Abstract

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.

© 2008 Optical Society of America

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2007 (4)

Y. Chang, H.-M. Wu, and Y.-F. Lin, "The axial misalignment between ocular lens and cornea observed by MRI(I)--at fixed accommodative state," Vision Res. 47, 71-84 (2007).
[CrossRef]

P. Rodríguez and R. Navarro, "Double-pass versus aberrometric modulation transfer function in green light," J. Biomed. Opt. 12, 0440181 (2007).
[CrossRef]

Y. Benny, S. Manzanera, P. Prieto, E. Ribak, and P. Artal, "Wide-angle chromatic aberration corrector for the human eye," J. Opt. Soc. Am. A 24, 1538-1544 (2007).
[CrossRef]

J. Tabernero, A. Benito, E. Alarcón, and P. Artal, "Mechanism of compensation of aberrations in the human eye," J. Opt. Soc. Am. A 24, 3274-3283 (2007).
[CrossRef]

2006 (8)

F. Díaz-Douton, A. Benito, J. Pujol, M. Arjona, J. Guillen, and P. Artal, "Comparison of the retinal image quality with a Hartmann comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument," Invest. Ophthalmol. Visual Sci. 47, 1710-1716 (2006).
[CrossRef]

E. Acosta, D. Vazquez, R. Flores, L. F. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. A 23, 2551-2565 (2006).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignment of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef] [PubMed]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 4, 1-7 (2006).
[CrossRef]

P. Rosales, M. Dubbleman, S. Marcos, and G. van der Heijde, "Crystalline lens radii of curvature from Purkinje and Scheimpflug imaging," J. Vision 6, 1057-1067 (2006).
[CrossRef]

M. Dubbleman, V. A. D. P. Sicam, and G. L. van der Heijde, "The shape of the anterior and posterior surface of the aging human cornea," Vision Res. 46, 993-1001 (2006).

D. A. Atchison, "Optical models for human myopic eyes," Vision Res. 46, 2236-2250 (2006).
[CrossRef] [PubMed]

Y. Huang and D. T. Moore, "Human eye modelling using a single equation of gradient index crystalline lens for relaxed and accommodated states," in International Optical Design Conference, G.G.Gregory, J.M.Howard, and R.J.Koshel, eds. (SPIE, 2006), Vol. 6342, pp. 6342D1-6342D9.

2005 (10)

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

J. A. Díaz, J. A. Martínez, R. G. Anera, and J. R. Jiménez, "Permissible lateral misaligments in corneal ablation for myopic eyes," J. Opt. A, Pure Appl. Opt. 7, 364-367 (2005).
[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. F. Deering, "A photon accurate model of the human eye," ACM Trans. Graphics 24, 649-658 (2005).
[CrossRef]

D. A. Atchison, N. Pritchard, K. L. Schmid, D. H. Scott, C. Jones, and J. Pope, "Shape of the retinal surface in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 46, 2698-2707 (2005).
[CrossRef]

M. V. Pérez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. Gómez-Reino, "Description of gradient-index crystalline lens by a first order optical system," J. Opt. A, Pure Appl. Opt. 7, 103-110 (2005).
[CrossRef]

D. A. Atchison, "Recent advances in measurement of monochromatic aberrations of human eyes," Clin. Exp. Optom. 88, 5-27 (2005).
[CrossRef] [PubMed]

D. A. Atchison and G. Smith, "Chromatic dispersion of the ocular media of human eyes," J. Opt. Soc. Am. A 22, 29-37 (2005).
[CrossRef]

E. Acosta, D. Vazquez, R. Flores, L. F. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. A 22, 424-433 (2005).
[CrossRef]

D. A. Atchison and W. N. Charman, "Influence of reference plane and direction of measurement on eye aberration measurement," J. Opt. Soc. Am. A 22, 2589-2597 (2005).
[CrossRef]

2004 (5)

P. Piers, N. E. S. Norby, and U. Mester, "Eye models for the prediction of contrast vision in patients with new intraocular lens designs," Opt. Lett. 29, 733-735 (2004).
[CrossRef] [PubMed]

ZEMAX Development Corporation, ZEMAX Optical Design Program: User's Guide, Version 10 (Zemax Software Development, 2004).

