Fringe visibility estimation in Michelson stellar interferometry: asymptotic performances

This paper is devoted to the computation of a theoretical lower bound on the variance of the squared visibility amplitude, estimated by optical long-baseline Michelson interferometry with large apertures. A solution to this problem is to compute the Cramer-Rao lower bound. This derivation is tractable under the Gaussian distribution assumption. This requires the first and second order moment of the image itself, for which analytical expressions are obtained. The resulting lower bound is compared to the variance of the amplitude visibility estimator proposed by Mourard. This variance, computed by Berio for images recorded in the photon-counting mode, is derived herein for the classical CCD camera.