Abstract

We consider a schematic human eye with four centered aspheric surfaces. We show that by introducing recent experimental average measurements of cornea and lens into the Gullstrand–Le Grand model, the average spherical aberration of the actual eye is predicted without any shape fitting. The chromatic dispersions are adjusted to fit the experimentally observed chromatic aberration of the eye. The polychromatic point-spread function and modulation transfer function are calculated for several pupil diameters and show good agreement with previous experimental results. Finally, from this schematic eye an accommodation-dependent model is proposed that reproduces the increment of refractive power of the eye during accommodation. The variation of asphericity with accommodation is also introduced in the model and the resulting optical performance studied.

© 1985 Optical Society of America

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References

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  1. H. von Helmholtz, Physiologische Optik, 3rd ed. (Voss, Hamburg, 1909).
  2. A. Gullstrand, appendix in H. von Helmholtz, Physiologische Optic, 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.
  3. Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).
  4. W. Lotmar, “Theoretical eye model with aspherics,” J. Opt. Soc. Am. 61, 1522–1529 (1971).
    [CrossRef]
  5. S. G. El Hage, F. Berny, “Contribution of the crystalline lens to the spherical aberration of the eye,” J. Opt. Soc. Am. 63, 205–211 (1973).
    [CrossRef] [PubMed]
  6. S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.
  7. O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
    [CrossRef]
  8. F. W. Fitzke, “A new schematic eye and its applications to psychophysics,” presented at the Optical Society of America Meeting on Recent Advances in Vision, Sarasota, Florida, April 30–, May 3, 1980.
  9. A. C. Kooijman, “Light distribution on the retina of a wide-angle theoretical eye,” J. Opt. Soc. Am. 73, 1544–1550 (1983).
    [CrossRef] [PubMed]
  10. J. W. Blaker, “Toward and adaptive model of the human eye,” J. Opt. Soc. Am. 70, 220–223 (1980).
    [CrossRef] [PubMed]
  11. P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
    [CrossRef]
  12. M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
    [CrossRef] [PubMed]
  13. A. Ivanoff, Les Aberrations de l’Oeil (Masson, Paris, 1953).
  14. G. Wald, D. T. Griffin, “The change in refractive power of the human eye in dim and bright light,” J. Opt. Soc. Am. 37, 321–329 (1947).
    [CrossRef] [PubMed]
  15. A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. Paris 9, 498 (1923).
  16. Y. Le Grand, L’Espace Visuel, Vol. III of Optique Physiologique (Masson, Paris, 1956).
  17. J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
    [CrossRef] [PubMed]
  18. D. A. Palmer, J. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 7, 780–782 (1981).
    [CrossRef]
  19. M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
    [CrossRef]
  20. A. Van Meeteren, “Calculations on the optical modulation transfer function of the human eye,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  21. M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 39, 370–376 (1949).
    [CrossRef] [PubMed]
  22. M. Françon, “Aberration spérique chromatisme et puvoir séparateur de l’oeil,” Rev. Opt. Theor. Instrum. 30, 71–86 (1951).
  23. H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
    [CrossRef]
  24. M. Millodot, J. G. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision. Res. 19, 685–687 (1979).
    [CrossRef] [PubMed]
  25. M. Millodot, J. A. Newton, “A possible change of refractive index with age and its relevance to chromatic aberration,” Albrecht V. Graefes Arch. Ophthalmol. 201, 159–167 (1976).
  26. M. Gomez, “Estudio sobre la acomodación del ojo en presencia de estímulos exteriores próximos a los umbrales de perceptión,” Ph.D. dissertation (Universidad Complutense de Madrid, Madrid, 1965).
  27. F. W. Campbell, J. A. E. Primrose, “The state of accommodation of the human eye in darkness,” Trans. Ophthalmol. Soc. UK 73, 353–361 (1953).
  28. J. Bescós, J. Santamaría, “Colour based quality parameters for white light imagery,” Opt. Acta 28, 43–55 (1981).
    [CrossRef]
  29. A. Arnulf, “Le systeme optique de l’oeil en vision photopique et mesopique,” Excerpta Med. Int. Congr. Ser. 125, 135–151 (1965).
  30. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
    [PubMed]
  31. R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 407–415 (1967).
    [CrossRef]
  32. M. S. Smirnov, “Measurement of the wave aberrations of the human eye,” Biophysics (USSR) 6, 776–795 (1961).
  33. M. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [CrossRef] [PubMed]
  34. R. F. Fisher, “The significance of the shape of the lens and capsular energy changes in accommodation,” J. Physiol. 201, 21–47 (1969).
    [PubMed]
  35. E. F. Fincham, The Mechanism of Accommodation (Pullman, London, 1937).
  36. N. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
    [CrossRef] [PubMed]
  37. B. Patnaik, “A photographic study of accommodative mechanisms: changes in the lens nucleus during accommodation,” Invest. Ophthalmol. 6, 601–611 (1967).
    [PubMed]
  38. F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
    [CrossRef] [PubMed]
  39. K. Ukai, H. Ohzu, “Dynamic laser speckle pattern used to determine eye refraction. I. Changes in chromatic aberration of the eye with accommodation,” presented at ICO-11, Madrid, September 10–17, 1978.

