Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.