Mutual coherence function for a double-passage retroreflected optical wave in atmospheric turbulence

Abstract

The mutual coherence function in the source-receiver plane of a reflected Gaussian beam wave from a retroreflector is calculated and analyzed for two refractive-index spectral models and compared with similar results for the case of a plane mirror. Specific expressions are calculated for the mean irradiance and spatial coherence radius based on a Gaussian model for the finite reflector. Results that we obtained here using a modified spectrum with a high wave-number rise and inner scale generally show greater amplitude enhancements in the reflected wave than predicted by the pure power-law spectrum of Kolmogorov. In contrast, a finite outer scale in the spectral model leads to a reduction in the amount of beam spreading caused by turbulence and, in the case of a retroreflector, also leads to a reduction in the peak amplitude enhancement on the optical axis. This last result is in contrast with a plane mirror reflector, in which outer scale effects tend to increase the peak amplitude enhancement on the optical axis. The theory also predicts that, except for small reflectors, the coherence radius associated with a retroreflector can be as much as 1.4 times larger than that associated with a plane mirror, and 1.2 times that of a bistatic configuration for a plane mirror. All calculations are based on weak fluctuation theory and generalized spectral representations that use complex ABCD ray matrices.