Abstract

A simple, parametric model of the gradient refractive index distribution (GRIN) of the human lens with conicoid surfaces able to adapt to individual distributions as well as to the changes of the lens shape and structure with age and accommodation is presented. The first part of this work was published in a companion paper [J. Opt. Soc. Am. A 24, 2175 (2007) ]. It included the development of the mathematical formulation of the adaptive model; the validation of its customization capability by fitting, sample by sample, a set of in vitro refractive index distributions of lenses of different ages, ranging from 7 to 82 years, from the recent literature; and an average model of the (in vitro) aging crystalline lens. Here we extrapolate that in vitro GRIN model by assuming that the same structural parameters are valid for the living lens. Then, recent data of the changes of the shape of the aging lens with accommodation from the literature are used to build an aging and accommodating lens model. This is straightforward since the GRIN model adapts automatically to the chosen external lens geometry. A strong coupling was found between the adaptive GRIN distributions and the conic constants affecting the refractive power. To account for the lens paradox and the reported changes in lens spherical aberration with age and accommodation, age- and accommodation-dependent functions for the anterior and posterior internal conic constants were derived through optimization.

© 2007 Optical Society of America

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  1. N. Brown, "The change in lens curvature with age," Exp. Eye Res. 19, 175-183 (1974).
    [CrossRef] [PubMed]
  2. J. F. Koretz, C. A. Cook, and 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).
  3. J. F. Koretz, C. A. Cook, and 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]
  4. M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
    [CrossRef]
  5. 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]
  6. M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
    [CrossRef] [PubMed]
  7. P. Artal, M. Ferro, I. Miranda, and R. Navarro, "Effects of aging in retinal image quality," J. Opt. Soc. Am. A 10, 1656-1662 (1993).
    [CrossRef] [PubMed]
  8. I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
    [CrossRef]
  9. A. Ivanoff, Les aberrations de l'oeil. Leur role dans l'accommodation (Éditions de la Revue d'Optique Théorique et Instrumentale, Paris, 1953).
  10. J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
    [CrossRef] [PubMed]
  11. M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
    [CrossRef] [PubMed]
  12. P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
    [CrossRef]
  13. P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. A 19, 137-143 (2002).
    [CrossRef]
  14. A. Popiolek-Masajada, "Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye," Ophthalmic Physiol. Opt. 19, 41-49 (1999).
    [CrossRef]
  15. G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
    [CrossRef] [PubMed]
  16. M. C. W. Campbell, "Measurement of refractive index in an intact crystalline lens," Vision Res. 24, 409-415 (1984).
    [CrossRef] [PubMed]
  17. B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
    [CrossRef]
  18. R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).
  19. B. K. Pierscionek, "Refractive index contours in the human lens," Exp. Eye Res. 64, 887-893 (1997).
    [CrossRef] [PubMed]
  20. C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
    [CrossRef] [PubMed]
  21. S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).
  22. G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
    [CrossRef] [PubMed]
  23. D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," J. Opt. Soc. Am. A 14, 1684-1695 (1995).
  24. H.-L. Liou and N. A. Brennan, "Anatomically accurate finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1695 (1997).
    [CrossRef]
  25. J. W. Blaker, "Toward an adaptive model of the human eye," J. Opt. Soc. Am. 70, 220-223 (1980).
    [CrossRef] [PubMed]
  26. A. Popiolek-Masajada and H. Kasprzak, "Model of the optical system of the human eye during accommodation," Ophthalmic Physiol. Opt. 22, 201-208 (2002).
    [CrossRef] [PubMed]
  27. G. Smith, D. A. Atchison, and B. K. Pierscionek, "Modeling the power of the aging human eye," J. Opt. Soc. Am. A 9, 2111-2117 (1992).
    [CrossRef] [PubMed]
  28. R. Navarro, F. Palos, and L. González, "Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses," J. Opt. Soc. Am. A 24, 2175-2185 (2007).
    [CrossRef]
  29. R. Navarro, L. González, and J. L. Hernández-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom. Vision Sci. 83, 371-381 (2006).
    [CrossRef]
  30. S. Norrby, "The Dubbelman eye model analysed by ray tracing through aspheric surfaces," Ophthalmic Physiol. Opt. 25, 153-161 (2005).
    [CrossRef] [PubMed]
  31. M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
    [CrossRef]
  32. M. Dubbelman, Department of Physics and Medical Technology, VU University Medical Center, Amsterdam; m.dubbelman@vumc.nl (personal communication, 2007).
  33. R. Navarro, J. Santamaría, and J. Bescós, "Accommodation-dependent model of the human eye with aspherics," J. Opt. Soc. Am. A 2, 1273-1281 (1985).
    [CrossRef] [PubMed]
  34. Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980), pp. 54-55.
  35. G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997).
    [CrossRef]
  36. L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vision Sci. 74, 114-119 (1997).
    [CrossRef]
  37. R. L. Calver, M. L. Cox, and D. B. Elliot, "Effects of aging on the monochromatic aberrations of the human eye," J. Opt. Soc. Am. A 16, 2069-2078 (1999).
    [CrossRef]
  38. A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
    [CrossRef]

