Abstract

Accommodation in the human eye occurs through controlled changes in crystalline lens shape, thickness, and refractive surface placement relative to the cornea. The changes in lens curvatures, whether surface or internal, have been characterized as a function of accommodation and subject age by use of quantitative analysis of Scheimpflug slit-lamp photographic images. Radii of curvature of the major lens refractive surfaces—the external and nuclear boundaries—decrease linearly with increasing accommodation in all eyes that are capable of accommodation. The rates at which they change with accommodation are age dependent, decreasing steadily toward zero with increased age. For the curves visible in each lens half, arising from boundaries between adjacent zones of discontinuity, radius of curvature and location are linearly related over the entire accommodative range for a given lens and over the age range for the population. The slope of this relationship changes with both accommodation and age, decreasing linearly in both cases. The relationship between these geometric changes and the loss of accommodative amplitude is discussed.

© 2002 Optical Society of America

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  1. A. Duane, “Studies in monocular and binocular accommodation with their clinical applications,” Am. J. Ophthalmol. 5, 867–877 (1922).
  2. D. A. Atchison, “Accommodation and presbyopia,” Ophthalmic Physiol. Opt. 15, 255–272 (1995).
    [CrossRef] [PubMed]
  3. A. P. Beers, G. L. van der Heijde, “Age-related changes in the accommodation mechanism,” Optom. Vision Sci. 73, 235–242 (1996).
    [CrossRef]
  4. A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
    [CrossRef] [PubMed]
  5. D. J. Coleman, “Unified model for accommodative mechanism,” Am. J. Ophthalmol. 69, 1063–1079 (1970).
    [PubMed]
  6. J. F. Koretz, “Development and aging of human visual focusing mechanisms,” in Trends in Optonics and Photonics: Vision Science and Its Applications, V. Lakshminarayanan, ed. (Optical Society of America, Washington, D.C., 2000), Vol. 35, pp. 246–258.
  7. B. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76, 83–91 (1993).
    [CrossRef]
  8. H. J. Wyatt, R. F. Fisher, “A simple view of age-related changes in the shape of the lens of the human eye,” Eye 9, 772–775 (1995).
    [CrossRef] [PubMed]
  9. 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]
  10. J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
    [CrossRef] [PubMed]
  11. J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).
  12. N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
    [CrossRef] [PubMed]
  13. J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
    [CrossRef]
  14. J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
    [CrossRef] [PubMed]
  15. C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
    [CrossRef] [PubMed]
  16. J. F. Koretz, C. A. Cook, P. L. Kaufman, “Aging of the human lens: changes in lens shape at zero-diopter accommodation,” J. Opt. Soc. Am. A 18, 265–272 (2001).
    [CrossRef]
  17. N. Brown, “An advanced slit-image camera,” Br. J. Ophthamol. 56, 624–631 (1972).
    [CrossRef]
  18. C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit lamp images: an application of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
    [CrossRef] [PubMed]
  19. C. A. Cook, J. F. Koretz, “Methods to obtain quantitative parametric descriptions of the optical surfaces of the human crystalline lens from Scheimpflug slit-lamp images. I. Image processing methods,” J. Opt. Soc. Am. A 15, 1473–1485 (1998).
    [CrossRef]
  20. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  21. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).
  22. C. A. Cook, J. F. Koretz, “The geometric theory of accommodation and presbyopia: new insights and new results,” J. Math. Game Theory Algebra 5, 55–76 (1996).
  23. J. F. Koretz, G. H. Handelman, “Model of the accommodative mechanism in the human eye,” Vision Res. 22, 917–927 (1982).
    [CrossRef] [PubMed]
  24. J. F. Koretz, G. H. Handelman, “A model for accommodation in the young human eye: the effects of lens elastic anisotropy on the mechanism,” Vision Res. 23, 1679–1686 (1983).
    [CrossRef] [PubMed]
  25. B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).
  26. S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).
  27. M. T. Pardue, J. G. Sivak, “The functional anatomy of the ciliary muscle in four avian species,” Brain Behav. Evol. 49, 295–311 (1997).
    [CrossRef] [PubMed]
  28. J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
    [CrossRef] [PubMed]
  29. J. F. Koretz, G. H. Handelman, “How the human eye focuses,” Sci. Am. 259(1), 92–99 (1988).
    [CrossRef] [PubMed]
  30. O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics (Springer-Verlag, Berlin, 1983), pp. 12–21.
  31. J. F. Koretz, G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in The Lens: Transparency and Cataract, G. Duncan, ed. (EURAGE, Rijswijk, The Netherlands, 1986), Vol. 6, pp. 57–64.
  32. B. K. Pierscionek, D. Y. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66(1), 822–829 (1989).
    [CrossRef]
  33. G. Smith, D. A. Atchison, B. K. Pierscionek, “Modeling the power of the aging human eye,” J. Opt. Soc. Am. A 9, 2111–2117 (1992).
    [CrossRef] [PubMed]
  34. I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
    [CrossRef] [PubMed]
  35. J. F. Koretz, C. A. Cook, “Aging of the optics of the human eye: lens refraction models and principal plane locations,” Optom. Vision Sci. 78 , (special issue on the aging eye), 396–404 (2001).
    [CrossRef]

