Eigenvectors of polarization coherency matrices

Sheppard, Colin J. R.; Bendandi, Artemi; Gratiet, Aymeric Le; Diaspro, Alberto

doi:10.1364/josaa.391902

Cited by 11 publications

(14 citation statements)

References 37 publications

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“…Such a barycentric eigenvalue space has been described as a way of representing a general depolarizing transformation in Refs. [87,91,92]. The origin represents a perfect depolarizer.…”

Section: Barycentric Eigenvalue Spacementioning

confidence: 99%

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

et al. 2022

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Depolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples.

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“…Such a barycentric eigenvalue space has been described as a way of representing a general depolarizing transformation in Refs. [87,91,92]. The origin represents a perfect depolarizer.…”

Section: Barycentric Eigenvalue Spacementioning

confidence: 99%

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

et al. 2022

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“…A depolarization space gives information not just on how much light is depolarized but also on how it is depolarized by the sample. The definition of a depolarization space is not unique 52 , 53 and a choice must be done based on multiple criteria such as discrimination power between depolarization metrics, computation time, adequacy to the physical problem treated among others 54 . The depolarization space used in this work is composed by the IPPs 55 , which can be directly deduced from the measured Mueller matrix of the sample.…”

Section: Methodsmentioning

confidence: 99%

Polarimetric imaging microscopy for advanced inspection of vegetal tissues

Eeckhout

García-Caurel

Garnatje

et al. 2021

Sci Rep

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Optical microscopy techniques for plant inspection benefit from the fact that at least one of the multiple properties of light (intensity, phase, wavelength, polarization) may be modified by vegetal tissues. Paradoxically, polarimetric microscopy although being a mature technique in biophotonics, is not so commonly used in botany. Importantly, only specific polarimetric observables, as birefringence or dichroism, have some presence in botany studies, and other relevant metrics, as those based on depolarization, are underused. We present a versatile method, based on a representative selection of polarimetric observables, to obtain and to analyse images of plants which bring significant information about their structure and/or the spatial organization of their constituents (cells, organelles, among other structures). We provide a thorough analysis of polarimetric microscopy images of sections of plant leaves which are compared with those obtained by other commonly used microscopy techniques in plant biology. Our results show the interest of polarimetric microscopy for plant inspection, as it is non-destructive technique, highly competitive in economical and time consumption, and providing advantages compared to standard non-polarizing techniques.

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“…The Poincaré sphere [1] provides a simple and meaningful representation of those polarization states whose electric field fluctuates in a fixed plane (2D states). Despite the interest of such a particular type of polarization states, which is commonly applied in many problems involving paraxial fields and is characterized through the conventional four Stokes parameters [2], or (equivalently) by means of the 2 × 2 polarization matrix (or coherency matrix) [3][4][5][6][7][8], the description of a general polarization state involves nine generalized Stokes parameters [9][10][11][12][13][14][15][16][17][18][19][20][21][22] instead of the conventional four ones, and therefore their geometric representation through a generalized Poincaré sphere is determined by an eight-dimensional object, which does not admit a simple geometric and physical interpretation.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the geometric representation introduced by Dennis [33] for general three-dimensional (3D) polarization states is studied and interpreted in terms of the intrinsic Stokes parameters [21] and other meaningful descriptors that are invariant under rotations of the reference frame [17][18][19][20][21][22][33][34][35][36][37][38][39][40][41][42][43][44][45]. The classification introduced in Refs.…”

Section: Introductionmentioning

confidence: 99%

Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

Gil

2021

Photonics

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In contrast with what happens for two-dimensional polarization states, defined as those whose electric field fluctuates in a fixed plane, which can readily be represented by means of the Poincaré sphere, the complete description of general three-dimensional polarization states involves nine measurable parameters, called the generalized Stokes parameters, so that the generalized Poincaré object takes the complicated form of an eight-dimensional quadric hypersurface. In this work, the geometric representation of general polarization states, described by means of a simple polarization object constituted by the combination of an ellipsoid and a vector, is interpreted in terms of the intrinsic Stokes parameters, which allows for a complete and systematic classification of polarization states in terms of meaningful rotationally invariant descriptors.

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Eigenvectors of polarization coherency matrices

Cited by 11 publications

References 37 publications

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Polarimetric imaging microscopy for advanced inspection of vegetal tissues

Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

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