Abstract

Light propagation through a cataractous lens was modeled on the basis of a phase-aberrating medium. The optical frequency characteristics of the modeled optical system were estimated, and examples of foveal images with different values of aberration characteristics were calculated. The phase-aberration effects caused by relatively smooth fluctuations of the refractive index were found to cause a significant deterioration of the foveal image. This theoretical result gives an indication of the main factor that produces image degradation as shown in previous experiments and that is likely to occur in the cataractous eye.

© 2002 Optical Society of America

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    [CrossRef] [PubMed]
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  55. B. A. Wichmann, I. D. Hill, “Algorithm AS 183: an efficient and portable pseudo-random number generator,” Appl. Statist. 31, 188–190 (1982).
    [CrossRef]
  56. R. P. Hemenger, “Small-angle intraocular light scatter: a hypothesis concerning its source,” J. Opt. Soc. Am. A 5, 577–582 (1988).
    [CrossRef] [PubMed]
  57. R. P. Hemenger, “Dependence on angle and wavelength of light scattered by the ocular lens,” Ophthalmic Physiol. Opt. 16, 237–238 (1996).
    [CrossRef] [PubMed]
  58. J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of lens aberrations by means of holography,” Appl. Opt. 5, 589–593 (1966).
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    [CrossRef] [PubMed]

2001 (1)

2000 (1)

1997 (2)

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).

1996 (1)

R. P. Hemenger, “Dependence on angle and wavelength of light scattered by the ocular lens,” Ophthalmic Physiol. Opt. 16, 237–238 (1996).
[CrossRef] [PubMed]

1995 (4)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[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]

P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[CrossRef]

P. Artal, I. Iglesias, N. López-Gil, D. G. Green, “Doublepass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system,” J. Opt. Soc. Am. A 12, 2358–2366 (1995).
[CrossRef]

1993 (1)

G. Suarez, A. L. Oronsky, M. H. L. J. Koch, “Age dependent structural changes in intact human lenses detected by synchrotron radiation x-ray scattering. Correlation with Maillard reaction protein fluorescence,” J. Biol. Chem. 268, 1716–1721 (1993).

1990 (1)

1989 (1)

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

1988 (3)

1987 (3)

J. Santamarı́a, P. Artal, J. Becós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[CrossRef]

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

1985 (1)

1984 (1)

H. H. Hopkins, “Image shift, phase distortion and the optical transfer function,” Opt. Acta 31, 345–368 (1984).
[CrossRef]

1982 (1)

B. A. Wichmann, I. D. Hill, “Algorithm AS 183: an efficient and portable pseudo-random number generator,” Appl. Statist. 31, 188–190 (1982).
[CrossRef]

1981 (1)

B. Philipson, P. P. Fagerholm, “Human subcapsular cataract-distribution of protein in relation to opacification,” Exp. Eye Res. 33, 621–630 (1981).
[CrossRef] [PubMed]

1977 (1)

G. Chan, A. T. A. Wood, “An algorithm for simulating stationary Gaussian random fields,” Appl. Statist. 46, 171–181 (1977).

1973 (4)

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]

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

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

1971 (4)

F. A. Bettelheim, M. J. Vinciguerra, “Laser-diffraction patterns of highly ordered super-structures in the lenses of bovine eyes,” Ann. N.Y. Acad. Sci. 172, 429–439 (1971).
[CrossRef]

M. J. Vinciguerra, F. A. Bettelheim, “Packing and orientation of fiber cells,” Exp. Eye Res. 1, 214–219 (1971).
[CrossRef]

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

J. E. Ward, D. C. Auth, F. P. Carlson, “Lens aberration correction by holography,” Appl. Opt. 10, 896–900 (1971).
[CrossRef] [PubMed]

1969 (1)

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

1968 (1)

1966 (2)

J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of lens aberrations by means of holography,” Appl. Opt. 5, 589–593 (1966).
[CrossRef] [PubMed]

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

1965 (1)

F. W. Campbell, F. W. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 558–578 (1965).

1964 (1)

