Advanced fringe tracking algorithms for low-light level ground-based stellar interferometry

Advanced nonlinear fringe tracking algorithms are used to improve the state-of-the-art in ground-based optical stellar interferometric fringe tracking by allowing the tracking of stars one to two bolometric magnitudes dimmer than currently possible. Even more significantly, the authors demonstrate active fringe locking for dim stars with less than 10% loss of lock probability. Enabling fringe locking through the atmosphere for dim stars has significant implications for ground-based interferometric stellar imaging. These results are a consequence of the powerful estimation framework in which the discrete Bayesian algorithm (DBA) is developed. This framework makes it possible to incorporate all the available nonlinear model and statistical information, including the known statistics of atmospheric variations, into the tracking algorithm and thus results in the highest performing fringe tracker. The authors made use of Zernike polynomial representations in order both to simulate atmospheric variations for algorithm evaluation and comparison, and also to incorporate the atmospheric information into the statistical mechanism of the nonlinear filters developed. All simulations are performed using parameters for the CHARA Array of Georgia State University. The formulation of the DBA for ground-based fringe tracking is presented. The nature of the data structures in the DBA makes it especially well suited to the incorporation of experimental data. A detailed formulation and preliminary evaluation is carried out on the Variation-Invariant Subspace Tracking Algorithm (VISTA). VISTA offers the possibility of making the interferometric measurements invariant to atmospheric disturbances through the optimal projection of many "sub-aperture interferometers" onto one invariant subspace. The DBA can fringe lock dim stars with a 50% loss of lock probability where state-of-the-art fringe tracking techniques fail. The use of VISTA in the fringe locking regime resulted in an improvement on the DBA results by up to one bolometric magnitude dimmer stars.