Reflector synthesis for generalized far-fields

The theoretical foundations of a proposed new method of reflector design are presented. The geometric-optics approximation is used to synthesise a reflector surface to produce a generalized far-field when illuminated by a point source. The far-field can have a prescribed variation in two variables and source blockage can be removed. The technique of differential geometry are used to show that a nonlinear second-order partial differential equation, the Monge-Ampere equation, must be solved subject to nonlinear boundary conditions. Particular consideration is given to the special case of fields with even azimuthal symmetry when referred to spherical polar coordinates. The method is applicable to problems in optics acoustics and microwave antenna design where shaped beams are required.