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This overview paper deals with the statistical properties of a speckle pattern. After the introduction, in which the speckle and its origin is shortly described, the first-order statistics of a polarized speckle pattern are derived. Further, a special case of the sum of a speckle pattern and a coherent background is briefly mentioned. The first-order statistics of this special case are presented, too.
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Pavel Horvath, Miroslav Hrabovsky, Zdenek Baca, "Statistical properties of a speckle pattern," Proc. SPIE 4888, First International Workshop on Classical and Quantum Interference, (22 July 2002); https://doi.org/10.1117/12.475874