H. Goldmann, “Senile changes of the lens and the vitreous,” Am. J. Ophthalmol. 57, 1–12 (1964).
[PubMed]

1962 (1)

S. Trokel, “The physical basis for transparency of the crystalline lens,” Invest. Ophthalmol. 1, 493–501 (1962).
[PubMed]

1956 (1)

J. A. Ratcliffe, “Some aspects of diffraction theory and their application to the ionosphere,” Rep. Prog. Phys. 19, 188–267 (1956).
[CrossRef]

1955 (1)

H. H. Hopkins, “The frequency response of a defocusing system,” Proc. R. Soc. London, Ser. A 231, 91–102 (1955).
[CrossRef]

1949 (1)

P. Debye, A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[CrossRef]

1947 (1)

C. L. Pekeris, “Note on the scattering of radiation in an inhomogeneous medium,” Phys. Rev. 71, 268–269 (1947).
[CrossRef]

Artal, P.

Auth, D. C.

Bará, S.

Becós, J.

Benedek, G. B.

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

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

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

Benedek, G. P.

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

Bettelheim, F. A.

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

M. J. Vinciguerra, F. A. Bettelheim, “Packing and orientation of fiber cells,” Exp. Eye Res. 1, 214–219 (1971).
[CrossRef]

F. A. Bettelheim, M. J. Vinciguerra, “Laser-diffraction patterns of highly ordered super-structures in the lenses of bovine eyes,” Ann. N.Y. Acad. Sci. 172, 429–439 (1971).
[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).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Bowen, M. S.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Bueche, A. M.

P. Debye, A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[CrossRef]

Burrows, P.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Campbell, F. W.

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

F. W. Campbell, F. W. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 558–578 (1965).

Carlson, F. P.

Chan, D. Y. C.

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

Chan, G.

G. Chan, A. T. A. Wood, “An algorithm for simulating stationary Gaussian random fields,” Appl. Statist. 46, 171–181 (1977).

Charman, W. N.

W. N. Charman, “Optics of the eye” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

Chylack, L. T.

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

Clark, J. I.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Courant, R.

R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York1962), Vol. 1.

Courogen, M.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Davson, H.

H. Davson, Visual Optics, Vol. 4 of The Eye (Academic, London, 1969).

Debye, P.

P. Debye, A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[CrossRef]

Delaye, M.

A. Tardieu, M. Delaye, “Eye lens proteins and transparency: from light transmission theory to solution x-ray structural analysis,” Annu. Rev. Biophys. Biophys. Chem. 17, 47–70 (1988).
[CrossRef] [PubMed]

Dolgobrodov, S. G.

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]

Dyes, W. A.

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Fagerholm, P. P.

B. Philipson, P. P. Fagerholm, “Human subcapsular cataract-distribution of protein in relation to opacification,” Exp. Eye Res. 33, 621–630 (1981).
[CrossRef] [PubMed]

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Françon, M.

M. Françon, Diffraction. Conherence in Optics (Pergamon, Oxford, UK, 1966).

Fry, G. A.

G. A. Fry, Blur of the Retinal Image (The Ohio State University Press, Columbus, Ohio, 1955).

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Goldmann, H.

H. Goldmann, “Senile changes of the lens and the vitreous,” Am. J. Ophthalmol. 57, 1–12 (1964).
[PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1968, 1996).

Green, D. G.

Green, F. W.

F. W. Campbell, F. W. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 558–578 (1965).

Green, R. J.

Gubisch, R. W.

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

Hemenger, R. P.

R. P. Hemenger, “Dependence on angle and wavelength of light scattered by the ocular lens,” Ophthalmic Physiol. Opt. 16, 237–238 (1996).
[CrossRef] [PubMed]

R. P. Hemenger, “Small-angle intraocular light scatter: a hypothesis concerning its source,” J. Opt. Soc. Am. A 5, 577–582 (1988).
[CrossRef] [PubMed]

Hilbert, D.

R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York1962), Vol. 1.

Hill, I. D.

