  Mueller matrix polarimetry constitutes a nondestructive powerful tool for the
analysis of material samples that is used today in an enormous variety of
applications. Depolarizing samples exhibit, in general, a complicated physical
behavior that requires appropriate mathematical formulation through models
involving decomposition theorems in terms of simpler components. In this work,
the general conditions for identifying retarding incoherent components of a
given Mueller matrix M are obtained. It is found that when the coherency matrix
C associated with M has rank C = 3,4 it is always possible to identify one or
two retarding incoherent components respectively, while in the case where rank
C =2, such retarding component only can be achieved if and only if the
diattenuation and the polarizance of M are equal. Since the Mueller matrices
associated with retarders have a simple structure, the results obtained open
new perspectives for the exploitation of polarimetric techniques in optics,
remote sensing and other areas.
