ABSTRACT
This chapter describes the analysis of all the possible parallel decompositions of Mueller matrices. In general, two kinds of decompositions of a Mueller matrix (M) can be performed: serial decompositions and parallel decompositions. Furthermore, both decompositions can be combined, leading to serial-parallel decompositions. Parallel decompositions consist of representing a M as a convex sum of Mueller matrices. The physical meaning of parallel decompositions is that the incoming electromagnetic wave splits into a set of pencils that respectively interact with each of a number of components spatially distributed in the illuminated area, without overlapping, and the emerging pencils are incoherently recombined into an output beam. The choice of a particular passive realization of the arbitrary decomposition whose first pure component has the largest coefficient must replace the spectral decomposition and a parallel decomposition akin to the characteristic one must be formulated in terms of mixtures of the components of the said particular decomposition.