2001 (2)

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Aging of the human lens: changes in lens shape at zero-diopter accommodation,” J. Opt. Soc. Am. A 18, 265–272 (2001).
[CrossRef]

J. F. Koretz, C. A. Cook, “Aging of the optics of the human eye: lens refraction models and principal plane locations,” Optom. Vision Sci. 78 , (special issue on the aging eye), 396–404 (2001).
[CrossRef]

2000 (1)

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

1999 (1)

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

1998 (1)

1997 (2)

M. T. Pardue, J. G. Sivak, “The functional anatomy of the ciliary muscle in four avian species,” Brain Behav. Evol. 49, 295–311 (1997).
[CrossRef] [PubMed]

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).

1996 (2)

A. P. Beers, G. L. van der Heijde, “Age-related changes in the accommodation mechanism,” Optom. Vision Sci. 73, 235–242 (1996).
[CrossRef]

C. A. Cook, J. F. Koretz, “The geometric theory of accommodation and presbyopia: new insights and new results,” J. Math. Game Theory Algebra 5, 55–76 (1996).

1995 (2)

H. J. Wyatt, R. F. Fisher, “A simple view of age-related changes in the shape of the lens of the human eye,” Eye 9, 772–775 (1995).
[CrossRef] [PubMed]

D. A. Atchison, “Accommodation and presbyopia,” Ophthalmic Physiol. Opt. 15, 255–272 (1995).
[CrossRef] [PubMed]

1994 (1)

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

1993 (1)

B. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76, 83–91 (1993).
[CrossRef]

1992 (1)

1991 (2)

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit lamp images: an application of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
[CrossRef] [PubMed]

1989 (3)

B. K. Pierscionek, D. Y. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66(1), 822–829 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

1988 (1)

J. F. Koretz, G. H. Handelman, “How the human eye focuses,” Sci. Am. 259(1), 92–99 (1988).
[CrossRef] [PubMed]

1987 (1)

B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).

1985 (1)

J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
[CrossRef] [PubMed]

1984 (1)

J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

1983 (1)

J. F. Koretz, G. H. Handelman, “A model for accommodation in the young human eye: the effects of lens elastic anisotropy on the mechanism,” Vision Res. 23, 1679–1686 (1983).
[CrossRef] [PubMed]

1982 (1)

J. F. Koretz, G. H. Handelman, “Model of the accommodative mechanism in the human eye,” Vision Res. 22, 917–927 (1982).
[CrossRef] [PubMed]

1974 (1)

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

1973 (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]

1972 (1)

N. Brown, “An advanced slit-image camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

1970 (1)

D. J. Coleman, “Unified model for accommodative mechanism,” Am. J. Ophthalmol. 69, 1063–1079 (1970).
[PubMed]

1922 (1)

A. Duane, “Studies in monocular and binocular accommodation with their clinical applications,” Am. J. Ophthalmol. 5, 867–877 (1922).

