zemax simulations are in visual angle. Strehl values are referred to the centroid of the geometrical spot diagram, i.e. tip/tilt errors are excluded.

3.1. Navarro 99 eye model simulations

According to our calculations the diameter of the diffraction-limited FOV (Strehl ≥ 0.8) at a wavelength of 834 nm increased from around 2.5 deg with SCAO to just over 8.4 deg with DCAO (Fig. 5, top left and right, respectively). The change in wavelength from 834 nm to 575 nm results in a chromatic focal shift at the imaging camera of -11.2 mm and refocusing is needed to compensate for this longitudinal chromatic aberration. There will be a Strehl loss over the entire FOV due to chromaticity of aberrations inherent in the eye [22

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990). [CrossRef] [PubMed]

] and the eye models. Furthermore, Strehl loss is induced when imaging at a shorter wavelength than the wavefront sensing wavelength even for an achromatic eye because of the Strehl value dependence on the optical path difference RMS in waves. The result is a slightly smaller corrected FOV and lower on-axis Strehl ratio at the imaging wavelength. The diameter of the diffraction-limited FOV at an imaging wavelength of 575 nm increased from around 1.5 deg with SCAO to approximately 6.5 deg with DCAO (see Fig. 5 and Fig. 6). For a wavefront error of 1 rad or less (Strehl ≤ 0.37) the isoplanatic patch increases from a diameter of around 3.0 deg with SCAO to approximately 7.4 deg with DCAO.

The estimated required stroke range for DM2 (conjugate to a plane inside the eye) is 25.3 μm PTV over an active diameter of 24 mm. The estimate for DM1 (conjugate to the pupil) was a stroke of 3.3 μm PTV over an active diameter of 10 mm.

Fig. 5. Strehl maps for the Navarro 99 eye model of the corrected FOV obtained with SCAO and DCAO at wavelengths of 834 nm and 575 nm (top row and bottom row, respectively). Each field is 6.7 deg (1.95 mm) square in size.

Fig. 6. Plot for the Navarro 99 eye model of simulated image plane Strehl ratio vs. field angle (vertical meridian) for SCAO and DCAO at 834 nm (left) and at 575 nm for the refocused system (right). Dashed lines indicate diffraction-limited performance, i.e. Strehl ≤ 0.8 (upper), and the less stringent criteria of Strehl ≤ 0.37 (lower).

3.2. Liou-Brennan eye model simulations

The predicted performance may depend upon the implemented eye model, and since the only previous MCAO simulations [16

] were based on the Liou-Brennan eye model the DCAO setup was also analyzed using this model. The main differences from the Navarro 99 eye are the gradient index lens, dispersion characteristics, and that the Liou-Brennan eye was designed for central visual axis performance. However, to include off axis performance a retinal radius of curvature of 12 mm was used in our simulations in correspondence with [16

]. The model was implemented in Zemax using the “Gradient 5” surface for the gradient index lens. Dispersion was emulated by changing the refractive index in the lens-model according to the formula given in [21

H.-L. Liou and N.A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1694 (1997). [CrossRef]

]. The chromatic focal shift at the retinal image plane was -5.1 mm, depicting significantly lower dispersion. The diameter of the diffraction-limited FOV (Strehl ≤ 0.8) at a wavelength of 834 nm increased from a diameter of about 4 deg with SCAO to just over 9 deg with DCAO. The corresponding FOV at 575 nm increased from a diameter of around 3.1 deg with SCAO to approximately 8.2 deg with DCAO (see Fig. 7 and Fig. 8). This is in reasonable agreement with [16

] at the imaging wavelength of 575 nm. For a wavefront error of 1 rad the isoplanatic patch increased from a diameter of around 4.8 deg with SCAO to approximately 9.6 deg with DCAO.

Fig. 7. Strehl maps for the Liou-Brennan eye model of the corrected FOV obtained with SCAO and DCAO at wavelengths of 834 nm and 575 nm (top row and bottom row, respectively). Each field is 6.7 deg (1.95 mm) square in size.

Fig. 8. Plot for the Liou-Brennan eye model of simulated image plane Strehl ratio vs. field angle (vertical meridian) for SCAO and DCAO at 834 nm (left) and at 575 nm for the refocused system (right). Dashed lines indicate diffraction-limited performance, i.e. Strehl ≤ 0.8 (upper), and the less stringent criteria of Strehl ≤ 0.37 (lower).

