Effect of the turbulent atmosphere on the autocovariance function for a speckle field generated by a laser beam with random pointing error

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Abstract
An analytic formulation for the speckle-intensity autocovariance function generated by a laser beam with random pointing error is developed. The analysis utilizes the extended Huygens–Fresnel principle and includes the effects of atmospheric turbulence on propagation of the misaligned laser beam to a diffuse target and on propagation of the speckle field back to the receiver. The main object of the development is to estimate the effects of deterministic and random pointing errors of the illuminating source on the statistics of the received intensity. In addition, methods for numerical evaluation of the autocovariance function are discussed, and some numerical results are shown. It is found that the autocovariance can be substantially increased above its vacuum value by the atmospheric turbulence.