Geometric-optic synthesis of single-reflector antennas with distributed sources

Previous systematic treatments of reflector synthesis have usually assumed that the feed is a point source producing a spherical wave, or a line source producing a cylindrical wave. To cater for a more general source, such as a feed array or a feed/subreflector system, within the existing methodology of geometric-optic synthesis, it is convenient to define a source aperture over which the field can be arbitrarily specified. The basic equations necessary to synthesize a single reflector to meet a prespecified output aperture field distribution are derived under general conditions, and the relationship with existing work is indicated. The Monge-Ampere partial differential equation occupies a central role in the discussion.