Zemax simulations with the Liou-Brennan eye model estimate the required stroke range for DM2 (conjugate to a plane inside the eye) to 10.7 μm PTV over an active diameter of 24 mm. The estimate for DM1 (conjugate to the pupil) was a stroke of 0.7 μm PTV over an active diameter of 10 mm.

4. Experimental results

A through focus image sequence of five separate GS beams passing the pinhole in the multi-object wavefront sensor is shown in Fig. 9. We found the arrangement of the array of five collimating lenses in this DCAO setup extremely useful, since it enables the use of a single spatial filter at a point conjugate to the retina to simultaneously filter the light from all five GS. It greatly reduces the complexity of spatial filtering by only requiring the alignment of one instead of five pinholes. Experimental results show that filtering is absolutely necessary in order to get rid of spurious reflections when using multiple GS. Crossed polarizers could be an alternative option, but this would require double the total intensity needed for wavefront sensing, an intensity that increases with the number of implemented GS.

Due to malfunction of the fiber splitter only three GS could be used during the closed loop evaluation, hence limiting the performance of DCAO correction to a subregion of the full FOV. The setup was first tested in the laboratory by imaging a model retina (a raster pattern) placed in the retinal conjugate plane before the Badal focus corrector, with added defocus of 0.5 D and a phase screen placed in front of DM2 to emulate a model eye (Fig. 10). The result of the SCAO correction is primarily a corrected central field around the GS, but also a general improvement of image quality. During DCAO correction the loop could be reliably locked on the three GS (center, lower left and right) resulting in improvement of image quality in a region around these beacons.

Fig. 9. Experimental through focus images of the five separate GS paths passing through the WFS pinhole (middle image). See Fig. 4 for a detailed description of the WFS spatial filter.

Single shot in-vivo retinal images focused on the photoreceptor layer are shown to the left in Fig. 11. Magnified corresponding regions from the uncorrected, SCAO corrected, and DCAO corrected images are shown to the right in Fig. 11 for clarity. SCAO correction is primarily obtained in the center of the FOV, but peripheral areas remain uncorrected. DCAO correction results in an improved image quality in the regions around the three GS. The SVD cutoff value λ_i /λ ₁ was set to 0.06 – 0.07 and the gain g was usually chosen to 0.25 – 0.30. Closed loop correction frequency was around 12 Hz.

Both model and real eye images were flat-fielded using a low-pass filtered image (original image convolved with a σ = 50 pixels Gaussian kernel) to reduce uneven illumination [23

S.B. Howell, Handbook of CCD Astronomy (Cambridge University Press, Cambridge, U.K., 2000)

]. The resulting images were post-processed with a σ = 0.75 pixel Gaussian kernel to reduce shot and readout noise. Gray scale levels were equalized across images.

Power spectra of the subregions in the real eye images are shown in Fig. 12. An increase in amplitude for subregion 4 (approximately 1 deg eccentricity) is seen for the SCAO and DCAO corrected power spectra at a spatial frequency of roughly 220 cycles/mm. The power spectrum amplitude of the more peripheral subregion 5 (approximately 2 deg eccentricity) is further enhanced by DCAO at a spatial frequency of roughly 170 cycles/mm. This corresponds to cone separations of 4.5 and 6 μm, respectively, and is in good agreement with morphological data [24

C.A. Curcio, K.R. Sloan, R.E. Kalina, and A.E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1990). [CrossRef] [PubMed]

5. Discussion and further work

The major gain of DCAO is a clinically useful corrected FOV that potentially has a more than 10 times larger image area than SCAO. This should be sufficient to provide diffraction-limited images with a 6 mm pupil of the central visual field. The primary motivation for DCAO in the eye is that if spherical aberration (SA) is distributed over several surfaces [25

P. Artal, A. Guirao, E. Berrio, and D.R. Williams, “Compensation of corneal aberrations by the internal optics in the human eye,” J. Vis. 1, 1–8 (2001). [CrossRef]

], correction of SA only in the pupil plane will lead to coma across the field. This coma can be reduced by distributing the correction for SA over two separate surfaces, manifested by the two DM in our setup. Additionally, two DM will allow for distributed focus adjustment over the FOV. Unfortunately we could only use three GS in the model and real eye experiments due to a malfunction of the fiber splitter that limited DCAO correction to a subregion of the full FOV. The benefit of this is that we can observe DCAO correction in the lower part of the retinal image, whereas the correction is not obvious in the upper part.

