Statistical properties of Gaussian-Schell beam from diffuse target in turbulent atmosphere

We utilize the extended Huygens-Fresnel principle to make an analysis of the scattering of a Gaussian Schell-model beam from a diffuse target in a turbulent atmosphere. It is assumed that the wave structure function is dominated by the phase structure function. Using the cross-spectral density function of the GSM beam, the analytical expressions are developed for the mutual coherence function (MCF) of the speckle field at the receiver, and then time-delayed variance of the scattering intensity in strong turbulence is derived. From the normalized MCF, estimates are given for the speckle size at receiver. We also analyze the influences of the coherence length of the source, wavelength, and turbulence strength on the mutual coherence function. For a diffuse target, the speckle size is only determined by the waist width, the coherence length of the source and the turbulence strength. With the turbulence strength increasing, the speckle radius will decrease at the receiver. In weak turbulence, speckle radius is dominated by the value of source coherence.