Invariants in copolar interferometry: An Abelian gauge theory

Thyagarajan, Nithyanandan and Nityananda, Rajaram and Samuel, Joseph (2022) Invariants in copolar interferometry: An Abelian gauge theory. Physical Review D, 105 (4). ISSN 2470-0010

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Abstract

An �-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), so closure quantities are naturally gauge invariant. Using this perspective, we provide a simple and effective formalism and identify the complete set of independent closure invariants from copolar interferometric correlations using only quantities defined on (�−1)⁢(�−2)/2 elementary and independent triangular loops. The (�−1)⁢(�−2)/2 closure phases and �⁢(�−3)/2 closure amplitudes (totaling �²−3�+1 real invariants), familiar in astronomical interferometry, naturally emerge from this unified formalism, which brings together treatments that were previously separate. We do not require autocorrelations, though they can be included if reliably measured. This unified view clarifies issues relating to noise and the inference of object model parameters, and it allows us to extend the rule of parallel transport associated with the Pancharatnam phase in optics to amplitudes as well. The framework presented here extends to GL⁡(2,ℂ) for full polarimetric interferometry, as developed 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 aimed at determining features very near the event horizons of black holes at the centers of M87, Centaurus A, and the Milky Way.

Item Type:	Article
Authors:	Thyagarajan, Nithyanandan and Nityananda, Rajaram and Samuel, Joseph
Document Language:	Language English
Subjects:	Natural Sciences > Astronomy & allied sciences Natural Sciences > Physics
Divisions:	Azim Premji University - Bengaluru > School of Arts and Sciences
Full Text Status:	Restricted
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/7109
Publisher URL:	https://doi.org/10.1103/PhysRevD.105.043019

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