On the equivalent parabola technique to predict the performance characteristics of a Cassegrainian system with an offset feed

The so-called equivalent parabola technique has been used extensively in the design of Cassegrainian systems. Hannan substantiated the validity of the technique by showing the excellent agreement between his measured data on a Cassegrainian system and the calculated results obtained using the equivalent parabola technique. However, his demonstration was restricted to an on-axis feed Cassegrainian. This paper derives an analytical expression involving only a 2-dimensional vector integral for the secondary vector field from the Cassegrain system with an offset feed by integrating over the surface currents on both the main dish and subdish with the integrations performed in closed form, and proceeds to compare its results with those obtained from the equivalent parabola technique, for different of the main dish, eccentricities of the subdish, illumination patterns, and lateral displacements of the primary radiator. The agreement in general is good for Cassegrainians with an on-axis feed. For Cassegrainians with an offset feed, the error in using the equivalent parabola technique remains negligible for a beam scan of as much as four beamwidths.