Correlation between light-flux fluctuations of two counter-propagating waves in weak atmospheric turbulence

Expressions for the correlation coefficient between light-flux fluctuations of two waves counter-propagating along a common path in weak turbulence are developed. Only the aperture and inner-scale Fresnel parameters are needed for evaluation of the correlation coefficient if the turbulence spectrum has no path dependence, and of the path weighting functions for the cross-covariance and variances of normalized light-flux fluctuations if the turbulence spectrum is dependent on path locations. Under the condition that atmospheric turbulence is statistically homogeneous over a path, although good correlation between light-flux fluctuations of two counter-propagating spherical waves may be achieved for a relatively small aperture Fresnel parameter or relatively large inner-scale Fresnel parameter, the correlation coefficient between light-flux fluctuations of two counter-propagating plane waves is always lower than 1 obviously. When the aperture Fresnel parameter becomes larger than the inner-scale Fresnel parameter, the inner scale of turbulence tends to play an unimportant role in determining the correlation coefficient.