On the First-order Probability Density Function of Integrated Laser Speckle

Abstract

We present a solution for the theoretical first-order probability density function of laser speckle measured with a finite aperture. A two-dimensional Kac-Siegert analysis is made. This involves the solution of an eigenvalue problem. For the spatial speckle correlation function and the spatial profile of the detector we assume gaussian models. The eigenvalues are then exactly expressed by simple formulae, and the probability density is calculated for slit apertures and a two-dimensional aperture. Experimental results are presented, and they agree well with the theory.