Interpretation of Mueller matrices based on polar decomposition
01 May 1996-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 13, Iss: 5, pp 1106-1113
TL;DR: In this paper, the authors decompose a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by depolarizer.
Abstract: We present an algorithm that decomposes a Mueller matrix into a sequence of three matrix factors: a diattenuator, followed by a retarder, then followed by a depolarizer. Those factors are unique except for singular Mueller matrices. Based on this decomposition, the diattenuation and the retardance of a Mueller matrix can be defined and computed. Thus this algorithm is useful for performing data reduction upon experimentally determined Mueller matrices.
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TL;DR: The foundations of passive imaging polarimetry, the phenomenological reasons for designing a polarimetric sensor, and the primary architectures that have been exploited for developing imaging polarimeters are discussed.
Abstract: Imaging polarimetry has emerged over the past three decades as a powerful tool to enhance the information available in a variety of remote sensing applications. We discuss the foundations of passive imaging polarimetry, the phenomenological reasons for designing a polarimetric sensor, and the primary architectures that have been exploited for developing imaging polarimeters. Considerations on imaging polarimeters such as calibration, optimization, and error performance are also discussed. We review many important sources and examples from the scientific literature.
1,374 citations
TL;DR: A summary of issues pertinent to the polarized light methodologies in tissues, including polarized light basics, Stokes-Muller formalism, methods of polarization measurements, polarized light modeling in turbid media, applications to tissue imaging, inverse analysis for polarimetric results quantification, Applications to quantitative tissue assessment, etc.
Abstract: Polarimetry has a long and successful history in various forms of clear media. Driven by their biomedical potential, the use of the polarimetric approaches for biological tissue assessment has also recently received considerable attention. Specifically, polarization can be used as an effective tool to discriminate against multiply scattered light (acting as a gating mechanism) in order to enhance contrast and to improve tissue imaging resolution. Moreover, the intrinsic tissue polarimetry characteristics contain a wealth of morphological and functional information of potential biomedical importance. However, in a complex random medium-like tissue, numerous complexities due to multiple scattering and simultaneous occurrences of many scattering and polarization events present formidable challenges both in terms of accurate measurements and in terms of analysis of the tissue polarimetry signal. In order to realize the potential of the polarimetric approaches for tissue imaging and characterization/diagnosis, a number of researchers are thus pursuing innovative solutions to these challenges. In this review paper, we summarize these and other issues pertinent to the polarized light methodologies in tissues. Specifically, we discuss polarized light basics, Stokes-Muller formalism, methods of polarization measurements, polarized light modeling in turbid media, applications to tissue imaging, inverse analysis for polarimetric results quantification, applications to quantitative tissue assessment, etc.
540 citations
Cites background from "Interpretation of Mueller matrices ..."
...(23), any possible state of polarization can be generated by selectively varying δ1 and δ2....
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TL;DR: The relationship between system condition and signal-to-noise ratio (SNR) in reconstructed Stokes parameter images is investigated for rotating compensator, variable retardance, and rotating analyzer Stokes vector (SV) polarimeters and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters.
Abstract: The relationship between system condition and signal-to-noise ratio (SNR) in reconstructed Stokes parameter images is investigated for rotating compensator, variable retardance, and rotating analyzer Stokes vector (SV) polarimeters. A variety of optimal configurations are presented for each class of systems. The operation of polarimeters is discussed in terms of a four-dimensional conical vector space; and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters. Although SNR is an important consideration, performance of a polarimeter in the presence of errors in the calibration and alignment of the optical components is also important. The relationship between system condition and error performance is investigated, and it is shown that an optimum system from the point of view of SNR is not always an optimum system with respect to error performance. A detailed theory of error performance is presented, and the error of a SV polarimeter is shown to be related to the stability and condition number of the polarization processing matrices. The rms error is found to fall off as the inverse of the number of measurements taken. Finally, the concepts used to optimize SV polarimeters are extended to be useful for full Mueller matrix polarimeters.
318 citations
TL;DR: Polarization sensitive (PS) OCT draws advantage from the fact that several materials and tissues can change the light's polarization state, adding an additional contrast channel and providing quantitative information.
Abstract: Optical coherence tomography (OCT) is now a well-established modality for high-resolution cross-sectional and three-dimensional imaging of transparent and translucent samples and tissues. Conventional, intensity based OCT, however, does not provide a tissue-specific contrast, causing an ambiguity with image interpretation in several cases. Polarization sensitive (PS) OCT draws advantage from the fact that several materials and tissues can change the light's polarization state, adding an additional contrast channel and providing quantitative information. In this paper, we review basic and advanced methods of PS-OCT and demonstrate its use in selected biomedical applications.
269 citations
TL;DR: 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, which constitutes a powerful tool for analyzing and exploiting experimental and industrial polarimetry.
Abstract: 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.
239 citations
References
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Journal Article•
TL;DR: In this paper, the authors propose an approach unifiee a l'algebre de la polarisation en utilisant les groupes unitaires speciaux SU(2) et SU(4) and leurs homomorphismes respectifs.
298 citations
TL;DR: In this paper, the classification of polarization properties of polarization elements is studied to derive data-reduction equations for extracting the diattenuation, retardance, and other polarization properties from their Jones matrices.
Abstract: The classification of polarization properties of polarization elements is studied to derive data-reduction equations for extracting the diattenuation, retardance, and other polarization properties from their Jones matrices. Polarization elements, and Jones matrices as well, are divided into two classes: homogeneous, with orthogonal eigenpolarizations, and inhomogeneous, with nonorthogonal eigenpolarizations. The basic polarization properties, diattenuation and retardance, of homogeneous polarization elements are straightforward and well known; these elements are characterized by their eigenvalues and eigenpolarizations. Polarization properties of inhomogeneous polarization elements are not so evident. By applying polar decomposition, the definitions of diattenuation and retardance are generalized to inhomogeneous polarization elements, providing an understanding of their polarization characteristics. Furthermore, an inhomogeneity parameter is introduced to describe the degree of inhomogeneity in a polarization element. These results are then adapted to degenerate polarization elements, which have only one linearly independent eigenpolarization.
261 citations
Journal Article•
TL;DR: Les proprietes de polarisation et de retard sont donnees par les parametres du polariseur partiel elliptique equivalent and du retardateur elliptique equivalent, which forme un systeme optique equivalent.
219 citations
TL;DR: In this article, the authors consider methods suitable for analyzing systems for which the assumption of uniform amplitude and constant polarization state is not valid, and define the basic classes of polarization phenomena and a review of the Jones calculus are included to form a basis for the discussion.
Abstract: For most optical systems it is typically assumed that the transmitted wavefront has uniform for Gaussian) amplitude and constant polarization state. This is the default assumption of geometrical optics. This paper considers methods suitable for analyzing systems for which this assumption is not valid. Such methods of polarization analysis include polarization ray tracing and polarization aberration theory. Definitions of the basic classes of polarization phenomena and a review of the Jones calculus are included to form a basis for the discussion.
142 citations
TL;DR: In this article, it was shown that a Mueller matrix can be expressed as a linear combination of at most four trace orthonormal Mueller-Jones matrices, and an algorithm for the construction was given.
Abstract: Necessary and sufficient conditions for an optical system characterized by a Mueller matrix to be characterized by a Mueller–Jones, and thence by a Jones, matrix are considered, and the issue of measurement error is examined. It is shown that a Mueller matrix can be expressed as a linear combination of at most four trace orthonormal Mueller–Jones matrices, and an algorithm for the construction is given.
141 citations