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, pp2331-2354, April 2016.

Calibration artefacts, like the self-calibration 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 east-west interferometer for a simple two-source 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 ghost-patten for a two-source 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 two-peak structure with which some ghosts manifest during imaging. We illustrate our mathematical predictions using simulations of the KAT-7 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 two-source example discussed here, incomplete sky models or full synthesis observations including direction dependent effects.

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