A new method of designing circularly symmetric shaped dual reflector antennas using distorted conics is presented. The surface of the shaped subreflector is expressed using a new set of equations employing differential geometry. The proposed equations require only a small number of parameters to accurately describe practical shaped subreflector surfaces. A geometrical optics (GO) based method is used to synthesize the shaped main reflector surface corresponding to the shaped subreflector. Using the proposed method, a shaped Cassegrain dual reflector system is designed. The field scattered from the subreflector is calculated using uniform geometrical theory of diffraction (UTD). Finally, a numerical example is provided showing how a shaped subreflector produces more uniform illumination over the main reflector aperture compared to an unshaped subreflector.
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