1983 (1)

1982 (2)

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

1981 (2)

J. Bescós, J. Santamaría, “Colour based quality parameters for white light imagery,” Opt. Acta 28, 43–55 (1981).
[CrossRef]

D. A. Palmer, J. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 7, 780–782 (1981).
[CrossRef]

1980 (1)

1979 (1)

M. Millodot, J. G. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision. Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

1977 (2)

1976 (1)

M. Millodot, J. A. Newton, “A possible change of refractive index with age and its relevance to chromatic aberration,” Albrecht V. Graefes Arch. Ophthalmol. 201, 159–167 (1976).

1974 (1)

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

1973 (2)

N. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

S. G. El Hage, F. Berny, “Contribution of the crystalline lens to the spherical aberration of the eye,” J. Opt. Soc. Am. 63, 205–211 (1973).
[CrossRef] [PubMed]

1972 (1)

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

1971 (1)

1969 (2)

R. F. Fisher, “The significance of the shape of the lens and capsular energy changes in accommodation,” J. Physiol. 201, 21–47 (1969).
[PubMed]

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

1968 (1)

H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
[CrossRef]

1967 (2)

B. Patnaik, “A photographic study of accommodative mechanisms: changes in the lens nucleus during accommodation,” Invest. Ophthalmol. 6, 601–611 (1967).
[PubMed]

R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 407–415 (1967).
[CrossRef]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

1965 (1)

A. Arnulf, “Le systeme optique de l’oeil en vision photopique et mesopique,” Excerpta Med. Int. Congr. Ser. 125, 135–151 (1965).

1961 (1)

M. S. Smirnov, “Measurement of the wave aberrations of the human eye,” Biophysics (USSR) 6, 776–795 (1961).

1959 (1)

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

1953 (1)

F. W. Campbell, J. A. E. Primrose, “The state of accommodation of the human eye in darkness,” Trans. Ophthalmol. Soc. UK 73, 353–361 (1953).

1951 (1)

M. Françon, “Aberration spérique chromatisme et puvoir séparateur de l’oeil,” Rev. Opt. Theor. Instrum. 30, 71–86 (1951).

1949 (1)

1947 (1)

1923 (1)

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. Paris 9, 498 (1923).

Arnulf, A.

A. Arnulf, “Le systeme optique de l’oeil en vision photopique et mesopique,” Excerpta Med. Int. Congr. Ser. 125, 135–151 (1965).

Berny, F.

S. G. El Hage, F. Berny, “Contribution of the crystalline lens to the spherical aberration of the eye,” J. Opt. Soc. Am. 63, 205–211 (1973).
[CrossRef] [PubMed]

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

Bescós, J.

J. Bescós, J. Santamaría, “Colour based quality parameters for white light imagery,” Opt. Acta 28, 43–55 (1981).
[CrossRef]

Blaker, J. W.

Brown, N.

N. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

F. W. Campbell, J. A. E. Primrose, “The state of accommodation of the human eye in darkness,” Trans. Ophthalmol. Soc. UK 73, 353–361 (1953).

Carney, G.

P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

El Hage, S. G.

Fincham, E. F.

E. F. Fincham, The Mechanism of Accommodation (Pullman, London, 1937).

Fish, H.

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

Fisher, R. F.

R. F. Fisher, “The significance of the shape of the lens and capsular energy changes in accommodation,” J. Physiol. 201, 21–47 (1969).
[PubMed]

Fitzke, F. W.

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

Françon, M.

