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A theoretical analysis of the radiating properties of the paraboloid reflector and the hyperboloid lens shows that low amplitude cross-polarized radiation and high gain factors can be obtained from a paraboloid reflector excited by a plane-wave source. Low amplitude, cross-polarized radiation can also be obtained from the hyperboloid lens with a plane-wave feed, but with a lower gain factor. It is found that the measured properties of the antennas agree reasonably well with the theoretical predictions. Also it is found experimentally that principal plane side lobes of the order of -40 db can be obtained with a short focal length hyperboloid lens.