Dual Approaches to Express the Generalized Degree of Polarimetric Purity

The degree of polarimetric purity is an invariant dimensionless quantity that characterizes the closeness of a polarization state of a wave to a pure state and is related to the Von Neumann entropy. The polarimetric purity of a plane wave characterized by the second-order statistics (i.e., the covariance matrix) is uniquely described by the degree of polarization. However, the 2D formalism is only applicable when the wave propagation direction is fixed. This assumption is typical in optical and radar polarimetric measurements. Therefore, one must consider all the components to describe the general state of wave polarization. Starting from Samson and Barakat, several different concepts have been proposed in the literature to describe the 3D degree of polarization. We discuss two new ways of achieving such description: by the Coefficient of Variation and by a Direct Sum Decomposition.