Lens internal curvature effects on age-related eye model and lens paradox


B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

B. E. Klein, K. E. Lee, and R. Klein, “Refraction in adults with diabetes,” Arch. Ophthalmol. 129(1), 56–62 (2011).
[Crossref] [PubMed]

T. Evans and W. F. Harris, “Dependence of the transference of a reduced eye on frequency of light,” S. Afr. Optom. 70, 149–155 (2011).

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

S. Norrby, “The Dubbelman eye model analysed by ray tracing through aspheric surfaces,” Ophthalmic Physiol. Opt. 25(2), 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(18), 2352–2366 (2005).
[Crossref] [PubMed]

W. F. Harris, “Magnification, blur, and ray state at the retina for the general eye with and without a general optical instrument in front of it: 1. Distant Objects,” Optom. Vis. Sci. 78(12), 888–900 (2001).
[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. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: Curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

G. Smith and B. K. Pierscionek, “The optical structure of the lens and its contribution to the refractive status of the eye,” Ophthalmic Physiol. Opt. 18(1), 21–29 (1998).
[Crossref] [PubMed]

B. Pierscionek, “Presbyopia–effect of refractive index,” Clin. Exp. Optom. 73(1), 23–30 (1990).
[Crossref]

D. Lahm, L. K. Lee, and F. A. Bettelheim, “Age dependence of freezable and nonfreezable water content of normal human lenses,” Invest. Ophthalmol. Vis. Sci. 26(8), 1162–1165 (1985).
[PubMed]

R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2(8), 1273–1281 (1985).
[Crossref] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[Crossref] [PubMed]

P. R. Eva, P. T. Pascoe, and D. G. Vaughan, “Refractive change in hyperglycaemia: hyperopia, not myopia,” Br. J. Ophthalmol. 66(8), 500–505 (1982).
[Crossref] [PubMed]

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19(2), 175–183 (1974).
[Crossref] [PubMed]

N. Drasdo and C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58(8), 709–714 (1974).
[Crossref] [PubMed]

W. N. Charman, Adnan, and D. A. Atchison, “Gradients of refractive index in the crystalline lens and transient changes in refraction among patients with diabetes,” Biomed. Opt. Express 3(12), 3033–3042 (2012).
[PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[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(18), 2352–2366 (2005).
[Crossref] [PubMed]

G. Smith, D. A. Atchison, and B. K. Pierscionek, “Modelling the ageing human eye,” J. Opt. Soc. Am. A 9(12), 2111–2117 (1992).
[Crossref]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

D. Lahm, L. K. Lee, and F. A. Bettelheim, “Age dependence of freezable and nonfreezable water content of normal human lenses,” Invest. Ophthalmol. Vis. Sci. 26(8), 1162–1165 (1985).
[PubMed]

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19(2), 175–183 (1974).
[Crossref] [PubMed]

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

N. Drasdo and C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58(8), 709–714 (1974).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[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. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: Curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[Crossref] [PubMed]

P. R. Eva, P. T. Pascoe, and D. G. Vaughan, “Refractive change in hyperglycaemia: hyperopia, not myopia,” Br. J. Ophthalmol. 66(8), 500–505 (1982).
[Crossref] [PubMed]

T. Evans and W. F. Harris, “Dependence of the transference of a reduced eye on frequency of light,” S. Afr. Optom. 70, 149–155 (2011).

N. Drasdo and C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58(8), 709–714 (1974).
[Crossref] [PubMed]

T. Evans and W. F. Harris, “Dependence of the transference of a reduced eye on frequency of light,” S. Afr. Optom. 70, 149–155 (2011).