Atchison, D. A.

Beers, A. P.

A. P. Beers, G. L. van der Heijde, “Age-related changes in the accommodation mechanism,” Optom. Vision Sci. 73, 235–242 (1996).
[CrossRef]

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Bron, A. J.

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

Brown, N.

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

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]

N. Brown, “An advanced slit-image camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

Brown, N. P.

J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

Chan, D. Y.

B. K. Pierscionek, D. Y. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66(1), 822–829 (1989).
[CrossRef]

Coleman, D. J.

D. J. Coleman, “Unified model for accommodative mechanism,” Am. J. Ophthalmol. 69, 1063–1079 (1970).
[PubMed]

Cook, C. A.

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Aging of the human lens: changes in lens shape at zero-diopter accommodation,” J. Opt. Soc. Am. A 18, 265–272 (2001).
[CrossRef]

J. F. Koretz, C. A. Cook, “Aging of the optics of the human eye: lens refraction models and principal plane locations,” Optom. Vision Sci. 78 , (special issue on the aging eye), 396–404 (2001).
[CrossRef]

C. A. Cook, J. F. Koretz, “Methods to obtain quantitative parametric descriptions of the optical surfaces of the human crystalline lens from Scheimpflug slit-lamp images. I. Image processing methods,” J. Opt. Soc. Am. A 15, 1473–1485 (1998).
[CrossRef]

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).

C. A. Cook, J. F. Koretz, “The geometric theory of accommodation and presbyopia: new insights and new results,” J. Math. Game Theory Algebra 5, 55–76 (1996).

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit lamp images: an application of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
[CrossRef] [PubMed]

de Mul, F. F.

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

DeMarco, J. K.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Duane, A.

A. Duane, “Studies in monocular and binocular accommodation with their clinical applications,” Am. J. Ophthalmol. 5, 867–877 (1922).

Dufault, P.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics (Springer-Verlag, Berlin, 1983), pp. 12–21.

Fisher, R. F.

H. J. Wyatt, R. F. Fisher, “A simple view of age-related changes in the shape of the lens of the human eye,” Eye 9, 772–775 (1995).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).

Goeckner, P. A.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Goldstein, R.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics (Springer-Verlag, Berlin, 1983), pp. 12–21.

Greve, J.

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

Gronlund-Jacob, J.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Handelman, G. H.

J. F. Koretz, G. H. Handelman, “How the human eye focuses,” Sci. Am. 259(1), 92–99 (1988).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “A model for accommodation in the young human eye: the effects of lens elastic anisotropy on the mechanism,” Vision Res. 23, 1679–1686 (1983).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “Model of the accommodative mechanism in the human eye,” Vision Res. 22, 917–927 (1982).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in The Lens: Transparency and Cataract, G. Duncan, ed. (EURAGE, Rijswijk, The Netherlands, 1986), Vol. 6, pp. 57–64.

Harding, J. J.

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

Hildebrand, T.

J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
[CrossRef] [PubMed]

Hyun, J.

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

Kappelhof, J.

B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).

Kaufman, P. L.

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Aging of the human lens: changes in lens shape at zero-diopter accommodation,” J. Opt. Soc. Am. A 18, 265–272 (2001).
[CrossRef]

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

Koretz, J.

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

Koretz, J. F.

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Aging of the human lens: changes in lens shape at zero-diopter accommodation,” J. Opt. Soc. Am. A 18, 265–272 (2001).
[CrossRef]

J. F. Koretz, C. A. Cook, “Aging of the optics of the human eye: lens refraction models and principal plane locations,” Optom. Vision Sci. 78 , (special issue on the aging eye), 396–404 (2001).
[CrossRef]

C. A. Cook, J. F. Koretz, “Methods to obtain quantitative parametric descriptions of the optical surfaces of the human crystalline lens from Scheimpflug slit-lamp images. I. Image processing methods,” J. Opt. Soc. Am. A 15, 1473–1485 (1998).
[CrossRef]

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).

