Investigating Frequency Dependency in Characteristic Basis Function Pattern Modelling with Geometric Perturbations

This paper presents a comparison between three Characteristic Basis Function Pattern (CBFP) methods when reconstructing beams of multi-frequency antennas with geometric perturbations. The methods differ mainly in their handling of the frequency parameter. They are assessed by calculating the error of a reconstructed beam as a function of the number of basis functions used. Two examples of existing radio telescope antenna elements, substantially different in shape and function, are analyzed to evaluate each method: a REACH (Radio Experiment for the Analysis of Cosmic Hydrogen) dipole and a MeerKAT offset Gregorian dual-reflector antenna excited by a generic feed horn. It is shown that treating frequency as a normal parameter requires fewer geometric samples to reconstruct a beam to a certain degree of accuracy, compared to performing the CBFP expansion across geometry variation, either per frequency slice or by including all frequencies. The results indicate that some geometric perturbation information is captured in the frequency data.