J. Kelly, T. Mihashi, and H. Howland, "Compensation of corneal horizontal/vertical astigmatism, lateral coma and spherical aberration by internal optics of the eye," J. Vision 4, 262-271 (2004).
[CrossRef]

J. A. Díaz, M. Irlbauer, and J. A. Martínez, "Diffractive-refractive hybrid doublet to achromatize the human eye," J. Mod. Opt. 51, 2223-2234 (2004).
[CrossRef]

H. Cheng, J. K. Barnett, A. S. Vilipuru, J. D. Marsack, S. Kasthuriragan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vision 16, 272-280 (2004).

2003 (3)

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

J. A. Díaz, R. G. Anera, J. R. Jiménez, and L. J. del Barco, "Optimum corneal asphericity of myopic eyes for refractive surgery," J. Mod. Opt. 50, 1903-1915 (2003).
[CrossRef]

M. V. Pérez, C. Bao, M. T. Flores-Arias, M. Rama, and C. Gómez-Reino, "Gradient parameter and axial and field rays in the gradient-index crystalline lens model," J. Opt. A, Pure Appl. Opt. 5, S293-S297 (2003).
[CrossRef]

2002 (8)

Y. Yang, K. Thompson, and S. A. Burns, "Pupil location under mesopic, phottopic, and pharmacologically dilated conditions," Invest. Ophthalmol. Visual Sci. 43, 2508-2512 (2002).

B. A. Moffat, D. A. Atchsion, and J. M. Pope, "Explanation of the lens paradox," Optom. Vision Sci. 79, 148-150 (2002).
[CrossRef]

T. Fujikado, T. Kuroda, S. Nimomiya, N. Maeda, Y. Tanao, Y. Hirohara, and T. Mihashi, "Age-related changes of ocular and corneal aberrations," Am. J. Ophthalmol. 183, 143-146 (2002).

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]

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in the refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

J. T. Holladay, P. A. Piers, G. Koranyi, M. van der Nooren, and N. E. S. Norby, "A new intraocular lens design to reduce spherical aberration of pseudophakic eyes," J. Refract. Surg. 18, 683-691 (2002).
[PubMed]

E. Acosta, R. Flores, D. Vazquez, S. Rios, L. F. Garner, and G. Smith, "Tomographic method for measurement of the refractive index profile of optical fibre forms and rod GRIN lenses," Jpn. J. Appl. Phys., Part 1 41, 4821-4824 (2002).
[CrossRef]

P. Artal, E. Berrio, and A. Guirao, "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]

2001 (7)

D. A. Atchison, D. H. Scott, A. Joblin, and G. Smith, "Influence of Stiles-Crawford effect apodization on spatial visual performance with decentered pupils," J. Opt. Soc. Am. A 18, 1201-1211 (2001).
[CrossRef]

G. Smith, M. Cox, R. Calver, and L. Garner, "The spherical aberration of the crystalline lens of the human eye," Vision Res. 41, 235-243 (2001).
[CrossRef] [PubMed]

M. Dubbleman, 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. S. McLellan, S. Marcos, and S. A. Burns, "Age-related changes in monochromatic wave aberrations of the human eye," Invest. Ophthalmol. Visual Sci. 42, 1390-1395 (2001).

M. Dubbleman and G. L. van der Heijde, "The shape of the human lens: curvature, equivalent refractive index and the lens paradox," Vision Res. 41, 1867-1877 (2001).
[CrossRef]

S. A. Burns and S. Marcos, "Measurement of the image quality of the eye with a spatially resolved refractometer," in Customized Corneal Ablations (Slack, 2001), pp. 201-209.

