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Optical Eye Modeling and Applications

analysis to determine how critical the optimized values of the variables are for the prediction of the total wave aberration of the eye. Navarro has developed the following procedure for this particular optical design problem: once the optimization algorithm finds the minimum of the merit function, 1D plots of this merit function are obtained in the vicinity of the optimal or minimal value versus each independent variable (such as surface curvature, conic constant, decentrations, and tip/tilt angle in Navarro’s study). Here, we perform a similar procedure. Once the optimization algorithm finds the minimum of the merit function, we obtain plots of this merit function against the varied RMS for each order of Zernike coefficients of anterior lens around the optimal (minimum) value. From these plots, we can see which order is the most significant and dominant (the smallest tolerance).

13.2.2. Population-Based Eye Modeling

13.2.2.1. Accommodative eye modeling

Most schematic eyes represent emmetropic and relaxed adult eyes. Under accommodation demand for near vision, the ciliary muscles holding the crystalline lens tighten, thereby causing the lens to become more rounded. The thickness and curvatures on both surfaces of lens increase. In the history of eye modeling, a few accommodative models exist. The Gullstrand No. 1 model1 is constructed at about 10.9 diopter accommodation. The Gullstrand-Emsley9 and Le Grand models10 present full schematic eyes that are in accommodated forms of 8.6 and 7.1 diopters, respectively. The Navarro model eye is “adaptive” in the sense that it offers the variability of lens parameters (the thickness, the radius of curvatures, and conic constants on both surfaces) and the anterior chamber and vitreous depth. In this popular eye model, these ocular parameters are given as functions of accommodation level. Atchinson summarized the four accommodative eye models in Appendix A3.11

As shown in previous studies,1215 the lens biometry is fundamentally independent of eye refractive error. However, in addition to the variation under accommodation, lens shape and refractive index are also significantly related to age. With an increase in age during adulthood, the lens becomes thicker and more curved in its relaxed state, and its refractive

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Ying-Ling Chen et al.

index distribution changes. Therefore, modeling the accommodative eye should be performed with specification of a limited age range.

13.2.2.2. Ametropic eye modeling

In 2006, Atchison published the optical models for myopic eyes11 according to the analysis of statistical relevance obtained from the subjects and studies primarily of his research group. Table 13.2 compares the refraction dependence of the Atchison myopic eye model and the emmetropic Navarro eye model.2 Not included in the table is the information regarding the decenters of the pupil and the lens, the tilt of the lens, and the fovea location that are also used in the models. These parameters contribute to ocular

Table 13.2. Comparison of parameters between Atchison myopia model11 and Navarro emmetropic model.2

 

 

Emmetropic

 

 

 

condition

Refractive error (K)

Ocular parameter

Model

(K = 0)

dependence

Anterior corneal radius

Atchison

7.77 mm

+0.022 mm/diopter

of curvature

Navarro

7.72 mm

 

Asphericity of anterior

Atchison

0.15

Not significant

cornea

Navarro

0.26

 

 

 

Central corneal

Atchison

0.55 mm

Not significant

thickness

Navarro

0.55 mm

 

Index of refraction of

Atchison

1.3975, 1.3807, 1.37405, 1.3668, for

cornea

Navarro

λ = 365, 486.1, 656.3, 1014 nm

 

Posterior corneal radius

Atchison

6.40 mm

Not significant

 

Navarro

6.50 mm

 

Asphericity of posterior

Atchison

0.275

Not significant

cornea

Navarro

0

 

Anterior chamber depth

Atchison

3.15 mm

Not significant

 

Navarro

3.05 mm

 

Index of refraction of

Atchison

1.3593, 1.3422, 1.3354, 1.3278, for

aqueous humor

Navarro

λ = 365, 486.1, 656.3, 1014 nm

 

(Continued)

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Optical Eye Modeling and Applications

Table 13.2. (Continued)

 

 

Emmetropic

 

 

 

condition

Refractive error (K)

Ocular parameter

Model

(K = 0)

dependence

Anterior lens

Atchison

11.48 mm

Not significant

radius

 

 

 

 

Navarro

10.20 mm

 

Anterior lens

Atchison

5

Not significant

asphericity

Navarro

3.1316

 

 

 

Lens thickness

Atchison

3.6 mm

Not significant

 

Navarro

4.0 mm

 

Refractive index of

Atchison

Gradient index

 

crystalline lens

Navarro

1.4492, 1.4263, 1.4175, 1.4097, for

 

 

λ = 365, 486.1, 656.3, 1014 nm

Posterior lens

Atchison

5.9 mm

Not significant

radius

 

 

 

Posterior lens asphericity

Vitreous chamber depth

Refractive index of vitreous humor

Radius of retina curvature

Navarro

6.0 mm

 

Atchison

2

Omit; not significant

Navarro

1

0.299 mm/diopter

Atchison

16.28 mm

Navarro

16.32 mm

 

Atchison

1.3565, 1.3407, 1.3341, 1.3273, for

Navarro

α = 365, 486.1, 656.3, 1014 nm.

Atchison

12.91 mm (x);

0.094 mm/diopter (x);

 

12.72 mm(y)

+0.004 mm/diopter (y)

Navarro

12 mm

 

asymmetry and introduce astigmatism, coma, and irregular aberrations, and, therefore, have important effect upon optical performance. The significance of using these parameters depends on the types of applications.

13.2.2.3. Modeling with consideration of ocular growth and aging

Age is an important factor in ocular biometry. The ocular dimension increases significantly during the first year of life. During infancy, the ocular refraction develops from mild hyperopia to emmetropia. From the age

399