Young's interference experiment with light of any state of coherence and of polarization

A general expression is derived for the electric cross-spectral density matrix of a random electromagnetic beam in an observation plane parallel to the plane of the pinholes in a Young interference experiment when the pinholes are illuminated by light of any state of coherence and of polarization. It is shown that the degree of polarization P in the observation plane may take on values different from those it takes at each pinhole, depending on the value of the degree of coherence of the light incident on the pinholes.