Effect of Spatial Coherence on the Photoelectric Counting Statistics of Gaussian Light

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Abstract
Exact formulas are derived for the factorial cumulants of the photoelectric counting distribution of partially polarized Gaussian and Gaussian-plus-coherent light for arbitrary detector areas. The results make it possible to follow the transition from Bose-Einstein statistics in the small-area limit to Poisson statistics in the large-area limit. Numerical results are presented for a circular geometry. These methods, which enable experimentally measured photocount statistics to be extrapolated to zero detector area, are expected to be useful in measurements of small departures from Gaussian statistics. Other theoretical results make it possible to express the statistics of the sum of photocounts from different photocathodes, or the multiaperture, single-cathode (MASC) photocount statistics of light of arbitrary coherence properties, in terms of the multicathode (MC) counting statistics. Explicit expressions are derived for the MASC photocount cumulants for the special case of partially polarized Gaussian light.