High-dimensional inference of radio interferometer beam patterns I: Parametric model of the HERA beams

TL;DR

This paper develops a Bayesian parametric model for high-dimensional inference of radio interferometer beam patterns, specifically applied to the HERA array, enabling accurate beam characterization crucial for 21cm intensity mapping.

Contribution

It introduces a compact basis for modeling complex radio telescope beams, making Bayesian inference computationally feasible for large arrays.

Findings

32 coefficients per feed suffice for percent-level accuracy in beam modeling.

Increasing to 128 coefficients reduces errors to below 1%.

The method effectively describes HERA's single-element beam with high precision.

Abstract

Accurate modelling of the primary beam is an important but difficult task in radio astronomy. For high dynamic range problems such as 21cm intensity mapping, small modelling errors in the sidelobes and spectral structure of the beams can translate into significant systematic errors. Realistic beams exhibit complex spatial and spectral structure, presenting a major challenge for beam measurement and calibration methods. In this paper series, we present a Bayesian framework to infer per-element beam patterns from the interferometric visibilities for large arrays with complex beam structure, assuming a particular (but potentially uncertain) sky model and calibration solution. In this first paper, we develop a compact basis for the beam so that the Bayesian computation is tractable with high-dimensional sampling methods. We use the Hydrogen Epoch of Reionization Array (HERA) as an example, verifying that the basis is capable of describing its single-element E-field beam (i.e. without considering array effects like mutual coupling) with a relatively small number of coefficients. We find that 32 coefficients per feed, incident polarization, and frequency, are sufficient to give percent-level and $\sim$10\% errors in the mainlobe and sidelobes respectively for the current HERA Vivaldi feeds, improving to $\sim 0.1\%$ and $\sim 1\%$ for 128 coefficients.