The main limitation of our DCAO system is the corrective power (stroke) of the two DM. The available stroke to correct higher order aberrations is very limited in this type of DM [26

E. Dalimier and J. C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express. 13, 4275–4285 (2005). [CrossRef] [PubMed]

]. This is the most probable explanation for the saturation of DM1 since higher order aberrations are more prominent in real eyes than in eye model predictions. With regards to DM2, the predicted stroke from the Navarro 99 eye model simulations exceeds the specified stroke. However, the 40 mm OKO MMDM was chosen to demonstrate the feasibility of the presented DCAO concept. Numerous actuators on both mirrors are close to or at saturation levels for all subjects, and as such we do not obtain the levels of correction predicted by simulations. A solution to this problem could be to replace one or both DM with a mirror that has larger stroke. There are currently DM on the market that fulfill this need, and this will be a subject of future investigations.

Fig. 10. Images of model retina with 0.5 D defocus introduced by the Badal focus corrector and a phase screen at DM2. FOV corresponds to 6.7 × 6.7 deg² (1.95 × 1.95 mm²) on the retina. Top row (a) is without AO correction, middle row (b) is with SCAO correction, and bottom row (c) is with DCAO correction. Numbered insets centered on GS positions in the original images to the left are shown magnified to the right. GS positions are marked with a white cross.

Fig. 11. Retinal images of foveal region of subject TW; upper (a) uncorrected, middle (b) with SCAO correction, and lower (c) with DCAO correction. FOV corresponds to 6.7 × 6.7 deg² (1.95 × 1.95 mm²) on the retina. GS positions are marked with a white cross. Numbered insets in the original images to the left are shown magnified to the right. Insets 1–3 are centered on GS positions. Insets 4–5 are magnifications of identical regions in the three retinal images.

Fig. 12. Log scaled power spectra with equal inverted gray scales of subregions 4a–c and 5a–c from Fig.11.

We find, in accordance with [16

], that moving DM2 closer to DM1 slightly improves the size of the corrected field, but may require extra relay optics. Hence the location of DM2 was chosen to provide adequate correction over the desired FOV and to avoid extra relay optics. It should be noticed that moving the two DM too close together would cause the optimal distribution of correction between the two to become undetermined and thus affect the stability of the DCAO correction. This was confirmed by our Zemax analysis and is also in accordance with the prediction of [16

] that moving the mirrors together will increase stroke.

It has been suggested that the correction quality of the central beacon must be sacrificed in MCAO compared to SCAO [27

D. C. Johnston and B.M. Welsh, ”Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]

]. Our simulations, however, were performed on a rotationally symmetric eye with very low contributions from higher order aberrations, and including an on axis beacon. This is a very different setting than the layered atmospheric turbulence simulated in [27

D. C. Johnston and B.M. Welsh, ”Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]

]. Simulation results shown in Fig. 6 and Fig. 8 show a decrease of on axis correction in the case of DCAO, however not as pronounced as in [27

D. C. Johnston and B.M. Welsh, ”Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]

] where SCAO outperforms MCAO over the central third of the corrected FOV. Our simulation data are similar to results from [16

] where SCAO outperforms MCAO over a small central region of the FOV.

There are two principal advantages of delivering the GS light over the two DM. Firstly, the system does not suffer from global tip/tilt, i.e. the Hartmann spots are stationary with respect to motion of the GS in the retinal object plane. The second advantage is that delivery of GS light through a large pupil might prove beneficial when investigating older patients with local ocular media opacities that could interfere with GS formation. This demands that the GS light is corrected before entering the eye. Backed by simulations and observations we have noticed that the peripheral GS suffer from astigmatism when imaged through the passive section of the setup. Careful calibration of the system is thus essential for correct DCAO performance. Once this is accomplished the five GS beams act as five individual subsystems.

Constructing a mosaic of several retinal images can enlarge the corrected retinal imaging area even further. A mosaic of just five images, centered on each of the GS, will yield a corrected FOV of approximately 10 × 10 deg. An array of nine images with an overlap of one degree will extend the corrected FOV to approximately 16 × 16 deg. The advantage over a system with a smaller FOV is evident if one considers that it will take around 120 images using an individual 1 deg FOV with an overlap of 0.1 deg to cover 10 × 10 deg, or equivalently around 50 images with a FOV of 1.5 deg.

