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Large reflector antennas, from cost and weight considerations, appear to be the best configurations for achieving the very large apertures needed for antennas mounted on orbiting spacecraft. Radiation pattern calculations for such antennas are, in general, quite costly both in terms of computer time and the considerable memory required to perform the large surface integrations. The method presented here treats the large aperture as a set of small subapertures for which the radiation fields are computed separately, stored and then added with due regard to phase to yield the radiation pattern of the large reflector. Numerical methods developed to provide the illumination of each subaperture to avoid overlap of the aperture fields of adjacent subapertures and to simplify the surface integrations are discussed. The algorithm is straightforward and has considerable intuitive appeal. The methods of geometrical optics (GO) are used to calculate the aperture plane tangential field components; and electric vector potential is then used to compute the antenna radiation fields. The algorithm includes a set of options for different reflector surfaces. If high accuracy of the far sidelobe levels is required, a subroutine accounting for edge diffraction should be added to the algorithm given here. Calculations made with this algorithm are compared with calculations made by other methods and with measured patterns.