<title>Kalman-filter fringe tracking in an optical interferometer</title>

Abstract

In a class of optical interferometers, two samples of the captured light are combined in the pupil plane, dispersed, and focused to form a channeled spectrum. Shifts of the resulting fringe pattern due, for example, to the rotation of the instrument or changes in the propagation medium, must be tracked and, in some cases, compensated for the instrument to perform properly. The performance of the fringe-tracking estimator sets the faint limit of the instrument for a given suite of disturbances to the optical path difference (OPD) through the two sides of the interferometer. A nearly optimal fringe tracker may be constructed as a Kalman filter that includes a correct representation of the statistical properties of the OPD time series and that processes the detected photons individually. The use of a suboptimal filter is likely to be necessary both because of the difficulty of properly representing the OPD statistics and because of the computational burden of the complete, nonlinear, photon-by-photon estimator running in real time. We discuss a portion of the study of fringe trackers that has been carried out at SAO for the IOTA (ground-based) and POINTS (space-based) interferometry projects. We also present the results obtained from a Kalman filter fringe tracker running on simulated data. When the simulated OPD is obtained by numerically solving a second order differential equation with a white Gaussian driving term, an augmented state extended Kalman filter substantially outperforms a similar filter with an unaugmented state.