According to our simulations the Liou-Brennan eye model overestimates the corrected FOV compared to the Navarro 99 eye model (cf. Figs. 5–8), presumably due to the fact that the Liou-Brennan eye model was not designed for off axis modeling. Furthermore the Liou-Brennan eye model does not suffer from chromatic errors to the same extent as the Navarro 99 eye model. The dispersion formula in [21

H.-L. Liou and N.A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1694 (1997). [CrossRef]

] is only valid up to a wavelength of 750 nm, whereas the Navarro 99 eye model dispersion is designed for wavelengths up to 1 μm [28

R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,’ J. Opt. Soc. Am. A 2, 1273–1281 (1985). [CrossRef] [PubMed]

]. Our experimental observations of chromatic shift support the simulated performance of the Navarro 99 eye since we have to significantly refocus the imaging camera during retinal imaging.

The chromatic shift when sensing the wavefront at a wavelength different from the imaging wavelength is a problem for both SCAO and DCAO. An alternative to refocusing the imaging camera is to place a chromatic compensator in the imaging arm [29

Y. Benny, S. Manzanera, P. M. Prieto, E. N. Ribak, and P. Artal, “Wide-angle chromatic aberration corrector for the human eye,” J. Opt. Soc. Am. A 24, 1538–1544 (2007). [CrossRef]

]. Furthermore, higher order aberrations are not predicted by the eye models but are frequent in real eyes [17

]. The consequence of this would be that the two eye models overestimate the size of the isoplanatic patch.

6. Conclusion

We have investigated the performance of a DCAO instrument for wide-field retinal imaging. The expected corrected FOV provided by simulations has been experimentally rendered probable on both a model eye and a real human eye. Preliminary measurements have documented the novel multiobject WFS with spatial filtering to be of crucial importance to acquire clean Hartmann images. Despite limited DM corrective power the preliminary results indicate that DCAO is a feasible method for wide-field high-resolution retinal imaging. However, there is room for improvement, and an increase of DM corrective power is essential in order to enable imaging of patients with larger refractive errors. Further modifications and testing are needed to evaluate the full potential of the DCAO instrument.

Acknowledgments

Swedish research council grant 2003-6254; the Göteborg Medical Society, Göteborg, Sweden; De Blindas Vänner Foundation, Göteborg, Sweden; KMA Foundation, Stockholm, Sweden; Stiftelsen Synfrämjandets Forskningsfond, Stockholm, Sweden. We are greatly in debt to David Landell for writing the custom software for this application, and to Professor emeritus Johan Sjöstrand for his endless support and encouragement. We would also like to acknowledge the support and encouragement from Professor Torben Andersen of the Lund Telescope Group. Special thanks are extended to Professores emeriti Berndt Ehinger and Arne Ardeberg for initiating this collaboration.