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

2000 (5)

R. E. Fisher and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and V. S. T. Members, "Standards for reporting the optical aberrations of eyes," Opt. Photonics News 35, 232-244 (2000).

D. Atchison and G. Smith, Optics of the Human Eye (Butterwoth-Heinemann, 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]

H. T. Kasprzak, "New approximation for the whole profile of the human crystalline lens," Ophthalmic Physiol. Opt. 20, 31-43 (2000).
[CrossRef] [PubMed]

1999 (3)

A. Guirao, C. González, M. Redondo, E. Geraghty, N. E. S. Norby, and P. Artal, "Average optical performance of the human eye as a function of age in a normal population," Invest. Ophthalmol. Visual Sci. 40, 210-213 (1999).

I. Escudero-Sanz and R. Navarro, "Off-axis aberrations of a wide-angle schematic eye," J. Opt. Soc. Am. A 16, 1881-1891 (1999).
[CrossRef]

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

1998 (3)

1997 (3)

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

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, 1997).

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

1995 (4)

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," Vision Res. 35, 2529-2538 (1995).
[CrossRef] [PubMed]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christiensen, and M. D. Waterworth, "Measurements of monochromatic ocular aberrations of human eyes as a fuction of accommodation by the Howland aberroscope technique," Vision Res. 35, 313-323 (1995).
[CrossRef] [PubMed]

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

W. J. Tropf, M. E. Thomas, and T. J. Harris, "Optical properties of crystal and glasses," in Handbook of Optics (Optical Society of America, 1995), Vol. 2, pp. 33.25-33.28.

1994 (1)

B. K. Pierscionek, "Refractive index of the human lens surface measured with an optic fiber sensor," Ophthalmic Res. 26, 32-35 (1994).
[CrossRef] [PubMed]

1993 (2)

1992 (2)

1991 (4)

J. W. Blaker, "A comprehensive optical model of the aging, accommodating adult eye," in Techical Digest on Ophthalmic and Visual Optics, Vol. 2 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), p. 2831.

A. Morrell, H. D. Whitefoot, and W. N. Charman, "Ocular chromatic aberration and age," Ophthalmic Physiol. Opt. 11, 385-390 (1991).
[CrossRef] [PubMed]

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

M. C. Dunne, J. M. Royston, and D. A. Barnes, "Posterior corneal surface toricity and total corneal astigmatism," Optom. Vision Sci. 68, 708-710 (1991).
[CrossRef]

1990 (1)

E. H. Roth and G. Kluxen, "In vivo measurements of the distribution of the refractive index of the human lens with a Sheimpflug procedure of the anterior segment of the eye and a He-Ne laser beam," Fortschr. Ophthalmol. 87, 312-316 (1990).
[PubMed]

1989 (1)

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

1988 (2)

B. K. Pierscionek, D. Y. C. Chan, J. P. Ennis, G. Smith, and R. C. Augusteyn, "Nondestructive method of constructing three dimensional gradient index models for crystalline lenses: 1. theory and experiment," Am. J. Optom. Physiol. Opt. 65, 481-491 (1988).
[PubMed]

P. A. Howarth, X. Zhang, A. Bradley, D. L. Still, and L. N. Thibos, "Does the chromatic aberration of the eye vary with age?" J. Opt. Soc. Am. A 5, 2087-2092 (1988).
[CrossRef] [PubMed]

1985 (1)

1984 (2)

R. P. Hemenger, "Intraocular light scattering in normal vision loss with age," Appl. Opt. 23, 1972-1974 (1984).
[CrossRef] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, "Wide-angle optical mode of the eye," Am. J. Optom. Physiol. Opt. 61, 166-176 (1984).
[PubMed]

1983 (2)

O. Pomerantzeff, P. Dufault, and R. Goldstein, "Wide-angle model of the eye," in Advances in Diagnostic Visual Optics, Springer Series in Optical Sciences, G.Breinin and I.Siegel, eds. (Springer-Verlag, 1983), pp. 12-21.

