Fresnel and fraunhofer patterns of overmoded feeds and reflector antennas

This paper describes the performance of feeds and reflector antennas at frequencies outside the design bandwidth where the feed can become overmoded, producing primary patterns that are functions of the mode content. The secondary patterns are then characteristic of the reflector's modal illumination. For an overmoded rectangular waveguide or horn feed, the secondary (Fraunhofer) pattern shows a cluster of sharp beams near the axis and substantially within the main beam at the fundamental frequency. A backscatter technique was applied to an array of shaped reflectors to simulate an arbitrary combination of modes. This avoided the construction of complicated multimode launchers. A TEmnmode in rectangular waveguide radiates an angular spectrum of plane waves. Simple methods of pattern computation use\sin x/xtables for the Fraunhofer field and tables of half-integer order Lommel functions for the Fresnel region (included in this paper). Moding feeds investigated included waveguides, waveguide arrays, pyramid horns, and box horns. A 6-foot paraboloid antenna was used as a secondary reflector.