W. F. Harris, “Magnification, blur, and ray state at the retina for the general eye with and without a general optical instrument in front of it: 1. Distant Objects,” Optom. Vis. Sci. 78(12), 888–900 (2001).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[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(18), 2352–2366 (2005).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[Crossref] [PubMed]

B. E. Klein, K. E. Lee, and R. Klein, “Refraction in adults with diabetes,” Arch. Ophthalmol. 129(1), 56–62 (2011).
[Crossref] [PubMed]

B. E. Klein, K. E. Lee, and R. Klein, “Refraction in adults with diabetes,” Arch. Ophthalmol. 129(1), 56–62 (2011).
[Crossref] [PubMed]

D. Lahm, L. K. Lee, and F. A. Bettelheim, “Age dependence of freezable and nonfreezable water content of normal human lenses,” Invest. Ophthalmol. Vis. Sci. 26(8), 1162–1165 (1985).
[PubMed]

B. E. Klein, K. E. Lee, and R. Klein, “Refraction in adults with diabetes,” Arch. Ophthalmol. 129(1), 56–62 (2011).
[Crossref] [PubMed]

D. Lahm, L. K. Lee, and F. A. Bettelheim, “Age dependence of freezable and nonfreezable water content of normal human lenses,” Invest. Ophthalmol. Vis. Sci. 26(8), 1162–1165 (1985).
[PubMed]

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[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(18), 2352–2366 (2005).
[Crossref] [PubMed]

R. Navarro and N. Lopez-Gil, “Impact of the internal curvature gradient on the power and accommodation of the crystalline lens,” Optica 4(3), 334–340 (2017).
[Crossref]

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(8), 2175–2185 (2007).
[Crossref] [PubMed]

R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2(8), 1273–1281 (1985).
[Crossref] [PubMed]

S. Norrby, “The Dubbelman eye model analysed by ray tracing through aspheric surfaces,” Ophthalmic Physiol. Opt. 25(2), 153–161 (2005).
[Crossref] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[Crossref] [PubMed]

P. R. Eva, P. T. Pascoe, and D. G. Vaughan, “Refractive change in hyperglycaemia: hyperopia, not myopia,” Br. J. Ophthalmol. 66(8), 500–505 (1982).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

B. Pierscionek, “Presbyopia–effect of refractive index,” Clin. Exp. Optom. 73(1), 23–30 (1990).
[Crossref]

B. K. Pierscionek and J. W. Regini, “The gradient index lens of the eye: an opto-biological synchrony,” Prog. Retin. Eye Res. 31(4), 332–349 (2012).
[Crossref] [PubMed]

G. Smith and B. K. Pierscionek, “The optical structure of the lens and its contribution to the refractive status of the eye,” Ophthalmic Physiol. Opt. 18(1), 21–29 (1998).
[Crossref] [PubMed]

G. Smith, D. A. Atchison, and B. K. Pierscionek, “Modelling the ageing human eye,” J. Opt. Soc. Am. A 9(12), 2111–2117 (1992).
[Crossref]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[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(18), 2352–2366 (2005).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

B. K. Pierscionek and J. W. Regini, “The gradient index lens of the eye: an opto-biological synchrony,” Prog. Retin. Eye Res. 31(4), 332–349 (2012).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[Crossref] [PubMed]

G. Smith and B. K. Pierscionek, “The optical structure of the lens and its contribution to the refractive status of the eye,” Ophthalmic Physiol. Opt. 18(1), 21–29 (1998).
[Crossref] [PubMed]

G. Smith, D. A. Atchison, and B. K. Pierscionek, “Modelling the ageing human eye,” J. Opt. Soc. Am. A 9(12), 2111–2117 (1992).
[Crossref]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[Crossref] [PubMed]

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[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. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: Curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

P. R. Eva, P. T. Pascoe, and D. G. Vaughan, “Refractive change in hyperglycaemia: hyperopia, not myopia,” Br. J. Ophthalmol. 66(8), 500–505 (1982).
[Crossref] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[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. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, “Wide-angle optical model of the eye,” Am. J. Optom. Physiol. Opt. 61(3), 166–176 (1984).
[Crossref] [PubMed]

B. E. Klein, K. E. Lee, and R. Klein, “Refraction in adults with diabetes,” Arch. Ophthalmol. 129(1), 56–62 (2011).
[Crossref] [PubMed]

