Abstract

Intraocular light scatter is modeled through a stratified medium. It is shown that the eye lens possesses properties of an interference filter. In conditions that may mimic opacification, as found with cataract formation, such a filter may have stop zones with reflectance up to 1 in the band of visible light.

© 2001 Optical Society of America

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  1. G. B. Benedek, “Theory of transparency of the eye,” Appl. Opt. 10, 459–473 (1971).
    [CrossRef] [PubMed]
  2. G. B. Benedek, “Cataract as a protein condensation disease: the Proctor lecture,” Invest. Ophthalmol. Visual Sci. 38, 1911–1921 (1997).
  3. B. K. Pierscionek, N. Y. C. Chan, “The refractive index gradient of the human lens,” Invest. Ophthalmol. Visual Sci. 66, 822–829 (1989).
  4. B. K. Pierscionek, “Variation in refractive index and absorbance of 670 nm light with eye in cataract formation in human lens,” Exp. Eye Res. 60, 407–413 (1995).
    [CrossRef] [PubMed]
  5. F. A. Bettelheim, L. Siew, “Biological-physical basis of lens transparency,” in Cell Biology of the Eye, D. S. McDevitt, ed. (Academic, New York, 1982).
    [CrossRef]
  6. J. M. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).
  7. R. P. Hemenger, “Small-angle intraocular light scatter: a hypothesis concerning its source,” J. Opt. Soc. Am. A 5, 577–582 (1988).
    [CrossRef] [PubMed]
  8. R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. 5, pp. 247–286.
    [CrossRef]
  9. L. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42, 806–810 (1952).
    [CrossRef]
  10. H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1969).
  11. M. Born, E. Wolf, eds., Principles of Optics (Pergamon, New York, 1970).
  12. F. A. Bettelheim, S. Ali, “Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses,” Exp. Eye Res. 41, 1–9 (1985).
    [CrossRef] [PubMed]
  13. B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
    [CrossRef]
  14. T. J. Jacob, “The relationship between cataract, cell swelling and volume regulation,” Prog. Retinal Eye Res. 12, 223–233 (1999).
    [CrossRef]
  15. R. Courant, D. Hilbert, Methoden der Mathematischen Physic (Springer-Verlag, Berlin, 1993).
    [CrossRef]
  16. W. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978).
  17. F. A. Bettelheim, M. Paunovic, “Light scattering of normal human lens,” Biophys. J. 26, 85–100 (1973).
    [CrossRef]
  18. F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
    [CrossRef] [PubMed]
  19. P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
    [CrossRef] [PubMed]
  20. A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
    [PubMed]
  21. F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés. Application aux couches minges,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).
  22. A. Herpin, “Calcul du pouvoir réflecteur d’un systéme stratifié quelconque,” C. R. Sceances Acad. Sci. 225, 182–183 (1947).
  23. C. Dufour, A. Herpin, “Propogation des ondes électromagnétiques dans un milieu stratifié périodique transparent,” Rev. Opt. Theor. Instrum. 32, 321–348 (1953).
  24. W. Weinstein, “Computations in thin film optics,” Vacuum 4, 3–19 (1954).
    [CrossRef]
  25. M. Abramovitz, I. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables (Dover, New York, 1965).
  26. G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
    [CrossRef]
  27. B. K. Pierscionek, “Refractive index contours in the human lens,” Exp. Eye Res. 64, 887–893 (1997).
    [CrossRef] [PubMed]
  28. A. Thelen, “Multilayer filters with wide transmittance bands,” J. Opt. Soc. Am. 53, 1266–1270 (1963).
    [CrossRef]
  29. A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1538 (1966).
    [CrossRef]
  30. B. Pierscionek, R. Green, S. G. Dolgobrodov are preparing a manuscript to be called “Calculation of retinal image for cataractous eye as modeled through a phase aberrating medium.”
  31. J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
    [PubMed]
  32. B. Philipson, “Changes in the lens related to the reduction of transparency,” Exp. Eye Res. 16, 29–39 (1973).
    [CrossRef] [PubMed]
  33. B. Philipson, “Biophysical studies on normal and cataractous rat lenses,” Acta Ophthalmol. Suppl. 103, 1–30 (1969).

