An objective analysis is carried out of the matricial models representing the polarimetric properties of light and material media leading to the identification and definition of their corresponding physical quantities, using the concept of the coherency matrix. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is constructed. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic nondepolarizing transformations. Through this framework, the relevant physical quantities, including indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.

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Polarimetric characterization of light and media - Physical quantities involved in polarimetric phenomena

A product decomposition of a depolarizing Mueller matrix consisting in the sequence of five factors—a diagonal depolarizer stacked between two retarder and diattenuator pairs—is proposed. This novel “symmetric” decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on experimentally determined Mueller matrices.

Analysis of depolarizing Mueller matrices through a symmetric decomposition.

We propose a new algorithm, the pseudopolar decomposition, to decompose a Jones or a Mueller-Jones matrix into a sequence of matrix factors: J≅JRJDJ1CJ2C or M≅MRMDM1CM2C. The matrices JR(MR) and JD(MD) parameterize, respectively, the retardation and dichroic properties of J(M) in a good approximation, while JiC(MiC) are correction factors that arise from the noncommutativity of the polarization properties. The exponential versions of the general Jones matrix are used to demonstrate the pseudopolar decomposition and to calculate each one of the matrix factors. The decomposition preserves all the polarization properties of the system on the factorized JR(MR) and JD(MD) matrix terms. The algorithm that calculates the pseudopolar decomposition for experimentally determined Mueller matrices is presented.

Pseudopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices.

Conversion of 3×3 Mueller matrix to 4×4 Mueller matrix for non-depolarizing samples

The measured Mueller matrices contain up to 16 independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of inci- dence, observation direction, etc.) 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 struc- ture of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. The main approaches for serial and parallel decompositions as well as for the geometric representation of measured Mueller matrices are reviewed. Furthermore, the physically invariant polarimetric quantities are identified and decoupled. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the origi- nal publication, including its DOI. (DOI: 10.1117/1.JRS.8.081599)

Review on Mueller matrix algebra for the analysis of polarimetric measurements

A generalized equivalence theorem for polarization theory is formulated and proven. It is shown that anisotropic properties of homogeneous nondepolarizing media can be presented as a combination of four basic mechanisms: linear and circular phase and linear and circular amplitude anisotropy. Expressions for the generalized effect operators of algebraic (or operator) optics are obtained and the inverse problem of crystal optics is solved in terms of physically realizable anisotropy parameters.

Generalized matrix equivalence theorem for polarization theory.

The problem of measurement of block-diagonal scattering matrix as being part of the so-called incomplete or partial Mueller polarimetry is addressed. It has been shown that non-zero elements of the scattering matrix with block-diagonal structure can be measured using only two elliptical polarizations of input light. Optimal pairs of these polarizations are derived. Utilization of the optimal input polarizations results in halving measurement time and decreasing measurement errors by 30%.

Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

The problem of measurement of the block-diagonal scattering matrix is addressed. It has been shown that non-zero elements of the scattering matrix with block-diagonal structure can be measured using only two polarizations of input radiation. Optimal pairs of these polarizations are derived. Utilization of the optimal input polarization results in half the measurement time and a decrease in measurement errors of approximately 30%.

E. Oberemok

Papers

Generalized matrix equivalence theorem for polarization theory.

Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

Measurement of block-diagonal scattering matrix