Abstract
Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others. For each given scattering measurement configuration, absolute Mueller polarimeters provide the most complete polarimetric information, intricately encoded in the 16 parameters of the corresponding Mueller matrix. Thus, the determination of the mathematical structure of the polarimetric information contained in a Mueller matrix constitutes a topic of great interest. In this work, besides a structural decomposition that makes explicit the role played by the diattenuation-polarizance of a general depolarizing medium, a universal synthesizer of Muller matrices is developed. This is based on the concept of an enpolarizing ellipsoid, whose symmetry features are directly linked to the way in which the polarimetric information is organized.
Highlights
Instituto Aragonés de Estadística, Gobierno de Aragón, Bernardino Ramazzini 5, 50015 Zaragoza, Spain; Abstract: Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others
This is based on the concept of an enpolarizing ellipsoid, whose symmetry features are directly linked to the way in which the polarimetric information is organized
The serial and parallel compositions of different kinds of pure media, the coherency matrix associated with a Mueller matrix, the arrow form of a Mueller matrix, etc., together with some original approaches presented in this work such as the structured composition–decomposition of a Mueller matrix and the enpolarizing ellipsoid
Summary
Instituto Aragonés de Estadística, Gobierno de Aragón, Bernardino Ramazzini 5, 50015 Zaragoza, Spain; Abstract: Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others. Among the different techniques for determining the polarimetric properties of material media, absolute (or complete) Mueller polarimetry is prominent because the measured Mueller matrix for each experimental configuration (transmission, reflection, scattering, angle of incidence and observation, spectral profile and spot-size of the probing light, measurement time, etc.) provides up to 16 independent parameters. Such parameters contain complete information of the second-order properties of the medium regarding its linear polarimetric interaction with the probing electromagnetic wave, but they are affected by bilinear and quadratic constraining inequalities derived from the physical exigency that the eigenvalues of the positive semidefinite Hermitian coherency matrix C associated with a given Mueller matrix M are nonnegative. A way to understand the physical information provided by M is to design a general algebraic or geometric synthesizer of Mueller matrices, where the way in which the overall polarimetric properties are generated arises in a natural manner
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