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We investigate interference of optical fields by examining the probabilitydistribution of photon detection. The usual description of interferencepatterns in terms of superposition of classical mean fields with definitephases is elucidated in quantum fashion. Especially, for interference of twoindependent mixtures of number states with Poissonian or sub-Poissonianstatistics, despite lack of intrinsic phases, it is found that the jointprobability has a distinct peak manifold in the multi-dimensional space of thedetector outcomes, which is along the trajectory of the mean-field values asthe relative phase varies on the unit circle. Then, an interference patternshould mostly appear in each shot of measurement as a point in the peakmanifold with a randomly chosen relative phase. On the other hand, forsuper-Poissonian sources the mean-field description is likely invalidated withrather broad probability distributions.

Optical interference in view of the probability distribution of photon detection