Discussion
What is the aperture field of an ideal feed for a symmetric reflector?
Answer: A
A feed whose pattern is the same in every plane illuminates a circular reflector evenly around its rim, which is what a corrugated horn achieves and a simple rectangular horn does not. Uniform illumination to the edge would maximise taper efficiency but spill badly, asymmetric patterns waste part of the aperture, and a phase gradient would steer the beam off boresight. Matching the symmetry of the feed to the symmetry of the reflector is the first requirement in any feed specification.
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