Three-dimensional coherence of light speckles: Theory

We provide a detailed analysis of the three-dimensional spatial coherence properties of light speckles, based on very general assumptions. We show that, while in the deep Fresnel region close to the source the longitudinal coherence of speckles is ruled by the laws of ordinary diffraction, on approach to the Fraunhofer zone the longitudinal coherence length tends to become infinite. We offer both a quantitative and a qualitative description of the emergence of these different behaviors. © 2008 The American Physical Society.