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Calculations are carried out with regard to the aperture illumination efficiency, spillover efficiency, and blockage efficiency of a shaped Cassegrainian antenna system whose feed pattern is not similar to that for which the antenna was designed. It appears that a maximum overall efficiency may be expected for antenna systems with a feed pattern having a slightly narrower beamwidth than those for which the systems were originally designed. It is further proved that the radiation pattern of mismatched systems is very unfavorable in the case of the beamwidth of the feed pattern being wider than the beamwidth of the feed pattern for which the system was designed. This is due to overillumination of the edges.