Optical Design of Single Reflector Systems and the Monge–kantorovich Mass Transfer Problem

نویسندگان

  • T. Glimm
  • V. Oliker
چکیده

We 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. In earlier approaches, it was shown that in the geometric optics approximation this problem is reduced to solving a second order nonlinear elliptic partial differential equation of Monge–Ampère type. We show that this problem can be solved as a variational problem within the framework of Monge–Kantorovich mass transfer problem. We develop the techniques used in [1], where the design problem for a system with two reflectors was considered. An important consequence of this approach is that the design problem can be solved numerically by tools of linear programming. A known convergent numerical scheme for this problem [2] was based on the construction of very special approximate solutions to the corresponding Monge–Ampère equation. Bibliography: 14 titles.

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تاریخ انتشار 2003