A generic eye model by reverse building based on Chinese population

Mei-mei Kong; Zhi-shan Gao; Xin-hua Li; Shu-hua Ding; Xiao-mei Qu; Mei-qun Yu

doi:10.1364/OE.17.013283

Optics Express
Vol. 17,
Issue 16,
pp. 13283-13297
(2009)
•https://doi.org/10.1364/OE.17.013283

A generic eye model by reverse building based on Chinese population

Mei-mei Kong, Zhi-shan Gao, Xin-hua Li, Shu-hua Ding, Xiao-mei Qu, and Mei-qun Yu

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Mei-mei Kong, Zhi-shan Gao, Xin-hua Li, Shu-hua Ding, Xiao-mei Qu, and Mei-qun Yu, "A generic eye model by reverse building based on Chinese population," Opt. Express 17, 13283-13297 (2009)

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- Vision, Color, and Visual Optics
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About this Article
History
- Original Manuscript: June 11, 2009
- Revised Manuscript: June 28, 2009
- Manuscript Accepted: June 29, 2009
- Published: July 20, 2009
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 4, Iss. 10

Abstract

The human eye has ethnic difference, the existing typical eye models are based on western eyes. A generic eye model based on Chinese population is presented for the first time. The statistical analyzed ocular parameters based on measured data are used for the initial generic eye model, and the wavefront aberration data obtained at two different pupil diameters are used for reproduction by optimizing the initial generic eye model. The differences and similarities between Chinese generic eye model and western eye models are given. The Chinese generic eye model provides a suitable model for the related further researches and applications on Chinese eye.

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Fig. 1. the flow diagram of reverse building Chinese generic eye model

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Fig. 2. the Q-Q plots of the anterior corneal surface steep curvature radius R_x with normality test

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Fig. 3. the Q-Q plots of the anterior corneal surface flat curvature radius R_y with normality test

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Fig. 4. the Normal distribution histogram of the anterior corneal surface steep curvature radius R_x

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Fig. 5. the Normal distribution histogram of the anterior corneal surface flat curvature radius R_y

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Fig. 6. the average values of Zernike polynomials coefficients at 3mm pupil diameter

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Fig. 7. the average values of Zernike polynomials coefficients at 6mm pupil diameter

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Fig. 8. the contrast curves of fitting new GRIN with others in axial direction

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Fig. 9. the contrast curves of fitting new GRIN with others in radial direction

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Fig. 10. the contrast curves of the fitting Conrady equations for ocular media with various sources of chromatic dispersion data in the visible spectrum

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Fig. 11. the measured wavefront aberrations with opposite signs (a) & (b) and predicted wavefront aberrations obtained by the generic eye model (c) & (d) at pupil diameter of 3mm (left) and 6mm (right)

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Fig. 12. the schematic plots of Chinese generic eye model at the pupil diameter of 3mm (a) and 6mm (b)

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Fig. 13. the MTF of Chinese generic eye model compared with experimental result and two western eye models

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Tables (7)

Table 1. the measurement apparatuses used

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Table 2. the mean values and 95% confidence intervals of measured parameters

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Table 3. Conrady equations fitted to various sources of chromatic dispersion data [21, 12–14]

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Table 4. some averages of various sources [12–14,21] in the visible spectrum

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Table 5. Conrady equations fitted to averages of various sources [12–14,21] in the visible spectrum

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Table 6. the structural parameters of Chinese generic eye model

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Table 7. the surface performance comparison of main refractive elements in Chinese generic eye model with existing western eye models

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Equations (16)

