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

Abstract

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.

Improving the Calibration Efficiency of an Array Fed Reflector Antenna Through Constrained Beamforming

“…The reference pattern employed in [11] to constrain the main beam shape of a scanned reflector is based on the JB-series solution for modeling reflector antenna far field patterns. The first term in this series is the near-boresight approximation of the co-polarized far field pattern radiated by a circular aperture with a uniform amplitude and phase distribution [16], i.e.,…”

“…Previously, beamforming techniques have been used to create similarly shaped beams over the FoV by conforming them to an elliptical reference pattern, but at the cost of a significant loss in sensitivity [6] (up to 25%). An initial study has shown that this loss can be reduced by applying the same beamforming technique, but using a reference pattern that more closely matches the natural radiation characteristics of large aperture antennas [11]. Therein, the first term of the Jacobi-Bessel (JB) series solution of reflector antenna far field patterns [12], [13] was used as a reference pattern to define directional constraints in a Linearly Constrained Minimum Variance (LCMV) beamforming Phased Array Feed (PAF).…”

“…Here, the reference pattern of [11] is extended to model the widening of the scanned beam as well as the change in the phase distribution for an offset dual-reflector antenna by introducing two additional model parameters. It will be shown that this model allows for the accurate characterization of multiple beams over a wide FoV without the need to perform additional calibration measurements.…”