P. R. Eva, P. T. Pascoe, and D. G. Vaughan, “Refractive change in hyperglycaemia: hyperopia, not myopia,” Br. J. Ophthalmol. 66(8), 500–505 (1982).
[Crossref] [PubMed]

N. Drasdo and C. W. Fowler, “Non-linear projection of the retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58(8), 709–714 (1974).
[Crossref] [PubMed]

B. Pierscionek, “Presbyopia–effect of refractive index,” Clin. Exp. Optom. 73(1), 23–30 (1990).
[Crossref]

N. Brown, “The change in lens curvature with age,” Exp. Eye Res. 19(2), 175–183 (1974).
[Crossref] [PubMed]

D. Lahm, L. K. Lee, and F. A. Bettelheim, “Age dependence of freezable and nonfreezable water content of normal human lenses,” Invest. Ophthalmol. Vis. Sci. 26(8), 1162–1165 (1985).
[PubMed]

R. Navarro, J. Santamaría, and J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2(8), 1273–1281 (1985).
[Crossref] [PubMed]

H. L. Liou and N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14(8), 1684–1695 (1997).
[Crossref] [PubMed]

A. V. Goncharov and C. Dainty, “Wide-field schematic eye models with gradient-index lens,” J. Opt. Soc. Am. A 24(8), 2157–2174 (2007).
[Crossref] [PubMed]

G. Smith, D. A. Atchison, and B. K. Pierscionek, “Modelling the ageing human eye,” J. Opt. Soc. Am. A 9(12), 2111–2117 (1992).
[Crossref]

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(8), 2175–2185 (2007).
[Crossref] [PubMed]

D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29 (2008).
[Crossref] [PubMed]

B. Pierscionek, M. Bahrami, M. Hoshino, K. Uesugi, J. Regini, and N. Yagi, “The eye lens: age-related trends and individual variations in refractive index and shape parameters,” Oncotarget 6(31), 30532–30544 (2015).
[Crossref] [PubMed]

G. Smith and B. K. Pierscionek, “The optical structure of the lens and its contribution to the refractive status of the eye,” Ophthalmic Physiol. Opt. 18(1), 21–29 (1998).
[Crossref] [PubMed]

S. Norrby, “The Dubbelman eye model analysed by ray tracing through aspheric surfaces,” Ophthalmic Physiol. Opt. 25(2), 153–161 (2005).
[Crossref] [PubMed]

S. F. Lin, P. K. Lin, F. L. Chang, and R. K. Tsai, “Transient hyperopia after intensive treatment of hyperglycemia in newly diagnosed diabetes,” Ophthalmologica 223(1), 68–71 (2009).
[Crossref] [PubMed]

W. F. Harris, “Magnification, blur, and ray state at the retina for the general eye with and without a general optical instrument in front of it: 1. Distant Objects,” Optom. Vis. Sci. 78(12), 888–900 (2001).
[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. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

B. K. Pierscionek and J. W. Regini, “The gradient index lens of the eye: an opto-biological synchrony,” Prog. Retin. Eye Res. 31(4), 332–349 (2012).
[Crossref] [PubMed]

T. Evans and W. F. Harris, “Dependence of the transference of a reduced eye on frequency of light,” S. Afr. Optom. 70, 149–155 (2011).

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(18), 2352–2366 (2005).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: Curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

H. von Helmholtz, Physiologische Optik, 3rd ed. (Voss, Hamburg 1909).

A. Gullstrand, appendix in Physiologische Optik, 3rd ed., H. von Helmholtz, Ed., Voss, Hamburg (1909).

H. H. Emsley, Visual Optics, 5th ed., Vol. 1, (Hatton Press Ltd., London 1952).

Y. Le Grand Optique Physiologique I, eds., Rev. Opt., Paris (1953).

C. J. Sheil, Modelling accommodation and ageing of the crystalline lens in the human eye, Ph.D. Thesis National University of Ireland, Galway (2016).

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