Freeform design of a two-reflector system to collimate and shape a point source distribution

Abstract

We present a method to design a freeform two-reflector system to collimate and shape a beam from a point source. An important generalization compared to previous research is that the output beam can be in an arbitrary direction. The design problem is based on a generalized Monge-Ampère equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. We test our algorithm on two cases, first, uniform source and target distributions, and second, an elliptic Gaussian intensity of a laser diode to a ring-shaped illuminance. We are able to obtain good solutions in both cases.