STATISTICAL APPROACH TO BIAS EFFECTS IN THE TECHNIQUES OF SPECKLE INTERFEROMETRY AND SPECKLE MASKING

We present an approach to the speckle interferometry techniques of Labeyrie and Weigelt that is based on the use of the moment-generating function (MGF). The remarkable properties of the MGF's of photodetected images make it possible to obtain the expression for the photon-bias terms by a method completely different from the usual Goodman-Belsher approach [J. W Goodman, Statistical Optics (Wiley, New York, 1985)]. It gives us the mathematical relations to predict the effect of a clipped photodetection of the image on the autocorrelation and triple correlation functions. As a result, clipping ruins the linear relationship between object and reference source for these functions. The effect of photon recentering is also investigated and is directly related to a single-photon clipping effect. Analytical expressions for a normal speckle pattern are given.