Abstract

Aberrations of both astronomical telescopes and the human eye can be successfully corrected with conventional adaptive optics. This produces diffraction-limited imagery over a limited field of view called the isoplanatic patch. A new technique, known as multiconjugate adaptive optics, has been developed recently in astronomy to increase the size of this patch. The key is to model atmospheric turbulence as several flat, discrete layers. A human eye, however, has several curved, aspheric surfaces and a gradient index lens, complicating the task of correcting aberrations over a wide field of view. Here we utilize a computer model to determine the degree to which this technology may be applied to generate high resolution, wide-field retinal images, and discuss the considerations necessary for optimal use with the eye. The Liou and Brennan schematic eye simulates the aspheric surfaces and gradient index lens of real human eyes. We show that the size of the isoplanatic patch of the human eye is significantly increased through multiconjugate adaptive optics.

© 2006 Optical Society of America

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References

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  1. J. Liang and D. R. Williams, "Aberrations and retinal image quality of the normal human eye," J. Opt. Soc. Am. A 14, 2873-2883 (1997).
    [CrossRef]
  2. 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]
  3. R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
    [CrossRef] [PubMed]
  4. D. C. Johnston and B. M. Welsh, "Analysis of multiconjugate adaptive optics," J. Opt. Soc. Am. A 11, 394-408 (1994).
    [CrossRef]
  5. P. Piatrou and L. Gilles, "Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics," Appl. Opt. 44, 1003-1010 (2005).
    [CrossRef] [PubMed]
  6. B. L. Ellerbroek, L. Gilles, and C. R. Vogel, "Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes," Appl. Opt. 42, 4811-4818 (2003).
    [CrossRef] [PubMed]
  7. M. Lloyd-Hart and N. M. Milton, "Fundamental limits on isoplanatic correction with multiconjugate adaptive optics," J. Opt. Soc. Am. A 20, 1949-1957 (2003).
    [CrossRef]
  8. 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]
  9. A. Tokovinin, M. Le Louarn, and M. Sarazin, "Isoplanatism in a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 17, 1819-1827 (2000).
    [CrossRef]
  10. G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
    [CrossRef] [PubMed]
  11. 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]
  12. H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
    [CrossRef] [PubMed]
  13. J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, "Monochromatic aberrations of the human eye in a large population," J. Opt. Soc. Am. A 18, 1793-1803 (2001).
    [CrossRef]
  14. 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]
  15. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition ed. (John Wiley and Sons, Inc., 1982).
  16. L. Levine, "Effective degree of mydriasis with phenylephrine and tropicamide," Am. J. Optom. Physiol. Opt. 53, 774-785 (1976).
    [CrossRef] [PubMed]
  17. M. Le Louarn and M. Tallon, "Analysis of modes and behavior of a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 19, 912-925 (2002).
    [CrossRef]
  18. G. Smith and D. Atchison, The Eye and Visual Optical Instruments (Cambridge University Press, 1997).
    [CrossRef]
  19. B. L. Ellerbroek, "First-order performance evaluation of adaptive-optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes," J. Opt. Soc. Am. A 11, 783-804 (1994).
    [CrossRef]
  20. A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE Press, 1988).
  21. M. Born and E. Wolf, Principles of Optics, Fifth ed. (Oxford: Pergamon Press, 1975).
  22. 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]
  23. D. A. Atchison, "Design of aspheric intraocular lenses," Ophthalmic Physiol. Opt. 11, 137-146 (1991).
    [CrossRef] [PubMed]

2005 (2)

2004 (1)

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

2001 (3)

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, "Monochromatic aberrations of the human eye in a large population," J. Opt. Soc. Am. A 18, 1793-1803 (2001).
[CrossRef]

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

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]

2000 (2)

R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
[CrossRef] [PubMed]

A. Tokovinin, M. Le Louarn, and M. Sarazin, "Isoplanatism in a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 17, 1819-1827 (2000).
[CrossRef]

1999 (1)

1997 (3)

1994 (2)

1991 (1)

D. A. Atchison, "Design of aspheric intraocular lenses," Ophthalmic Physiol. Opt. 11, 137-146 (1991).
[CrossRef] [PubMed]

1976 (1)

L. Levine, "Effective degree of mydriasis with phenylephrine and tropicamide," Am. J. Optom. Physiol. Opt. 53, 774-785 (1976).
[CrossRef] [PubMed]

Applegate, R. A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Artal, P.

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]

Atchison, D. A.

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

D. A. Atchison, "Design of aspheric intraocular lenses," Ophthalmic Physiol. Opt. 11, 137-146 (1991).
[CrossRef] [PubMed]

Barnett, J. K.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Berrio, E.

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]

Brennan, N. A.

Cheng, H.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Cox, I. G.

Dainty, J. C.

Ellerbroek, B. L.

Escudero-Sanz, I.

Esposito, S.

Gilles, L.

Goncharov, A. V.

Guirao, A.

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]

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, "Monochromatic aberrations of the human eye in a large population," J. Opt. Soc. Am. A 18, 1793-1803 (2001).
[CrossRef]

Johnston, D. C.

Kasthurirangan, S.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Le Louarn, M.

Levine, L.

