Phase and power density distributions on plane apertures of reflector antennas

Abstract

Complex coordinates are used under the assumptions of geometrical optics to study the relations between phase and power density distributions on plane apertures of reflector antenna systems. No symmetry assumptions are made and the results form a generalisation of existing work in the field. The synthesis of a dual reflector system to produce given aperture phase and power distributions when illuminated by a point source of prescribed power density is shown to depend on the solution of a particular partial differential equation of the Monge-Ampere type. Finally it is shown that even in cases of symmetry the use of complex coordinates simplifies the design equations.