Numerical Algorithms

doi:10.1117/3.975277.ch6

Book: Modeling the Optical and Visual Performance of the Human Eye

Author(s): Pier Giorgio Gobbi

Published: 2013

https://doi.org/10.1117/3.975277.ch6

Author Affiliations +

Abstract

Numerical ray tracing is required to evaluate the wave aberration function Wp,λ (rp), which is the OPD cumulated from the plane of the corneal apex to the Gaussian reference sphere tangent to the exit pupil. Due to cylindrical symmetry, wave aberration is a function of ray height only, and it can be equally represented at the entrance or exit pupil planes. The geometry of the Campbell-Gubisch experiment simply involves tracing a bundle of meridional rays parallel to the optical axis throughout the eye model. The presence of aspheric surfaces requires modification of the standard ray tracing equations, but the choice of conic sections greatly simplifies the task. While the Gullstrand exact model is entirely optically homogeneous and ray tracing is straightforward, for the GRIN lens model it is necessary to solve the differential equation for the ray trajectory in an inhomogeneous medium. The computational scheme followed here is the method illustrated by Sharma, Kumar, and Ghatak, which is a Runge-Kutta method extended to 3D (in the present case, circular symmetry reduces the problem to bidimensional). Maximum accuracy in the evaluation of the ray-surface intersection was achieved using a fifth-order interpolation method.