Comparison of Abbe Sine shaped offset dual reflectors

Spaceborne multiple beam antennas (MBAs) generally consist of a reflector fed by multiple feeds, with each feed (or cluster) corresponding to a single beam directed at a separate geographic region. In general, spaceborne reflector antennas must provide high aperture efficiency and focusing reflectors are preferred (e.g. paraboloids, conics with eccentricity close to 1.0, or high efficiency surface shapes). Focusing reflector systems provide high aperture efficiency when a feed is located on or near the antenna boresight but gain degrades significantly for feeds that are displaced in the focal plane and can limit the field of regard of the MBA to a few beamwidths about the reflector boresight. Reflector "scan losses" can be reduced by increasing the equivalent focal length of a dual reflector system. Enforcement of the Abbe Sine condition can provide significant scan improvement for short equivalent focal lengths, and in some cases short focal length Abbe Sine designs have superior scan performance than longer focal length Cassegrains (particularly if subreflector size is small).