Remarks on the concept of equivalent parabolas for Cassegrain antennas

In Cassegrain antennas, the whole focusing system is usually replaced by an equivalent paraboloid of focal length mf, where f is the focal length of the paraboloid and m is the magnification of the Cassegrain system. Here, it is shown that this equivalent paraboloid is useful only for feeds near the Cassegrainian focus. The discussion of series expansions of the phase in the system aperture yields severe differences between the Cassegrain system and the prime focus-fed equivalent paraboloid for larger radial or axial defocusing.