Abstract

The optical quality of the human eye varies across the visual field. Hence an exact compensation of the eye aberration for a given field point can give rise to a less-than-optimum compensation in neighboring field regions. We have studied some aspects of this problem and present here an approach to design wide-field (<10°) optically thin correcting elements, e.g., phase plates, deformable mirrors, and liquid-crystal displays. Their expected performance is assessed using actual eye aberration data. Particular attention is given to the design of elements providing a minimum averaged rms residual aberration and those providing a nearly uniform rms residual aberration across a given field.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  10. P. M. Prieto, F. Vargas-Martin, S. Goelz, P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
    [CrossRef]
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    [CrossRef]
  13. E. Moreno-Barriuso, S. Marcos, R. Navarro, S. A. Burns, “Comparing laser ray tracing, spatially resolved refractometer and Hartmann–Shack sensor to measure the ocular wavefront aberration,” Optom. Vision Sci. 78, 152–156 (2001).
    [CrossRef]
  14. R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
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    [CrossRef]
  16. J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]
  17. L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
    [CrossRef]
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    [CrossRef]
  23. R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
    [CrossRef]
  24. L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
    [CrossRef]
  25. G. Smith, D. A. Atchinson, C. Avudainayagam, K. Avudainayagam, “Designing lenses to correct peripheral refractive errors of the eye,” J. Opt. Soc. Am. A 19, 10–18 (2002).
    [CrossRef]
  26. A. Guirao, J. Porter, D. R. Williams, I. G. Cox, “Calculated impact of high-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19, 620–628 (2002).
    [CrossRef]
  27. G. Y. Yoon, D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19, 266–275 (2002).
    [CrossRef]
  28. S. Bará, T. Mancebo, E. Moreno-Barriuso, “Positioning tolerances for phase plates compensating aberrations of the human eye,” Appl. Opt. 39, 3413–3420 (2000).
    [CrossRef]
  29. J. Porter, A. Guirao, I. G. Cox, D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001).
    [CrossRef]
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2002 (4)

2001 (3)

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

E. Moreno-Barriuso, S. Marcos, R. Navarro, S. A. Burns, “Comparing laser ray tracing, spatially resolved refractometer and Hartmann–Shack sensor to measure the ocular wavefront aberration,” Optom. Vision Sci. 78, 152–156 (2001).
[CrossRef]

E. J. Fernández, I. Iglesias, P. Artal, “Closed-loop adaptive optics in the human eye,” Opt. Lett. 26, 746–748 (2001).
[CrossRef]

2000 (4)

1999 (2)

1998 (4)

1997 (3)

1994 (1)

1992 (1)

1980 (1)

1977 (2)

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce members, “Standards for Reporting the Optical Aberrations of Eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Artal, P.

Atchinson, D. A.

Avudainayagam, C.

Avudainayagam, K.

Bará, S.

Bartsch, D. W.

L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Bille, J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), Chap. 5, pp. 203–207.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), pp. 464–468, 767–772.

Burns, S. A.

Cox, I. G.

DeVore, S. L.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

Dorronsoro, C.

Elsner, A. E.

Fainman, Y.

L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Fernández, E. J.

Freeman, W. R.

L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Goelz, S.

Grimm, B.

Guirao, A.

He, J. C.

Herrmann, J.

Howland, B.

Howland, H. C.

Iglesias, I.

Liang, J.

Love, G. D.

Malacara, D.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

Mancebo, T.

Marcos, S.

Medoff, B. P.

B. P. Medoff, “Image reconstruction from limited data: theory and applications in computerized tomography,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), Chap. 9.

Miller, D. T.

Moreno, E.

Moreno-Barriuso, E.

Navarro, R.

Penney, C. M.

Porter, J.

Prieto, P. M.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce members, “Standards for Reporting the Optical Aberrations of Eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Silva, D. E.

Smith, G.

Sun, P.

L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce members, “Standards for Reporting the Optical Aberrations of Eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Thompson, K. P.

Vargas-Martin, F.

von Helmholtz, H.

H. von Helmholtz, Popular Scientific Lectures, M. Kline, ed. (Dover, New York, 1962).

Wang, J. Y.

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce members, “Standards for Reporting the Optical Aberrations of Eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

Webb, R. H.

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), pp. 464–468, 767–772.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), Chap. 5, pp. 203–207.

Yoon, G. Y.

Zhu, L.

L. Zhu, P. Sun, D. W. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (12)

J. Liang, B. Grimm, S. Goelz, J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eye across the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
[CrossRef]

F. Vargas-Martin, P. M. Prieto, P. Artal, “Correction of the aberrations in the human eye with a liquid-crystal spatial light modulator: limits to performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998).
[CrossRef]

J. Liang, 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, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

E. Moreno-Barriuso, R. Navarro, “Laser ray-tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000).
[CrossRef]

P. M. Prieto, F. Vargas-Martin, S. Goelz, P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

J. Porter, A. Guirao, I. G. Cox, 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, D. A. Atchinson, C. Avudainayagam, K. Avudainayagam, “Designing lenses to correct peripheral refractive errors of the eye,” J. Opt. Soc. Am. A 19, 10–18 (2002).
[CrossRef]

