S. J. Wijnholds, T. L. Grobler and O. M. Smirnov, "Calibration
artefacts in radio interferometry.  II. Ghost patterns for irregular
arrays," Monthly Notices of the Royal Astronomical Society, V457,
no. 3, pp23312354, April 2016.
abstract:
Calibration artefacts, like the selfcalibration bias, usually emerge
when data is calibrated using an incomplete sky model. In the first
paper of this series, in which we analyzed calibration artefacts in
data from the WSRT, we showed that these artefacts take the form of
spurious positive and negative sources, which we refer to as ghosts or
ghost sources. We also developed a mathematical framework with which
we could predict the ghost pattern of an eastwest interferometer for
a simple twosource test case. In this paper, we extend our analysis
to more general array layouts. This provides us with a useful method
for the analysis of ghosts that we refer to as
extrapolation. Combining extrapolation with a perturbation analysis,
we are able to: 1. analyse the ghostpatten for a twosource test case
with one modeled and one unmodeled source for an arbitrary array
layout, 2. explain why some ghosts are brighter than others, 3. define
a taxonomy allowing us to classify the different ghosts, 4. derive
closed form expressions for the fluxes and positions of the brightest
ghosts, and 5. explain the strange twopeak structure with which some
ghosts manifest during imaging. We illustrate our mathematical
predictions using simulations of the KAT7 array. These results show
the explanatory power of our mathematical model. The insights gained
in this paper provide a solid foundation to study calibration
artefacts in arbitrary, i.e., more complicated than the twosource
example discussed here, incomplete sky models or full synthesis
observations including direction dependent effects.
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