L. Levine, "Effective degree of mydriasis with phenylephrine and tropicamide," Am. J. Optom. Physiol. Opt. 53, 774-785 (1976).
[CrossRef] [PubMed]

Liang, J.

Liou, H.-L.

Lloyd-Hart, M.

Marchetti, E.

R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
[CrossRef] [PubMed]

Marsack, J. D.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Miller, D. T.

Milton, N. M.

Navarro, R.

Piatrou, P.

Porter, J.

Puglisi, A.

Ragazzoni, R.

R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
[CrossRef] [PubMed]

Roorda, A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Sarazin, M.

Smith, G.

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

Tallon, M.

Tokovinin, A.

Valente, G.

R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
[CrossRef] [PubMed]

Vilupuru, A. S.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

Vogel, C. R.

Welsh, B. M.

Williams, D. R.

Am. J. Optom. Physiol. Opt. (1)

L. Levine, "Effective degree of mydriasis with phenylephrine and tropicamide," Am. J. Optom. Physiol. Opt. 53, 774-785 (1976).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Opt. Soc. Am. A (10)

M. Lloyd-Hart and N. M. Milton, "Fundamental limits on isoplanatic correction with multiconjugate adaptive optics," J. Opt. Soc. Am. A 20, 1949-1957 (2003).
[CrossRef]

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

B. L. Ellerbroek, "First-order performance evaluation of adaptive-optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes," J. Opt. Soc. Am. A 11, 783-804 (1994).
[CrossRef]

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]

J. Liang and D. R. Williams, "Aberrations and retinal image quality of the normal human eye," J. Opt. Soc. Am. A 14, 2873-2883 (1997).
[CrossRef]

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]

A. Tokovinin, M. Le Louarn, and M. Sarazin, "Isoplanatism in a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 17, 1819-1827 (2000).
[CrossRef]

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, "Monochromatic aberrations of the human eye in a large population," J. Opt. Soc. Am. A 18, 1793-1803 (2001).
[CrossRef]

M. Le Louarn and M. Tallon, "Analysis of modes and behavior of a multiconjugate adaptive optics system," J. Opt. Soc. Am. A 19, 912-925 (2002).
[CrossRef]

J. Vis. (2)

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vis. 4, 272-280 (2004).
[CrossRef] [PubMed]

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]

Nature (1)

R. Ragazzoni, E. Marchetti, and G. Valente, "Adaptive-optics corrections available for the whole sky," Nature 403, 54-56 (2000).
[CrossRef] [PubMed]

Ophthalmic Physiol. Opt. (2)

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

D. A. Atchison, "Design of aspheric intraocular lenses," Ophthalmic Physiol. Opt. 11, 137-146 (1991).
[CrossRef] [PubMed]

Opt. Express (1)

Other (4)

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition ed. (John Wiley and Sons, Inc., 1982).

G. Smith and D. Atchison, The Eye and Visual Optical Instruments (Cambridge University Press, 1997).
[CrossRef]

A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE Press, 1988).

M. Born and E. Wolf, Principles of Optics, Fifth ed. (Oxford: Pergamon Press, 1975).

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Figures (9)

Fig. 1.
Fig. 1.

Geometry of reference beacons on retina.

Fig. 2.
Fig. 2.

Contour plot of RMS error vs eccentricity in the uncorrected Liou Brennan schematic eye. Initials denote retinal position with respect to the optical axis, where S = superior, I = inferior, N = nasal, T = temporal.

Fig. 3.
Fig. 3.

Contour plot of RMS error vs eccentricity in the Liou Brennan schematic eye corrected with a phase plate conjugate to the pupil.

Fig. 4.
Fig. 4.

Plot of RMS error vs eccentricity in horizontal meridian, for the uncorrected Liou Brennan eye, the same eye corrected with a phase plate at the exit pupil, and the theoretical diffraction limit given by the Marechal criterion.

Fig. 5.
Fig. 5.

Radius of the isoplanatic patch depends on the angular separation of the beacons. The zero degree separation case indicates the patch obtained with conventional adaptive optics. The mean radius was calculated from the radii of the whole patch (i.e. not just from the average of the horizontal/vertical and oblique meridia).

Fig. 6.
Fig. 6.

Contour plot of RMS error vs eccentricity in the Liou Brennan schematic eye for the MCAO case (solid line) compared to the conventional AO case (dashed line).

Fig. 7.
Fig. 7.

Plot of RMS error vs eccentricity in the horizontal meridian, for conventional AO at the pupil, the same eye corrected via MCAO with 5 mirrors and 5 beacons, and the theoretical diffraction limit given by the Marechal criterion.

Fig. 8.
Fig. 8.

Plot of corrector position combinations vs total corrector stroke for the simplified case of 2 correctors and 2 beacons. Combinations were measured in 0.5mm increments and the results interpolated to produce the color map. The black region represents redundant combinations of corrector positions.

Fig. 9.
Fig. 9.

Plot of corrector position combinations vs patch diameter in the horizontal meridian for the simplified case of 2 correctors and 2 beacons. Combinations were measured in 0.5mm increments, and wavefronts were measured in 1.25° increments. The results were interpolated to produce the color map. The black region represents redundant combinations of corrector positions.

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