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 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.
