Characterizing beam errors for radio interferometric observations of reionization

A limiting systematic effect in 21-cm interferometric experiments is the chromaticity due to the coupling between the sky and the instrument. This coupling is sourced by the instrument primary beam; therefore it is important to know the beam to extremely high precision. Here, we demonstrate how known beam uncertainties can be characterized using data bases of beam models. In this introductory work, we focus on beam errors arising from physically offset and/or broken antennas within a station. We use the public code OSKAR to generate an 'ideal' SKA beam formed from 256 antennas regularly spaced in a 35-m circle, as well as a large data base of 'perturbed' beams sampling distributions of broken/offset antennas. We decompose the beam errors ('ideal' minus 'perturbed') using principal component analysis (PCA) and Kernel PCA (KPCA). Using 20 components, we find that PCA/KPCA can reduce the residual of the beam in our data sets by 60-90 per cent compared with the assumption of an ideal beam. Using a simulated observation of the cosmic signal plus foregrounds, we find that assuming the ideal beam can result in 1 per cent error in the epoch of reionization (EoR) window and 10 per cent in the wedge of the 2D power spectrum. When PCA/KPCA is used to characterize the beam uncertainties, the error in the power spectrum shrinks to below 0.01 per cent in the EoR window and <= 1 per cent in the wedge. Our framework can be used to characterize and then marginalize over uncertainties in the beam for robust next-generation 21-cm parameter estimation.