Speckle statistical properties of Gaussian beam from a semi-rough target in the atmospheric turbulence

Based on extended Huygens–Fresnel principle and Goodman model for target surface, analytic expression is developed for the mutual coherent function (MCF) of a reflected Gaussian-beam from a semi-rough target in single-pass atmospheric turbulence. Then according to the MCF we derive expression about the mean intensity and average speckle size at the receiver. The analysis indicates that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length; in addition, the speckle size is associated with turbulence strength and roughness of target. Our results agree with well-known the limiting cases of perfectly smooth and Lambertian target.