Ensemble approach to coherence between two scalar harmonic light vibrations and the phase difference

We develop an approach to coherence between two scalar harmonic light vibrations derived from the ensemble interpretation of statistical optics. Coherence is presented as a statistical variable itself that turns out to be the phase difference between the two vibrations. This provides a natural and simple extension of second-order coherence to cover more complicated situations. This includes in a single formalism both classic and quantum light states, allowing the most accurate interferometric measurements, even if they are incoherent according to the standard second-order approach.