Synthesis of the primary fields of a transmitting feed for a circular reflector

A two-dimensional electromagnetic boundary-value problem consisting in the synthesis of the primary fields of a transmitting feed antenna for a circular-cylindrical reflector is considered. A primary field that corrects for the phase aberration of the reflector is synthesized as a sum of circular waves whose common origin is displaced from the center of curvature of the reflector. Limitations on the gain of the feed-reflector combination as a function of the number of waves and the displacement are discussed. The synthesized fields are compared with those obtained from geometrical optics.