It has long been recognized that, in the low signal-to-noise 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. It eliminates heuristics by fitting a parameterized model for the phase as a function of time and wavelength 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. When bootstrapping several baselines, the noise variance is about a factor of two smaller than normally assumed. This technique has been applied to both simulated and stellar data.
|