Coherence properties of a reflected optical wave in atmospheric turbulence

The transverse spatial coherence radius is studied for both the monostatic and bistatic laser radar problems involving an optical wave propagating through atmospheric turbulence in the weak-fluctuation regime over a path of length L and then reflected in the reverse direction from a finite mirror with finite focal length F-R. Formal expressions are developed for the wave structure function and the modulus of the complex degree of coherence in the general Gaussian-beam wave ease, and tractable analytic results are derived for the special case of a diverging (or spherical) wave at the transmitter and observation points in the beam symmetrically located with respect to the beam centerline. By varying the focal length of the mirror, one minimizes the spatial coherence radius of a reflected spherical. wave when the receiver is located near the plane defined by the radius of curvature of the mirror (i.e., L/F-R similar to 2) and maximizes it when L/F-R is approximately 6-7. Effects of inner scale, outer scale, and the high wave-number deviation from pure power-law behavior are taken into account in the assumed spectral models for refractive-index fluctuations. Analogous to line-of-sight propagation, the spatial coherence radius based on a modified spectrum is generally less than that based on the von Karman spectrum, particularly when the coherence radius is of the order of the inner scale of turbulence. (C) 1996 Optical Society of America