Depolarizing mueller matrices: How to decompose them?

The various decompositions of depolarizing Mueller matrices into products of basic optical devices, i.e. retarders, diattenuators and depolarizers, are critically revisited and discussed. Both classic as well as recently proposed factorizations are reviewed. Physical and calculation aspects such as depolarization and matrix singularity are comparatively addressed. The problems of physical realizability and matrix filtering are treated in connection with the sum decomposition of a depolarizing Mueller matrix. Experimental matrices are factorized using the different decompositions and physically interpreted.