A. C. Kooijman, "Light distribution on the retina of a wide-angle theoretical eye," J. Opt. Soc. Am. 73, 1544-1550 (1983).
[CrossRef] [PubMed]

1982 (1)

G. Wyszecki and W. S. Stiles, Color Science: Formula and Quantitative Data (Wiley, 1982).

1981 (1)

P. P. Fagerholm, B. T. Philipson, and B. Lindström, "Normal human lens, the distribution of protein," Exp. Eye Res. 33, 615-620 (1981).
[CrossRef] [PubMed]

1980 (2)

1971 (1)

O. Pomerantzeff, H. Fish, J. Govingnon, and C. L. Schepens, "Wide-angle optical model of the human eye," Ann. Ophthalmol. 3, 815-819 (1971).
[PubMed]

1968 (1)

1947 (1)

R. E. Bedford and G. Wyszecki, "Axial chromatic aberration of the human eye," J. Opt. Soc. Am. 37, 564-565 (1947).

1924 (1)

A. Gullstrand, Hemholtz's Handbuch der Physiologischen Optik, 3rd. ed., English translation edited by J.P.Southall (Optical Society of America, 1924), Vol. 1, Appendix II, pp. 301-358.

1882 (1)

L. Matthiessen, "Untersuchungen über den aplanatismus und die periscopie der krystalllinsen in den augen der fische," Pfluegers Arch. Gesamte Physiol. Menschen Tiere 27, 510-523 (1882).
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1880 (1)

L. Matthiessen, "Untersuchungen über den aplanatismus und die periscopie der krystalllinsen in den augen der fische," Pfluegers Arch. Gesamte Physiol. Menschen Tiere 231, 287-307 (1880).
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Acosta, E.

Alarcón, E.

Anera, R. G.

J. A. Díaz, J. A. Martínez, R. G. Anera, and J. R. Jiménez, "Permissible lateral misaligments in corneal ablation for myopic eyes," J. Opt. A, Pure Appl. Opt. 7, 364-367 (2005).
[CrossRef]

J. A. Díaz, R. G. Anera, J. R. Jiménez, and L. J. del Barco, "Optimum corneal asphericity of myopic eyes for refractive surgery," J. Mod. Opt. 50, 1903-1915 (2003).
[CrossRef]

Applegate, R. A.

H. Cheng, J. K. Barnett, A. S. Vilipuru, J. D. Marsack, S. Kasthuriragan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vision 16, 272-280 (2004).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and V. S. T. Members, "Standards for reporting the optical aberrations of eyes," Opt. Photonics News 35, 232-244 (2000).

Arjona, M.

F. Díaz-Douton, A. Benito, J. Pujol, M. Arjona, J. Guillen, and P. Artal, "Comparison of the retinal image quality with a Hartmann comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument," Invest. Ophthalmol. Visual Sci. 47, 1710-1716 (2006).
[CrossRef]

Artal, P.

J. Tabernero, A. Benito, E. Alarcón, and P. Artal, "Mechanism of compensation of aberrations in the human eye," J. Opt. Soc. Am. A 24, 3274-3283 (2007).
[CrossRef]

Y. Benny, S. Manzanera, P. Prieto, E. Ribak, and P. Artal, "Wide-angle chromatic aberration corrector for the human eye," J. Opt. Soc. Am. A 24, 1538-1544 (2007).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignment of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef] [PubMed]

F. Díaz-Douton, A. Benito, J. Pujol, M. Arjona, J. Guillen, and P. Artal, "Comparison of the retinal image quality with a Hartmann comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument," Invest. Ophthalmol. Visual Sci. 47, 1710-1716 (2006).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 4, 1-7 (2006).
[CrossRef]

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

A. Guirao, C. González, M. Redondo, E. Geraghty, N. E. S. Norby, and P. Artal, "Average optical performance of the human eye as a function of age in a normal population," Invest. Ophthalmol. Visual Sci. 40, 210-213 (1999).

