Abstract
The author studies an inverse problem consisting in recovering a reflecting surface such that for a given point source of light the directions of reflected rays cover a prescribed region of the far sphere and the density of the distribution of reflected rays is a function of the reflected directions prescribed in advance. The power density of the source as well as the aperture of the incident cone are also given and the laws of geometric optics are applied. In this form the problem has been posed by Westcott and Norris (1975). For circular far field and aperture and distribution densities close to radially symmetric ones (in some Holder norm) he shows that the above problem can be solved, provided a natural energy conservation condition is satisfied.
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