B. A. Wichmann, I. D. Hill, “Algorithm AS 183: an efficient and portable pseudo-random number generator,” Appl. Statist. 31, 188–190 (1982).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “Image shift, phase distortion and the optical transfer function,” Opt. Acta 31, 345–368 (1984).
[CrossRef]

H. H. Hopkins, “The frequency response of a defocusing system,” Proc. R. Soc. London, Ser. A 231, 91–102 (1955).
[CrossRef]

Hyden, D. L.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Iglesias, I.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. I and II.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Kandel, J.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[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]

Koch, M. H. L. J.

G. Suarez, A. L. Oronsky, M. H. L. J. Koch, “Age dependent structural changes in intact human lenses detected by synchrotron radiation x-ray scattering. Correlation with Maillard reaction protein fluorescence,” J. Biol. Chem. 268, 1716–1721 (1993).

Kogelnik, H.

Leith, E.

Libondi, T.

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

López-Gil, N.

Magnante, P.

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

Mancebo, T.

Marcos, S.

Miller, D.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

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

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

Moreno-Barriuso, E.

Navarro, R.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

Oronsky, A. L.

G. Suarez, A. L. Oronsky, M. H. L. J. Koch, “Age dependent structural changes in intact human lenses detected by synchrotron radiation x-ray scattering. Correlation with Maillard reaction protein fluorescence,” J. Biol. Chem. 268, 1716–1721 (1993).

Paunovic, M.

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

Peetermans, J. A.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Pekeris, C. L.

C. L. Pekeris, “Note on the scattering of radiation in an inhomogeneous medium,” Phys. Rev. 71, 268–269 (1947).
[CrossRef]

Pennett, M.

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

Pennington, K. S.

Philipson, B.

B. Philipson, P. P. Fagerholm, “Human subcapsular cataract-distribution of protein in relation to opacification,” Exp. Eye Res. 33, 621–630 (1981).
[CrossRef] [PubMed]

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 (1969).

Pierscionek, B.

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

Ratcliffe, J. A.

J. A. Ratcliffe, “Some aspects of diffraction theory and their application to the ionosphere,” Rep. Prog. Phys. 19, 188–267 (1956).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

Santamari´a, J.

Shack, R. V.

R. V. Shack, “On the optical significance of the phase transfer function,” in Quantitative Imagery in the Biomedical Sciences II, R. E. Herron, ed., Proc. SPIE4, 39–43 (1974).
[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).

Stern, H.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Storb, R.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Suarez, G.

G. Suarez, A. L. Oronsky, M. H. L. J. Koch, “Age dependent structural changes in intact human lenses detected by synchrotron radiation x-ray scattering. Correlation with Maillard reaction protein fluorescence,” J. Biol. Chem. 268, 1716–1721 (1993).

Sullivan, K. L.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Tardieu, A.

A. Tardieu, M. Delaye, “Eye lens proteins and transparency: from light transmission theory to solution x-ray structural analysis,” Annu. Rev. Biophys. Biophys. Chem. 17, 47–70 (1988).
[CrossRef] [PubMed]

Taret, V. G.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Thurston, G. M.

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Trokel, S.

S. Trokel, “The physical basis for transparency of the crystalline lens,” Invest. Ophthalmol. 1, 493–501 (1962).
[PubMed]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, San Diego, Calif., 1998).

Upatnieks, J.

Vander Lugt, A.

Vinciguerra, M. J.

F. A. Bettelheim, M. J. Vinciguerra, “Laser-diffraction patterns of highly ordered super-structures in the lenses of bovine eyes,” Ann. N.Y. Acad. Sci. 172, 429–439 (1971).
[CrossRef]

M. J. Vinciguerra, F. A. Bettelheim, “Packing and orientation of fiber cells,” Exp. Eye Res. 1, 214–219 (1971).
[CrossRef]

von Helmholtz, H.

H. von Helmholtz, Physiological Optics (The Optical Society of America, New York, 1924), Vol. I.

Ward, J. E.

