A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source
Abstract
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We give a rigorous analysis of this problem. The reflectors we construct are (parts of) the boundaries of convex sets. We prove existence of solutions for a large class of input data and give a uniqueness result. To the author's knowledge, this is the first time that a rigorous mathematical analysis of this problem is given. The approach is based on optimal transportation theory. It yields a practical algorithm for finding the reflectors. Namely, the problem is equivalent to a constrained linear optimization problem.
Cite
@article{arxiv.0908.2464,
title = {A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source},
author = {Tilmann Glimm},
journal= {arXiv preprint arXiv:0908.2464},
year = {2015}
}
Comments
5 Figures - pdf files attached to submission, but not shown in manuscript