Fringe tracking in optical interferometry: a robust control framework for higher sensitivity limits

Fringe tracking (FT) is the adaptive optics component of an Optical Long Baseline Interferometer (OLBIN). It is a critical element in particular for high spectral resolution spectro-interferometric observations. The FT must be accurate and stable, which implies high frequency sampling of the optical path differences introduced by the atmosphere and the interferometer vibrations. It must also be as sensitive as possible, which needs to minimize this sampling frequency. The optimum between these contradictory requirements must be maintained through atmospheric and instrument conditions that change very rapidly. We describe a control framework to face this robustness challenge. First, we approximate the sampled-data feedback system as a discrete time feedback system and we show that the closed-loop FT behavior is entirely determined by key closed-loop transfer functions. To fix the closed-loop bandwith in order to limit the loss of vadidity of the discrete time feedback system, we propose a loop shaping control method based on H-infinity optimization. This H-infinity framework allows to bound the frequency response of the key closed-loop transfer function. First numerical experiments are presented showing satisfactory performance when the sampling frequency disminishes. Extensive simulations to demonstate the effectivness of the proposed approach are in progress. Open issues and perspectives of applicative and/or theoretical interests are discussed.