Resolving phase ambiguities in the calibration of redundant interferometric arrays: implications for array design
MIT Lincoln Laboratory Lexington United States
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We provide new results enabling robust interferometric image reconstruction in the presence of unknown aperture piston variation via the technique of Redundant Spacing Calibration RSC. The RSC technique uses redundant measurements of the same interferometric baseline with different pairs of apertures to reveal the piston variation among these pairs. In both optical and radio interferometry, the presence of phase wrapping in the measurements is a fundamental issue that needs to be addressed for reliable image reconstruction. In this paper, we show that these ambiguities affect recently-developed RSC phasor-based reconstruction approaches operating on the complex visibilities, as well as the traditional phase-based approaches operating on their logarithm. We also derive new sufficient conditions for an interferometric array to be immune to these ambiguities in two different senses immunity up to an image shift in the reconstruction, and absolute immunity. We show the implications of these results for imaging via phase closures and extend existing results involving the classical three-baseline closures to generalized closures. Furthermore we show that absolute immunity is conferred upon arrays whose interferometric graph satisfies a certain loop-free condition. We specify this condition and, for cases in which this condition is not satisfied, we provide a simple algorithm for identifying those graph cycles which prevent its satisfaction. Finally we apply this algorithm to diagnose and correct a member of a pattern family popular in the literature.