ABSTRACT
The analysis of the physical quantities that remain unchanged under certain transformations has proven to be very useful for the interpretation of two-dimensional and three-dimensional coherency matrices associated with polarization states. This chapter aims to provide the study of the quantities involved in a Mueller matrix (M) that are invariant with respect to physically realizable transformations. Moreover, the depolarization of a medium represented by an M is also closely related to the randomness of the covariance matrix associated with M. The chapter deals with a synthesis procedure for generating any depolarizing M from an associated reference pure M through appropriate adjustment of a set of indices of polarimetric purity. The components of purity of an M have a peculiar physical meaning, different from that of polarization states. The degree of polarizance of an M contributes to purity in a peculiar way, which may mask a certain lack of purity due to depolarization effects.