M. Françon, “Aberration spérique chromatisme et puvoir séparateur de l’oeil,” Rev. Opt. Theor. Instrum. 30, 71–86 (1951).

Gomez, M.

M. Gomez, “Estudio sobre la acomodación del ojo en presencia de estímulos exteriores próximos a los umbrales de perceptión,” Ph.D. dissertation (Universidad Complutense de Madrid, Madrid, 1965).

Govignon, J.

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

Griffin, D. T.

Gubisch, R. W.

R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 407–415 (1967).
[CrossRef]

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

Gullstrand, A.

A. Gullstrand, appendix in H. von Helmholtz, Physiologische Optic, 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.

Herzberger, M.

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

Howcroft, M. J.

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

Howland, B.

Howland, M. C.

Ivanoff, A.

A. Ivanoff, Les Aberrations de l’Oeil (Masson, Paris, 1953).

Kamiya, S.

S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.

Kiely, P. H.

P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Kooijman, A. C.

Koomen, M.

Le Grand, Y.

Y. Le Grand, L’Espace Visuel, Vol. III of Optique Physiologique (Masson, Paris, 1956).

Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

Lotmar, W.

Mandelman, T.

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

Millodot, M.

M. Millodot, J. G. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision. Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

M. Millodot, J. A. Newton, “A possible change of refractive index with age and its relevance to chromatic aberration,” Albrecht V. Graefes Arch. Ophthalmol. 201, 159–167 (1976).

Mine, K.

S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.

Nakao, S. N.

S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.

Newton, J. A.

M. Millodot, J. A. Newton, “A possible change of refractive index with age and its relevance to chromatic aberration,” Albrecht V. Graefes Arch. Ophthalmol. 201, 159–167 (1976).

Nishioka, K.

S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.

Nunker, H.

H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
[CrossRef]

Ohzu, H.

K. Ukai, H. Ohzu, “Dynamic laser speckle pattern used to determine eye refraction. I. Changes in chromatic aberration of the eye with accommodation,” presented at ICO-11, Madrid, September 10–17, 1978.

Palmer, D. A.

D. A. Palmer, J. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 7, 780–782 (1981).
[CrossRef]

Parker, J. A.

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

Patnaik, B.

B. Patnaik, “A photographic study of accommodative mechanisms: changes in the lens nucleus during accommodation,” Invest. Ophthalmol. 6, 601–611 (1967).
[PubMed]

Polack, A.

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. Paris 9, 498 (1923).

Pomerantzeff, O.

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

Primrose, J. A. E.

F. W. Campbell, J. A. E. Primrose, “The state of accommodation of the human eye in darkness,” Trans. Ophthalmol. Soc. UK 73, 353–361 (1953).

Santamaría, J.

J. Bescós, J. Santamaría, “Colour based quality parameters for white light imagery,” Opt. Acta 28, 43–55 (1981).
[CrossRef]

Schepens, C. L.

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

Schober, H.

H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
[CrossRef]

Scolnik, R.

Sivak, J.

D. A. Palmer, J. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 7, 780–782 (1981).
[CrossRef]

Sivak, J. G.

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

M. Millodot, J. G. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision. Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberrations of the human eye,” Biophysics (USSR) 6, 776–795 (1961).

Smith, G.

P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Tousey, R.

Ukai, K.

K. Ukai, H. Ohzu, “Dynamic laser speckle pattern used to determine eye refraction. I. Changes in chromatic aberration of the eye with accommodation,” presented at ICO-11, Madrid, September 10–17, 1978.

Van Meeteren, A.

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

von Helmholtz, H.

H. von Helmholtz, Physiologische Optik, 3rd ed. (Voss, Hamburg, 1909).

A. Gullstrand, appendix in H. von Helmholtz, Physiologische Optic, 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.

Wald, G.

Zolleis, F.

H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
[CrossRef]

Albrecht V. Graefes Arch. Ophthalmol. (1)

M. Millodot, J. A. Newton, “A possible change of refractive index with age and its relevance to chromatic aberration,” Albrecht V. Graefes Arch. Ophthalmol. 201, 159–167 (1976).

Biophysics (USSR) (1)

M. S. Smirnov, “Measurement of the wave aberrations of the human eye,” Biophysics (USSR) 6, 776–795 (1961).

Bull. Soc. Ophthalmol. Paris (1)

A. Polack, “Le chromatisme de l’oeil,” Bull. Soc. Ophthalmol. Paris 9, 498 (1923).

Excerpta Med. Int. Congr. Ser. (1)

A. Arnulf, “Le systeme optique de l’oeil en vision photopique et mesopique,” Excerpta Med. Int. Congr. Ser. 125, 135–151 (1965).

