An efficient technique for the computation of vector secondary patterns of offset paraboloid reflectors

A series approach for the rapid computation of the vector secondary pattern of offset paraboloid reflectors wherein the feed is displaced is presented. We show that the Jacobi polynomial series method, which has been demonstrated to provide an efficient means for evaluating the radiation integral of symmetric paraboloid reflectors, can be extended to the case of an offset paraboloid without compromising the ease or speed of computation. The analysis leading to the series formula is also useful for deriving an analytic expression for the optimum scan plane for the displacement of the feed. Representative numerical results illustrating the application of the method and the properties of the offset paraboloid are presented.