Recently, a set of polarimetric indicators, the Indices of Polarimetric Purity (IPPs), were described in the literature. These indicators allow synthesize depolarization content of samples, and provide further analysis of depolarizers than other existing polarimetric indicators. We demonstrate the potential of the IPPs as a criterion to characterize and classify depolarizing samples. In particular, the method is firstly analyzed through a series of basic polarization experiments, and we prove how differences in the depolarizing capability of samples, concealed from the commonly used depolarization index PΔ, are identified with the IPPs.
In the second part of this work, the method is experimentally highlighted by studying a rabbit leg ex-vivo sample. The obtained images of the ex-vivo sample illustrate how IPPs provide a significant enhancement in the image contrast of some biological tissues and, in some cases, present new information hidden in the usual polarimetric channels. Moreover, new physical interpretation of the sample can be derived from the IPPs which allow us to synthesize the depolarization behavior.
Finally, we also propose a pseudo-colored encoding of the IPPs information that provides an improved visualization of the samples. This last technique opens the possibility to highlight a specific tissue structure by properly adjusting the pseudo-colored formula.
We highlight the interest of using the Indices of Polarimetric Purity (IPPs) for the biological tissue inspection. These are three polarimetric metrics focused on the study of the depolarizing behaviour of the sample. The IPPs have been recently proposed in the literature and provide different and synthetized information than the commonly used depolarizing indices, as depolarization index (PΔ) or depolarization power (Δ). Compared with the standard polarimetric images of biological samples, IPPs enhance the contrast between different tissues of the sample and show differences between similar tissues which are not observed using the other standard techniques. Moreover, they present further physical information related to the depolarization mechanisms inherent to different tissues. In addition, the algorithm does not require advanced calculations (as in the case of polar decompositions), being the indices of polarimetric purity fast and easy to implement. We also propose a pseudo-coloured image method which encodes the sample information as a function of the different indices weights. These images allow us to customize the visualization of samples and to highlight certain of their constitutive structures. The interest and potential of the IPP approach are experimentally illustrated throughout the manuscript by comparing polarimetric images of different ex-vivo samples obtained with standard polarimetric methods with those obtained from the IPPs analysis. Enhanced contrast and retrieval of new information are experimentally obtained from the different IPP based images.
The polarimetric properties of a material medium are summarized in the sixteen elements of its associated Mueller matrix. The quantities carrying specific information on the significant polarimetric features have to be defined on the basis of the analysis of the mathematical structure of Mueller matrices. It is found that any Mueller matrix can be parameterized through two retardance vectors and ten quantities that are invariant under dual retarder transformations. This parameterization leads to proper definitions of the retardance and depolarization properties, which together with the diattenuation and polarizance properties provide complete polarimetric characterization of the sample under consideration.
The measured Mueller matrices contain until sixteen independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of incidence, observation direction...) and for each spatially resolved element of the sample (imaging polarimetry). Thus, the polarimetric techniques are widely used for the study of a great variety of material samples in optics and remote sensing. Nevertheless, the relevant physical information does not appear explicitly in the measured parameters and thus the best knowledge of the structure of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. In this paper, the physically invariant polarimetric quantities are identified and decoupled, and the main approaches for serial and parallel decompositions of measured Mueller matrices into simple components are reviewed.
The physical magnitudes involved in polarimetric phenomena are studied under a unified mathematical model based on coherency matrices. These magnitude arise as the real coefficients of the expansion of the coherency matrices on the basis constituted by n-1 the generators of SU(n) group and the nxn identity matrix. The states of polarization of light beams are analyzed in the general case where the three components of the wave field must be considered. The 3D polarization magnitudes are obtained and two non-dimensional invariant magnitudes are defined to represent the stability of the polarization ellipse and the stability of the propagation direction. These "indices of purity" derive in the well known degree of polarization when the propagation direction does not fluctuate. The model is also applied to the polarimetric properties of material media, where three non-dimensional invariant "indices of purity" are defined to represent the mixture of pure components resulting in depolarization behavior of the media as a whole.