The Bias and Uncertainty of Redundant and Sky-based Calibration Under Realistic Sky and Telescope Conditions

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.

Redundant-baseline calibration of the hydrogen epoch of reionization array

“…Perhaps unsurprisingly, the strongest apparent variations occur during the transit of Fornax A, further evidence for our hypothesis that bright point sources, combined with antenna-to-antenna beam variation cause redundant gains to be erroneously dragged around. The phases are contiguous, so this does not appear to be an LSTdependence due to phase wrapping as was simulated in Joseph et al (2018). The particulars of the peaks and troughs vary from antenna to antenna and frequency to frequency, but the general features seen in the Figure 16 are representative.…”

“…In practice, redundant-baseline calibration must be performed as a series of iterative steps, each bringing us closer to a solution that minimizes 2 . Without a good starting point, phase wrapping issues plague logcal while lincal and omnical converge slowly, if at all (Zheng et al 2014;Joseph et al 2018). Getting "good enough" gain phases is key to achieving convergence and avoiding the introduction of spectral structure in the degeneracies (Dillon et al 2018).…”

Science with the Murchison Widefield Array: Phase I results and Phase II opportunities

“…A number of other theoretical studies are under way to determine optimal strategies for calibrating data from the compact array for EoR science, augmenting existing literature of results from other arrays (Thyagarajan et al 2018;Orosz et al 2018). Joseph et al (2018) demonstrate how the flux density distribution of the sky can affect redundant calibration techniques, despite the lack of explicit reference to a sky model. Byrne et al (2019) study the subset of parameters that cannot be constrained by redundant calibration and show how sky model incompleteness errors still affect these terms, which, in turn, introduce contamination into the EoR window.…”

Gridded and direct Epoch of Reionisation bispectrum estimates using the Murchison Widefield Array

“…Figure 1 shows the tile layout, including the two 36-tile hexagonal subarrays of redundantly spaced tiles. The minimum redundant spacing is 14 m. The primary motivations for the hexagons are twofold: (1) to increase the sensitivity to angular scales of relevance for the EoR, allowing coherent addition of measurements from redundant baselines, and (2) enabling additional methods for calibrating the array (redundant calibration, Li et al 2018, Joseph et al 2018. For the bispectrum, there is an additional advantage of multiple, redundant equilateral triangle baselines being formed from the short spacings.…”