Análisis Competitivo del País

Ametropic eyes are eyes with sphero-cylindrical refractive errors and are discussed in Chapter 3. In my M.S. thesis [Tan 2005], I constructed 3 types of ametropic eye models according to the possible causes of the defocus: mismatches of the cornea curvature, the lens power, and the axial length. Based on the well accepted Navarro Eye Model [Navarro 1985], the axial type of ametropic eye model is constructed by varying only the posterior axial length (Model I). The pure refractive type of ametropic eye model depends only on the variable of corneal surface curvature (Model II). The pure index ametropic eye model varies only the virtual power of near pupil and lens position (Model III). Since then, I have changed the use of merit function slightly to obtain the ametropic eye models. The modeling procedures of the three ametropic eye models are summarized as the following:

Model I --- The only adjustable parameter in this modeling is the vitreous chamber thickness. This thickness value is optimized to approach the desired spherical refractive error. To do so, a virtual Gaussian thin lens is placed in front of the optical model eye. The power of the thin lens is set to be the compensation of the defocus. For example, a clinically near-sighted eye of -5.5 diopter is an over- powered eye of +5.5 diopter from emmetropia. The compensation virtual lens is, therefore, -5.5 diopter. Before the optimization, in the lens editor in ZEMAX, the vitreous body thickness is set to be the only variable in the base Navarro model. In my M.S. thesis, I used the default RMS WFA as the merit function to optimize VCD alone. Based on my previous investigation and comparison of the results, I now use the maximization of the Strehl Ratio as the merit function for a finely-tuned optimization following the first optimization. As discussed in Chapter 3, the minimal difference between SRX and the diffraction limited case of ―1‖ will be approached in the iteration. The same merit function is used for the optimizations in constructing models B and C. All the iterations are run under paraxial eye condition (i.e. small pupil diameter) because the Navarro model eye is emmetropic only under the paraxial condition. With a larger pupil diameter and the resulting aberrations, the refractive error of the Navarro model eye will not be zero. For example, in a 3-mm-pupil Navarro eye, a small refractive error of -0.18 diopter (slightly near- sighted) is present. Therefore, in my eye modeling that uses the Navarro model as the emmetropic standard, the refractive result of final model is always determined under the paraxial assumption.

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Model II --- The vertex curvature radius of anterior cornea surface is set to be the only variable to provide the result refractive error. Curvature contributions in the posterior cornea and the two lens surfaces were omitted because they provide very small refractive influence compared to the front cornea surface. For example, the influence of the posterior cornea surface is only about 10% of the anterior surface. According to the ocular biometry studies in Chapter 2, the lens parameters have very little to do with refractive error. Therefore, with the single variable of curvature of the first surface of the Navarro eye, the refractive ametropic eye is obtained by similar optimization process as it is done in model A. Model III --- The single adjustable parameter in this model is an extra virtual thin lens that is specified with a uniform power at the location of pupil. Similar to the process in Model A, the power of virtual thin lens is varied to approach the desired conjugate point of the retina and to obtain the corresponding ametropic condition.

One thing to be noted in this ametropic eye modeling is the role played by the conic constants in these models. The conic surface is the standard surface type in ZEMAX and is also the most commonly used surface type in today‘s eye modeling community to produce the adequate asphericity of human eye elements. Unless additional parameters or the user-defined surface(s) are introduced in the modeling, the conic constants and the radius on surfaces of cornea and lens are the parameters that determine the final high-order aberrations of these models. Although the conic constants will not change the results of refractive error in paraxial region, they affect the resulting spherical aberration significantly. From the discussion in Chapter 2, the conic constant of the anterior cornea varies significantly from one person to another, and the reported values are also very different between studies. Even when examining a single eye, the Q number is rarely the same in the temporal, nasal, upper and lower quarters of the eyes. From the spherical aberration measurements among populations, the corresponding Q value tends to be near - 1.0 for infants and toddlers and tends to increase toward zero with age. It has been shown in my M.S. thesis [Tan 2005] that the deviation of the cornea surface from Q = 0 to Q = -1.0 is observable only near the periphery of cornea. Surprisingly, this ‗small‘ deviation results in a significant difference in the spherical aberration of the eye up to several diopters in the periphery vision in a darkened environment. The conic constant, Q, in the anterior cornea surface of Navarro model is -0.26 for adult. The validation of this model as described in the paper makes sure that the final model provides the result spherical aberration that is equivalent to the clinically measured values in Navarro‘s study. In my ametropic eye models A, B, and C, the final spherical aberrations were not examined or validated since the statistical data in Chapter 2 do not provide evidence of aberrations on the refraction dependence.

