Statistics of speckle propagation through the turbulent atmosphere

Abstract

We have utilized the extended Huygens-Fresnel principle to make an analysis of the first- and second-order statistics of the received intensity for speckle propagation through the turbulent atmosphere. The treatment includes the effects of the turbulent atmosphere on the laser beam as it propagates to the target and on the speckle as it propagates back to the receiver. Formulations have been developed for both the focused and collimated cases. It is assumed in the analysis that phase perturbation of the waves is the dominant effect due to the atmosphere. Utilizing this assumption it can be shown that the fields at the receiver are marginally Gaussian and that the space-averaged, spatial power spectral density at the receiver is “white“. Because of these results, we have assumed that the field statistics at the receiver are jointly Gaussian. This appears to be a reasonable assumption and allows a closed form solution for the variance and covariance to be derived. For a point detector it is found that the normalized variance is unity and independent of the turbulence strength, and that the transverse correlation length becomes proportional to ρ0 as the turbulence strength increases.