Abstract

A schematic eye model based on anatomical data, which had been previously designed to reproduce image quality on axis, has been transformed into a wide-angle model by simply adding a spherical image surface that plays the role of the retina. This model captures the main features of the wide-angle optical design of the human eye with minimum complexity: four conic optical surfaces plus a spherical image surface. Seidel aberrations (spherical aberration, coma, astigmatism, field curvature, and distortion), longitudinal and transverse chromatic aberrations, and overall monochromatic spot diagrams have been computed for this eye model and for field angles ranging from 0° to 60° by both finite and third-order ray tracing. The modulation transfer function for each field angle has been computed as well. In each case our results have been compared with average experimental data found in the literature, showing a reasonably good agreement. The agreement between the model and experimental data is better off axis, mainly at moderate (10°–40°) field angles, than on axis. The model has been applied to simulate a variety of experimental methods in which image aberrations are estimated from measurements taken in the object space. Our results suggest that for some types of aberration, these methods may yield biased estimates.

© 1999 Optical Society of America

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  3. L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. Y. Wang, L. N. Thibos, “Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 557–562 (1997).
    [CrossRef]
  6. O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
    [CrossRef] [PubMed]
  7. F. W. Fitzke, “A new schematic eye and its applications to psychophysics,” presented at the Optical Society of America Topical Meeting on Recent Advances in Vision, Sarasota, Fla., April 30–May 3, 1980.
  8. H.-L. Liou, N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1695 (1997).
    [CrossRef]
  9. D. A. Atchison, G. Smith, “Continuous gradient index and shell models of the human lens,” Vision Res. 35, 2529–2538 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
    [CrossRef]
  13. 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, 1–8 (1998).
    [CrossRef]
  14. R. Navarro, J. Santamaría, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
    [CrossRef] [PubMed]
  15. W. Lotmar, “Theoretical eye model with aspherics,” J. Opt. Soc. Am. 61, 1522–1529 (1971).
    [CrossRef]
  16. W. Lotmar, T. Lotmar, “Peripheral astigmatism in the human eye: experimental data and theoretical model predictions,” J. Opt. Soc. Am. 64, 510–513 (1974).
    [CrossRef] [PubMed]
  17. M. C. M. Dunne, D. A. Barnes, “Modelling oblique astigmatism in eyes with known peripheral refraction and optical dimensions,” Ophthalmic Physiol. Opt. 10, 46–48 (1990).
    [CrossRef] [PubMed]
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  19. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
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  20. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986).
  21. M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 39, 370–376 (1949).
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  22. W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
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  23. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  24. 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]
  25. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); [Biophysics (USSR) 6, 776–795 (1962]. That basic idea was later adopted by different authors: M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990);R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular local wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
    [CrossRef] [PubMed]
  26. F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
    [CrossRef] [PubMed]
  27. M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).
  28. Y. U. Ogboso, H. E. Bedell, “Magnitude of lateral chromatic aberration across the retina of the human eye,” J. Opt. Soc. Am. A 4, 1666–1672 (1987).
    [CrossRef] [PubMed]
  29. R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [CrossRef] [PubMed]
  30. D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
    [CrossRef] [PubMed]

1998 (2)

1997 (5)

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

Y. Wang, L. N. Thibos, “Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 557–562 (1997).
[CrossRef]

H.-L. Liou, N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14, 1684–1695 (1997).
[CrossRef]

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

1996 (1)

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

1995 (1)

D. A. Atchison, G. Smith, “Continuous gradient index and shell models of the human lens,” Vision Res. 35, 2529–2538 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1992 (1)

1990 (2)

M. C. M. Dunne, D. A. Barnes, “Modelling oblique astigmatism in eyes with known peripheral refraction and optical dimensions,” Ophthalmic Physiol. Opt. 10, 46–48 (1990).
[CrossRef] [PubMed]

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

1987 (1)

1985 (2)

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[CrossRef] [PubMed]

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

1984 (1)

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

1983 (1)

1977 (1)

1974 (2)

W. Lotmar, T. Lotmar, “Peripheral astigmatism in the human eye: experimental data and theoretical model predictions,” J. Opt. Soc. Am. 64, 510–513 (1974).
[CrossRef] [PubMed]

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

1971 (2)

W. Lotmar, “Theoretical eye model with aspherics,” J. Opt. Soc. Am. 61, 1522–1529 (1971).
[CrossRef]

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[CrossRef] [PubMed]

1961 (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); [Biophysics (USSR) 6, 776–795 (1962]. That basic idea was later adopted by different authors: M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990);R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular local wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
[CrossRef] [PubMed]

1949 (1)

Artal, P.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

Atchison, D. A.