2007

2006

R. Navarro, L. González, and J. L. Hernández-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom. Vision Sci. 83, 371-381 (2006).
[CrossRef]

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

2005

S. Norrby, "The Dubbelman eye model analysed by ray tracing through aspheric surfaces," Ophthalmic Physiol. Opt. 25, 153-161 (2005).
[CrossRef] [PubMed]

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
[CrossRef]

2003

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

2002

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. A 19, 137-143 (2002).
[CrossRef]

A. Popiolek-Masajada and H. Kasprzak, "Model of the optical system of the human eye during accommodation," Ophthalmic Physiol. Opt. 22, 201-208 (2002).
[CrossRef] [PubMed]

2001

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
[CrossRef]

J. F. Koretz, C. A. Cook, and 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]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

2000

J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
[CrossRef] [PubMed]

1999

A. Popiolek-Masajada, "Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye," Ophthalmic Physiol. Opt. 19, 41-49 (1999).
[CrossRef]

R. L. Calver, M. L. Cox, and D. B. Elliot, "Effects of aging on the monochromatic aberrations of the human eye," J. Opt. Soc. Am. A 16, 2069-2078 (1999).
[CrossRef]

1997

G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997).
[CrossRef]

L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vision Sci. 74, 114-119 (1997).
[CrossRef]

H.-L. Liou and N. A. Brennan, "Anatomically accurate finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1695 (1997).
[CrossRef]

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

J. F. Koretz, C. A. Cook, and 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).

1995

R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," J. Opt. Soc. Am. A 14, 1684-1695 (1995).

1993

1992

1991

G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

1989

B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
[CrossRef]

1985

1984

M. C. W. Campbell, "Measurement of refractive index in an intact crystalline lens," Vision Res. 24, 409-415 (1984).
[CrossRef] [PubMed]

1980

1979

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

1974

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

1973

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]

1969

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Artal, P.

Atchison, D. A.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997).
[CrossRef]

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," J. Opt. Soc. Am. A 14, 1684-1695 (1995).

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

G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

Augusteyn, R. C.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Berrio, E.

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. A 19, 137-143 (2002).
[CrossRef]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Bescós, J.

Blaker, J. W.

Borja, D.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Brennan, N. A.

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]

Brunette, I.

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

Bueno, J. M.

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

Burns, S. A.

J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
[CrossRef] [PubMed]

Calver, R. L.

Campbell, M. C. W.

M. C. W. Campbell, "Measurement of refractive index in an intact crystalline lens," Vision Res. 24, 409-415 (1984).
[CrossRef] [PubMed]

Chan, D. Y. C.

B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
[CrossRef]

Cook, C. A.

J. F. Koretz, C. A. Cook, and 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, and 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).

Cox, M. L.

Denham, D. B.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Dubbelman, M.