P. Artal and A. Guirao, "Contribution of cornea and lens to the aberrations of the human eye," Opt. Lett. 23, 1713-1715 (1998).
[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]

Atchison, D.

D. Atchison and G. Smith, Optics of the Human Eye (Butterwoth-Heinemann, 2000).

Atchison, D. A.

D. A. Atchison, "Optical models for human myopic eyes," Vision Res. 46, 2236-2250 (2006).
[CrossRef] [PubMed]

D. A. Atchison and W. N. Charman, "Influence of reference plane and direction of measurement on eye aberration measurement," J. Opt. Soc. Am. A 22, 2589-2597 (2005).
[CrossRef]

D. A. Atchison, "Recent advances in measurement of monochromatic aberrations of human eyes," Clin. Exp. Optom. 88, 5-27 (2005).
[CrossRef] [PubMed]

D. A. Atchison, N. Pritchard, K. L. Schmid, D. H. Scott, C. Jones, and J. Pope, "Shape of the retinal surface in emmetropia and myopia," Invest. Ophthalmol. Visual Sci. 46, 2698-2707 (2005).
[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]

D. A. Atchison and G. Smith, "Chromatic dispersion of the ocular media of human eyes," J. Opt. Soc. Am. A 22, 29-37 (2005).
[CrossRef]

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in the refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

D. A. Atchison, D. H. Scott, A. Joblin, and G. Smith, "Influence of Stiles-Crawford effect apodization on spatial visual performance with decentered pupils," J. Opt. Soc. Am. A 18, 1201-1211 (2001).
[CrossRef]

D. A. Atchison, A. Joblin, and G. Smith, "Influence of Stiles-Crawford effect apodization on spatial visual performance," J. Opt. Soc. Am. A 15, 2545-2551 (1998).
[CrossRef]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christiensen, and M. D. Waterworth, "Measurements of monochromatic ocular aberrations of human eyes as a fuction of accommodation by the Howland aberroscope technique," Vision Res. 35, 313-323 (1995).
[CrossRef] [PubMed]

D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," Vision Res. 35, 2529-2538 (1995).
[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 modeling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
[CrossRef] [PubMed]

Atchsion, D. A.

B. A. Moffat, D. A. Atchsion, and J. M. Pope, "Explanation of the lens paradox," Optom. Vision Sci. 79, 148-150 (2002).
[CrossRef]

Augusteyn, R. C.

B. K. Pierscionek, D. Y. C. Chan, J. P. Ennis, G. Smith, and R. C. Augusteyn, "Nondestructive method of constructing three dimensional gradient index models for crystalline lenses: 1. theory and experiment," Am. J. Optom. Physiol. Opt. 65, 481-491 (1988).
[PubMed]

Bao, C.

M. V. Pérez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. Gómez-Reino, "Description of gradient-index crystalline lens by a first order optical system," J. Opt. A, Pure Appl. Opt. 7, 103-110 (2005).
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M. V. Pérez, C. Bao, M. T. Flores-Arias, M. Rama, and C. Gómez-Reino, "Gradient parameter and axial and field rays in the gradient-index crystalline lens model," J. Opt. A, Pure Appl. Opt. 5, S293-S297 (2003).
[CrossRef]

Barnes, D. A.

M. C. Dunne, J. M. Royston, and D. A. Barnes, "Posterior corneal surface toricity and total corneal astigmatism," Optom. Vision Sci. 68, 708-710 (1991).
[CrossRef]

Barnett, J. K.

H. Cheng, J. K. Barnett, A. S. Vilipuru, J. D. Marsack, S. Kasthuriragan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vision 16, 272-280 (2004).

Bedford, R. E.

