Interferometric Closure Phase Uncertainties in the Low Signal-to-Noise Ratio Regime

TL;DR

This paper introduces an efficient, analytic method to approximate the distribution of interferometric closure phase uncertainties in low signal-to-noise conditions, improving computational speed and accuracy.

Contribution

It demonstrates that the true phase distribution can be approximated by a von Mises distribution and provides a convolution-based method for better uncertainty estimation.

Findings

The von Mises distribution closely approximates the true phase distribution.

The convolution of three von Mises distributions yields a superior approximation to the normal distribution.

The method enables fast, analytic computation of closure phase uncertainties in low SNR regimes.

Abstract

Closure phases are critical in astronomical interferometry. However, their uncertainties are difficult to compute numerically. We provide a method to efficiently compute interferometric closure phase distributions in terms of an approximate distribution that is valid in the low signal-to-noise ratio regime. This is done by first showing that the true phase distribution is well approximated by the von Mises distribution, then performing a convolution of three von Mises distributions. The resulting approximation is superior than the normal distribution for all signal-to-noise ratios and, being fully analytic, allow for fast computations in statistical algorithms.