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

Dual Approaches to Express the Generalized Degree of Polarimetric Purity