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
[CrossRef]

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
[CrossRef]

M. Dubbelman, Department of Physics and Medical Technology, VU University Medical Center, Amsterdam; m.dubbelman@vumc.nl (personal communication, 2007).

El Hage, S. G.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980), pp. 54-55.

Elliot, D. B.

Fernandez, V.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Ferro, M.

Garner, L. F.

L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vision Sci. 74, 114-119 (1997).
[CrossRef]

R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).

González, L.

R. Navarro, F. Palos, and L. González, "Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses," J. Opt. Soc. Am. A 24, 2175-2185 (2007).
[CrossRef]

R. Navarro, L. González, and J. L. Hernández-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom. Vision Sci. 83, 371-381 (2006).
[CrossRef]

Guirao, A.

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. A 19, 137-143 (2002).
[CrossRef]

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Hamam, H.

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

He, J. C.

J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
[CrossRef] [PubMed]

Hemenger, R. P.

R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).

Hernández-Matamoros, J. L.

R. Navarro, L. González, and J. L. Hernández-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom. Vision Sci. 83, 371-381 (2006).
[CrossRef]

Ho, A.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Ivanoff, A.

A. Ivanoff, Les aberrations de l'oeil. Leur role dans l'accommodation (Éditions de la Revue d'Optique Théorique et Instrumentale, Paris, 1953).

Iwata, K.

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Jones, C. E.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Kasprzak, H.

A. Popiolek-Masajada and H. Kasprzak, "Model of the optical system of the human eye during accommodation," Ophthalmic Physiol. Opt. 22, 201-208 (2002).
[CrossRef] [PubMed]

Kaufman, P. L.

J. F. Koretz, C. A. Cook, and 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, and 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).

Koretz, J. F.

J. F. Koretz, C. A. Cook, and 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, and 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).

Le Grand, Y.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980), pp. 54-55.

Liou, H.-L.

Manns, F.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Marcos, S.

J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
[CrossRef] [PubMed]

Meder, R.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Millodot, M.

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

Miranda, I.

Nagata, R.

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Nakao, S.

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Navarro, R.

Norrby, S.

S. Norrby, "The Dubbelman eye model analysed by ray tracing through aspheric surfaces," Ophthalmic Physiol. Opt. 25, 153-161 (2005).
[CrossRef] [PubMed]

Ono, T.

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Ooi, C. S.

R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).

Palos, F.

Parel, J. M.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Parent, M.

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

Piers, P.

Pierscionek, B. K.

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

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

G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
[CrossRef]

Pope, J. M.

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

Popiolek-Masajada, A.

A. Popiolek-Masajada and H. Kasprzak, "Model of the optical system of the human eye during accommodation," Ophthalmic Physiol. Opt. 22, 201-208 (2002).
[CrossRef] [PubMed]

A. Popiolek-Masajada, "Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye," Ophthalmic Physiol. Opt. 19, 41-49 (1999).
[CrossRef]

Rosen, A. M.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

Santamaría, J.

Simonet, P.

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

Sivak, J.

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

Smith, G.

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vision Sci. 74, 114-119 (1997).
[CrossRef]

G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997).
[CrossRef]

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," J. Opt. Soc. Am. A 14, 1684-1695 (1995).

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

G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

van der Heijde, G. L.

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
[CrossRef]

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
[CrossRef]

Vrensen, G. F. J. M.

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

Weeber, H. A.

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
[CrossRef]

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
[CrossRef]

Williams, D. R.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Exp. Eye Res.

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]

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

Invest. Ophthalmol. Visual Sci.

R. P. Hemenger, L. F. Garner, and C. S. Ooi, "Change with age of the refractive index gradient of the human ocular lens," Invest. Ophthalmol. Visual Sci. 36, 703-707 (1995).

I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, "Monochromatic aberrations as a function of age, from childhood to advanced age," Invest. Ophthalmol. Visual Sci. 44, 5438-5446 (2003).
[CrossRef]

J. F. Koretz, C. A. Cook, and 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).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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

R. Navarro, F. Palos, and L. González, "Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses," J. Opt. Soc. Am. A 24, 2175-2185 (2007).
[CrossRef]

R. Navarro, J. Santamaría, and J. Bescós, "Accommodation-dependent model of the human eye with aspherics," J. Opt. Soc. Am. A 2, 1273-1281 (1985).
[CrossRef] [PubMed]

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," J. Opt. Soc. Am. A 14, 1684-1695 (1995).

