Comparison between relay propagation and direct propagation of Gaussian—Schell-model beam in turbulent atmosphere along a slant path

The relay propagation of Gaussian--Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens--Fresnel principle and a quadratic approximation, an analytical formula of average intensity for Gaussian--Schell-model beams in turbulent atmosphere along a slant path is derived, and some special cases are discussed. From the study and the comparison with the direct propagation, we can see that the relay propagation has an advantage over the direct propagation. When the altitude of the target is low, the peak intensity of relay propagation is much larger than that of direct propagation. However, because of the limitation of the relay system aperture for relay propagation and the variation of coherence length for direct propagation, the difference in peak intensity between the two propagations decreases with the increase of the target altitude.