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.
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