Invariant indices of polarimetric purity

Sets of orthogonal three-dimensional polarization states and their physical interpretation

“…, where I is the 3 × 3 identity matrix and P 1 , P 2 are the so-called indices of polarimetric purity (IPP) [28], defined as…”

Polarimetric purity and the concept of degree of polarization

“…The ability of P 3D to represent the degree of polarization (or degree of polarimetric purity) for electromagnetic waves, as well as some important features, has been studied by Setälä et al [8,[15][16][17] as well as by Gil et al [2,12,18,19]. It is worth noting that the mathematical definition of P 3D is, in fact, the 3D analog of the degree of polarimetric purity, P 4D , for the 4 × 4 Mueller matrices (depolarization index [20]) representing the transformation of polarization states by the action of a material medium [2].…”

“…It should be stressed that, in the case of 2D representation, P 2D is precisely the conventional 2D degree of polarization [19]. At this point, it is worth recalling that a generic concept of the nD polarization matrix can be applied in many different situations, like the superposition of n pencils of electromagnetic radiation (second-order statistics of n optical beams), which was formulated, very early on, by Wiener [21].…”

Purity indices yield more complete data than entropy

“…The overall degree of purity, P 3 , is derived from the first two indices of purity through a weighted quadratic average. 1 The indicated approach can be extended to characterize the polarimetric purity of material samples 1,3,4 in such a manner that the corresponding 4D purity space (see Figure 2) is built from a set of three indices of purity, P 1 , P 2 , P 3 , thereby satisfying 0 Ä P 1 Ä P 2 Ä P 3 Ä 1, which provide the complete required information and open non-destructive polarimetric techniques to a wide range of applications including medicine, remote sensing, and industry. These results have allowed us to establish a generalized polarization algebra 2, 3 as a common mathematical framework for polarized light (2D and 3D) and for the description of the polarimetric properties of material samples.…”

“…These are just a few of the applications for and significance of the indices of purity, which can be easily defined for Continued on next page 10.1117/2.1201306.004944 Page 2/2 covariance or density matrices of any dimensionality. 4 Our work has enabled us to show that, given a system characterized by n stochastic variables, the statistical purity of the system is determined by a set of n-1 nested indices P i (i D 1,2, . . .…”