Monte-carlo ray tracing for axisymmetrical optical elements

A modification of the Monte-Carlo ray tracing procedure for axisymmetric surfaces is proposed. The main idea consists in the approximation of optical surfaces by truncated cones and the use of an unconventional k-d tree. The simulation results show high performance of the proposed method, with the ray tracing procedure working 3-12 times faster than conventional algorithms based on a triangle approximation.