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Equivalent edge currents, derived from the edge diffraction theory for a half-plane, are used to obtain the radiation patterns of a parabeloidal reflector antenna when illuminated by a source at the focus. Cylindrical wave diffraction coefficients are used. The method avoids infinities at caustics and shadow boundaries thus giving solutions which are finite everywhere. A slope-wave equivalent current correction term is applied when the illumination is tapered towards the edge of the reflector. Comparisons are given with the physical optics approach and experimental results.