Comparison of Uniform and Gradient Paraxial Models of the Crystalline Lens

Abstract

Purpose: : To quantify errors in paraxial optical models of the unaccommodated crystalline lens using a uniform equivalent refractive index.

Methods: : Two paraxial models were compared: uniform and continuous refractive index gradient. The position of the principal and focal points of both models were calculated for age 18 to 50 years. For the gradient model, the differential equation for the ray path in an inhomogeneous medium was solved. Age-dependent radius of curvature and thickness were taken from Dubbelman et al, Vis Res 2001. The uniform model used the equivalent index of Borja et al, IOVS 2008. The gradient model used a power function for the axial variation of the index. The index was 1.378 at the surface and 1.410 at the equator, independent of age (Kasthurirangan et al, IOVS, 2008). At each age, the value of the power coefficient p was selected to match the published lens power.

Results: : The power coefficient ranged from p=3 at 18 years to p=11 at 50 years. The positions of the first and second principal point of the gradient model were, in mm from lens center: 0.267+0.0041*Age and 0.352+0.00473*Age. In both models the distance between the two principal points is less than 5% of the lens thickness. Assuming a uniform index produces an error smaller than 0.1D in the back vertex power.

Conclusions: : The unaccommodated crystalline lens can be modeled as a thin optical element with a back principal plane located between 0.39 (18 years) and 0.53mm (50 years) posterior to the lens center. The error introduced by assuming a uniform equivalent index is negligible.

Keywords: accommodation • optical properties