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Interest in reflector antennas due to attractive features including high gain, multiple beam, low side lobe level, and robustness have been growth both in military and commercial areas in microwave frequency range since World War I. In particular, low side lobe level radiation pattern, is an essential requirement for satellite communication systems. Offset reflector antennas featuring adjacent high gain beams with good isolation across the same frequency bandwidth make them good candidates for these applications. Depending on the required radiation pattern, feeds may or may not be located at the focus. A cluster of feeds can be used in the focal region of offset reflectors for multiple beams application [Skolnik, 1990; Chu and Turrin, 1973; Rudge, 1975; Janken et al., 1973; Ingerson and Wong, 1974; Tian et al., 2007]. There have been published lots of articles dealing with analyze and design of electrically small and large reflectors by analytical or numerical techniques [Love, 1978; Wood, 1986; Lo and Lee, 1988; Scott, 1990]. These methods vary from the traditional Aperture Field Method (AFM) that involves integrating the electric fields scattered by the reflector onto a projected planar aperture, to more modern hybrid methods that employ a variety of techniques each of which is applicable over different regions of the radiation pattern. Some of the aforementioned methods yield exact solutions such as, Method of Moments (MoM) but require significantly computational resources. Larger reflectors like large radio astronomy antennas need to be analysed using high-frequency techniques which use approximations based on asymptotic solutions for canonical problems. The approximate techniques have been proved to be quite successful in predicting both far and near-field patterns and are in very good agreement with the measurements. Methods of evaluating the electromagnetic fields radiated from a reflector antenna fall into two categories: exact and approximation methods. These various techniques have been explained as follows [Philips et al., 1996]. The Method of Moments is the most accurate technique in all known methods used in electromagnetic scattering analysis. The formulation of the governing equations of the problem (such as Electric Field Integral Equation (EFIE)) is exact, and highly accurate solutions can be obtained by a suitable choice of basis and testing functions. The induced 10

A Fast Method to Compute Radiation Fields of Shaped Reflector Antennas by FFT