Array Element Coupling in Radio Interferometry I: A Semi-Analytic Approach

Abstract

We derive a general formalism for interferometric visibilities, which considers first-order antenna-antenna coupling and assumes steady-state, incident radiation. We simulate such coupling features for non-polarized skies on a compact, redundantly-spaced array and present a phenomenological analysis of the coupling features. Contrary to previous studies, we find mutual coupling features manifest themselves at nonzero fringe rates. We compare power spectrum results for both coupled and non-coupled (noiseless, simulated) data and find coupling effects to be highly dependent on LST, baseline length, and baseline orientation. For all LSTs, lengths, and orientations, coupling features appear at delays which are outside the foreground 'wedge', which has been studied extensively and contains non-coupled astrophysical foreground features. Further, we find that first-order coupling effects threaten our ability to average data from baselines with identical length and orientation. Two filtering strategies are proposed which may mitigate such coupling systematics. The semi-analytic coupling model herein presented may be used to study mutual coupling systematics as a function of LST, baseline length, and baseline orientation. Such a model is not only helpful to the field of 21cm cosmology, but any study involving interferometric measurements, where coupling effects at the level of at least 1 part in 10^4 could corrupt the scientific result. Our model may be used to mitigate coupling systematics in existing radio interferometers and to design future arrays where the configuration of array elements inherently mitigates coupling effects at desired LSTs and angular resolutions.

References in corpus (10)

• Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe
• Improved upper limits on the 21-cm signal power spectrum of neutral hydrogen at $\mathbf{z}\approx 9.1$ from LOFAR
• Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism
• First Season MWA EoR Power Spectrum Results at Redshift 7
• Testing for calibration systematics in the EDGES low-band data using Bayesian model selection
• MITEoR: A Scalable Interferometer for Precision 21 cm Cosmology
• Mitigating Internal Instrument Coupling II: A Method Demonstration with the Hydrogen Epoch of Reionization Array
• Mitigating Internal Instrument Coupling for 21 cm Cosmology I: Temporal and Spectral Modeling in Simulations
• Cosmological constraints from 21cm surveys after reionization
• Revisiting Hybrid Interferometry with Low-Frequency Radio Astronomy Arrays

Cited by in corpus (12)

• Improved Constraints on the 21 cm EoR Power Spectrum and the X-Ray Heating of the IGM with HERA Phase I Observations
• Hydrogen Epoch of Reionization Array (HERA) Phase II Deployment and Commissioning
• The Impact of Beam Variations on Power Spectrum Estimation for 21-cm Cosmology I: Simulations of Foreground Contamination for HERA
• On the use of temporal filtering for mitigating galactic synchrotron calibration bias in 21 cm reionization observations
• A Differentiable, End-to-End Forward Model for 21 cm Cosmology: Estimating the Foreground, Instrument, and Signal Joint Posterior
• Understanding spectral artefacts in SKA-LOW 21-cm cosmology experiments: the impact of cable reflections
• Field-level Reconstruction from Foreground-Contaminated 21-cm Maps
• Strategy for mitigation of systematics for EoR experiments with the Murchison Widefield Array
• Low-cost, Low-loss, Ultra-wideband Compact Feed for Interferometric Radio Telescopes
• Primary Beam Chromaticity in HIRAX: I. Characterization from Simulations and Power Spectrum Implications
• The impact of lunar topography on the 21-cm power spectrum for grid-based arrays : Insights for the Dark-ages EXplorer (DEX)
• The Effects of the Local Environment on a Compact Radio Interferometer I: Cross-coupling in the Tianlai Dish Pathfinder Array