Wichmann, B. A.

B. A. Wichmann, I. D. Hill, “Algorithm AS 183: an efficient and portable pseudo-random number generator,” Appl. Statist. 31, 188–190 (1982).
[CrossRef]

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Wood, A. T. A.

G. Chan, A. T. A. Wood, “An algorithm for simulating stationary Gaussian random fields,” Appl. Statist. 46, 171–181 (1977).

Yaglom, A. M.

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, N.J., 1962).

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]

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

Acta Ophthalmol. Suppl. (1)

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

Am. J. Ophthalmol. (1)

H. Goldmann, “Senile changes of the lens and the vitreous,” Am. J. Ophthalmol. 57, 1–12 (1964).
[PubMed]

Ann. N.Y. Acad. Sci. (1)

F. A. Bettelheim, M. J. Vinciguerra, “Laser-diffraction patterns of highly ordered super-structures in the lenses of bovine eyes,” Ann. N.Y. Acad. Sci. 172, 429–439 (1971).
[CrossRef]

Annu. Rev. Biophys. Biophys. Chem. (1)

A. Tardieu, M. Delaye, “Eye lens proteins and transparency: from light transmission theory to solution x-ray structural analysis,” Annu. Rev. Biophys. Biophys. Chem. 17, 47–70 (1988).
[CrossRef] [PubMed]

Appl. Opt. (4)

Appl. Statist. (2)

G. Chan, A. T. A. Wood, “An algorithm for simulating stationary Gaussian random fields,” Appl. Statist. 46, 171–181 (1977).

B. A. Wichmann, I. D. Hill, “Algorithm AS 183: an efficient and portable pseudo-random number generator,” Appl. Statist. 31, 188–190 (1982).
[CrossRef]

Biophys. J. (1)

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

Curr. Eye Res. (2)

G. P. Benedek, L. T. Chylack, T. Libondi, P. Magnante, M. Pennett, “Quantitative detection of the molecular changes associated with early catarogenesis in living human lens using quasielastic light scattering,” Curr. Eye Res. 6, 1421–1432 (1987).
[CrossRef] [PubMed]

G. M. Thurston, D. L. Hyden, P. Burrows, J. I. Clark, V. G. Taret, J. Kandel, M. Courogen, J. A. Peetermans, M. S. Bowen, D. Miller, K. L. Sullivan, R. Storb, H. Stern, G. B. Benedek, “Quasielastic light scattering study of the living human lens as a function of age,” Curr. Eye Res. 16, 197–207 (1987).
[CrossRef]

Exp. Eye Res. (5)

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]

M. J. Vinciguerra, F. A. Bettelheim, “Packing and orientation of fiber cells,” Exp. Eye Res. 1, 214–219 (1971).
[CrossRef]

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

B. Philipson, P. P. Fagerholm, “Human subcapsular cataract-distribution of protein in relation to opacification,” Exp. Eye Res. 33, 621–630 (1981).
[CrossRef] [PubMed]

Invest. Ophthalmol. (2)

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

S. Trokel, “The physical basis for transparency of the crystalline lens,” Invest. Ophthalmol. 1, 493–501 (1962).
[PubMed]

Invest. Ophthalmol. Visual Sci. (2)

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

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

J. Appl. Phys. (1)

P. Debye, A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20, 518–525 (1949).
[CrossRef]

J. Biol. Chem. (1)

G. Suarez, A. L. Oronsky, M. H. L. J. Koch, “Age dependent structural changes in intact human lenses detected by synchrotron radiation x-ray scattering. Correlation with Maillard reaction protein fluorescence,” J. Biol. Chem. 268, 1716–1721 (1993).