References and links

1.	I. Newton, Opticks, or A treatise of the reflections, refractions, inflections & colours of light (New York, Dover publ. 1952).
2.	H. W. Babcock, “The Possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pacif. 65, 229–236 (1953). [CrossRef]
3.	R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 29–31 (1985).
4.	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). [CrossRef]
5.	H. Hofer, J. Carroll, J. Neitz, M. Neitz, and D. R. Williams, “Organization of the human trichromatic cone mosaic,” J. Neurosci. 25, 9669–9679 (2005). [CrossRef] [PubMed]
6.	D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982). [CrossRef]
7.	R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys J. 198, 605–615 (1975). [CrossRef]
8.	J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference and Workshop on Very Large Telescopes and their Instrumentation. Garching, Germany: European Southern Observatory (ESO) (1988).
9.	I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, and J.-P. Veran, “Design of the dual conjugate adaptive optics test-bed,” in Beyond conventional adaptive optics: a conference devoted to the development of adaptive optics for extremely large telescopes. Venice, Italy: European Southern Observatory (ESO) (2001).
10.	B. Wallace, C. Bradley, H. Richardson, J. Kennedy, O. Keskin, P. Hampton, D. Robertson, L. Jolissaint, and A. Hilton, “Dual conjugate adaptive optics testbed: progress report,” Proc. SPIE 5169, 255–261 (2003). [CrossRef]
11.	P.A. Knutsson and M. Owner-Petersen, “Emulation of dual-conjugate adaptive optics on an 8-m class telescope,” Opt. Express 11, 2231–2237 (2003). [CrossRef] [PubMed]
12.	M. Langlois, C. Saunter, C. Dunlop, R. Myers, and G. Love, “Multiconjugate adaptive optics: laboratory experience,” Opt. Express 12, 1689–1699 (2004). [CrossRef] [PubMed]
13.	A. V. Goncharov, J. C. Dainty, S. Esposito, and A. Puglisi, “Laboratory MCAO test-bed for developing wavefront sensing concepts,” Opt. Express 13, 5580–5590 (2005). [CrossRef] [PubMed]
14.	O. von der Lühe, T. Berkefeld, and D. Soltau, “Multi-conjugate solar adaptive optics at the Vacuum Tower Telescope on Tenerife,” C. R. Physique 6, 1139–1147 (2005) [CrossRef]
15.	E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J.-L. Lizon, M. Marchesi, S. Oberti, R. Reiss, J. Santos, C. Soenke, S. Tordo, A. Baruffolo, and P. Bagnara, and The CAMCAO Consortium, “On-sky Testing of the Multi-Conjugate Adaptive Optics Demonstrator,” The Messenger , 129, 8–13 (2007)
16.	P. A. Bedggood, R. Ashman, G. Smith, and A. B. Metha, “Multiconjugate adaptive optics applied to an anatomically accurate human eye model,” Opt. Express 14, 8019–8030 (2006). [CrossRef] [PubMed]
17.	P. Bedggood, M. Daaboul, R. Ashman, G. Smith, and A. Metha, “Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging,” J. Biomed. Opt. 13, 024008 (2008). [CrossRef] [PubMed]
18.	W.S. Stiles and B.H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. B. 112, 428–450 (1933). [CrossRef]
19.	D. Landell, Implementation and optimization of a multi conjugate adaptive optics software system for vision research (Güteborg, Chalmers University of Technology 2005).
20.	I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A 16, 1881–1891 (1999). [CrossRef]
21.	H.-L. Liou and N.A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1694 (1997). [CrossRef]
22.	L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990). [CrossRef] [PubMed]
23.	S.B. Howell, Handbook of CCD Astronomy (Cambridge University Press, Cambridge, U.K., 2000)
24.	C.A. Curcio, K.R. Sloan, R.E. Kalina, and A.E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1990). [CrossRef] [PubMed]
25.	P. Artal, A. Guirao, E. Berrio, and D.R. Williams, “Compensation of corneal aberrations by the internal optics in the human eye,” J. Vis. 1, 1–8 (2001). [CrossRef]
26.	E. Dalimier and J. C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express. 13, 4275–4285 (2005). [CrossRef] [PubMed]
27.	D. C. Johnston and B.M. Welsh, ”Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994). [CrossRef]
28.	R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,’ J. Opt. Soc. Am. A 2, 1273–1281 (1985). [CrossRef] [PubMed]
29.	Y. Benny, S. Manzanera, P. M. Prieto, E. N. Ribak, and P. Artal, “Wide-angle chromatic aberration corrector for the human eye,” J. Opt. Soc. Am. A 24, 1538–1544 (2007). [CrossRef]

OCIS Codes
(330.4300) Vision, color, and visual optics : Vision system - noninvasive assessment
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(330.7326) Vision, color, and visual optics : Visual optics, modeling
(330.7327) Vision, color, and visual optics : Visual optics, ophthalmic instrumentation
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: December 18, 2008
Revised Manuscript: February 19, 2009
Manuscript Accepted: March 2, 2009
Published: March 5, 2009

Virtual Issues
Vol. 4, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Jörgen Thaung, Per Knutsson, Zoran Popovic, and Mette Owner-Petersen, "Dual-conjugate adaptive optics for wide-field high-resolution retinal imaging," Opt. Express 17, 4454-4467 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-6-4454

