Deriving an Optimum Mapping Function for the SKA-Shaped Offset Gregorian Reflectors

Of primary importance for a radio telescope is its receiving sensitivity. The offset Gregorian reflector antennas, as used for the Square Kilometer Array (SKA) radio telescope, can be shaped to make efficient use of the reflector's aperture and thus to maximize sensitivity for a given sidelobe level. The shape of the reflector is controlled by a mapping function. This paper presents a method to derive the optimum mapping function given a selected set of single pixel feeds. In this case, the feeds were optimized for a geometrically similar classical conic section (unshaped) reflector system. Realistic performance results are given for reflector systems with various subreflector sizes, extensions, and subtended angles.