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The implementation of fringe tracking for optical interferometers isinevitable when optimal exploitation of the instrumental capacities is desired.Fringe tracking allows continuous fringe observation, considerably increasingthe sensitivity of the interferometric system. In addition to the correction ofatmospheric path-length differences, a decent control algorithm should correctfor disturbances introduced by instrumental vibrations, and deal with othererrors propagating in the optical trains. We attempt to construct controlschemes based on Kalman filters. Kalman filtering is an optimal data processingalgorithm for tracking and correcting a system on which observations areperformed. As a direct application, control schemes are designed for GRAVITY, afuture four-telescope near-infrared beam combiner for the Very Large TelescopeInterferometer (VLTI). We base our study on recent work in adaptive-opticscontrol. The technique is to describe perturbations of fringe phases in termsof an a priori model. The model allows us to optimize the tracking of fringes,in that it is adapted to the prevailing perturbations. Since the model is of aparametric nature, a parameter identification needs to be included. Differentpossibilities exist to generalize to the four-telescope fringe tracking that isuseful for GRAVITY. On the basis of a two-telescope Kalman-filtering controlalgorithm, a set of two properly working control algorithms for four-telescopefringe tracking is constructed. The control schemes are designed to take intoaccount flux problems and low-signal baselines. First simulations of thefringe-tracking process indicate that the defined schemes meet the requirementsfor GRAVITY and allow us to distinguish in performance. In a future paper, wewill compare the performances of classical fringe tracking to our Kalman-filtercontrol.

Kalman-filter control schemes for fringe tracking. Development and application to VLTI/GRAVITY