Rigorous techniques for synthesis of offset reflector antennas

Summary form only given. The author describes a geometric method that allows to prove, in a completely rigorous fashion, that under some natural restrictions the problem of synthesis of a reflector transforming a given energy pattern from a point source into a prespecified output energy pattern on a prespecified far-field aperture always has a solution. The uniqueness question has also been investigated. The existence proof is constructive and admits a numerical implementation. The numerical procedure produces an approximate solution built of a finite number of pieces of confocal paraboloids of revolution. The numerical solutions converge to the true solution when a certain parameter associated with the problem tends to zero. A modification of the method allows to solve the corresponding near-field problem.