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On reconstructing a reflecting surface from the scattering data in the geometric optics approximation. (English) Zbl 0702.35242
It is suggested to use the Authors’s summary: Consider a reflector- antenna system, consisting of a point light source O, a reflecting surface F, and an object T in space, to be illuminated in this system. Under the assumptions of the geometric optics theory it is required to reconstruct the surface F when the position of the light source and the object T are given, and the power distribution is a function prescribed in aevance on T. In addition, the aperture of the incidence ray cone is also prescribed. Using differential geometric methods we study this inverse problem and obtain relations between elements of the system. In the radially symmetric case we establish conditions for existence and uniqueness of a solution to the problem.
Reviewer: H.Ding

35R30 Inverse problems for PDEs
35J60 Nonlinear elliptic equations
78A05 Geometric optics
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