R. E. Bedford and G. Wyszecki, "Axial chromatic aberration of the human eye," J. Opt. Soc. Am. 37, 564-565 (1947).

Benito, A.

J. Tabernero, A. Benito, E. Alarcón, and P. Artal, "Mechanism of compensation of aberrations in the human eye," J. Opt. Soc. Am. A 24, 3274-3283 (2007).
[CrossRef]

F. Díaz-Douton, A. Benito, J. Pujol, M. Arjona, J. Guillen, and P. Artal, "Comparison of the retinal image quality with a Hartmann comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument," Invest. Ophthalmol. Visual Sci. 47, 1710-1716 (2006).
[CrossRef]

P. Artal, A. Benito, and J. Tabernero, "The human eye is an example of robust optical design," J. Vision 4, 1-7 (2006).
[CrossRef]

J. Tabernero, A. Benito, V. Nourrit, and P. Artal, "Instrument for measuring the misalignment of ocular surfaces," Opt. Express 14, 10945-10956 (2006).
[CrossRef] [PubMed]

Benny, Y.

Berrio, E.

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

Bescós, J.

Blaker, J. W.

J. W. Blaker, "A comprehensive optical model of the aging, accommodating adult eye," in Techical Digest on Ophthalmic and Visual Optics, Vol. 2 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), p. 2831.

J. W. Blaker, "Toward an adaptative model of the human eye," J. Opt. Soc. Am. 70, 220-283 (1980).
[CrossRef] [PubMed]

Bradley, A.

Brennan, N. A.

Burns, S. A.

Y. Yang, K. Thompson, and S. A. Burns, "Pupil location under mesopic, phottopic, and pharmacologically dilated conditions," Invest. Ophthalmol. Visual Sci. 43, 2508-2512 (2002).

S. A. Burns and S. Marcos, "Measurement of the image quality of the eye with a spatially resolved refractometer," in Customized Corneal Ablations (Slack, 2001), pp. 201-209.

J. S. McLellan, S. Marcos, and S. A. Burns, "Age-related changes in monochromatic wave aberrations of the human eye," Invest. Ophthalmol. Visual Sci. 42, 1390-1395 (2001).

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.

G. Smith, M. Cox, R. Calver, and L. Garner, "The spherical aberration of the crystalline lens of the human eye," Vision Res. 41, 235-243 (2001).
[CrossRef] [PubMed]

Calver, R. I.

Campbell, M. C. W.

A. Glasser and M. C. W. Campbell, "Presbyopia and the optical changes in the human crystalline lens with age," Vision Res. 38, 209-229 (1998).
[CrossRef] [PubMed]

Carroll, J. P.

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]

B. K. Pierscionek, D. Y. C. Chan, J. P. Ennis, G. Smith, and R. C. Augusteyn, "Nondestructive method of constructing three dimensional gradient index models for crystalline lenses: 1. theory and experiment," Am. J. Optom. Physiol. Opt. 65, 481-491 (1988).
[PubMed]

Chang, Y.

Y. Chang, H.-M. Wu, and Y.-F. Lin, "The axial misalignment between ocular lens and cornea observed by MRI(I)--at fixed accommodative state," Vision Res. 47, 71-84 (2007).
[CrossRef]

Charman, W. N.

D. A. Atchison and W. N. Charman, "Influence of reference plane and direction of measurement on eye aberration measurement," J. Opt. Soc. Am. A 22, 2589-2597 (2005).
[CrossRef]

A. Morrell, H. D. Whitefoot, and W. N. Charman, "Ocular chromatic aberration and age," Ophthalmic Physiol. Opt. 11, 385-390 (1991).
[CrossRef] [PubMed]

Cheng, H.

H. Cheng, J. K. Barnett, A. S. Vilipuru, J. D. Marsack, S. Kasthuriragan, R. A. Applegate, and A. Roorda, "A population study on changes in wave aberrations with accommodation," J. Vision 16, 272-280 (2004).