H.-L. Liou and N. A. Brennan, "Anatomically accurate finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1695 (1997).
[CrossRef]

J. F. Koretz, C. A. Cook, and 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]

P. Artal, M. Ferro, I. Miranda, and R. Navarro, "Effects of aging in retinal image quality," J. Opt. Soc. Am. A 10, 1656-1662 (1993).
[CrossRef] [PubMed]

P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J. Opt. Soc. Am. A 19, 137-143 (2002).
[CrossRef]

G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997).
[CrossRef]

R. L. Calver, M. L. Cox, and D. B. Elliot, "Effects of aging on the monochromatic aberrations of the human eye," J. Opt. Soc. Am. A 16, 2069-2078 (1999).
[CrossRef]

J. Vision

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by internal optics in the human eye," J. Vision 1, 1-8 (2001).
[CrossRef]

Jpn. J. Clin. Ophthalmol.

S. Nakao, T. Ono, R. Nagata, and K. Iwata, "Model of refractive indices in the human crystalline lens," Jpn. J. Clin. Ophthalmol. 23, 903-906 (1969).

Ophthalmic Physiol. Opt.

G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

S. Norrby, "The Dubbelman eye model analysed by ray tracing through aspheric surfaces," Ophthalmic Physiol. Opt. 25, 153-161 (2005).
[CrossRef] [PubMed]

A. Popiolek-Masajada and H. Kasprzak, "Model of the optical system of the human eye during accommodation," Ophthalmic Physiol. Opt. 22, 201-208 (2002).
[CrossRef] [PubMed]

A. Popiolek-Masajada, "Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye," Ophthalmic Physiol. Opt. 19, 41-49 (1999).
[CrossRef]

G. Smith and D. A. Atchison, "The gradient index and spherical aberration of the lens of the human eye," Ophthalmic Physiol. Opt. 21, 317-326 (2001).
[CrossRef] [PubMed]

Optom. Vision Sci.

R. Navarro, L. González, and J. L. Hernández-Matamoros, "On the prediction of optical aberrations by personalized eye models," Optom. Vision Sci. 83, 371-381 (2006).
[CrossRef]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "The thickness of the aging human lens obtained from corrected Scheimpflug images," Optom. Vision Sci. 78, 411-416 (2001).
[CrossRef]

B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
[CrossRef]

L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vision Sci. 74, 114-119 (1997).
[CrossRef]

Vision Res.

A. M. Rosen, D. B. Denham, V. Fernandez, D. Borja, A. Ho, F. Manns, J. M. Parel, and R. C. Augusteyn, "In vitro dimensions and curvatures of human lenses," Vision Res. 46, 1002-1009 (2006).
[CrossRef]

C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005).
[CrossRef] [PubMed]

M. C. W. Campbell, "Measurement of refractive index in an intact crystalline lens," Vision Res. 24, 409-415 (1984).
[CrossRef] [PubMed]

J. C. He, S. A. Burns, and S. Marcos, "Monochromatic aberrations in the accommodated human eye," Vision Res. 40, 41-48 (2000).
[CrossRef] [PubMed]

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

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, "Change in shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005).
[CrossRef]

M. Dubbelman, G. L. van der Heijde, H. A. Weeber, and G. F. J. M. Vrensen, "Changes in the internal structure of the human crystalline lens with age and accommodation," Vision Res. 43, 2363-2375 (2003).
[CrossRef] [PubMed]

Other

A. Ivanoff, Les aberrations de l'oeil. Leur role dans l'accommodation (Éditions de la Revue d'Optique Théorique et Instrumentale, Paris, 1953).

M. Dubbelman, Department of Physics and Medical Technology, VU University Medical Center, Amsterdam; m.dubbelman@vumc.nl (personal communication, 2007).