J. Opt. Soc. Am. (1)

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

J. Physiol. (2)

F. W. Campbell, F. W. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 558–578 (1965).

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

Ophthalmic Physiol. Opt. (1)

R. P. Hemenger, “Dependence on angle and wavelength of light scattered by the ocular lens,” Ophthalmic Physiol. Opt. 16, 237–238 (1996).
[CrossRef] [PubMed]

Opt. Acta (1)

H. H. Hopkins, “Image shift, phase distortion and the optical transfer function,” Opt. Acta 31, 345–368 (1984).
[CrossRef]

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[CrossRef]

Opt. Eng. (1)

G. O. Reynolds, J. L. Zuckerman, W. A. Dyes, D. Miller, “Holographic phase compensation techniques applied to human cataracts,” Opt. Eng. 12, 23–34 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

C. L. Pekeris, “Note on the scattering of radiation in an inhomogeneous medium,” Phys. Rev. 71, 268–269 (1947).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

H. H. Hopkins, “The frequency response of a defocusing system,” Proc. R. Soc. London, Ser. A 231, 91–102 (1955).
[CrossRef]

Rep. Prog. Phys. (1)

J. A. Ratcliffe, “Some aspects of diffraction theory and their application to the ionosphere,” Rep. Prog. Phys. 19, 188–267 (1956).
[CrossRef]

Other (18)

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, San Diego, Calif., 1998).

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, N.J., 1962).

R. Navarro, “Objective measurements of the optical image quality in the human eye,” in Optical Technologies in Biophysics and Medicine II, V. V. Tuchin, ed., Proc. SPIE4241, 127–137 (2001), www.io.csic.es/saratov.pdf .
[CrossRef]

R. Navarro, “Objective measurement of the optical image quality in the human eye,” www.io.csic.es/tutor_rn1/v3dcmnt.htm (2002).

R. V. Shack, “On the optical significance of the phase transfer function,” in Quantitative Imagery in the Biomedical Sciences II, R. E. Herron, ed., Proc. SPIE4, 39–43 (1974).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1968, 1996).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

M. Françon, Diffraction. Conherence in Optics (Pergamon, Oxford, UK, 1966).

R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York1962), Vol. 1.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. I and II.

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).

W. N. Charman, “Optics of the eye” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II.

H. von Helmholtz, Physiological Optics (The Optical Society of America, New York, 1924), Vol. I.

H. Davson, Visual Optics, Vol. 4 of The Eye (Academic, London, 1969).

G. A. Fry, Blur of the Retinal Image (The Ohio State University Press, Columbus, Ohio, 1955).

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Figures (9)

Fig. 1
Fig. 1

Simplified model of the light ray tracing through the eye lens in the paraxial approximation.

Fig. 2
Fig. 2

Simplified model of a lens section along the fiber cells.

Fig. 3
Fig. 3

Foveal image suffering from phase aberrations caused by the refractive index n d + n s with different deviation parameters: A, Δ n d = 0 , σ s = 0 ; B, Δ n d = 0 , σ s = 0.65 × 10 - 4 ; C, Δ n d = 3 × 10 - 3 , σ s = 0 ; D, Δ n d = 3 × 10 - 3 , σ s = 0.5 × 10 - 4 .

Fig. 4
Fig. 4

Effect of phase aberrations caused by quadratically distributed refractive index n d . The frequency response is plotted against spatial frequency f and deviations in the refractive-index gradient: Δ n d = 0 6 × 10 - 3 .

Fig. 5
Fig. 5

Effect of phase aberrations caused by refractive index n s normally distributed in the lens. Normalized frequency response is plotted against spatial frequency f and deviations in the localized refractive index: σ s = 0 1.2 × 10 - 4 .

Fig. 6
Fig. 6

Foveal image of a sine-wave grating suffering from phase aberrations caused by refractive index n d + n s with different deviations: A, Δ n d = 0 ; B, 2 × 10 - 3 ; C, 4 × 10 - 3 ; σ s = 0 for all three images. The spatial frequency increases logarithmically from 0 to 36 cycles/deg.

Fig. 7
Fig. 7

Foveal image of a sine-wave grating suffering from phase aberrations caused by refractive index n d + n s with the deviations Δ n d = 5.5 × 10 - 3 and σ s = 0 . On the top of the image zones of contrast reversal are indicated by signs ↓ and ↑ for contrast decreasing and increasing, respectively. The spatial frequency increases logarithmically from 0 to 36 cycles/deg.

