Approximate Formulas for Photoelectric Counting Distributions

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Abstract
The validity of a simple approximate formula for the photoelectric counting probability in a thermal optical field, which was proposed by one of us (L.M.) in 1959, is investigated. The formula is based on a generalization of the Bose-Einstein distribution and should hold for light of arbitrary spectral density. It is shown by explicit calculation for three different spectral distributions that the formula holds with good accuracy over a very wide range of conditions. It should therefore prove useful when the spectral distribution of the light being studied is not known.