Scattering from a hyperboloidal reflector in a cassegrainian feed system

The scattered field from a hyperboloidal reflector is calculated by integrating the induced current density over the front of the hyperboloid. The resulting integral expressions for the fields possess a stationary term which, when evaluated, yields the geometrical ray-optics approximation to the scattering problem. The complete field, including diffraction effects, may be obtained by numerical evaluation of the integrals. The formulas are applied to a hyperboloid illuminated by an idealized, sharply cut off uniform feed pattern. Characteristic diffraction phenomena are reduced with increasing
D/\lambda
until the geometrical ray-optics result is obtained in the limit of vanishing wavelength. Theoretical field patterns are also obtained for a horn-fed hyperboloidal subreflector in a Cassegrainian feed system; they indicate that for moderately large hyperboloidal reflectors spillover may be reduced to an acceptable level, but there is a tendency toward increased forward spillover. The results of 9600-Mc model tests compare favorably with the theoretical patterns.