Integral decomposition and polarization properties of depolarizing Mueller matrices

We show that, by suitably defining the integral decomposition of a depolarizing Mueller matrix, it becomes possible to fully interpret the polarization response of the medium or structure under study in terms of mean values and variances-covariances of a set of six integral polarization properties. The latter appear as natural counterparts of the elementary (differential) polarization properties stemming from the differential decomposition of the Mueller matrix. However, unlike the differential decomposition, the integral one is always mathematically and physically realizable and is furthermore unambiguously defined inasmuch as a nondepolarizing estimate of the initial Mueller matrix is secured. The theoretical results are illustrated on an experimental example.