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We consider the following geometric optics problem: Construct a system of tworeflectors which transforms a spherical wavefront generated by a point sourceinto a beam of parallel rays. This beam has a prescribed intensitydistribution. We give a rigorous analysis of this problem. The reflectors weconstruct are (parts of) the boundaries of convex sets. We prove existence ofsolutions for a large class of input data and give a uniqueness result. To theauthor's knowledge, this is the first time that a rigorous mathematicalanalysis of this problem is given. The approach is based on optimaltransportation theory. It yields a practical algorithm for finding thereflectors. Namely, the problem is equivalent to a constrained linearoptimization problem.

A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source