Christiensen, J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christiensen, and M. D. Waterworth, "Measurements of monochromatic ocular aberrations of human eyes as a fuction of accommodation by the Howland aberroscope technique," Vision Res. 35, 313-323 (1995).
[CrossRef] [PubMed]

Collins, M. J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christiensen, and M. D. Waterworth, "Measurements of monochromatic ocular aberrations of human eyes as a fuction of accommodation by the Howland aberroscope technique," Vision Res. 35, 313-323 (1995).
[CrossRef] [PubMed]

Cox, M.

G. Smith, M. Cox, R. Calver, and L. Garner, "The spherical aberration of the crystalline lens of the human eye," Vision Res. 41, 235-243 (2001).
[CrossRef] [PubMed]

Cox, M. J.

Deering, M. F.

M. F. Deering, "A photon accurate model of the human eye," ACM Trans. Graphics 24, 649-658 (2005).
[CrossRef]

del Barco, L. J.

J. A. Díaz, R. G. Anera, J. R. Jiménez, and L. J. del Barco, "Optimum corneal asphericity of myopic eyes for refractive surgery," J. Mod. Opt. 50, 1903-1915 (2003).
[CrossRef]

Díaz, J. A.

J. A. Díaz, J. A. Martínez, R. G. Anera, and J. R. Jiménez, "Permissible lateral misaligments in corneal ablation for myopic eyes," J. Opt. A, Pure Appl. Opt. 7, 364-367 (2005).
[CrossRef]

J. A. Díaz, M. Irlbauer, and J. A. Martínez, "Diffractive-refractive hybrid doublet to achromatize the human eye," J. Mod. Opt. 51, 2223-2234 (2004).
[CrossRef]

J. A. Díaz, R. G. Anera, J. R. Jiménez, and L. J. del Barco, "Optimum corneal asphericity of myopic eyes for refractive surgery," J. Mod. Opt. 50, 1903-1915 (2003).
[CrossRef]

Díaz-Douton, F.

F. Díaz-Douton, A. Benito, J. Pujol, M. Arjona, J. Guillen, and P. Artal, "Comparison of the retinal image quality with a Hartmann comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument," Invest. Ophthalmol. Visual Sci. 47, 1710-1716 (2006).
[CrossRef]

Dubbleman, M.

M. Dubbleman, V. A. D. P. Sicam, and G. L. van der Heijde, "The shape of the anterior and posterior surface of the aging human cornea," Vision Res. 46, 993-1001 (2006).

P. Rosales, M. Dubbleman, S. Marcos, and G. van der Heijde, "Crystalline lens radii of curvature from Purkinje and Scheimpflug imaging," J. Vision 6, 1057-1067 (2006).
[CrossRef]

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

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

M. Dubbleman, 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. Dubbleman and G. L. van der Heijde, "The shape of the human lens: curvature, equivalent refractive index and the lens paradox," Vision Res. 41, 1867-1877 (2001).
[CrossRef]

Dufault, P.

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, "Wide-angle optical mode of the eye," Am. J. Optom. Physiol. Opt. 61, 166-176 (1984).
[PubMed]

O. Pomerantzeff, P. Dufault, and R. Goldstein, "Wide-angle model of the eye," in Advances in Diagnostic Visual Optics, Springer Series in Optical Sciences, G.Breinin and I.Siegel, eds. (Springer-Verlag, 1983), pp. 12-21.

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M. C. Dunne, J. M. Royston, and D. A. Barnes, "Posterior corneal surface toricity and total corneal astigmatism," Optom. Vision Sci. 68, 708-710 (1991).
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Piers, P. A.

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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).
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Pritchard, N.

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M. V. Pérez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. Gómez-Reino, "Description of gradient-index crystalline lens by a first order optical system," J. Opt. A, Pure Appl. Opt. 7, 103-110 (2005).
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Rios, S.

