Abstract

A model for the human eye is proposed, similar to Gullstrand’s well-known 4-radius model, however with the front surface of the cornea and the back surface of the crystalline lens taken to be rotationally symmetric aspherics. Whereas for the cornea a polynomial is used based on experimental data of Bonnet, a second-order parabola was tentatively adopted for the back surface of the lens. This model results in slight spherical undercorrection, in agreement with experimental findings. On the other hand, the sine condition is not well satisfied, probably due to neglect of the shell structure of the lens. By ray tracing, astigmatism and coma as well as the meridional and sagittal focal lengths were computed up to a visual angle of 90°. Calculations were also made for the same model preceded by a plano-concave contact lens (Goldmann 3-mirror contact glass), showing that this combination results in considerably reduced astigmatism.

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  1. F. Fankhauser and W. Lotmar, Arch. OphthalmoL 77, 320 (1967).
  2. W. Lotmar, F. Fankhauser, and A. Roulier, Arch. Ophthalmol. 82, 314 (1969).
  3. T. Schmidt, Ophthalmologica 129,303 (1955).
  4. F. Fankhauser and J. M. Enoch, Arch. Ophthalmol. 68, 240 (1962).
  5. C. E. Ferree and G. Rand, in Report of a Joint Discussion on Vision (Cambridge U. P., New York, 1932), p. 244.
  6. F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).
  7. F. Fankhauser and W. Lotmar, Acta Ophthalmol. 48, 253 (1970).
  8. P. Lee, O. Pomerantzeff, and C. L. Schepens, Arch. Ophthalmol. 84, 650 (1970).
  9. Y. Le Grand, Optique Physiologique I (Ed. Rev. Opt., Paris, 1953), p. 52.
  10. S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).
  11. G. van den Brink, Vision Res. 2, 233 (1962).
  12. H. Schober, H. Munker., and F. Zolleis, Opt. Acta 15, 47 (1968)
  13. F. Berny, Vision Res. 9, 977 (1969).
  14. R. Bonnet, La Topographie Cornéenne (Desroches, Paris, 1964).
  15. R. Bonnet and P. Cochet, Bull. Soc. Franç. Ophtalmol. 73, 688 (1960).
  16. Visual angle α (Fig. 1) is different from the angle a in Fig. 2 and Eq. (1) as used by Bonnet.
  17. W. Merté, in Handbuchder Physik XVIII, edited by R. Geiger and K. Scheel (Springer, Berlin, 1927), p. 73.
  18. S. Nakao, personal communication.
  19. H. Goldmann and T. Schmidt, Ophthalmologica 149, 481 (1965).

Berny, F.

F. Berny, Vision Res. 9, 977 (1969).

Bonnet, R.

R. Bonnet and P. Cochet, Bull. Soc. Franç. Ophtalmol. 73, 688 (1960).

R. Bonnet, La Topographie Cornéenne (Desroches, Paris, 1964).

Cochet, P.

R. Bonnet and P. Cochet, Bull. Soc. Franç. Ophtalmol. 73, 688 (1960).

Enoch, J. M.

F. Fankhauser and J. M. Enoch, Arch. Ophthalmol. 68, 240 (1962).

Fankhauser, F.

F. Fankhauser and J. M. Enoch, Arch. Ophthalmol. 68, 240 (1962).

F. Fankhauser and W. Lotmar, Acta Ophthalmol. 48, 253 (1970).

F. Fankhauser and W. Lotmar, Arch. OphthalmoL 77, 320 (1967).

W. Lotmar, F. Fankhauser, and A. Roulier, Arch. Ophthalmol. 82, 314 (1969).

Ferree, C. E.

C. E. Ferree and G. Rand, in Report of a Joint Discussion on Vision (Cambridge U. P., New York, 1932), p. 244.

Fujimoto, S.

S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).

Goldmann, H.

H. Goldmann and T. Schmidt, Ophthalmologica 149, 481 (1965).

Grand, Y. Le

Y. Le Grand, Optique Physiologique I (Ed. Rev. Opt., Paris, 1953), p. 52.

Hoogenboom, W. P. H.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).