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x^{2} + y^{2} + (1 + k) z^{2} - 2 R z = 0

z = \frac{c_{x} x^{2} + c_{y} y^{2}}{1 + \sqrt{1 - (1 + k_{x}) c_{x}^{2} x^{2} - (1 + k_{y}) c_{y}^{2} y^{2}}}

n (r, z) = n_{0} (z) + n_{1} (z) r^{2} + n_{2} (z) r^{4} + n_{3} (z) r^{6} + \dots

n (r, z) = 1.406 - 0.0062685 {(z - 1.7)}^{2} + 0.0003834 {(z - 1.7)}^{3}

- [0.00052375 + 0.00005735 (z - 1.7) + 0.00027875 {(z - 1.7)}^{2}] r^{2} - 0.000066716 r^{4}

n (r, z) = 1.387 + 0.014 z - 0.00384 z^{2} - 0.0012 r^{2}

n (r, z) = {\begin{array}{c} 1.368 + 0.049057 z - 0.015427 z^{2} - 0.001978 r^{2} & 0 < z \leq 1.59 \\ 1.407 + 0.0 (z - 1.59) - {0.006605 (z - 1.59)}^{2} - 0.001978 r^{2} & 1.59 < z \leq 4.02 \end{array}

n (r, z) = 1.362 - 0.0021490 r^{2} - 0.0000106 r^{4}

+ 0.049467 z - 0.015958 z^{2} + 0.0001715 z^{3} + 0.000141 z^{4}

n (r, z) = 1.379 + 0.035118 z - 0.012214 z^{2} + 0.00076664 z^{3} - 0.0018073 r^{2}

n (λ) = A + \frac{B}{λ^{2}} + \frac{C}{λ^{4}} + \frac{D}{λ^{6}} + \dots

n (λ) = n_{0} + \frac{A}{λ} + \frac{B}{λ^{3.5}}

{n (λ)}_{cornea} = 1.3625 + \frac{6.6460 \times 10^{- 3}}{λ} + \frac{3.5752 \times 10^{- 4}}{λ^{3.5}}

{n (λ)}_{aqueous} = 1.3229 + \frac{6.7866 \times 10^{- 3}}{λ} + \frac{3.5976 \times 10^{- 4}}{λ^{3.5}}

{n (λ)}_{lens} = 1.4050 + \frac{6.3200 \times 10^{- 3}}{λ} + \frac{6.4981 \times 10^{- 4}}{λ^{3.5}}

{n (λ)}_{vitreous} = 1.3222 + \frac{6.6518 \times 10^{- 3}}{λ} + \frac{3.4545 \times 10^{- 4}}{λ^{3.5}}

Ocular parameters	Apparatuses
Anterior surface	CRS-Master Twinline ^a
Cornea Posterior surface		Orbscan ‖ ^b
Central thickness	Pentacam ^a
Anterior chamber depth	Pentacam ^a
Lens central thickness		A/B scanner ^b
Overall axial length	IOL-Master ^a	A/B scanner ^b
Wavefront aberrations	CRS-Master Twinline ^a and Zywave ^b

Measured parameters		Mean ± SD	95% confidence intervals
Anterior corneal surface curvature radii (mm)	Steep curvature radius R_x	7.77±0.21	(7.71, 7.83)
Anterior corneal surface curvature radii (mm)	Flat curvature radius R_y	7.93±0.23	(7.86, 8.00)
Anterior corneal surface conic coefficient		-0.18±0.12	(-0.21, -0.14)
Posterior corneal surface curvature radii (mm)	Steep curvature radius R_x	6.23±0.18	(6.16, 6.31)
Posterior corneal surface curvature radii (mm)	Flat curvature radius R_y	6.62±0.24	(6.52, 6.72)
Posterior corneal surface conic coefficient		-0.07±0.23	(-0.17, 0.02)
Corneal central thickness (mm)		0.53±0.03	(0.52, 0.53)
Anterior chamber depth (mm)		3.28±0.37	(3.17, 3.38)
Lens central thickness (mm)		3.76±0.30	(3.63, 3.89)
Vitreous depth (mm)		16.16±0.56	(15.92, 16.40)
Overall axial length (mm)		23.79±0.71	(23.59, 23.99)