Exp. Eye Res. (1)

N. Brown, “The change in shape and internal form of the lens of the eye on accommodation,” Exp. Eye Res. 15, 441–459 (1973).
[CrossRef] [PubMed]

Invest. Ophthalmol. (1)

B. Patnaik, “A photographic study of accommodative mechanisms: changes in the lens nucleus during accommodation,” Invest. Ophthalmol. 6, 601–611 (1967).
[PubMed]

J. Opt. Soc. Am. (9)

J. Physiol. (2)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966).
[PubMed]

R. F. Fisher, “The significance of the shape of the lens and capsular energy changes in accommodation,” J. Physiol. 201, 21–47 (1969).
[PubMed]

Opt. Acta (6)

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

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

H. Schober, H. Nunker, F. Zolleis, “Die Aberration des menschlichen Auges und ihre Messung,” Opt. Acta 15, 47–55 (1968).
[CrossRef]

O. Pomerantzeff, H. Fish, J. Govignon, C. L. Schepens, “Wide-angle optical model of the eye,” Opt. Acta 19, 387–388 (1972).
[CrossRef]

P. H. Kiely, G. Smith, G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

J. Bescós, J. Santamaría, “Colour based quality parameters for white light imagery,” Opt. Acta 28, 43–55 (1981).
[CrossRef]

Rev. Opt. Theor. Instrum. (1)

M. Françon, “Aberration spérique chromatisme et puvoir séparateur de l’oeil,” Rev. Opt. Theor. Instrum. 30, 71–86 (1951).

Trans. Ophthalmol. Soc. UK (1)

F. W. Campbell, J. A. E. Primrose, “The state of accommodation of the human eye in darkness,” Trans. Ophthalmol. Soc. UK 73, 353–361 (1953).

Vision Res. (3)

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[CrossRef] [PubMed]

M. J. Howcroft, J. A. Parker, “Aspheric curvatures for the human lens,” Vision Res. 17, 1217–1223 (1977).
[CrossRef] [PubMed]

F. Berny, “Etude de la formation des images retiniennes et determination de l’aberration de sphericite de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

Vision. Res. (1)

M. Millodot, J. G. Sivak, “Contribution of the cornea and lens to the spherical aberration of the eye,” Vision. Res. 19, 685–687 (1979).
[CrossRef] [PubMed]

Other (10)

Y. Le Grand, L’Espace Visuel, Vol. III of Optique Physiologique (Masson, Paris, 1956).

A. Ivanoff, Les Aberrations de l’Oeil (Masson, Paris, 1953).

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

H. von Helmholtz, Physiologische Optik, 3rd ed. (Voss, Hamburg, 1909).

A. Gullstrand, appendix in H. von Helmholtz, Physiologische Optic, 3rd ed. (Voss, Hamburg, 1909), Bd. 1, p. 299.

Y. Le Grand, S. G. El Hage, Physiological Optics (Springer-Verlag, Berlin, 1980).

S. N. Nakao, K. Mine, K. Nishioka, S. Kamiya, “New schematic eye and its clinical applications,” presented at the Twenty-First International Congress of Ophthalmology, México DF, México, March 8–14, 1970.

M. Gomez, “Estudio sobre la acomodación del ojo en presencia de estímulos exteriores próximos a los umbrales de perceptión,” Ph.D. dissertation (Universidad Complutense de Madrid, Madrid, 1965).

E. F. Fincham, The Mechanism of Accommodation (Pullman, London, 1937).

K. Ukai, H. Ohzu, “Dynamic laser speckle pattern used to determine eye refraction. I. Changes in chromatic aberration of the eye with accommodation,” presented at ICO-11, Madrid, September 10–17, 1978.

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Figures (11)

Fig. 1
Fig. 1

Schematic eye.

Fig. 2
Fig. 2

LSA of the cornea (- – - –), of the lens (– –), and of the whole theoretical eye (—). The results corresponding to the Gullstrand–Le Grand eye (…) and to Van Meeteren’s parabolic adjustment (- - – - -) are also represented, (dp, diopters.)

