Extrapolation Technique for Shaping Tri-Reflectors

Abstract

A linear extrapolation technique is described here for shaping reflectors to achieve a prescribed aperture distribution. The technique is so simple that a typical design with some 2 x 40, 000 reflector surface points takes less than one minute on a Cray XMP. There is no restriction on the number of reflectors (with two reflectors shaped) or their geometry (symmetrical or offset). The technique is applied to design a Watanabe-type tri-reflector antenna, in which the main reflector is spherical and two subreflectors are shaped to correct the spherical aberration. With an oversized main reflector, the beam of the antenna can be steered over a very wide angular range by rotating subreflectors, while keeping the main reflector and feed stationary. A design example for high directivity is given.