D. A. Atchison, G. Smith, “Continuous gradient index and shell models of the human lens,” Vision Res. 35, 2529–2538 (1995).
[CrossRef] [PubMed]

Barnes, D. A.

M. C. M. Dunne, D. A. Barnes, “Modelling oblique astigmatism in eyes with known peripheral refraction and optical dimensions,” Ophthalmic Physiol. Opt. 10, 46–48 (1990).
[CrossRef] [PubMed]

Bedell, H. E.

Bescós, J.

Bille, J. F.

Bradley, A.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

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

Brainard, D. H.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Brennan, N. A.

Burns, S. A.

Charman, W. N.

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[CrossRef] [PubMed]

Dorronsoro, C.

Dufault, P.

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

Dunne, M. C. M.

M. C. M. Dunne, D. A. Barnes, “Modelling oblique astigmatism in eyes with known peripheral refraction and optical dimensions,” Ophthalmic Physiol. Opt. 10, 46–48 (1990).
[CrossRef] [PubMed]

Fitzke, F. W.

F. W. Fitzke, “A new schematic eye and its applications to psychophysics,” presented at the Optical Society of America Topical Meeting on Recent Advances in Vision, Sarasota, Fla., April 30–May 3, 1980.

Goelz, S.

Grimm, B.

Gullstrand, A.

A. Gullstrand, Appendix II in Handbuch der Physiologischen Optik, H. von Helmholtz, ed., 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.

He, J. C.

Hoogenboom, W. P. H.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[CrossRef] [PubMed]

Hoogerheide, J.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[CrossRef] [PubMed]

Howarth, P. A.

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

Howland, B.

Howland, H. C.

Kooijman, A. C.

Koomen, M.

Le Grand, Y.

Y. Le Grand, La Dioptrique de l’Oeil et sa Correction, Tome I of Optique Physiologique (Masson, Paris, 1956); rev. ed. translated into English: Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

Liang, J.

Liou, H.-L.

Losada, M. A.

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

Lotmar, T.

Lotmar, W.

Marcos, S.

McMahon, M. J.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Moreno, E.

Navarro, R.

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]

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

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

Ogboso, Y. U.

Pankratov, M.

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

Pomerantzeff, O.

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

Rempt, F.

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[CrossRef] [PubMed]

Rynders, M. C.

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

Santamaría, J.

Scolnik, R.

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); [Biophysics (USSR) 6, 776–795 (1962]. That basic idea was later adopted by different authors: M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990);R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular local wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
[CrossRef] [PubMed]

Smith, G.

D. A. Atchison, G. Smith, “Continuous gradient index and shell models of the human lens,” Vision Res. 35, 2529–2538 (1995).
[CrossRef] [PubMed]

Still, D. L.

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

Thibos, L. N.

Y. Wang, L. N. Thibos, “Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 557–562 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

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

Tousey, R.

van Meeteren, A.

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Walsh, G.

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[CrossRef] [PubMed]

Wang, G.-J.

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, L. N. Thibos, “Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 557–562 (1997).
[CrossRef]

Webb, R. H.

Welford, T.

T. Welford, Aberrations of Optical Systems (Hilger, London, 1986).

Williams, D. R.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

Ye, M.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

Zhang, X.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

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

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

O. Pomerantzeff, M. Pankratov, G.-J. Wang, P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61, 166–176 (1984).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biofizika (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); [Biophysics (USSR) 6, 776–795 (1962]. That basic idea was later adopted by different authors: M. C. W. Campbell, E. H. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990);R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular local wavefront distortion with a spatially resolved refractometer,” Appl. Opt. 31, 3678–3686 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (7)

Ophthalmic Physiol. Opt. (1)

M. C. M. Dunne, D. A. Barnes, “Modelling oblique astigmatism in eyes with known peripheral refraction and optical dimensions,” Ophthalmic Physiol. Opt. 10, 46–48 (1990).
[CrossRef] [PubMed]

Ophthalmologica (1)

F. Rempt, J. Hoogerheide, W. P. H. Hoogenboom, “Peripheral retinoscopy and the skiagram,” Ophthalmologica 162, 1–10 (1971).
[CrossRef] [PubMed]

