This paper presents a new ray method to synthesize shaped offset multireflector antennas which involves solving linear equations. In the other existing techniques, differential equations have to be solved. The advantage of the technique is that the solution is easier to control, so that, for example, low cross-polarization can be obtained and an exact solution can be found. The method is applied to synthesize a dual-reflector feed for the spherical reflector of the radio telescope in Arecibo.
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