Speckle dynamics resulting from multiple interfering beams

The space-time intensity covariance function for illuminating an object giving rise to fully developed speckle is considered in the case where the object is illuminated with two spatially separated beams, or with a multitude of equidistant but spatially separated spots. Specifically, and to the best of our knowledge for the first time, we obtain the result that the larger speckles will be covered by a fine structure that, in general, translates at a different velocity from that of the larger speckles. In particular, closed-form analytical expressions are found for the space- and time-lagged covariance of irradiance as well as the corresponding power spectrum for each of the two spatially separated, N equidistant separated illuminating beams. The present analysis is valid not only for free-space propagation but also for an arbitrary real ABCD optical system. Finally, the corresponding statistical signal properties, including the power spectrum, are derived and discussed for the (practical) case where the comprehensive speckle field is spatially filtered by a gratinglike structure. (C) 2008 Optical Society of America.