Age-dependence of the average and equivalent refractive indices of the crystalline lens

W Neil Charman,David A Atchison

doi:10.1364/boe.5.000031

Abstract

Lens average and equivalent refractive indices are required for purposes such as lens thickness estimation and optical modeling. We modeled the refractive index gradient as a power function of the normalized distance from lens center. Average index along the lens axis was estimated by integration. Equivalent index was estimated by raytracing through a model eye to establish ocular refraction, and then backward raytracing to determine the constant refractive index yielding the same refraction. Assuming center and edge indices remained constant with age, at 1.415 and 1.37 respectively, average axial refractive index increased (1.408 to 1.411) and equivalent index decreased (1.425 to 1.420) with age increase from 20 to 70 years. These values agree well with experimental estimates based on different techniques, although the latter show considerable scatter. The simple model of index gradient gives reasonable estimates of average and equivalent lens indices, although refinements in modeling and measurements are required.

Highlights

With the development of optical coherence tomography (OCT) and related non-contact optical methods for measurement of the axial and other dimensions of the eye, the reliability with which these distances can be determined in vivo has improved considerably
Are the values of the average and equivalent refractive indices the same? Is an equivalent index derived from measurements of the other ocular parameters the correct one to use when converting lenticular optical path to true lens thickness and are any differences of importance? We present here an analysis which suggests that generally the average and equivalent refractive indices are not the same, and we consider our results in relation to experimental findings
3.1 Average refractive index We assumed that ns = 1.37 and nc = 1.415, similar to those found by Jones et al [16] of 1.371 for ns and 1.418 for nc, and to those used by Bahrami & Goncharov [11] of 1.376 and 1.416

Summary

Introduction

With the development of optical coherence tomography (OCT) and related non-contact optical methods for measurement of the axial and other dimensions of the eye, the reliability with which these distances can be determined in vivo has improved considerably. At the present time the exact nature of these changes remains uncertain and it is necessary to use some form of average index. If this index is selected correctly, the measured optical path can be converted to the true thickness of the lens. If the assumed index is 0.001 in error, the error in the estimated lens thickness will be about 3 μm While this may seem small, it is of about the magnitude that is found by OCT for the changes in the total axial length of the eye when it accommodates [1,2,3]. Atchison and Smith [4] have suggested that the results found in such studies are influenced by the values of the average refractive index used in deriving the measurements and their dependence on the accommodation state of the eye

Methods

Results

Discussion

Conclusion