1999 (2)

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

T. J. Jacob, “The relationship between cataract, cell swelling and volume regulation,” Prog. Retinal Eye Res. 12, 223–233 (1999).
[CrossRef]

1998 (1)

A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
[PubMed]

1997 (3)

F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
[CrossRef] [PubMed]

B. K. Pierscionek, “Refractive index contours in the human lens,” Exp. Eye Res. 64, 887–893 (1997).
[CrossRef] [PubMed]

G. B. Benedek, “Cataract as a protein condensation disease: the Proctor lecture,” Invest. Ophthalmol. Visual Sci. 38, 1911–1921 (1997).

1995 (1)

B. K. Pierscionek, “Variation in refractive index and absorbance of 670 nm light with eye in cataract formation in human lens,” Exp. Eye Res. 60, 407–413 (1995).
[CrossRef] [PubMed]

1989 (1)

B. K. Pierscionek, N. Y. C. Chan, “The refractive index gradient of the human lens,” Invest. Ophthalmol. Visual Sci. 66, 822–829 (1989).

1988 (1)

1985 (1)

F. A. Bettelheim, S. Ali, “Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses,” Exp. Eye Res. 41, 1–9 (1985).
[CrossRef] [PubMed]

1979 (1)

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

1973 (3)

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

B. Philipson, “Changes in the lens related to the reduction of transparency,” Exp. Eye Res. 16, 29–39 (1973).
[CrossRef] [PubMed]

F. A. Bettelheim, M. Paunovic, “Light scattering of normal human lens,” Biophys. J. 26, 85–100 (1973).
[CrossRef]

1971 (2)

G. B. Benedek, “Theory of transparency of the eye,” Appl. Opt. 10, 459–473 (1971).
[CrossRef] [PubMed]

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

1969 (1)

B. Philipson, “Biophysical studies on normal and cataractous rat lenses,” Acta Ophthalmol. Suppl. 103, 1–30 (1969).

1966 (1)

1963 (1)

1954 (1)

W. Weinstein, “Computations in thin film optics,” Vacuum 4, 3–19 (1954).
[CrossRef]

1953 (1)

C. Dufour, A. Herpin, “Propogation des ondes électromagnétiques dans un milieu stratifié périodique transparent,” Rev. Opt. Theor. Instrum. 32, 321–348 (1953).

1952 (1)

1947 (1)

A. Herpin, “Calcul du pouvoir réflecteur d’un systéme stratifié quelconque,” C. R. Sceances Acad. Sci. 225, 182–183 (1947).

Abelès, F.

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés. Application aux couches minges,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).

Abramovitz, M.

M. Abramovitz, I. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables (Dover, New York, 1965).

Ali, S.

F. A. Bettelheim, S. Ali, “Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses,” Exp. Eye Res. 41, 1–9 (1985).
[CrossRef] [PubMed]

Alvarado, J. A.

J. M. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Bagg, A.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Beers, A. P.

A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
[PubMed]

Benedek, G. B.

G. B. Benedek, “Cataract as a protein condensation disease: the Proctor lecture,” Invest. Ophthalmol. Visual Sci. 38, 1911–1921 (1997).

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

G. B. Benedek, “Theory of transparency of the eye,” Appl. Opt. 10, 459–473 (1971).
[CrossRef] [PubMed]

Benedek, K.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Bettelheim, F. A.

F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
[CrossRef] [PubMed]

F. A. Bettelheim, S. Ali, “Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses,” Exp. Eye Res. 41, 1–9 (1985).
[CrossRef] [PubMed]

F. A. Bettelheim, M. Paunovic, “Light scattering of normal human lens,” Biophys. J. 26, 85–100 (1973).
[CrossRef]

F. A. Bettelheim, L. Siew, “Biological-physical basis of lens transparency,” in Cell Biology of the Eye, D. S. McDevitt, ed. (Academic, New York, 1982).
[CrossRef]

Bracchi, P. G.

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

Carta, F.

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

Chan, N. Y. C.

B. K. Pierscionek, N. Y. C. Chan, “The refractive index gradient of the human lens,” Invest. Ophthalmol. Visual Sci. 66, 822–829 (1989).

Churchill, A. C.

F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
[CrossRef] [PubMed]

Clark, J. I.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Courant, R.

R. Courant, D. Hilbert, Methoden der Mathematischen Physic (Springer-Verlag, Berlin, 1993).
[CrossRef]

Dolgobrodov, S. G.

B. Pierscionek, R. Green, S. G. Dolgobrodov are preparing a manuscript to be called “Calculation of retinal image for cataractous eye as modeled through a phase aberrating medium.”

Dubbelman, M.

A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
[PubMed]

Dufour, C.

