Parallel decompositions have proved to be powerful tools for the analysis and interpretation of the physical information provided by Mueller matrices experimentally obtained. In this work, the procedure for the so-called arbitrary decomposition of Mueller matrices is validated through its application to a set of representative experimentally determined Mueller matrices. The covariance and passivity criteria required for the physical realizability of the Mueller matrices involved in the parallel decompositions are integrated in the procedure, which ensures the physical consistency of the results presented.

Through the arrow decomposition of the Mueller matrix, respective sets of sixteen independent polarimetric images of biological tissues are obtained for enpolarizing, retarding and depolariz-ing descriptors. In addition to the mean intensity coefficient and the three indices of polarimetric purity, the absolute values and Poincaré orientations of diattenuation, polarizance, entrance re-tardance and exit retardance vectors are considered. In this work we use for the first time this set of polarimetric observables for the visualization of biological structures, both of animal and vege-tal origin. Results show images with enhanced visualization derived from the spatial variation of such significant polarimetric properties. The experimental results are discussed, showing the suit-ability of such set of observables for applications in biophotonics imaging, providing not only ex-cellent visualization of biological tissues, but also showing structures not visible in non-polarimetric images.

The transformation of the state of polarization of a light beam by its linear interaction with a material medium can be modeled through the Stokes-Mueller formalism. The Mueller matrix associated with a given interaction depends on many aspects of the measurement configuration. In particular, different Mueller matrices can be measured for a fixed material sample depending on the spectral profile of the light probe. For a given light probe and a given sample with inhomogeneous spatial behavior, the polarimetric descriptors of the point-to-point Mueller matrices can be mapped leading to respective polarimetric images. The procedure can be repeated sequentially by using light probes with different central frequencies. In addition, the point-to-point Mueller matrices consecutively measured can be combined synthetically through convex sums leading to respective new Mueller matrices, in general with increased polarimetric randomness, thus exhibiting specific values for the associated polarimetric descriptors, including the indices of polarimetric purity, and generating new polarimetric images which are different from those obtained from the original Mueller matrices. In this work, the fundamentals for such synthetic generation of additional polarimetric images are described, providing a new tool that enhances the exploitation of Mueller polarimetry.

The transformation of the states of polarization of electromagnetic waves that interact with polarimetrically linear media can be represented by means of the associated Mueller matrix. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as a distance of the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion transforms the Stokes quaternion for depolarizing process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general, quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.