An approximation of the radiation integral for distorted reflector antennas using surface-error decomposition

The physical optics/aperture integration (PO/AI) formulation is often used to analyze the radiation patterns of reflector antennas. In this study, the PO/AI radiation integrals for distorted reflector antennas are addressed. The surface error of the antennas is approximated by a series of surface expansion functions. The radiation integral is decomposed into a series of radiation-type integrals, each of which corresponds to one of the surface expansion functions. Each of these radiation-type integrals is then weighted by amplitude coefficients. The advantage of performing the decomposition is that each of the radiation-type integrals can be computed and the pattern data stored. The computation of the pattern for a distorted reflector antenna with a changing error profile is performed by recalling the pattern data for each perturbation term and weighting it with the amplitude coefficient. This facilitates rapid evaluation of the radiation integral in cases where the error profile is changing (for example, time-varying errors). The superposition of integrals presented in this paper was shown to be valid for surface-error profiles up to 0.1 λ rms amplitude