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

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.


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