Performance evaluation of far field patterns for radio astronomy applications through the use of the Jacobi-Bessel series

The Jacobi-Bessel (JB) series representation for modeling reflector antenna patterns is proposed to be used as a reference tool to assess and improve the pattern shape of multi-beam wide-scan radio telescopes. After expanding each beam in JB functions, the number of dominant JB functions per beam not only serves as an indication of the beam calibratability (beam smoothness), but is a measure for the uniformity of the scanned patterns as well (inter-beam comparison). It is demonstrated that the first term in the JB series can be used to define directional constraints in a linear constrained minimum variance beamformer, so that each realized scanned beam pattern conforms to this first term. As a result, multiple beams cover a wide field of view in an almost undistorted manner.