COHERENCE PROPERTIES OF A REFLECTED OPTICAL-WAVE IN ATMOSPHERIC-TURBULENCE

The transverse spatial coherence radius is studied for both the monost atic and bistatic laser radar problems involving an optical wave propa gating through atmospheric turbulence in the weak-fluctuation regime o ver a path of length L and then reflected in the reverse direction fro m a finite mirror with finite focal length F-R. Formal expressions are developed for the wave structure function and the modulus of the comp lex degree of coherence in the general Gaussian-beam wave ease, and tr actable analytic results are derived for the special case of a divergi ng (or spherical) wave at the transmitter and observation points in th e beam symmetrically located with respect to the beam centerline. By v arying the focal length of the mirror, one minimizes the spatial coher ence radius of a reflected spherical. wave when the receiver is locate d 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 devia tion from pure power-law behavior are taken into account in the assume d spectral models for refractive-index fluctuations. Analogous to line -of-sight propagation, the spatial coherence radius based on a modifie d spectrum is generally less than that based on the von Karman spectru m, particularly when the coherence radius is of the order of the inner scale of turbulence. (C) 1996 Optical Society of America