Design of a freeform two-reflector system to collimate and shape a point source distribution

TL;DR

This paper introduces a novel method for designing freeform two-reflector systems that can shape and collimate light from a point source into arbitrary directions using a generalized Monge-Ampère equation and a least-squares algorithm.

Contribution

It presents a new approach to designing freeform reflectors for arbitrary beam directions, extending previous work with a generalized Monge-Ampère equation and a specialized numerical solution.

Findings

Successfully designed reflectors for uniform source and target distributions.

Demonstrated shaping of laser diode light into a ring-shaped target.

Validated the method's flexibility in arbitrary beam direction control.

Abstract

In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target. An important generalization in our approach compared to previous research is that the output beam can be in an arbitrary direction. The design problem is approached by using a generalized Monge-Amp\`ere equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. This algorithm calculates the optical map, from which we can then compute the surfaces. We test our algorithm on two cases. First we consider a uniform source and target distribution. Next, we use the model of a laser diode light source and a ring-shaped target distribution.