Coherent diffusion of partial spatial coherence

Partially coherent light is abundant in many physical systems, and its propagation properties are well understood. Here we extend current theory of propagation of partially coherent light beams to the field of coherent diffusion. Based on a unique four-wave mixing scheme of electro-magnetically induced transparency, an optical speckle pattern is coupled to diffusing atoms in a warm vapor. The spatial coherence propagation properties of light speckles is studied experimentally under diffusion, and is compared to the familiar spatial coherence of speckles under diffraction. An analytic model explaining the results is presented, based on a diffusion analogue of the famous Van Cittert-Zernike theorem.