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In this paper we propose a method to compute a freeform reflector system forcollimating and shaping a beam from a point source. We construct thesereflectors such that the radiant intensity of the source is converted into adesired target. An important generalization in our approach compared toprevious research is that the output beam can be in an arbitrary direction. Thedesign problem is approached by using a generalized Monge-Amp\`ere equation.This equation is solved using a least-squares algorithm for non-quadratic costfunctions. This algorithm calculates the optical map, from which we can thencompute the surfaces. We test our algorithm on two cases. First we consider auniform source and target distribution. Next, we use the model of a laser diodelight source and a ring-shaped target distribution.

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