On the proper polarimetric scattering matrix formulation of the forward propagation versus backscattering radar systems description

Jones matrices and Sinclair matrices are 2×2 complex matrices that determine forward (transmission) and backward scattering, respectively. Under a unitary change of polarization basis they transform by ordinary unitary similarity and by unitary consimilarity, respectively, forming equivalence classes with common invariant polarimetric features. In most applications the Jones matrices T are normal and, thus, have orthogonal eigenvectors; whereas, Sinclair matrices S are symmetric and have orthogonal coneigenvectors. For forward scattering the term homogeneous is used in this case. Recently, inhomogeneous Jones and Sinclair matrices characterized by non-orthogonal eigenvectors and coneigenvectors have attracted attention. The present contribution considers some characteristics of these matrices. In particular it is shown that the graphical field-of-value representation of inhomogeneous Jones matrices leads to an interesting characterization of the degree of inhomogeneity, often characterized by the (cosine of the) angle between the normalized eigenvectors. Applications of the resulting theorems to both optical (transmission) and radar (backscattering) polarimetry are demonstrated, together with identifying the inherent mathematical intricacies and physical complexities which are integral to radar and optical polarimetry