# Primary beam effects of radio astronomy antennas: I. Modelling the Karl G. Jansky Very Large Array (VLA) L-band beam using holography

## TL;DR

This paper develops and compares data-driven and parametric models for the VLA L-band antenna beam using holography, enhancing calibration accuracy for high dynamic range imaging in radio astronomy.

## Contribution

It introduces PCA and Zernike polynomial-based beam models from holography data, improving beam representation and calibration efficiency for large radio arrays.

## Key findings

- PCA provides the most accurate beam model.
- Models capture frequency ripple due to standing waves.
- Low-rank approximations enable efficient on-the-fly calibration.

## Abstract

Modern interferometric imaging relies on advanced calibration that incorporates direction-dependent effects. Their increasing number of antennas (e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the accuracy of their calibration. Beam accuracy drives particularly the capability for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio Interferometric Measurement Equation (RIME) proposes a refined calibration framework for wide field of views (i.e. beyond the primary lobe and first null) using beam models. We have used holography data taken on 12 antennas of the Very Large Array (VLA) with two different approaches: a `data-driven' representation derived from Principal Component Analysis (PCA) and a projection on the Zernike polynomials. We determined sparse representations of the beam to encode its spatial and spectral variations. For each approach, we compressed the spatial and spectral distribution of coefficients using low-rank approximations. The spectral behaviour was encoded with a Discrete Cosine Transform (DCT). We compared our modelling to that of the Cassbeam software which provides a parametric model of the antenna and its radiated field. We present comparisons of the beam reconstruction fidelity vs. `compressibility'. We found that the PCA method provides the most accurate model. In the case of VLA antennas, we discuss the frequency ripple over L-band which is associated with a standing wave between antenna reflectors. The results are a series of coefficients that can easily be used `on-the-fly' in calibration pipelines to generate accurate beams at low computing costs.