Fig. 8
Fig. 8

Foveal image of a sine-wave grating suffering from phase aberrations caused by refractive index n d + n s with different deviations: A, Δ n d = 0 , σ s = 0.1 × 10 - 4 ; B, σ s = 0.5 × 10 - 4 ; C, σ s = 0.65 × 10 - 4 ; D, Δ n d = 3 × 10 - 3 , σ s = 0.5 × 10 - 4 . The spatial frequency increases logarithmically from 0 to 36 cycles/deg.

Fig. 9
Fig. 9

Normalized frequency response plotted against Δ n d , σ s for varying spatial frequencies f = 2 , 8, and 15 cycles/deg.

Equations (22)

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

x o = MX o , y o = MY o ,
I i = U i ,   U i * t ,
I i ( x i ,   y i ) = - I o ( x o ,   y o ) × | K ( x i - x o ,   y i - y o ) | 2 d x o d y o ,
K ( x i - x o ,   y i - y o ) = 1 ( λ R ) 2 - P ( ξ ,   η ) × exp - 2 π i λ R [ ( x i - x o ) ξ + ( y i - y o ) η ] d ξ d η ,
0 P ( ξ ,   η ) 1 when ( ξ ,   η ) Σ ,
P ( ξ ,   η ) = 0 elsewhere .
P ( ξ ,   η ) = P ( ξ ,   η ) exp [ i Φ ( ξ ,   η ) ] .
L ξ λ R ,   η λ R = 1 ( λ R ) 2 - P ( ξ + ξ ,   η + η ) × P * ( ξ ,   η ) d ξ d η ,
L ξ λ R ,   η λ R 2 = 1 ( λ R ) 2 - P ( ξ + ξ ,   η + η ) P * ( ξ ,   η ) d ξ d η 2 1 ( λ R ) 2 - | P | 2 · - | P * | 2 = 1 ( λ R ) - P ( ξ + ξ ,   η + η ) d ξ d η 2 .
W ( ξ ,   η ) = z a z p [ n d ( ξ ,   η ,   z ) + n s ( ξ ,   η ,   z ) ] d z = z a z p n d ( ξ ,   η ,   z ) d z + z a z p n s ( ξ ,   η ,   z ) d z = W d ( ξ ,   η ) + W s ( ξ ,   η ) ,
δ ( r ) = δ 0 - 2 R c [ 1 - ( 1 - r 2 / R c 2 ) 1 / 2 ] ,
W s ( ξ ,   η ) = n s ( ξ ,   η ) δ ( r ) = n s ( ξ ,   η ) { δ 0 - 2 R c [ 1 - ( 1 - r 2 / R c 2 ) 1 / 2 ] } .
W s ( ξ ,   η ) = n s ( ξ ,   η ) ( δ 0 - r 2 / R c ) .
W s ( ξ ,   η ) = λ ζ ( ξ ,   η ) ( 1 - α r 2 / R c 2 ) .
D n s ( r ) = def [ n ˜ s ( r 0 + r ) - n ˜ s ( r 0 ) ] 2 ¯ .
D n s ( r ) = 8 π 0 Ψ n s ( k ) k 2 ( 1 - sin   kr / kr ) d k .
W d ( ξ ,   η ) = W d ( r ) = n d ( r ) δ ( r ) = [ n d 0 + Δ n d ( 1 - r 2 / R a 2 ) ] δ ( r ) = n d 0 δ ( r ) + Δ n d ( 1 - r 2 / R a 2 ) δ ( r ) .
W d ( r ) = Δ n d ( 1 - r 2 / R a 2 ) δ ( r ) .
A Δ n d = 0 , σ s = 0 ,
B Δ n d = 0 , σ s = 0.65 × 10 - 4 ,
C Δ n d = 3 × 10 - 3 , σ s = 0 ,
D Δ n d = 3 × 10 - 3 , σ s = 0.5 × 10 - 4 .

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