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 thepresence 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 variationamong these pairs. In both optical and radio interferometry, the presence of phasewrapping in the measurements is a fundamental issue that needs to be addressedfor 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 traditional phase-based approaches operating on theirlogarithm. We also derive new sucient conditions for an interferometric array to beimmune to these phase-wrap ambiguities in the sense that their effect can be rendered benign in image reconstruction. We show the implications of this property ofwrap-invariance for imaging via phase closures and extend existing results involving the classical three-baseline closures to generalized closures. Furthermore we show that this property is conferred upon arrays whose interferometric graph satisfies a certaincycle-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. We apply this algorithm to diagnose and correct a member of a pattern family popular in the literature. Finally, we show that wrap-invarianceis a fundamental property which is important in certifying reliability of powerful existing RSC techniques in the literature.