ABSTRACT
The statistical concept of the Mueller matrix entails more restrictive conditions than the very fact that a Mueller matrix is a linear transformation of Stokes vectors into Stokes vectors. Several physical arguments support the concept of Mueller matrices as ensemble averages of pure, passive Mueller matrices. The particular forms of Jones and Mueller matrices with respect to the bases commonly used in radar polarimetry for forward and backward scattering, as well as their respective relations with the coherent scattering matrix, covariance and coherency matrices, and Kennaugh matrix. The transformations for both nondepolarizing and depolarizing Mueller matrices when they are represented with respect to different coordinate frames are derived from the rule for Stokes vectors. Moreover, the rigorous characterization of Mueller matrices is the appropriate basis for identifying representative physical quantities, as well as serial and parallel decompositions in terms of easily interpretable components.
