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The inverse scattering problem considered here is that of finding the shape of a reflector which produces a prescribed scattered wave. The scattered wave is characterized by its angular pattern, which determines the differential scattering cross section of the reflector. The problem is solved by means of explicit formulas for cylindrical and for rotationally symmetric objects. Plane, cylindrical, and spherical incident waves are considered. The general three dimensional object is also treated. The method of geometrical optics is used throughout.