The Bias and Uncertainty of Redundant and Sky-Based Calibration under Realistic Sky and Telescope Conditions

TL;DR

This paper investigates how antenna position offsets and sky flux distribution affect the bias and uncertainty in redundant calibration of low-frequency interferometers, highlighting the importance of precise antenna positioning for accurate EoR observations.

Contribution

It provides a simulation-based analysis of calibration biases under realistic sky and instrument conditions, comparing redundant and sky-based calibration methods.

Findings

Position offsets cause phase bias in calibration solutions.

Bias increases with proximity to bright sources and their flux.

Redundant calibration outperforms sky-based calibration for MWA.

Abstract

The advent of a new generation of low frequency interferometers has opened a direct window into the Epoch of Reionisation (EoR). However, key to a detection of the faint 21-cm signal, and reaching the sensitivity limits of these arrays, is a detailed understanding of the instruments and their calibration. In this work we use simulations to investigate the bias and uncertainty of redundancy based calibration. Specifically, we study the influence of the flux distribution of the radio sky and the impact of antenna position offsets on the complex calibration solutions. We find that the position offsets introduce a bias into the phase component of the calibration solutions. This phase bias increases with the distance between bright radio sources and the pointing center, and with the flux density of these sources. This is potentially problematic for redundant calibration on MWA observations of EoR fields 1 and 2. EoR field 0, however, lacks such sources. We also compared the simulations with theoretical estimates for the bias and uncertainty in sky model based calibration on incomplete sky models for the redundant antenna tiles in the MWA. Our results indicate that redundant calibration outperforms sky based calibration due to the high positional precision of the MWA antenna tiles.