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P. Rosales, M. Dubbleman, S. Marcos, and G. van der Heijde, "Crystalline lens radii of curvature from Purkinje and Scheimpflug imaging," J. Vision 6, 1057-1067 (2006).
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J. W. Blaker, "A comprehensive optical model of the aging, accommodating adult eye," in Techical Digest on Ophthalmic and Visual Optics, Vol. 2 of 1991 OSA Technical Digest Series (Optical Society of America, 1991), p. 2831.

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Figures (7)

Fig. 1
Fig. 1

Modeling the crystalline lens in current eye models with two GRIN profiles (top) and with a single profile.

Fig. 2
Fig. 2

Example of the schematic eye model used for an emmetropic subject. This view is from the top of the right eye. The right eye was used in all calculations.

Fig. 3
Fig. 3

GRIN profile parameters as a function of age (symbols). The solid line is the linear fit of the data, and the dashed lines represent the confidence interval at 95%.

Fig. 4
Fig. 4

Contour index values in the equatorial Y Z plane (left column), index profile along the lens axis (middle column) and index variation of the lens-center index along the equatorial radius (right column) at different ages. The dashed line in the graphs corresponding to the index profile along the lens axis indicates the position of the lens-center-index value.

Fig. 5
Fig. 5

Refractive index values corresponding to the lens edge and lens center (curves) as a function of wavelength compared to the data (symbols) from Atchison [9].

Fig. 6
Fig. 6

Comparison of the chromatic difference on refraction (CDRx) corresponding to the ages of 25 and 65   years . Solid curve is that of the chromatic eye [57].

Fig. 7
Fig. 7

Average modulation transfer function (MTF) at 543 nm for three representative ages, each one within the group adopted by Guirao et al. [34]. Data with the standard error from the normal population reported in that study are also plotted for comparison.

Tables (3)

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Table 1 Schematic Eye Parameters as a Function of Age ( A ) a

Tables Icon

Table 2 Value of the GRIN Profile Parameters as a Function of Age ( A ) a

Tables Icon

Table 3 Values of the A B C D Matrix Elements ( A G , B G , C G , D G ) of the GRIN Lens Profile, Anterior Lens Power ( ϕ 1 ) , Posterior Lens Power ( ϕ 2 ) , Surface Power ( ϕ L ϕ G ) , GRIN Power ( ϕ G ) , and Total Lens Power ( ϕ L ) as Age Increases

Equations (13)

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Q c 1 = 0.24 + 0.003 age , Q c 2 = 0.006 age .
A C D = 3.87 0.01 age ,
R l 1 = 12.7 0.058 age ; Q l 1 = 5 ,
R l 2 = 5.9 + 0.0015 age ; Q l 2 = 4 .
n ( λ , x , y , z ) = n 0 ( λ ) + n 1 ( cos ( n 2 z ) 1 ) + n 3 sin ( n 4 z ) + n 5 ( x 2 + y 2 ) ,
n o 2 ( λ ) 1 = K 1 λ 2 L 1 λ 2 + K 2 λ 2 L 2 λ 2 + K 3 λ 2 L 3 λ 2 ,
d L = 2.93 + 0.0236 age .
V C = 16.79 0.0136 age .
ψ = [ ω j 2 ( α j α j t ) 2 ] 1 2 ,
ϕ L = ϕ G + ϕ 2 A G + ϕ 1 D G ϕ 1 ϕ 2 B G n ,
A B C D G = [ A G B G C G D G ] = [ H f ( d ) H a ( d ) H ̇ f ( d ) H ̇ a ( d ) ] ,
A B C D L = [ A L B L C L D L ] = R 2 A B C D G R 1 = [ 1 0 ϕ 2 n v n e n v ] [ A G B G C G D G ] [ 1 0 ϕ 1 n e n a n e ] ,
ϕ L = C L = ϕ G + ϕ 2 A G + ϕ 1 D G ϕ 1 ϕ 2 B G n e ,

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