Determination of caustic surfaces using point spread function and ray Jacobian and Hessian matrices.

Abstract

Existing methods for determining caustic surfaces involve computing either the flux density singularity or the center of curvature of the wavefront. However, such methods rely rather heavily on ray tracing and finite difference methods for estimating the first- and second-order derivative matrices (i.e., Jacobian and Hessian matrices) of a ray. The main reason is that previously the analytical expressions of these two matrices have been tedious or even impossible. Accordingly, the present study proposes a robust numerical method for determining caustic surfaces based on a point spread function and the established analytical Jacobian and Hessian matrices of a ray by our group. It is shown that the proposed method provides a convenient and computationally straightforward means of determining the caustic surfaces of both simple and complex optical systems without the need for analytical equations, and is substantially different from the two existing methods.