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The paper describes an efficient method for evaluating the physical-optics radiation pattern of a dual-shaped-reflector antenna. The method consists in representing the integrands of the four- and two-dimensional (4-, 2-D) field integrals as Gaussian series and then analytically integrating each term, including the effects of diffraction by the edges of both reflectors. The method is applied to a multibeam antenna and compared to numerical integration. Similar radiation patterns are obtained but with the new method significantly reducing the computation time.