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980), pp. 54-55.

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Figures (8)

Fig. 1
Fig. 1

Changes of the isoindicial surfaces of the lens model with accommodation (upper row) and age (lower row). The step between the plotted isoindicial surfaces is 0.01, starting from the minimum value, 1.3709. The orientation is from the left (anterior surface) to the right (posterior surface).

Fig. 2
Fig. 2

Paraxial refractive power versus accommodation for homogeneous ( n = 1.42 , open symbols) and adaptive GRIN (solid symbols) lens models with the same geometry (by Dubbelman and co-workers) [30] and for different ages. We have assumed that the accommodation range declines with age, so that it was computed up to 8 D at 20 years (circles); 4 D at 40 years (diamonds), and 0 D at 60 years (squares). The GRIN model predicts a lower power than the homogeneous lens version does.

Fig. 3
Fig. 3

Paraxial refractive power versus accommodation for homogeneous ( n = 1.42 , open symbols) and adaptive GRIN (solid symbols) lens models, with the geometry corresponding to the Navarro et al. eye model [33].

Fig. 4
Fig. 4

Effect of the conic constants, Q a and Q p , on paraxial (solid dark bars) and effective (best image plane, solid white bars) refractive power of the adaptive GRIN lens model. The dotted bar represents the power of a homogeneous lens ( n = 1.42 ) with the same geometry. The hatched bars represent the fixed GRIN model from Liou and Brennan [24], using the labeled conic constants.

Fig. 5
Fig. 5

Plots of the LSA (in diopters), versus pupil radius, derived from the GRIN model using different possible conic constants: spheres ( Q a = Q p = 0 ) , paraboloids ( Q a = Q p = 1 ) , hyperboloid and paraboloid ( Q a = 3.1316 , Q p = 1 ), and the two hyperboloids of the present model ( Q a = 4 , Q p = 3 ). The dashed curve represents the Navarro et al. homogeneous lens model ( Q a = 3.1316 , Q p = 1 ) [33].

Fig. 6
Fig. 6

Changes of the LSA (in diopters) of the lens model with age and accommodation.

Fig. 7
Fig. 7

Comparison of paraxial (dotted line) and effective (solid line) refractive power of the lens model corresponding to the initial ( Q a = 4 0.5 D and Q p = 3 , open squares) and optimized (solid circles) conic constants. The effective power is constant only in the optimized version.

Fig. 8
Fig. 8

Changes with age of the LSA in the optimized lens model. The ages represented are 20 (open circles), 25 (solid circles), 40 (open diamonds), and 60 (open squares) years. The dashed curve represents the (sign-reversed) negative LSA of the cornea of a standard eye model [33].

Tables (1)

Tables Icon

Table 1 Expressions for the Changes of the Parameters of the Crystalline Lens Model with Age A (in Years) and Accommodation D (in Diopters)

Equations (5)

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n a n t ( z , ω ) = n o + δ n ( 1 1 f a n t ( z 2 2 Δ a n t z a a n t 2 + ε a n t ω 2 b a n t 2 ) ) p for ( z a n t , ω a n t ) ( z , ω ) < ( z i , ω i ) ,
n p o s ( z , ω ) = n o + δ n ( 1 f p o s ( z 2 t a n t 2 2 Δ p o s ( z t a n t ) a p o s 2 + ε p o s ω 2 b p o s 2 ) ) p for ( z i , ω i ) ( z , ω ) < ( z p o s , ω p o s ) ,
[ 1 f p a p 2 + 1 f a a a 2 ] z i 2 2 [ Δ p f p a p 2 + Δ a f a a a 2 ] z i + [ 1 f p b p 2 + 1 f a b a 2 ] ω i 2 + [ 2 Δ p t a t a 2 f p a p 2 ] = 1 .
Q a = 2.8 + 0.025 A 0.0013 A 2 , Q p = 0.1 0.06 A ,
Q a = 2.8 + 0.025 A 0.0013 A 2 0.25 D .

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