Coherent Integration in Astronomical Interferometry: Theory and Practice

Ground-based long-baseline astronomical interferometry operates in a regime where short integration exposures are demanded by working in the presence of a turbulent atmosphere. To reduce piston noise to less than one radian per aperture, these exposure times are on order 10 milliseconds or less in the visible. It has long been recognized that, in the low signal-to-noise ratio (SNR) regime, the visibility SNR is improved by co-adding frames, each rotated by an estimate of its phase. However, implementation of this technique is challenging. Where it is most needed, on low SNR baselines and when combining multiple phases to estimate the phase for a lower SNR baseline, phase errors reduce the amplitude by a large amount and in a way that has proven difficult to calibrate. In this paper, an improved coherent integration algorithm is presented. A parameterized model for the phase as a function of time and wavelength is fit to the entire data set. This framework is used to build a performance model which can be used in two ways. First, it can be used to test the algorithm; by comparing its performance to theory, one can test how well the parameter fitting has worked. Also, when designing future systems, this model provides a simple way to predict performance and compare it to alternative techniques such as hierarchical fringe tracking. This technique has been applied to both simulated and stellar data.