Spatial coherence function of partially coherent Gaussian beams in atmospheric turbulence

We introduce a new method of estimating the coherence function of a Gaussian-Schell model beam in the inertial subrange of atmospheric turbulence. It is compared with the previously published methods based on either the quadratic approximation of the parabolic equation or an assumed independence between the source's randomness and the atmosphere using effective beam parameters. This new method, which combines the results of the previous two methods to account for any random source/atmospheric coupling, was shown to more accurately estimate both the coherence radius and coherence functional shape across much of the relevant parameter space. The regions of the parameter space where one method or another is the most accurate in estimating the coherence radius are identified along with the maximum absolute estimation error in each region. By selecting the appropriate estimation method for a given set of conditions, the absolute estimation error can generally be kept to less than 5%, with a maximum error of 7%. We also show that the true coherence function is more Gaussian than expected, with the exponential power tending toward 9/5 rather than the theoretical value of 5/3 in very strong turbulence regardless of the nature of the source coherence.