C. Dufour, A. Herpin, “Propogation des ondes électromagnétiques dans un milieu stratifié périodique transparent,” Rev. Opt. Theor. Instrum. 32, 321–348 (1953).

Dyes, W.

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

Epstein, L.

Fasella, P.

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

Green, R.

B. Pierscionek, R. Green, S. G. Dolgobrodov are preparing a manuscript to be called “Calculation of retinal image for cataractous eye as modeled through a phase aberrating medium.”

Hemenger, R. P.

Herpin, A.

C. Dufour, A. Herpin, “Propogation des ondes électromagnétiques dans un milieu stratifié périodique transparent,” Rev. Opt. Theor. Instrum. 32, 321–348 (1953).

A. Herpin, “Calcul du pouvoir réflecteur d’un systéme stratifié quelconque,” C. R. Sceances Acad. Sci. 225, 182–183 (1947).

Hilbert, D.

R. Courant, D. Hilbert, Methoden der Mathematischen Physic (Springer-Verlag, Berlin, 1993).
[CrossRef]

Hogan, J. M.

J. M. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Jacob, T. J.

T. J. Jacob, “The relationship between cataract, cell swelling and volume regulation,” Prog. Retinal Eye Res. 12, 223–233 (1999).
[CrossRef]

Jacobsson, R.

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. 5, pp. 247–286.
[CrossRef]

Keller, M.

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

Landman, K. A.

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1969).

Maraimi, G.

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

Mengel, L.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Miller, D.

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

Moffat, B. A.

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

Paunovic, M.

F. A. Bettelheim, M. Paunovic, “Light scattering of normal human lens,” Biophys. J. 26, 85–100 (1973).
[CrossRef]

Philipson, B.

B. Philipson, “Changes in the lens related to the reduction of transparency,” Exp. Eye Res. 16, 29–39 (1973).
[CrossRef] [PubMed]

B. Philipson, “Biophysical studies on normal and cataractous rat lenses,” Acta Ophthalmol. Suppl. 103, 1–30 (1969).

Pierscionek, B.

B. Pierscionek, R. Green, S. G. Dolgobrodov are preparing a manuscript to be called “Calculation of retinal image for cataractous eye as modeled through a phase aberrating medium.”

Pierscionek, B. K.

B. K. Pierscionek, “Refractive index contours in the human lens,” Exp. Eye Res. 64, 887–893 (1997).
[CrossRef] [PubMed]

B. K. Pierscionek, “Variation in refractive index and absorbance of 670 nm light with eye in cataract formation in human lens,” Exp. Eye Res. 60, 407–413 (1995).
[CrossRef] [PubMed]

B. K. Pierscionek, N. Y. C. Chan, “The refractive index gradient of the human lens,” Invest. Ophthalmol. Visual Sci. 66, 822–829 (1989).

Pope, J. M.

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

Sauke, T.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Serrallach, E. N.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Siew, L.

F. A. Bettelheim, L. Siew, “Biological-physical basis of lens transparency,” in Cell Biology of the Eye, D. S. McDevitt, ed. (Academic, New York, 1982).
[CrossRef]

Stegun, I.

M. Abramovitz, I. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables (Dover, New York, 1965).

Sweeney, M. H.

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

Thelen, A.

Trascott, R. J.

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

van der Heijde, G. L.

A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
[PubMed]

Weddell, J. E.

J. M. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

Weinstein, W.

W. Weinstein, “Computations in thin film optics,” Vacuum 4, 3–19 (1954).
[CrossRef]

Young, C. Y.

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Zigler, J. S.

F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
[CrossRef] [PubMed]

Zuckerman, J. L.

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

Acta Ophthalmol. Suppl. (1)

B. Philipson, “Biophysical studies on normal and cataractous rat lenses,” Acta Ophthalmol. Suppl. 103, 1–30 (1969).

Appl. Opt. (1)

Biophys. J. (1)

F. A. Bettelheim, M. Paunovic, “Light scattering of normal human lens,” Biophys. J. 26, 85–100 (1973).
[CrossRef]

C. R. Sceances Acad. Sci. (1)

A. Herpin, “Calcul du pouvoir réflecteur d’un systéme stratifié quelconque,” C. R. Sceances Acad. Sci. 225, 182–183 (1947).

