Determination of intensity correlation functions from photoelectric counting distributions

Two techniques are described for obtaining information about the intensity correlation function of an optical field, from measurements of photoelectric counting distributions. The first method is based on double differentiation of the second factorial moment with respect to the counting time. It requires very accurate data, but is shown to be quite feasible, and yields the intensity-correlation function explicitly. The second procedure is less sensitive to inaccuracies and allows the correlation time and certain other parameters to be determined from the factorial moments. In addition, it yields some information about the general form of the correlation function, but no explicit function. The procedures are illustrated and compared by application to photoelectric counting measurements of a laser far below the threshold of oscillation.