Synthesis of multireflector antennas by kinematic and dynamic ray tracing

A technique for synthesizing reflector surfaces that transform a known input ray-field (e.g., the radiation field of a feed) to a desired output ray-field (e.g. an aperture distribution) is presented. The synthesis problem is reduced to solving linear equations by local biparabolic expansions of the reflector surfaces. Because the solution is easier to control, this is advantageous compared to existing techniques based on solving nonlinear differential equations. The condition to obtain low cross polarization can therefore be readily included, and the requirements for an exact solution to exist can be found clearly. The latter has been the subject of discussion in the literature for several years. The synthesis technique is applied to a shaped-offset dual-reflector antenna and to the proposed dual-reflector feed of the spherical reflector antenna in Arecibo. In both cases circular and elliptical apertures are considered