	n₀	A(×10^-3)	B(×10^-4)	Max fitting error(×10^-4)	Abbe number
Cornea
Le Grand [21]	1.3596	9.5761	0.1988	0.5006	56.13
Navarro [12]	1.3662	3.3770	6.1009	1.1866	55.66
Liou & Brennan [13]	1.3583	9.4379	1.04517	2.2711	63.77
Escudero-Sanz & Navarro [14]	1.3647	4.7808	4.9921	1.9254	56.96
Aqueous
Le Grand [21]	1.3210	8.8810	1.9688	0.2387	53.27
Navarro [12]	1.3272	3.5656	6.1842	1.7423	48.73
Liou & Brennan [13]	1.3183	9.4379	1.0452	2.2711	56.97
Escudero-Sanz & Navarro [14]	1.3263	4.4187	5.5639	0.7065	49.09
Lens
Le Grand [21]	1.3982	11.9622	2.4817	0.2217	50.05
Navarro [12]	1.4087	3.1737	8.8728	2.1370	47.20
periphery	1.3503	9.4379	1.04517	2.2711	62.41
Liou & Brennan [13]
core	1.3893	9.4379	1.0452	2.2711	69.04
Escudero-Sanz & Navarro [14]	1.4077	4.1884	8.006	0.5960	48.10
Vitreous
Le Grand [21]	1.3193	9.1927	1.8030	0.4844	52.79
Navarro [12]	1.3255	4.0605	5.5345	1.7666	50.46
Liou & Brennan [13]	1.3183	9.4379	1.0452	2.2711	56.97
Escudero-Sanz & Navarro [14]	1.3247	4.7808	4.9921	0.2824	50.90

Ocular media	n(0.4µm)	n(0.45µm)	n(0.5µm)	n(0.55µm)	n(0.6µm)	n(0.65µm)	n(0.7µm)
Cornea	1.3879	1.3831	1.3798	1.3774	1.3757	1.3743	1.3732
Aqueous	1.3488	1.3439	1.3406	1.3382	1.3364	1.3350	1.3339
Lens	1.4369	1.4297	1.4250	1.4218	1.4195	1.4177	1.4163
Vitreous	1.3474	1.3427	1.3395	1.3371	1.3354	1.3340	1.3330

Ocular media	n₀	A(×10^-3)	B(×10^-4)	Max fitting error(×10^-4)	Abbe number
Cornea	1.3625	6.6460	3.5752	4.1718	58.34
Aqueous	1.3229	6.7866	3.5976	1.3055	51.50
Lens	1.4050	6.3200	6.4981	4.6499	48.58
Vitreous	1.3222	6.6518	3.4545	4.4185	52.87

Surf	Type	Radius (mm) (meridional/sagittal)	Conic coefficient (meridional/sagittal)	Thickness (mm)
1	Biconic	7.94/7.80	-0.16/-0.21	0.52
2	Biconic	6.61/6.16	-0.14/-0.10	3.22
3(STO)	Standard	Infinity	0	0
4	Biconic	13.68/12.42	-5.69/-5.86	3.81
5	Biconic	-6.07/-6.73	-1.62/-1.05	16.28
6	Standard	-12.3	0	—

The main refractive optical elements		Existing western eye models		Chinese generic eye model (meridional/sagittal)
The main refractive optical elements		Radius (mm)	Conic coefficient	Radius (mm)	Conic coefficient
Cornea	Anterior surface	7.7, 7.72, 7.77, 7.8	0, -0.18, -0.25, -0.26	7.94/7.80	-0.16/-0.21
Cornea	Posterior surface	6.4, 6.5, 6.8	0, -0.60	6.61/6.16	-0.14/-0.10
Lens	Anterior surface	10, 11, 12.4	0, -0.94, -3.06, -3.1316	13.68/12.42	-5.69/-5.86
Lens	Posterior surface	-5.5, -6, -8.1	0.96, 0, -1	-6.07/-6.73	-1.62/-1.05

Abstract

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Figures (13)

Tables (7)

Equations (16)

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