Components of purity of a three-dimensional polarization state

The degree of polarimetric purity of a three-dimensional (3D) polarization state is a measure of the closeness to a pure state and can be expressed as a weighted quadratic average of two indices of polarimetric purity, invariant with respect to unitary transformations and defined in terms of the relative weights of certain incoherent components of the state. An alternative view of the polarimetric purity is formulated in terms of three contributions, namely, the degree of directionality, the degree of linear polarization, and the degree of circular polarization. While the indices of polarimetric purity give complete information on the structure of randomness but are insensitive to other attributes of the state of polarization, the three components of purity are invariant under orthogonal transformations (rotations in the real space) and provide a meaningful framework for the representation of 3D polarization states in terms of quantities that are intrinsic for each given state.