Modeling of micro cat's eye retroreflectors using a matrix-based three-dimensional ray tracing technique.

In this paper we develop a three-dimensional (3D) ray tracing tool based on the ABCD ray transfer matrices. With symmetric optical components and under paraxial approximation, two sets of 2×2 ABCD matrices, each for a two-dimensional subspace, can be used to describe the 3D ray propagation completely. Compared to commercial ray-tracing software packages, our tool requires no tedious drawing, and the results for various conditions, such as different device dimensions and incident angles, can be easily obtained by simply changing the parameter values used for the calculation. We have employed this matrix-based 3D ray tracing tool to model cat's eye retroreflectors. The cat's eye performance, including the retroreflection efficiency, acceptance angle (i.e., field of view), and beam divergence and deviation, is fully studied. The application of this 3D ray tracing technique can be further extended to other optical components.