C. A. Cook, J. F. Koretz, “The geometric theory of accommodation and presbyopia: new insights and new results,” J. Math. Game Theory Algebra 5, 55–76 (1996).

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

C. A. Cook, J. F. Koretz, “Acquisition of the curves of the human crystalline lens from slit lamp images: an application of the Hough transform,” Appl. Opt. 30, 2088–2099 (1991).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, G. H. Handelman, “How the human eye focuses,” Sci. Am. 259(1), 92–99 (1988).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “A model for accommodation in the young human eye: the effects of lens elastic anisotropy on the mechanism,” Vision Res. 23, 1679–1686 (1983).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “Model of the accommodative mechanism in the human eye,” Vision Res. 22, 917–927 (1982).
[CrossRef] [PubMed]

J. F. Koretz, “Development and aging of human visual focusing mechanisms,” in Trends in Optonics and Photonics: Vision Science and Its Applications, V. Lakshminarayanan, ed. (Optical Society of America, Washington, D.C., 2000), Vol. 35, pp. 246–258.

J. F. Koretz, G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in The Lens: Transparency and Cataract, G. Duncan, ed. (EURAGE, Rijswijk, The Netherlands, 1986), Vol. 6, pp. 57–64.

Lebert, C.

J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
[CrossRef] [PubMed]

Maraini, G.

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

Munoz, P.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Neider, M. W.

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye. 1: Evaluation of in vivo measurement techniques,” Appl. Opt. 28, 1097–1102 (1989).
[CrossRef] [PubMed]

Pardue, M. T.

M. T. Pardue, J. G. Sivak, “The functional anatomy of the ciliary muscle in four avian species,” Brain Behav. Evol. 49, 295–311 (1997).
[CrossRef] [PubMed]

Pfahnl, A.

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

Pierscionek, B.

B. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76, 83–91 (1993).
[CrossRef]

Pierscionek, B. K.

G. Smith, D. A. Atchison, B. K. Pierscionek, “Modeling the power of the aging human eye,” J. Opt. Soc. Am. A 9, 2111–2117 (1992).
[CrossRef] [PubMed]

B. K. Pierscionek, D. Y. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66(1), 822–829 (1989).
[CrossRef]

Pomerantzeff, O.

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics (Springer-Verlag, Berlin, 1983), pp. 12–21.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).

Semmlow, J. L.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Siebinga, I.

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

Sivak, J. G.

M. T. Pardue, J. G. Sivak, “The functional anatomy of the ciliary muscle in four avian species,” Brain Behav. Evol. 49, 295–311 (1997).
[CrossRef] [PubMed]

J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
[CrossRef] [PubMed]

Smith, G.

Strenk, L. M.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Strenk, S. A.

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).

van der Heijde, G. L.

A. P. Beers, G. L. van der Heijde, “Age-related changes in the accommodation mechanism,” Optom. Vision Sci. 73, 235–242 (1996).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).

Vrensen, G.

B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).

Vrensen, G. F.

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

Willekens, B.

B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).

Wyatt, H. J.

H. J. Wyatt, R. F. Fisher, “A simple view of age-related changes in the shape of the lens of the human eye,” Eye 9, 772–775 (1995).
[CrossRef] [PubMed]

Am. J. Ophthalmol. (2)

A. Duane, “Studies in monocular and binocular accommodation with their clinical applications,” Am. J. Ophthalmol. 5, 867–877 (1922).

D. J. Coleman, “Unified model for accommodative mechanism,” Am. J. Ophthalmol. 69, 1063–1079 (1970).
[PubMed]

Appl. Opt. (2)

Br. J. Ophthamol. (1)

N. Brown, “An advanced slit-image camera,” Br. J. Ophthamol. 56, 624–631 (1972).
[CrossRef]

Brain Behav. Evol. (1)

M. T. Pardue, J. G. Sivak, “The functional anatomy of the ciliary muscle in four avian species,” Brain Behav. Evol. 49, 295–311 (1997).
[CrossRef] [PubMed]

Clin. Exp. Optom. (1)

