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A microwave antenna can be designed in the form of two reflecting dishes and a feed, based on the principle of the Cassegrain optical telescope. There are a variety of shapes and sizes available, all described by the same set of equations. The essential performance of a Cassegrain double-reflector system may be easily analyzed by means of the equivalent-parabola single-reflector concept. Techniques are available for reducing the aperture blocking by the sub dish of the Cassegraln system: one method minimizes the blocking by optimizing the geometry of the feed and sub dish; other methods avoid the blocking by means of polarization-twisting schemes. The former method yields good performance in a simple Cassegrain antenna when the beamwidth is about or less. The latter methods are available for any application not requiring polarization diversity, and an optimized set of polarization-operative surfaces has been developed for these twisting Cassegrain antennas. Experimental results, presented for practical antennas of both types, illustrate the feasibility of these principles. A number of unusual benefits have been obtained in the various Cassegrain antenna designs, and additional interesting features remain to be exploited.