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

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 superior to the normal distribution for all signal-to-noise ratios and, being fully analytic, allows for fast computations in statistical algorithms.