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On the design of a reflector antenna. (English) Zbl 0858.35142

Summary: We consider the problem of recovering a reflecting surface such that for a given point source of light the directions of the reflected rays cover a prescribed region of a far field sphere and the density of the distribution of the reflected rays is a function prescribed in advance, where the aperture of the incident ray cone is also prescribed in advance. Mathematically this problem requires one to solve a nonlinear partial differential equation of Monge-Ampère type subject to a nonliner boundary condition. Numerical computations for the problem have been carried out by several authors. In this paper we study the existence, uniqueness, and smoothness of the reflecting surfaces for the above problem.

MSC:

35R30 Inverse problems for PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A50 Antennas, waveguides in optics and electromagnetic theory
93B51 Design techniques (robust design, computer-aided design, etc.)
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