Problem of fringe acquisition in high-precision space-based interferometers

This paper presents the results of an investigation of the problem of fringe acquisition (FA) as it applies to high-precision space-based optical interferometers. The POINTS (for Precision Optical INTerferometry in Space) instrument concept, being developed in a collaborative effort between the Smithsonian Astrophysical Observatory and the Jet Propulsion Laboratory as a wide-band space-based optical interferometer dedicated to astrometry, is used as a test baseline. In this study we analyze three candidate FA algorithms: linear correlation techniques (CT); nonlinear least squares (NLS); and, a discrete Bayes approach (DBA). Analytical methods of evaluating the probability of detection for the NLS are developed which enable a multi-parametric study of the FA problem. Among other parameters, the study examines the effects of varying the magnitude of the electronic readout noise of the focal plane detector cells (assumed to be CCD's), of increasing the bolometric magnitude of the target stars, of allowing constant drifts of the optical path difference, and of co-adding CCD cells to reduce readout noise. A signal-to-noise measure is selected that exhibits a high correlation with the FA performance and a study of the a posteriori density space reveals insight into the nonlinear nature of the interferometric measurement function. The study concludes with selected Monte Carlo simulations to confirm the analytical predictions and to compare the performance and robustness of the CT and NLS to those attainable with the DBA.