In a turbulent atmosphere, the log-amplitude, phase-correlation, and structure functions are formulated for light sources exhibiting arbitrary-field distribution. This is done by extending the formulations of the correlation and structure functions for the known general-type beam sources to cover any type of source having arbitrary-field distribution. To introduce the arbitrary field, the source is presented by an incidence that is a function of transverse source coordinates. The received field in the random medium is found by employing the Rytov method, which is a single-scattering solution obtained by the first-order approximation; thus our results are valid in weak turbulence. All the existing results can be correctly reproduced from our formulations when the corresponding source-field distributions are inserted into our presented correlation and structure-function expressions. Our results for the arbitrary-source field profiles can be utilized in finding the scintillation index and the angle-of-arrival fluctuations of any type of incidence in optical atmospheric links. Additionally, our formulations can find applications in reflection from rough surfaces and imaging in turbulence.
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