Fig. 3
Fig. 3

Longitudinal chromatic aberration (C.A., in diopters) of the theoretical eye (—). Experimental results of Wald and Griffin (Δ) and of Ivanoff (×) are also represented.

Fig. 4
Fig. 4

Influence of Stiles–Crawford effect on the monochromatic MTF of a 4-mm pupil-diameter schematic eye: aberration-free system (- -), eye model without apodization (—) and with apodization (- – - –).

Fig. 5
Fig. 5

Distribution of a) illuminance and b) chromaticity coordinates (x, y) of the polychromatic PSF and c) the polychromatic MTF for the schematic eye with the following pupil diameters: 2 mm (●), 3 mm (○), 4 mm (×), 5 mm (Δ), 6 mm (□), and 8 mm (▲), ν = 1 corresponds to the cutoff frequency at λ = 500 nm, ρ is the radial coordinate on the image plane, and α′ is the semiaperture angle. Dashed curves correspond to the aberration-free system.

Fig. 6
Fig. 6

Polychromatic MTF of the schematic eye (theoretical) computed for 4-mm pupil diameter, compared with experimental curves from Arnulf (○)29 and Campbell and Gubisch (∇).30 (The last corresponds to 3.8-mm pupil diameter.)

Fig. 7
Fig. 7

Strehl ratio versus pupil diameter for the schematic eye (theoretical) compared with experimental findings from Gubisch (●).31 They differ by an almost constant factor of the order of 0.7.

Fig. 8
Fig. 8

Variation of the anterior lens radius with accommodation. The figure shows the experimental mean curve from Ivanoff13 and that adopted for the schematic theoretical eye. They have similar shapes, but the theoretical eye curve differs somewhat from that of Ivanoff because our schematic eye starts from the Gullstrand–Le Grand eye, whose anterior unaccommodated radius differs from that of Ivanoff. (dp, diopters.)

Fig. 9
Fig. 9

Refractive power of the schematic eye versus accommodation (●). The straight line corresponds to the ideal fitting. (dp, diopters.)

Fig. 10
Fig. 10

LSA obtained for several accommodation states: unaccommodated (—), 3 D (- – - –), 5 D (- -), and 10 D (…). (dp, diopters.)

Fig. 11
Fig. 11

Distribution of a) illuminance and b) chromaticity coordinates (x, y) of the polychromatic PSF and the c) polychromatic MTF obtained for the 3 D accommodated eye with the following pupil diameters: 2 mm (●), 3 mm (○), 4 mm (×), 5 mm (Δ), 6 mm (□), and 8 mm (▲), ν = 1 corresponds to the cutoff frequency at λ = 500 nm, ρ is the radial coordinate on the image plane, and α′ is the semiaperture angle. Dashed curves correspond to the aberration-free system.

Tables (5)

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Table 1 Schematic Eye Parameters Compared with Those of Gullstrand–Le Grand and Kooijman

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Table 2 Refractive Indices of the Schematic Eye

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Table 3 Constringences of the Schematic Eye Compared with Data of Polack and Sivak and Mandelman

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Table 4 Accommodation Dependence of the Lens Parameters on Accommodation A (in diopters)

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Table 5 Test Parameters Used in Optical Performance Computations

Equations (4)

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x 2 + y 2 + ( 1 + Q ) z 2 2 R z = 0 ,
n ( λ ) = a 1 ( λ ) n * * + a 2 ( λ ) n F + a 3 ( λ ) n c + a 4 ( λ ) n * ,
a 1 ( λ ) = 0.66147196 0.040352796 λ 2 0.2804679 λ 2 λ 0 2 + 0.03385979 ( λ 2 λ 0 2 ) 2 , a 2 ( λ ) = 4.20146383 + 2.73508956 λ 2 + 1.50543784 λ 2 λ 0 2 0.11593235 ( λ 2 λ 0 2 ) 2 , a 3 ( λ ) = 6.29834237 4.69409935 λ 2 1.5750865 λ 2 λ 0 2 + 0.10293038 ( λ 2 λ 0 2 ) 2 , a 4 ( λ ) = 1.75835059 + 2.36253794 λ 2 + 0.35011657 λ 2 λ 0 2 0.02085782 ( λ 2 λ 0 2 ) 2 ,
P ( r ) = exp ( 0.05 R p 2 r 2 ln 10 ) [ exp i k ( δ 0 W 20 r 2 + W 40 r 4 + W 60 r 6 + W 80 r 8 + ) ] ,

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