B. Pierscionek, “What we know and understand about presbyopia,” Clin. Exp. Optom. 76, 83–91 (1993).
[CrossRef]

Exp. Eye Res. (3)

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]

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19, 175–183 (1974).
[CrossRef] [PubMed]

I. Siebinga, G. F. Vrensen, F. F. de Mul, J. Greve, “Age-related changes in local water and protein content of human eye lenses measured by Raman microspectroscopy,” Exp. Eye Res. 53, 233–239 (1991).
[CrossRef] [PubMed]

Eye (1)

H. J. Wyatt, R. F. Fisher, “A simple view of age-related changes in the shape of the lens of the human eye,” Eye 9, 772–775 (1995).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (2)

J. F. Koretz, C. A. Cook, P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Visual Sci. 38, 569–578 (1997).

S. A. Strenk, J. L. Semmlow, L. M. Strenk, P. Munoz, J. Gronlund-Jacob, J. K. DeMarco, “Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study,” Invest. Ophthalmol. Visual Sci. 40, 1162–1169 (1999).

J. Math. Game Theory Algebra (1)

C. A. Cook, J. F. Koretz, “The geometric theory of accommodation and presbyopia: new insights and new results,” J. Math. Game Theory Algebra 5, 55–76 (1996).

J. Opt. Soc. Am. A (3)

Lens Res. (1)

B. Willekens, J. Kappelhof, G. Vrensen, “Morphology of the aging human lens. I. Biomicroscopy and biometrics,” Lens Res. 4, 207–230 (1987).

Ophthalmic Physiol. Opt. (1)

D. A. Atchison, “Accommodation and presbyopia,” Ophthalmic Physiol. Opt. 15, 255–272 (1995).
[CrossRef] [PubMed]

Ophthalmologica (1)

A. J. Bron, G. F. Vrensen, J. Koretz, G. Maraini, J. J. Harding, “The ageing lens,” Ophthalmologica 214, 86–104 (2000).
[CrossRef] [PubMed]

Optom. Vision Sci. (3)

A. P. Beers, G. L. van der Heijde, “Age-related changes in the accommodation mechanism,” Optom. Vision Sci. 73, 235–242 (1996).
[CrossRef]

B. K. Pierscionek, D. Y. Chan, “Refractive index gradient of human lenses,” Optom. Vision Sci. 66(1), 822–829 (1989).
[CrossRef]

J. F. Koretz, C. A. Cook, “Aging of the optics of the human eye: lens refraction models and principal plane locations,” Optom. Vision Sci. 78 , (special issue on the aging eye), 396–404 (2001).
[CrossRef]

Sci. Am. (1)

J. F. Koretz, G. H. Handelman, “How the human eye focuses,” Sci. Am. 259(1), 92–99 (1988).
[CrossRef] [PubMed]

Vision Res. (6)

J. G. Sivak, T. Hildebrand, C. Lebert, “Magnitude and rate of accommodation in diving and nondiving birds,” Vision Res. 25, 925–933 (1985).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “Model of the accommodative mechanism in the human eye,” Vision Res. 22, 917–927 (1982).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, “A model for accommodation in the young human eye: the effects of lens elastic anisotropy on the mechanism,” Vision Res. 23, 1679–1686 (1983).
[CrossRef] [PubMed]

J. F. Koretz, G. H. Handelman, N. P. Brown, “Analysis of human crystalline lens curvature as a function of accommodative state and age,” Vision Res. 24, 1141–1151 (1984).
[CrossRef] [PubMed]

J. F. Koretz, P. L. Kaufman, M. W. Neider, P. A. Goeckner, “Accommodation and presbyopia in the human eye—aging of the anterior segment,” Vision Res. 29, 1685–1692 (1989).
[CrossRef]

C. A. Cook, J. F. Koretz, A. Pfahnl, J. Hyun, P. L. Kaufman, “Aging of the human crystalline lens and anterior segment,” Vision Res. 34, 2945–2954 (1994).
[CrossRef] [PubMed]

Other (5)

J. F. Koretz, “Development and aging of human visual focusing mechanisms,” in Trends in Optonics and Photonics: Vision Science and Its Applications, V. Lakshminarayanan, ed. (Optical Society of America, Washington, D.C., 2000), Vol. 35, pp. 246–258.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989).

