Single dispersive gradient-index profile for the aging human lens

José Antonio Díaz; Carles Pizarro; Josep Arasa

doi:10.1364/JOSAA.25.000250

Journal of the Optical Society of America A
Vol. 25,
Issue 1,
pp. 250-261
(2008)
•https://doi.org/10.1364/JOSAA.25.000250

Single dispersive gradient-index profile for the aging human lens

José Antonio Díaz, Carles Pizarro, and Josep Arasa

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José Antonio Díaz, Carles Pizarro, and Josep Arasa, "Single dispersive gradient-index profile for the aging human lens," J. Opt. Soc. Am. A 25, 250-261 (2008)

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Table of Contents Category
- Vision, color, and visual optics
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About this Article
History
- Original Manuscript: May 8, 2007
- Revised Manuscript: October 23, 2007
- Manuscript Accepted: November 4, 2007
- Published: December 21, 2007
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Virtual Journal for Biomedical Optics Vol. 3, Iss. 2

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.

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Surface	Medium	n $(555 nm)$	R (mm)	Asphericity	Thickness (mm)
1	Cornea	1.376	7.79	$- 0.24 + {0.003}^{*} A$	0.579
2	Aqueous	1.336	6.53	$- {0.006}^{*} A$	$3.291 - {0.01}^{*} A$
3 (iris)^b	Aqueous	1.336	∞	—	0
4^c	Lens	$1.371 + n_{1} (\cos (n_{2} z) - 1)$	$12.7 - {0.058}^{*} A$	$- 4.56$	$2.93 + {0.0236}^{*} A$
		$+ n_{3} \sin (n_{4} z) + n_{5} (x^{2} + y^{2})$
5	Vitreous	1.336	$- 5.9 + {0.0015}^{*} A$	$- 1.13$	$16.79 - {0.0136}^{*} A$
6 (retina)^d	—	—	$R_{x} = - 12.91$	$Q_{x} = 0.27$	—
			$R_{y} = - 12.72$	$Q_{y} = 0.25$

Coefficient	Value	p-value	$R^{2}$
$K_{1}$	$- 30.121153$
$L_{1} ({nm}^{2})$	$- 19.383097 \times 10^{6}$
$K_{2}$	$- 0.809941$
$L_{2} ({nm}^{2})$	$0.017803 \times 10^{6}$
$K_{3}$	$- 156.88487$
$L_{3} ({nm}^{2})$	$107.42008 \times 10^{6}$
$n_{1}$	$0.0394 (\pm 0.0018) - 0.000355 {(\pm 0.00004)}^{*} A$	$< 1 \times 10^{- 4}$	0.907
$n_{2} ({mm}^{- 1})$	$1.238 (\pm 0.031) - 0.00561 {(\pm 0.0007)}^{*} A$	$< 1 \times 10^{- 4}$	0.89
$n_{3}$	$0.1092 (\pm 0.0018) - 0.00077 {(\pm 0.000039)}^{*} A$	$< 1 \times 10^{- 8}$	0.979
$n_{4} ({mm}^{- 1})$	$0.79 (\pm 0.014) - 0.00312 {(\pm 0.00032)}^{*} A$	$< 1 \times 10^{- 4}$	0.921
$n_{5} ({mm}^{- 2})$	$- 0.00235 (\pm 0.00002) + 1.32 \times 10^{- 5} {(\pm 5 \times 10^{- 7})}^{*} A$	$< 1 \times 10^{- 8}$	0.991

Age	$A_{G}$	$B_{G} (mm)$	$C_{G} (D)$	$D_{G}$	$ϕ_{1}^{'}$ (D)	$ϕ_{2}^{'}$ (D)	$ϕ_{L}^{'} - ϕ_{G}^{'}$ (D)	$ϕ_{G}^{'}$ (D)	$ϕ_{L}^{'}$ (D)
20	0.99989	3.34731	$- 10.392$	0.96532	3.03	5.96	8.83	14.25	23.08
25	1.00479	3.45945	$- 10.4017$	0.959416	3.11	5.97	8.93	14.26	23.19
30	0.99876	3.57997	$- 10.274$	0.964415	3.19	5.97	8.99	14.09	23.08
35	0.99799	3.69642	$- 10.209$	0.96402	3.28	5.98	9.08	14.0	23.08
40	0.9977	3.81277	$- 10.1451$	0.963243	3.37	5.99	9.17	13.91	23.08
45	0.9978	3.92976	$- 9.9049$	0.962541	3.47	6.0	9.26	13.58	22.84
50	0.966867	4.04563	$- 10.09$	0.958305	3.57	6.0	9.36	13.72	23.08
55	0.996512	4.16215	$- 9.9286$	0.962031	3.68	6.01	9.46	13.61	23.07
60	0.995904	4.27847	$- 9.9102$	0.961538	3.79	6.02	9.57	13.59	23.16
65	0.995524	4.39507	$- 9.7603$	0.961406	3.92	6.03	9.69	13.38	23.07

Surface	Medium	n $(555 nm)$	R (mm)	Asphericity	Thickness (mm)
1	Cornea	1.376	7.79	$- 0.24 + {0.003}^{*} A$	0.579
2	Aqueous	1.336	6.53	$- {0.006}^{*} A$	$3.291 - {0.01}^{*} A$
3 (iris)^b	Aqueous	1.336	∞	—	0
4^c	Lens	$1.371 + n_{1} (\cos (n_{2} z) - 1)$	$12.7 - {0.058}^{*} A$	$- 4.56$	$2.93 + {0.0236}^{*} A$
		$+ n_{3} \sin (n_{4} z) + n_{5} (x^{2} + y^{2})$
5	Vitreous	1.336	$- 5.9 + {0.0015}^{*} A$	$- 1.13$	$16.79 - {0.0136}^{*} A$
6 (retina)^d	—	—	$R_{x} = - 12.91$	$Q_{x} = 0.27$	—
			$R_{y} = - 12.72$	$Q_{y} = 0.25$

Coefficient	Value	p-value	$R^{2}$
$K_{1}$	$- 30.121153$
$L_{1} ({nm}^{2})$	$- 19.383097 \times 10^{6}$
$K_{2}$	$- 0.809941$
$L_{2} ({nm}^{2})$	$0.017803 \times 10^{6}$
$K_{3}$	$- 156.88487$
$L_{3} ({nm}^{2})$	$107.42008 \times 10^{6}$
$n_{1}$	$0.0394 (\pm 0.0018) - 0.000355 {(\pm 0.00004)}^{*} A$	$< 1 \times 10^{- 4}$	0.907
$n_{2} ({mm}^{- 1})$	$1.238 (\pm 0.031) - 0.00561 {(\pm 0.0007)}^{*} A$	$< 1 \times 10^{- 4}$	0.89
$n_{3}$	$0.1092 (\pm 0.0018) - 0.00077 {(\pm 0.000039)}^{*} A$	$< 1 \times 10^{- 8}$	0.979
$n_{4} ({mm}^{- 1})$	$0.79 (\pm 0.014) - 0.00312 {(\pm 0.00032)}^{*} A$	$< 1 \times 10^{- 4}$	0.921
$n_{5} ({mm}^{- 2})$	$- 0.00235 (\pm 0.00002) + 1.32 \times 10^{- 5} {(\pm 5 \times 10^{- 7})}^{*} A$	$< 1 \times 10^{- 8}$	0.991

Abstract

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Figures (7)

Tables (3)

Equations (13)

Journal of the Optical Society of America A