Purity-depolarization relations and the components of purity of a Mueller matrix

A comprehensive physically realizable space, namely, the overall purity index-components of purity (PI_4D-CP) space is proposed for the characterization of the depolarization caused by random (or deterministic) media. The overall purity index (PI_4D)is obtained via indices of polarimetric purity which are incurred by the eigenvalues of the covariance matrix, whereas the components of purity (CP) are the functions of the elements of a Mueller matrix. On the one hand, the proposed space is useful in studying the depolarization caused by material media and on the other hand, it provides information on the diattenuation-polarizance properties of a Mueller matrix. Thus, it gives a remarkable physical insight of the depolarization problem.