Curr. Eye Res. (1)

F. A. Bettelheim, A. C. Churchill, J. S. Zigler, “On the nature of hereditary cataract in strain 13/N guinea pigs,” Curr. Eye Res. 16, 917–924 (1997).
[CrossRef] [PubMed]

Exp. Eye Res. (6)

P. G. Bracchi, F. Carta, P. Fasella, G. Maraimi, “Selective binding of age α-crystallin to lens fiber ghost,” Exp. Eye Res. 12, 151–154 (1971).
[CrossRef] [PubMed]

F. A. Bettelheim, S. Ali, “Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses,” Exp. Eye Res. 41, 1–9 (1985).
[CrossRef] [PubMed]

B. A. Moffat, K. A. Landman, R. J. Trascott, M. H. Sweeney, J. M. Pope, “Age-related changes in the kinetics of water transport in normal human lenses,” Exp. Eye Res. 69, 663–669 (1999).
[CrossRef]

B. K. Pierscionek, “Variation in refractive index and absorbance of 670 nm light with eye in cataract formation in human lens,” Exp. Eye Res. 60, 407–413 (1995).
[CrossRef] [PubMed]

B. K. Pierscionek, “Refractive index contours in the human lens,” Exp. Eye Res. 64, 887–893 (1997).
[CrossRef] [PubMed]

B. Philipson, “Changes in the lens related to the reduction of transparency,” Exp. Eye Res. 16, 29–39 (1973).
[CrossRef] [PubMed]

Invest. Ophthalmol. (1)

J. L. Zuckerman, D. Miller, W. Dyes, M. Keller, “Degradation of vision through a simulated cataract,” Invest. Ophthalmol. 12, 213–224 (1973).
[PubMed]

Invest. Ophthalmol. Visual Sci. (2)

G. B. Benedek, “Cataract as a protein condensation disease: the Proctor lecture,” Invest. Ophthalmol. Visual Sci. 38, 1911–1921 (1997).

B. K. Pierscionek, N. Y. C. Chan, “The refractive index gradient of the human lens,” Invest. Ophthalmol. Visual Sci. 66, 822–829 (1989).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Philos. Trans. R. Soc. London Ser. A (1)

G. B. Benedek, J. I. Clark, E. N. Serrallach, C. Y. Young, L. Mengel, T. Sauke, A. Bagg, K. Benedek, “Light scattering and reversible cataracts in the calf and human lens,” Philos. Trans. R. Soc. London Ser. A 293, 329–340 (1979).
[CrossRef]

Prog. Retinal Eye Res. (1)

T. J. Jacob, “The relationship between cataract, cell swelling and volume regulation,” Prog. Retinal Eye Res. 12, 223–233 (1999).
[CrossRef]

Rev. Opt. Theor. Instrum. (1)

C. Dufour, A. Herpin, “Propogation des ondes électromagnétiques dans un milieu stratifié périodique transparent,” Rev. Opt. Theor. Instrum. 32, 321–348 (1953).

Tijdschr. Gerontol. Geriatr. (1)

A. P. Beers, G. L. van der Heijde, M. Dubbelman, “Aging of crystalline lens and presbyopia,” Tijdschr. Gerontol. Geriatr. 29, 185–188 (1998).
[PubMed]

Vacuum (1)

W. Weinstein, “Computations in thin film optics,” Vacuum 4, 3–19 (1954).
[CrossRef]

Other (10)

M. Abramovitz, I. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables (Dover, New York, 1965).

B. Pierscionek, R. Green, S. G. Dolgobrodov are preparing a manuscript to be called “Calculation of retinal image for cataractous eye as modeled through a phase aberrating medium.”

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoidales dans les milieux stratifiés. Application aux couches minges,” Ann. Phys. (Paris)5, 596–640, 706–782 (1950).

R. Courant, D. Hilbert, Methoden der Mathematischen Physic (Springer-Verlag, Berlin, 1993).
[CrossRef]

W. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978).

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. 5, pp. 247–286.
[CrossRef]

H. A. Macleod, Thin-Film Optical Filters (Hilger, London, 1969).

M. Born, E. Wolf, eds., Principles of Optics (Pergamon, New York, 1970).

F. A. Bettelheim, L. Siew, “Biological-physical basis of lens transparency,” in Cell Biology of the Eye, D. S. McDevitt, ed. (Academic, New York, 1982).
[CrossRef]

J. M. Hogan, J. A. Alvarado, J. E. Weddell, Histology of the Human Eye (Saunders, Philadelphia, Pa., 1971).

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Figures (10)

Fig. 1
Fig. 1

Morphological structure of the crystalline lens, as on a normal cut. Thickness of the rhomboidal fibers: h c ≈ 8 µm, widths of the boundary regions h g from 20 nm up to 700 nm.

