Go Synthesis of Reflectors using Complex Coordinates

Recent theoretical work on direct GO synthesis of reflectors for two variable far-field and point source feed pattern specification is described. The mathematics is simplified by the use of complex coordinates and stereographic projection. Reflector properties are formulated in terms of the mapping between incident and reflected ray directions. Analytic transformations occur naturally in the new formalism and their application to reflector design appears to have interesting possibilities. Numerical methods of solution are briefly described. Finally progress in extending the work to demand aperture distributions of dual reflector systems is discussed.