Exact First-, Second-, and Third-Order Photocounting Cumulants for Lognormally Modulated Mixtures of Coherent and Chaotic Radiation

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Abstract
In this paper we investigate the photocount statistics of mixed coherent plus Gaussian light that has suffered lognormal fading, such as produced by the turbulent atmosphere. The Gaussian component need not be stationary, may have an arbitrary spectral distribution, and the mean frequency of the coherent and Gaussian components need not coincide. The first three cumulants of the phototelectric counts for a single detector and for an array of detectors are obtained for arbitrary ratios of counting time to source coherence time, β, while assuming the fading to be fully time correlated over the detection interval. In particular, the cumulants are evaluated for Gaussian light of Lorentzian spectrum. The variation of the cumulants with degree of turbulence and detector separation is exhibited graphically, for several values of β, and ratio of coherent to chaotic component, y. The effect of increasing the degree of turbulence is shown to cause the ratio of the second‐order cumulant for Gaussian light to the same cumulant for coherent light to approach a nominal value of 2, indicating the extent to which the fading dominates the counting statistics. As the detector separation is varied, the twofold cumulant exhibits the spatial correlations of the turbulence, when the source radiation alone is assumed to be approximately spatially coherent at the detector array. Furthermore, the cumulants are shown to increase exponentially with the turbulence level σ, the log‐intensity standard deviation.