High-performance fringe-tracking algorithms utilizing statistical models of atmospheric turbulence

This paper introduces a new method for tracking fringes in ground-based optical stellar interferometry at low light levels under conditions of variations in OPD due to atmospheric turbulence. Like the group delay tracking (GDT), the method involves processing of short-exposure frames of channeled spectra when operating in a fringe tracking mode. But while the GDT is based on the fast Fourier transform, the proposed method is base don the formalism of optical statistical decisions and Markov chain framework. The corresponding algorithm, doubled DBA makes it possible to utilize all available information about the problem's nonlinearities and statistics such as Poisson photon arrivals, Gaussian readout noise, the statistics of atmospheric turbulence. Simulation results show that the DBA tracks stars up to two bolometric magnitudes dimmer than is possible with the GDT.