O. Pomerantzeff, P. Dufault, R. Goldstein, “Wide-angle optical model of the eye,” in Advances in Diagnostic Visual Optics (Springer-Verlag, Berlin, 1983), pp. 12–21.

J. F. Koretz, G. H. Handelman, “The ‘lens paradox’ and image formation in accommodating human eyes,” in The Lens: Transparency and Cataract, G. Duncan, ed. (EURAGE, Rijswijk, The Netherlands, 1986), Vol. 6, pp. 57–64.

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Figures (9)

Fig. 1
Fig. 1

Cornea and lens curves for the illustrative example, a subject age 19 yr at 0 and 9.25 D accommodation. The center of the anterior corneal surface is the origin for all distances, but neither corneal curve is accurate. The lens curves, all of which are well fitted to second-order polynomials, exhibit reduced radii of curvature with accommodation. Changes in lens curve location relative to the cornea are much greater for the lens anterior, and they result primarily from changes in lens nucleus shape. LAS and LPS refer to lens anterior and posterior surfaces; NAB and NPB to the nuclear anterior and posterior boundaries; and FNPB and FNAB represent fetal nuclear boundaries.

Fig. 2
Fig. 2

Central radius of curvature as a function of accommodation for the four major lens surfaces of the illustrative example, data for which was taken on two different days and merged: lens anterior and posterior surfaces (LAS and LPS) and nuclear anterior and posterior boundaries (NAB and NPB).

Fig. 3
Fig. 3

Radius of curvature from the illustrative example as a function of vertex location yo along the sagittal axis for discernible boundaries in (a) the lens anterior half, where the diamonds represent 0 D, the triangles 4 D, and the inverted triangles 9.25 D and for (b) the lens posterior half, where the diamonds represent 0 D and the triangles 3.25 D. The error bars represent the error in R and y associated with fitting a second-order polynomial to each curve by using the Hough transform. Note that the slopes of the relationships become shallower with increasing accommodation.

Fig. 4
Fig. 4

Rate of change of the central radius of curvature Rm with accommodation, plotted as a function of age, for (a) the lens anterior surface (LAS) and (b) the lens posterior surface (LPS). Open circles and solid lines represent data to age 45 yr, while ×s and dashed lines represent the entire data set.

Fig. 5
Fig. 5

As in Fig. 4, but for (a) the nuclear anterior boundary (NAB) and (b) the nuclear posterior boundary (NPB).

Fig. 6
Fig. 6

Rate of change of lens curvature Cm, the inverse of radius of curvature, with accommodation plotted as a function of age, for (a) the lens anterior surface and (b) the lens posterior surface. Symbols as in Fig. 4.

Fig. 7
Fig. 7

As in Fig. 6, but for (a) the anterior and (b) the posterior nuclear boundaries. Symbols as in Fig. 4.

Fig. 8
Fig. 8

Slope λ of the relationship between radius of curvature and curve location at 0 D accommodation as a function of age for (a) the lens anterior and (b) the lens posterior. Open circles and solid lines represent the 0 D accommodation rate λ0, and ×s and dashed lines represent the intercept of the linear relationship between slope and accommodation state λb for each subject. Where direct measurement and extrapolated values are identical for a given subject, the × is centered in the open circle.

Fig. 9
Fig. 9

Change in slope of the relationship between radius of curvature and curve location λm as a function of accommodation, plotted as a function of age for (a) the lens anterior and (b) the lens posterior. Open circles and solid lines represent data from subjects up to age 45 yr, and the ×s and dashed lines represent the entire data set.

Tables (3)

Tables Icon

Table 1 Statistical Analysis of the Data Charted in Figs. 4 and 5

Tables Icon

Table 2 Statistical Analysis of the Data Charted in Figs. 6 and 7

Tables Icon

Table 3 Statistical Analysis of the Data Charted in Figs. 8 and 9

Metrics