Determination of reflector surfaces from near-field scattering data II. Numerical solution

Let be a nonisotropic point source of light, and the power intensity of this source in direction . Suppose that the light rays emitted by the source through an aperture fall on a perfectly reflecting surface and reflect off it so that the reflected rays illuminate a closed domain on some plane with intensity . The inverse problem consists of constructing the reflector surface from given position of the source , the input aperture , function , “target” set , and output intensity . For example, the input intensity may have a “bell”-like shape and we may wish to redistribute the energy uniformly over a prespecified region. The analytical formulation of the described above problem leads to a non-linear partial differential equation of Monge-Ampère type. In our previous paper we proved existence of weak solutions to this inverse problem and in this paper we describe and illustrate with examples an algorithm for its numerical solution. The proposed numerical method can be easily modified for the case when is a closed domain on an arbitrary surface. Received November 26, 1996