First-order correction of aberrations in Cassegrainian and Gregorian antennas

Cassegrainian and Gregorian reflector arrangements are needed for multibeam ground station and satellite antennas. In these antennas one or more feeds are displaced from the focus. This displacement normally causes aberrations, due primarily to astigmatism and coma. In a previous article, astigmatism was eliminated for small feed displacements by centering the antenna aperture with respect to the equivalent paraboloid axis. In this article coma is also removed by deforming the reflectors without causing spherical aberration, and simple expressions for the deformation coefficients are derived. The analysis applies in general to an arrangement of
N
reflectors. The deformations required to correct astigmatism, if the antenna aperture is not centered is also derived.