G. Y. Yoon, D. R. Williams, “Visual performance after correcting the monochromatic and chromatic aberrations of the eye,” J. Opt. Soc. Am. A 19, 266–275 (2002).
[CrossRef]

A. Guirao, J. Porter, D. R. Williams, I. G. Cox, “Calculated impact of high-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19, 620–628 (2002).
[CrossRef]

Opt. Lett. (4)

Optom. Vision Sci. (2)

E. Moreno-Barriuso, S. Marcos, R. Navarro, S. A. Burns, “Comparing laser ray tracing, spatially resolved refractometer and Hartmann–Shack sensor to measure the ocular wavefront aberration,” Optom. Vision Sci. 78, 152–156 (2001).
[CrossRef]

L. Zhu, D. W. Bartsch, W. R. Freeman, P. Sun, Y. Fainman, “Modeling human eye aberrations and their compensation for high-resolution retinal imaging,” Optom. Vision Sci. 75, 827–839 (1998).
[CrossRef]

Other (6)

B. P. Medoff, “Image reconstruction from limited data: theory and applications in computerized tomography,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), Chap. 9.

H. von Helmholtz, Popular Scientific Lectures, M. Kline, ed. (Dover, New York, 1962).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), Chap. 5, pp. 203–207.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1987), pp. 464–468, 767–772.

D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce members, “Standards for Reporting the Optical Aberrations of Eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.

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Figures (6)

Fig. 1
Fig. 1

Eye aberration maps for five different positions across the visual field of subjects EM, RN, and CD. Gray levels span one wavelength (543 nm). The on-axis defocus has been subtracted in all cases.

Fig. 2
Fig. 2

Overall rms aberration including all terms (excepting tilts) of subjects EM (circles), RN (squares), and CD (triangles) for five positions across the visual field.

Fig. 3
Fig. 3

Aberration coefficients ai for subject EM for five positions across the visual field. Circles, i=4 (defocus, including the on-axis measured value); squares, i=5 (astigmatism at 0° or 90°); diamonds, i=8 (third-order coma along x axis); and triangles, i=12 (spherical aberration).

Fig. 4
Fig. 4

Maps of the EM wave aberration, with the gray-scale levels spanning one wavelength of optical path (543 nm). Pupil diameter 6.7 mm. Each column corresponds to a different position within the foveal and parafoveal field: 0°, 5°, and 10°, as noted. All terms in the aberration function have been included, excepting for the tilt. Upper row, uncompensated eye; second row, eye compensated with w=[100]; third row, same with w=(1/2)[110]; fourth row, same with w=(1/3)[111]; fifth row, same with an optimal element designed to achieve the smallest uniform variance at these three positions of the field. Note the smaller residual aberration at 10° and the slightly higher one at 0° and 5° in comparison with the fourth row.

Fig. 5
Fig. 5

PSFs for subject EM computed from the wave aberrations shown in Fig. 4. The pupil diameter is 6.7 mm and the wavelength 543 nm.

Fig. 6
Fig. 6

Residual rms aberration for subjects (a) EM, (b) RN, and (c) CD. ●, before compensation; after compensation with an element designed with ■, w=[100]; ▲, w=(1/2)[110]; ♦, w=(1/3)[111]; ○, after compensation with optimum coefficients for maximum uniformity for three positions across the visual field. The pupil diameter is 6.7 mm and the wavelength 543 nm.

Equations (29)

Equations on this page are rendered with MathJax. Learn more.

We(r, α)=i=0ai(α)Zi(r/R),
1πR2 PZi(r/R)Zj(r/R)d2r,
σ2(α)=1Ap P[We(r, α)-W¯e(r, α)]2d2r,
σ2=i=1 ai2.
Wr(r, α)=WC(r)+We(r, α).
Wc(r)=i=1N ciZi(r/R),
Wr(r, α)=i=1[ci+ai(α)]Zi(r/R),
σ2(α)=i=1N[ci+ai(α)]2+i=N+1[ai(α)]2,
σ2σ2(α)=Aω(α)σ2(α)d2α,
Aω(α)d2α=1.
ci=-Aω(α)ai(α)d2α,(i=1, , N).
ci=-ai(α),(i=1, , N).
ω(α)=k=1Mωkδ(α-αk),
k=1Mωk=1,
σ2=k=1Mωkσ2(αk).
ci=-k=1Mωkai(αk).
η[σ2(α)-σ2(α)]2,
η=4Mk=1Mi=1N(Akici-δki)2,
Aki=ai(αk)-ai(αk),
δki=(-1/2)[ai2(αk)-ai2(αk)].
ν=Ac-d,
dk=i=1Ndki.
c=(ATA)-1ATd,
c=A+d+(I-A+A)y,
AA+A=A,A+AA+=A+,(AA+)T=AA+,(A+A)T=A+A.
σ2(α)=1Mk=1Mσ2(αk)=1Mk=1Mi=1N[ai(αk)+ci]2.
σ2(α)=1Mk=1Mi=1Nai(αk)+ci0+j=1NPijyj2.
c=c0+Pa=A+d+(I-A+A)a,
ai(α)=1Mk=1Mai(αk).

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