A three dimensional projection algorithm for evaluating the radiation integral on a curved surface with application to reflector antennas

A method of evaluating the radiation integral on the curved surface of a reflecting antenna is presented. A three-dimensional Fourier transform approach is used to generate a two-dimensional radiation cross-section along a planar cut at any angle\phithrough the far-field pattern. Salient to the method is a new algorithm for evaluating a subset of the total three-dimensional discrete fourier transform results. The subset elements are selectively evaluated to yield data along a geometric plane of constant\phi. The algorithm is extremely efficient so that computation of the induced surface currents via the physical optics approximation dominates the computer run-time required to compute a radiation pattern. Application to paraboloid reflectors with off-focus feeds is presented, but the method is easily extended to offset antenna systems and reflectors of arbitrary shapes. Numerical results have been computed for both gain and phase and are compared with other published work.