Fig. 2
Fig. 2

Refractive index in the normal eye: up to ≈1.4 in the center of the nucleus and a linear variation in the outer region of the nucleus from ≈1.37 at the cortex.5 The origin of frame references coincides with the anterior of the area with a higher refractive index. Axis 0, z coincides with the visual axis of the lens.

Fig. 3
Fig. 3

Displacement of a multiply reflected ray along the thin fluid-filled regions between two cellular layers with irregular surfaces and of greater refractive index. Two rhomboid fibers are shown schematically by dotted lines.

Fig. 4
Fig. 4

Dependence of the reflectivity ℛ for the normal incidence (θ1 = 0°), λ = 500–520 nm, h c = 7 µm. (a) h g = 0–100 nm, (b) h g = 100–200 nm, (c) h g = 200–300 nm, (d) h g = 300–500 nm. Parameters correspond to N ≈ 150–175.

Fig. 5
Fig. 5

Slice through Fig. 4(b). Reflectivity ℛ versus λ = 500–520 nm; θ1 = 0°; thickness of layers, h c = 7 µm, h g = 120 nm.

Fig. 6
Fig. 6

Reflectivity ℛ versus θ1 = 0°–8°; thickness of layers, h c = 7 µm, h g = 100–300 nm; λ = 500 nm.

Fig. 7
Fig. 7

Slice through Fig. 6. Reflectivity ℛ versus θ1 = 0°–8°; thickness of layers, h c = 7 µm, h g = 280 nm; λ = 500 nm.

Fig. 8
Fig. 8

Reflectivity ℛ dependence versus thickness of layers: (a) h c = 7–8 µm, h g = 120–200 nm; (b) h g = 200–280 nm, with θ1 = 0°, λ = 500 nm. The space pattern has two periods along the h g axis (short and long).

Fig. 9
Fig. 9

Reflectivity ℛ dependence versus angle of incidence θ1 = 0°–8° and wavelength λ = 500–520 nm; h c = 7 µm, h g = 150 nm.

Fig. 10
Fig. 10

Equivalent refractive index of the pile dependence versus thickness of gaps h g = 100–101.5 nm. h c = 7 µm and wavelength λ = 400 and 500 nm.

Equations (40)

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2=n2r.
ddsn drds=grad n.
r0=rs0,
s0=ss0,
n d2xds2=0,
n d2yds2=0,
n d2zds2+dndsdzds=nz=α.
x=axs+bx,
y=ays+by,
z+n0αd2zds2+dzds2=1.
z0=z0,
z0=z0,
z1,2s=1α-n0±n02+2sαz0αz0+n0+αz0αz0+2n0+α2s21/2.
d2Udz2+k02n2 cos2 θU=0,
d2Vdz2+k02n2 cos2 θV=0,
Mz=cosk0nz cos θ-ipsink0nz cos θ-ip sink0nz cos θcosk0nz cos θ,
U0V0=MzUzVz.
MzN=M1z1M2z2-z1MNzN-zN-1,
βc=2πλ0 nchc cos θc,
βg=2πλ0 nghg cos θg,
pc=nc cos θc,
pg=ng cos θg.
M2h=cos βc cos βg-pgpcsin βc sin βg-ipgcos βc sin βg-ipcsin βc cos βg-ipc sin βc cos βg-ipg cos βc sin βgcos βc cos βg-pcpgsin βc sin βg.
M2NNh=m11m12m21m22,
m11=cos βc cos βg-pgpcsin βc sin βgUN-1a-UN-2a,
m12=-i1pgcos βc sin βg+1pcsin βc cos βgUN-1a,
m21=-ipc sin βc cos βg+pg cos βc sin βgUN-1a,
m22=cos βc cos βg-pcpgsin βc sin βgUN-1a-UN-2a,
a=cos βc cos βg-12pcpg+pgpcsin βc sin βg,
M2N+1N+1h=cos βc-ipcsin βc-ipc sin βccos βc.
=M2NM2N+1.
r=RA=11+12pgpc-21+22pg11+12pgpc+21+22pg,
=|r|2.
+T=1.
λs=2mnchc+nghg, m=1, 2,.
tan αi=AA,
tan αr=cosθi-θtcosθi+θttan αi,
tan αt=cosθi-θttan αi,
cos βe=11=22,
ne=i sin βe12=-i21sin βe.

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