Determination of reflector antennas from the intensity distribution data in the geometric optics approximation

Two inverse problems are discussed. The first one, the reflector mapping problem, consists in recovering a reflector surface such that for a given 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 other problem concerns a reflector antenna system consisting of a point light source O, a reflecting surface F, and a target surface T in space to be illuminated in this system. Under the assumptions of the geometric optics theory it is desired to construct the surface F, given the positions of the light source and surface T and the light intensity distribution as a function on T. In addition, the aperture of the incidence ray cone is also prescribed. Situations in which questions of existence and uniqueness of reflector surfaces with required properties can be satisfactorily resolved are examined.<>