Array element coupling in radio interferometry I: a semi-analytic approach

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 non-zero 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 local sidereal time (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.