Information structure and general characterization of Mueller matrices

Gil, José J.; José, Ignacio San

doi:10.1364/josaa.448255

Cited by 9 publications

(4 citation statements)

References 38 publications

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“…Because of the fundamental role that P S plays in subsequent analyses, it is worth considering it in more detail by noting that the name degree of spherical purity originally coined for P S [9,16] comes from the fact that both the I-image and the characteristic ellipsoid [16,18] associated with M are spherical if and only if P S = 1. On the other hand, from a statistical point of view, P S can be expressed as [16,19]…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…where σ 2 k represent the variances of the coherency matrix (denoted by C) associated with M, so that P S formally adopts the form of the Mueller-algebra version of the dimensionality index defined originally for 3D polarization matrices [20] and then generalized for n-dimensional density matrices [21]. In contrast to the generic dimensionality index of a density matrix ρ defined from the variances of the symmetric matrix constituting the real part of ρ, P S is defined from the variances of C, which determine the diagonal elements of M by means of simple linear relations [19]…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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Thermodynamic Reversibility in Polarimetry

Gil

2022

Photonics

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The action of linear media on incident polarized electromagnetic waves can produce two kinds of thermodynamic irreversible effects, namely, loss of intensity, in general anisotropic, and reduction of the degree of polarization. Even though both phenomena can be described through specific properties, the overall degree of reversibility of polarimetric interactions can be characterized by means of a single parameter whose minimum and maximum values are achieved by fully irreversible and reversible polarimetric transformations, respectively. Furthermore, the sources of irreversibility associated to the entire family of Mueller matrices proportional to a given one are identified, leading to the definition of the specific reversibility as the square average of the degree of polarimetric purity and the polarimetric dimension index. The feasible values of the degree of reversibility with respect to the mean intensity coefficient and the degree of polarimetric purity are analyzed graphically, and the iso-reversibility branches are identified and analyzed. Furthermore, the behavior of the specific reversibility with respect to the achievable values of the polarimetric dimension index and the degree of polarizance is described by means of the purity figure, and it is compared to the iso-purity elliptical branches in such figure.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Thermodynamic Reversibility in Polarimetry

Gil

2022

Photonics

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“…where m 00 is the mean intensity coefficient (MIC), i.e., the transmittance or reflectance for incident unpolarized light; D and P are the diattenuation and polarizance vectors, with absolute values D (diattenuation) and P (polarizance); and m is a 3×3 submatrix. The positive semidefiniteness of the covariance matrix H associated with (the generally depolarizing) M leads to a general characterization of Mueller matrices through the nonnegativity property of the four eigenvalues (λ 0 , λ 1 , λ 2 , λ 3 ) of H (expressed through four covariance conditions) or through other formulations equivalent to it [9][10][11][15][16][17][18][19][20][21][22]. In addition, the fact that passive polarimetric interactions do not amplify the intensity of incident light leads to the additional passivity condition m 00 (1 + Q) ≤ 1 where Q ≡ max (D, P) [11,23].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Physical Significance of the Determinant of a Mueller Matrix

2022

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The determinant of a Mueller matrix M plays an important role in both polarization algebra and the interpretation of polarimetric measurements. While certain physical quantities encoded in M admit a direct interpretation, the understanding of the physical and geometric significance of the determinant of M (detM) requires a specific analysis, performed in this work by using the normal form of M, as well as the indices of polarimetric purity (IPP) of the canonical depolarizer associated with M. We derive an expression for detM in terms of the diattenuation, polarizance and a parameter proportional to the volume of the intrinsic ellipsoid of M. We likewise establish a relation existing between the determinant of M and the rank of the covariance matrix H associated with M, and determine the lower and upper bounds of detM for the two types of Mueller matrices by taking advantage of their geometric representation in the IPP space.

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“…The main advantage of polarimetric observables is that they present physical interpretation of the samples and focus on some characteristics that may be relevant in terms of contrast or classificatory potential, as can be the dichroism, retardance or depolarization associated to structures of interest. All those polarimetric observables can be deduced from the experimental measured Mueller matrix [35][36][37] of the sample, which represents the polarimetric transfer function of a polarimetric system, thus including all measurable information on linear polarimetric light-matter transformations [38]. As will be provided throughout this work, this situation places the MM coefficients as the ideal framework to establish comparisons with other MM-derived observables.…”

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confidence: 99%

Optimizing the classification of biological tissues using machine learning models based on polarized data

Rodríguez

Estévez

González‐Arnay

et al. 2022

Journal of Biophotonics

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Polarimetric data is nowadays used to build recognition models for the characterization of organic tissues or the early detection of some diseases. Different Mueller matrix‐derived polarimetric observables, which allow a physical interpretation of a specific characteristic of samples, are proposed in literature to feed the required recognition algorithms. However, they are obtained through mathematical transformations of the Mueller matrix and this process may loss relevant sample information in search of physical interpretation. In this work, we present a thorough comparative between 12 classification models based on different polarimetric datasets to find the ideal polarimetric framework to construct tissues classification models. The study is conducted on the experimental Mueller matrices images measured on different tissues: muscle, tendon, myotendinous junction and bone; from a collection of 165 ex‐vivo chicken thighs. Three polarimetric datasets are analyzed: (A) a selection of most representative metrics presented in literature; (B) Mueller matrix elements; and (C) the combination of (A) and (B) sets. Results highlight the importance of using raw Mueller matrix elements for the design of classification models.

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Information structure and general characterization of Mueller matrices

Cited by 9 publications

References 38 publications

Thermodynamic Reversibility in Polarimetry

Thermodynamic Reversibility in Polarimetry

Physical Significance of the Determinant of a Mueller Matrix

Optimizing the classification of biological tissues using machine learning models based on polarized data

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