Hoogerheide, J.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).

Iwata, K.

S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).

Lee, P.

P. Lee, O. Pomerantzeff, and C. L. Schepens, Arch. Ophthalmol. 84, 650 (1970).

Lotmar, W.

F. Fankhauser and W. Lotmar, Arch. OphthalmoL 77, 320 (1967).

W. Lotmar, F. Fankhauser, and A. Roulier, Arch. Ophthalmol. 82, 314 (1969).

F. Fankhauser and W. Lotmar, Acta Ophthalmol. 48, 253 (1970).

Merté, W.

W. Merté, in Handbuchder Physik XVIII, edited by R. Geiger and K. Scheel (Springer, Berlin, 1927), p. 73.

Munker., H.

H. Schober, H. Munker., and F. Zolleis, Opt. Acta 15, 47 (1968)

Nagata, R.

S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).

Nakao, S.

S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).

S. Nakao, personal communication.

Pomerantzeff, O.

P. Lee, O. Pomerantzeff, and C. L. Schepens, Arch. Ophthalmol. 84, 650 (1970).

Rand, G.

C. E. Ferree and G. Rand, in Report of a Joint Discussion on Vision (Cambridge U. P., New York, 1932), p. 244.

Rempt, F.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).

Roulier, A.

W. Lotmar, F. Fankhauser, and A. Roulier, Arch. Ophthalmol. 82, 314 (1969).

Schepens, C. L.

P. Lee, O. Pomerantzeff, and C. L. Schepens, Arch. Ophthalmol. 84, 650 (1970).

Schmidt, T.

H. Goldmann and T. Schmidt, Ophthalmologica 149, 481 (1965).

T. Schmidt, Ophthalmologica 129,303 (1955).

Schober, H.

H. Schober, H. Munker., and F. Zolleis, Opt. Acta 15, 47 (1968)

van den Brink, G.

G. van den Brink, Vision Res. 2, 233 (1962).

Zolleis, F.

H. Schober, H. Munker., and F. Zolleis, Opt. Acta 15, 47 (1968)

Other (19)

F. Fankhauser and W. Lotmar, Arch. OphthalmoL 77, 320 (1967).

W. Lotmar, F. Fankhauser, and A. Roulier, Arch. Ophthalmol. 82, 314 (1969).

T. Schmidt, Ophthalmologica 129,303 (1955).

F. Fankhauser and J. M. Enoch, Arch. Ophthalmol. 68, 240 (1962).

C. E. Ferree and G. Rand, in Report of a Joint Discussion on Vision (Cambridge U. P., New York, 1932), p. 244.

F. Rempt, J. Hoogerheide, and W. P. H. Hoogenboom, Ophthalmologica 162, 1 (1971).

F. Fankhauser and W. Lotmar, Acta Ophthalmol. 48, 253 (1970).

P. Lee, O. Pomerantzeff, and C. L. Schepens, Arch. Ophthalmol. 84, 650 (1970).

Y. Le Grand, Optique Physiologique I (Ed. Rev. Opt., Paris, 1953), p. 52.

S. Nakao, S. Fujimoto, R. Nagata, and K. Iwata, J. Opt. Soc. Am. 58, 1125 (1968).

G. van den Brink, Vision Res. 2, 233 (1962).

H. Schober, H. Munker., and F. Zolleis, Opt. Acta 15, 47 (1968)

F. Berny, Vision Res. 9, 977 (1969).

R. Bonnet, La Topographie Cornéenne (Desroches, Paris, 1964).

R. Bonnet and P. Cochet, Bull. Soc. Franç. Ophtalmol. 73, 688 (1960).

Visual angle α (Fig. 1) is different from the angle a in Fig. 2 and Eq. (1) as used by Bonnet.

W. Merté, in Handbuchder Physik XVIII, edited by R. Geiger and K. Scheel (Springer, Berlin, 1927), p. 73.

S. Nakao, personal communication.

H. Goldmann and T. Schmidt, Ophthalmologica 149, 481 (1965).

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