Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem. (English. Russian original) Zbl 1049.49030

Glimm, Tilmann; Oliker, Vladimir

J. Math. Sci., New York 117, No. 3, 4096-4108 (2003); translation from Probl. Mat. Anal. 26, 47-66 (2003).

The authors consider the problem of designing a reflector that transforms a spherical wave front with a given intensity into an output front illuminating a prespecified region of the far-sphere with prescribed intensity. They show that this problem can be solved as a variational problem within the framework of Monge-Kantorovich mass transfer problem and that the design problem can be solved numerically by tools of linear programming.

Reviewer: V. Grebenev (Novosibirsk)

MSC:

49Q20	Variational problems in a geometric measure-theoretic setting
49K20	Optimality conditions for problems involving partial differential equations
35J65	Nonlinear boundary value problems for linear elliptic equations
78A05	Geometric optics
90C05	Linear programming

Keywords:

Fermat’s principle; cost function; geometrical optics; geometry of convex reflectors