http://arxiv.org/abs/2108.11399
An $N$-element interferometer measures correlations between pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, local, element-based corruptions that occur in these measurements. Till now, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. Using an Abelian $\textrm{GL}(1,\mathbb{C})$ gauge theory, we provide a simple and effective formalism to isolate the complete set of independent closure invariants from co-polar interferometric correlations only using quantities defined on the $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. Our formalism does not require auto-correlations, but can easily include them if reliably measured, including potentially from cross-correlation between two short-spaced elements. The gauge theory framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry presented in a companion paper, which generalizes and clarifies earlier work. Our findings can be relevant to cutting-edge co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.
N. Thyagarajan, R. Nityananda and J. Samuel
Fri, 27 Aug 21
66/67
Comments: 10 pages (including references), 0 figures, submitted to Physical Review D