Gaussian mode analysis of Cassegrain antenna efficiency

Gaussian mode analysis is a convenient way to characterize long focal length systems, such as the Cassegrain antenna at the secondary focus. We use multimode Gaussian optics to derive several interesting results concerning the aperture efficiencies of Cassegrain antennas fed by corrugated conical horns. The highest efficiency is obtained when the antenna is illuminated by a wide-band, wide-angle horn which has its phase center at the secondary focus, or equivalently by a narrow-band diffraction limited horn with its phase-center located at a confocal tertiary focus. In both cases this corresponds to placing the horn aperture at a position where the incoming fields are frequency-independent and have limited spatial extent. We generalize these results to show that a true image of the aperture distribution can always be formed on the spherical cap in the aperture of any arbitrary scalar horn, by using a single refocusing tertiary lens or mirror. Since both the incoming fields and the horn aperture fields on this surface are frequency independent, it follows that the aperture efficiency is also independent of frequency with either of these arrangements. We suggest that devices for shaping the aperture illumination, such as shaped lenses or dual shaped subreflector systems, should, in general, be installed near an image of the telescope aperture distribution.