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Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle. (English) Zbl 1129.49309

Summary: It is shown that the problem of designing a two-reflector system transforming a plane wave front with given intensity into an output plane front with prescribed output intensity can be formulated and solved as the Monge-Kantorovich mass transfer problem.

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
35A15 Variational methods applied to PDEs
35Q15 Riemann-Hilbert problems in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A05 Geometric optics
90C48 Programming in abstract spaces
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