GROUP-DELAY TRACKING IN OPTICAL STELLAR INTERFEROMETRY WITH THE FAST FOURIER-TRANSFORM

Group-delay tracking is a method of fringe tracking used for optical stellar interferometry. It employs a photon-counting spectrometer to record short-exposure frames of channeled spectra. In each frame the number of fringes is proportional to the path difference, which can be extracted by power spectrum analysis. In this study the low-light-level limitations of the method are examined when the fast Fourier transform is used for data processing. Frame times are limited by the coherence time of the atmosphere, and for active tracking the sensitivity depends on the largest number of power spectra that can be integrated usefully. Rayleigh and Rician statistics are used to model the visibility amplitudes determined from the power spectra, and the probability of tracking loss is examined as a function of fringe visibility, the number of photons per frame, and the number of integrated frames. The effect of bracketing the fringe peak with a filter is also examined, and simulations are used to verify the predictions.