Title:	Invariants in copolar interferometry: An Abelian gauge theory
Authors:	Thyagarajan, Nithyanandan Nityananda, Rajaram Samuel, Joseph
Issue Date:	28-Feb-2022
Publisher:	American Physical Society
Citation:	Physical Review D, 2022, Vol.105, p043019
Abstract:	An N-element interferometer measures correlations among pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, element-based (“local”) corruptions that occur in these measurements. Till recently, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in copolar correlations as gauge transformations belonging to the gauge group GL(1,C). Closure quantities are then naturally gauge invariant. We use this to provide a simple and effective formalism and identify the complete set of independent closure invariants from copolar interferometric correlations using only quantities defined on (N−1)(N−2)/2 elementary and independent triangular loops. The (N−1)(N−2)/2 closure phases and N(N−3)/2 closure amplitudes (totaling N2−3N+1 real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. We do not require autocorrelations but can easily include them if reliably measured. This unified view clarifies issues relating to noise and inference of object model parameters. It also allows us to extend the rule of parallel transport associated with Pancharatnam phase in optics to apply to amplitudes as well. The framework presented here extends to GL(2,C) for full polarimetric interferometry as presented in a companion paper, which generalizes and clarifies earlier work. Our findings are relevant to state of the art copolar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of black holes at the centers of M87, Centaurus A, and the Milky Way.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7905
ISSN:	2470-0010 2470-0029 (Online)
Alternative Location:	https://arxiv.org/abs/2108.11399 https://doi.org/10.1103/PhysRevD.105.043019 https://ui.adsabs.harvard.edu/abs/2022PhRvD.105d3019T/abstract
Copyright:	2022 American Physical Society
Appears in Collections:	Research Papers (TP)

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