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References

I. Newton, Opticks, or A treatise of the reflections, refractions, inflections & colours of light (New York, Dover publ. 1952).
H. W. Babcock, "The Possibility of compensating astronomical seeing," Publ. Astron. Soc. Pacif. 65, 229-236 (1953). [CrossRef]
R. Foy and A. Labeyrie, "Feasibility of adaptive telescope with laser probe," Astron. Astrophys. 152, 29-31 (1985).
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). [CrossRef]
H. Hofer, J. Carroll, J. Neitz, M. Neitz, and D. R. Williams, "Organization of the human trichromatic cone mosaic," J. Neurosci. 25, 9669-9679 (2005). [CrossRef] [PubMed]
D. L. Fried, "Anisoplanatism in adaptive optics," J. Opt. Soc. Am. 72, 52-61 (1982). [CrossRef]
R. H. Dicke, "Phase-contrast detection of telescope seeing errors and their correction," Astrophys J. 198, 605-615 (1975). [CrossRef]
J. M. Beckers, "Increasing the size of the isoplanatic patch with multiconjugate adaptive optics," in ESO Conference and Workshop on Very Large Telescopes and their Instrumentation. Garching, Germany: European Southern Observatory (ESO) (1988).
I. Sharf, K. Bell, D. Crampton, J. Fitzsimmons, G. Herriot, L. Jolissaint, B. Lee, H. Richardson, D. van der Kamp, and J.-P. Veran, "Design of the dual conjugate adaptive optics test-bed," in Beyond conventional adaptive optics: a conference devoted to the development of adaptive optics for extremely large telescopes. Venice, Italy: European Southern Observatory (ESO) (2001).
B. Wallace, C. Bradley, H. Richardson, J. Kennedy, O. Keskin, P. Hampton, D. Robertson, L. Jolissaint, and A. Hilton, "Dual conjugate adaptive optics testbed: progress report," Proc. SPIE 5169, 255-261 (2003). [CrossRef]
P. A. Knutsson and M. Owner-Petersen, "Emulation of dual-conjugate adaptive optics on an 8-m class telescope," Opt. Express 11, 2231-2237 (2003). [CrossRef] [PubMed]
M. Langlois, C. Saunter, C. Dunlop, R. Myers, and G. Love, "Multiconjugate adaptive optics: laboratory experience," Opt. Express 12, 1689-1699 (2004). [CrossRef] [PubMed]
A. V. Goncharov, J. C. Dainty, S. Esposito, and A. Puglisi, "Laboratory MCAO test-bed for developing wavefront sensing concepts," Opt. Express 13, 5580-5590 (2005). [CrossRef] [PubMed]
O. von der Lühe, T. Berkefeld, and D. Soltau, "Multi-conjugate solar adaptive optics at the Vacuum Tower Telescope on Tenerife," C. R. Physique 6, 1139-1147 (2005). [CrossRef]
E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J.-L. Lizon, M. Marchesi, S. Oberti, R. Reiss, J. Santos, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, and The CAMCAO Consortium," On-sky Testing of the Multi-Conjugate Adaptive Optics Demonstrator," The Messenger, 129, 8-13 (2007).
P. A. Bedggood, R. Ashman, G. Smith, and A. B. Metha, "Multiconjugate adaptive optics applied to an anatomically accurate human eye model," Opt. Express 14, 8019-8030 (2006). [CrossRef] [PubMed]
P. Bedggood, M. Daaboul, R. Ashman, G. Smith, and A. Metha, "Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging," J. Biomed. Opt. 13, 024008 (2008). [CrossRef] [PubMed]
W. S. Stiles and B. H. Crawford, "The luminous efficiency of rays entering the eye pupil at different points," Proc. R. Soc. B. 112, 428-450 (1933). [CrossRef]
D. Landell, Implementation and optimization of a multi conjugate adaptive optics software system for vision research (Göteborg, Chalmers University of Technology 2005).
I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye model," J. Opt. Soc. Am. A 16, 1881-1891 (1999). [CrossRef]
H.-L. Liou and N. A. Brennan, "Anatomically accurate, finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1694 (1997). [CrossRef]
L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, and P. A. Howarth, "Theory and measurement of ocular chromatic aberration," Vision Res. 30, 33-49 (1990). [CrossRef] [PubMed]
S. B. Howell, Handbook of CCD Astronomy (Cambridge University Press, Cambridge, U.K., 2000)
C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, "Human photoreceptor topography," J. Comp. Neurol. 292, 497-523 (1990). [CrossRef] [PubMed]
P. Artal, A. Guirao, E. Berrio, D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vis. 1, 1-8 (2001). [CrossRef]
E. Dalimier and J. C. Dainty, "Comparative analysis of deformable mirrors for ocular adaptive optics," Opt. Express. 13, 4275-4285 (2005). [CrossRef] [PubMed]
D. C. Johnston and B. M. Welsh, "Analysis of multiconjugate adaptive optics," J. Opt. Soc. Am. A 11, 394-408 (1994). [CrossRef]
R. Navarro, J. Santamaría, and J. Bescós, ‘‘Accommodation-dependent model of the human eye with aspherics,’’J. Opt. Soc. Am. A 2, 1273-1281 (1985). [CrossRef] [PubMed]
Y. Benny, S. Manzanera, P. M. Prieto, E. N. Ribak, and P. Artal, "Wide-angle chromatic aberration corrector for the human eye," J. Opt. Soc. Am. A 24, 1538-1544 (2007). [CrossRef]

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