Over the past two decades there has been a renewed interest in the properties of light and its interactions with matter. In particular, the phenomenon of mixing on the surface of a quantum detector, first performed by Forrester and Gudmundsen, has had significant impact on the treatment of the interaction of light with matter. Mandel and Wolf have interpreted optical mixing of two fields in terms of wave-packet interactions. The wave packets of the fields were allowed to add in a classical manner, without any interaction between photons. In this paper, we consider the extension to an ensemble of statistical wave packets. This is accomplished by considering the wave-packet ensemble as a generalized shot-noise process, and generating statistical properties of the ensemble. The first-order probability density is obtained for the envelope of an ensemble in which each member has uniform and independently distributed phase. This is then used to compute the resulting photoelectron-counting distribution. The results can be shown to be somewhat different than would arise from a gaussian field, and a statistical test is derived to compare the two.
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