Opt. Acta (1)

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Optom. Vision Sci. (1)

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

Optom. Vision Sci. (2)

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

Y. Wang, L. N. Thibos, “Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 557–562 (1997).
[CrossRef]

Vision Res. (5)

D. A. Atchison, G. Smith, “Continuous gradient index and shell models of the human lens,” Vision Res. 35, 2529–2538 (1995).
[CrossRef] [PubMed]

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

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[CrossRef] [PubMed]

M. C. Rynders, R. Navarro, M. A. Losada, “Objective measurement of the off-axis longitudinal chromatic aberration in the human eye,” Vision Res. 37, 513–521 (1997).

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Other (4)

T. Welford, Aberrations of Optical Systems (Hilger, London, 1986).

F. W. Fitzke, “A new schematic eye and its applications to psychophysics,” presented at the Optical Society of America Topical Meeting on Recent Advances in Vision, Sarasota, Fla., April 30–May 3, 1980.

A. Gullstrand, Appendix II in Handbuch der Physiologischen Optik, H. von Helmholtz, ed., 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.

Y. Le Grand, La Dioptrique de l’Oeil et sa Correction, Tome I of Optique Physiologique (Masson, Paris, 1956); rev. ed. translated into English: Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

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Figures (12)

Fig. 1
Fig. 1

Plot of the schematic model of the human eye of Table 1 with a 3-mm entrance pupil diameter. Rays for three field objects at infinity are traced: minimum (0°), intermediate (40°), and maximum (60°) fields considered in this study.

Fig. 2
Fig. 2

Longitudinal spherical aberration (LSA) of the schematic eye with an 8-mm-diameter entrance pupil, compared with experimental data taken from the literature, in diopters (see the symbol key and the text for details).

Fig. 3
Fig. 3

Tangential and sagittal angular coma, in arcminutes, of the schematic eye, compared with experimental tangential coma.

Fig. 4
Fig. 4

Oblique astigmatism of the eye model compared with experimental data. Results of two computer simulations of experimental measurements, moving the object distance (I) and using trial cylinder lenses (II), are included.

Fig. 5
Fig. 5

Field curvature of the eye model, estimated as the offset, in diopters, between the least confusion disk (LCD) and the retina (solid curve); third-order LCD (dotted curve); experimental data (solid squares); and computer simulation of the experiment (open circles).

Fig. 6
Fig. 6

Shape and relative location of the different image surfaces of the eye: Model surface (solid curve), computed as the locus of the disks of least confusion for finite ray tracing with the use of a 3-mm pupil, is compared with the Petzval surface (asterisks), with the disks of least confusion in third-order approximation, and finally with the retinal surface that is approximated by a sphere in the eye model.

Fig. 7
Fig. 7

Angular distortion of the eye model. (We have not found experimental data available.)

Fig. 8
Fig. 8

Variation of longitudinal color (LCA) with field angle for the schematic eye model (solid curve), along with experimental data (solid squares) and simulations of that experiment, both direct simulation (open circles) and corrected from estimated bias (asterisks).

Fig. 9
Fig. 9

Transverse color TCA for the model, experimental data, and computer simulations.

Fig. 10
Fig. 10

Spot diagrams for the schematic eye, obtained by finite ray tracing, for a 6-mm entrance pupil diameter and for six field angles: 0°, 5°, 10°, 20°, 40°, and 60°.

Fig. 11
Fig. 11

Spot diagrams for 3-mm and 9-mm pupil diameters and for 0° and 40° field angles.

Fig. 12
Fig. 12

Radial profiles (orientation average) of the MTF of the eye model compared with experimental data available in the literature. (a) On-axis. Here the MTF has been computed for 0 and 0.15 D of defocus. (b) 20° off-axis.  

Tables (2)

Tables Icon

Table 1 Geometry of the Schematic Wide-Angle Eye Model

Tables Icon

Table 2 Refractive Indices for the Wavelengths Used in Computations

Equations (4)

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LCA(r)=(n/fr)-(n/fp)=(n/lp)-(n/lr),
(n/ft)-(n/fs)=(n/ls)-(n/lt),
(nr/fr)-(nb/fb)=(nb/lb)-(nr/lr).
(nr/fr)-(nb/fb)=(nb/lb)-(nr/lr)+(nr/lr)-(nb/lb).

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