The connection between the phase problem in optics, focusing of radiation, and the Monge-Kantorovich problem

We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge - Kantorovich optimal mass transport problem, and the variational methods for solving the equation of a modified Monge - Ampere equation. It is shown that the solution of the phase problem in optics within the framework of the asymptotic approach is closely related to the solution of the problem of optimal mass transport with a nonquadratic cost function.