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Journal of Mathematical Sciences

, Volume 117, Issue 3, pp 4096–4108 | Cite as

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

  • T. Glimm
  • V. Oliker
Article

Abstract

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–Ampere 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 by the authors in their work “Optical Design of Two-Reflector Systems, the Monge–Kantorovich Mass Transfer Problem and Fermat's Principle” [Preprint, 2003], 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 was based on the construction of very special approximate solutions to the corresponding Monge–Ampere equation. Bibliography: 14 titles.

Keywords

Design Problem Geometric Optic Optical Design Spherical Wave Elliptic Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • T. Glimm
  • V. Oliker

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