In 2006, Atchison published the optical models for myopic eyes [Atchison 2006] according to the analysis of statistical relevance obtained from the subjects and studies majorly of his research group. Table 4.1 compares the refraction dependence of Atchison‘s myopic eye model, the conclusion I obtained from the review in Chapter 2, and the emmetropic eye model of Navarro‘s [Isabel Escudero-Sanz 1999] (N). 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 used in the models. These parameters concerning ocular asymmetry 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.

After putting together an eye model, validations to optical performance of various types of aberrations are the next step to ensure that the model preserves the integrity of required characteristics. Because many parameters, especially the conic constants, are not confidently assigned, they can be set as variables within a given reasonable ranges for iteration to approach the target aberrations.

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Table 4.1 Comparison of ocular parameters in Atchison myopic eye model, the statistical finding in Chapter 2, and the emmetropic Navarro model.

Ocular parameter

Model

Emmetropic condition

(K=0) Refractive error,(K) dependence

Anterior Corneal Radius of Curvature (CR1): Atchison 7.77 mm +0.022 mm/diopter Tan 7.75 mm +0.016 mm/diopter Navarro 7.72 mm X Asphericity of anterior cornea surface (Q1):

Atchison -0.15 Not significant

Tan -0.2654 -0.0145 /diopter

Navarro -0.26 X

Central corneal thickness (CCT):

Atchison 0.55 mm Not significant

Tan 0.536 mm Not significant

Navarro 0.55 mm

Index of refraction of cornea, n1

Atchison use Navarro's

Tan use Navarro's

Navarro 1.3975,1.3807,1.37405,1.3668, for = 365,486.1,656.3,1014nm

Posterior Corneal Radius (CR2):

Atchison 6.40 mm Not significant

Tan 6.50 mm +0.013 mm/diopter

Navarro 6.50 mm X

Asphericity of posterior cornea surface (Q2):

Atchison -0.275 Not significant

Tan -0.4 Not enough info

Navarro 0 X

Anterior chamber depth (ACD)

Atchison 3.15 mm Not significant

Tan Adopt Navarro‘s Not significant

Navarro 3.05 mm X

Index of refraction of aqueous humor: n2

Atchison use Navarro's

Tan use Navarro's

Navarro 1.3593,1.3422,1.3354,1.3278, for= 365, 486.1,656.3,1014nm.

Anterior lens radius (LR1):

Atchison 11.48 mm Not significant

Tan 10.50 mm Not significant

Navarro 10.20 mm X

Anterior lens asphericity (Q3):

Atchison -5 Not significant

Tan use Navarro's No info

Navarro -3.1316 X

Lens thickness (LT):

Atchison 3.6 mm Not significant

Tan Adopt Navarro‘s Not significant

Navarro 4.0 mm X

Refractive index of crystalline lens: n3

Atchison Gradient index

Tan use Navarro's

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Table 4.1, cont.

Posterior lens radius (LR2)

Atchison -5.9 mm Not significant

Tan use Navarro's Not significant

Navarro -6.0 mm X

Posterior lens asphericity (Q4):

Atchison -2 Omit; Not significant

Tan use Navarro's Not significant

Navarro -1 X Vitreous chamber depth (VCD): Atchison 16.28 mm -0.299 mm / diopter Tan 16.15 mm -0.36 mm/ diopter Navarro 16.32 mm X Refractive index of vitreous humor (n4):

Atchison use Navarro's

Tan use Navarro's

Navarro 1.3565,1.3407,1.3341,1.3273, for =365,486.1, 656.3,1014nm.

Radius of retina curvature (RR):

Atchison Use Navarro‘s X

Tan use Navarro's X

Navarro -12 mm X