Piston control with adaptive optics in stellar interferometry -: Application to the GI2T interferometer and bimorph mirrors

The general purpose of an adaptive optics system is to correct for the wavefront corrugations due to atmospheric turbulence. When applied to a stellar interferometer, care must be taken in the control of the mean optical path length, commonly called differential piston. This paper defines a general formalism for the piston control of a deformable mirror in the linear regime. It is shown that the usual filtering of the piston mode in the command space is not sufficient, mostly in the case of a bimorph mirror. Another algorithm is proposed to cancel in the command space the piston produced in the pupil space. This analysis is confirmed by simulations in the case of the GI2T interferometer located on Plateau de Calern, France. The contrast of the interference fringes is severely reduced in the case of a classical wavefront correction, even in short exposures, but is negligible with our algorithm? assuming a realistic calibration of the mirror. For this purpose, a simple concept for the calibration of the piston induced by a deformable mirror is proposed.