RAY PATHS THROUGH A GRIN LENS: THE CRYSTALLINE CASE

Rays paths follow a complex trajectory through the human crystalline. This is due to the changes in refractive index with position: crystalline is a GRIN lens. To calculate these trajectories approximate methods are often employed. In this contribution our aim is to compare two numerical methods: the first one based in solving the vector differential equation of the ray paths, while the second one is based on Fermat's principle. For each method different numeric schema are applied, and the results compared based on precision and computing easiness. We found that the most efficient procedure is a Runge-Kuta algorithm with adaptive step for integrating the differential equation derived from Fermat's principle. This procedure will be applied in a ray tracing computer program and also in an optimization algorithm to determine the refraction index distribution inside crystalline.