Target detection with a liquid crystal-based passive Stokes polarimeter

International audienceWe present an imaging system that measures the polarimetric state of the light coming from each point of a scene. This system, which determines the four components of the Stokes vector at each spatial location, is based on a liquid-crystal polarization modulator, which makes it possible to acquire fourdimensional Stokes parameter images at a standard video rate. We show that using such polarimetric images instead of simple intensity images can improve target detection and segmentation performance

Modèles sous-jacents à certaines techniques d'interpolation géodésique dans l'espace des matrices de cohérence en optique de polarisation

International audienceNous montrons au travers de l'exemple particulier des matrices de cohérence optique, qu'il est possible de mettre en évidence des modèles physiques sous-jacents à différentes solutions d'interpolation de ces matrices au moyen de courbes géodésiques. Le choix de la méthode d'interpolation dépend donc de connaissances a priori que l'on a sur les données à traiter. Nous développons cette idée en conclusion à partir de la notion de matrices de covariance globale

Spatial propagation of coherency matrix in polarization optics

International audienceIn this work, the question of the coherency matrix propagation of a light beam is addressed by means of the analysis of interpolation processes between two physical situations. These physical situations are defined according to the second order statistical properties of the underlying process. Two states of a light beam or the path in a medium to go from a physical situation at distance z1 to another one at distance z2 is related to the correlation between both these physical situations. Equivalence classes are derived from the definition of a group action on the set of coherency matrices. The geodesic curves on each equivalence class define the process of interpolation. The general solution is derived as a symbolic equation, and the solution is explicitly developed for the situation of uncorrelated statistical processes. Interpolating coherency matrix in this particular case describes the propagation of a light beam into a uniform nondepolarizing medium characterized by a differential Jones matrix determined by the far points of the interpolation curve up to a unitary matrix

Mueller matrix interpolation in polarization optics

International audienceThe question of the physical significance of the Mueller matrix average is addressed by means of an analysis of interpolation processes. We draw a comparison between two interpolation processes. The first one is related to the classical Euclidean metrics and the second one is based on the log-Euclidean metrics. Both the associated interpolation procedures are depicted with their underlying physical models. Addressing the question of the physical meaning of the log-Euclidean process of interpolation is founded on a very similar approach to the layered-medium interpretation proposed by Jones [J. Opt. Soc. Am. 38, 671 (1948)] in the seventh paper of his series. Based on the analysis of their respective properties, we eventually show that the choice between both these interpolation processes may depend on what statistical situation is considered or what underlying physical model is assumed

Depolarizing differential Mueller matrix of homogeneous media under Gaussian fluctuation hypothesis

International audienceIn this paper, we address the issue of the existence of a solution of depolarizing differential Mueller matrix for a homogeneous medium. Such a medium is characterized by linear changes of its differential optical properties with z the thickness of the medium. We show that under a short correlation distance assumption, it is possible to derive such linear solution and we clarify this solution in the particular case where the random fluctuations processes associated to the optical properties are Gaussian white noise-like. A solution to the problem of non-commutativity of a previously proposed model [J. Opt. Soc. Am. 30, 2196 (2013)] is given by assuming a random permutation of the order of the layers and by averaging all the differential matrices resulting from these permutations. It is shown that the underlying assumption in this case is exactly the Gaussian white noise assumption. Finally, a recently proposed approach [Opt. Lett. 39, 4470 (2014)] for analysis of the statistical properties related to changes in optical properties is revisited and the experimental conditions of application of these results are specified

Etude des bruits numeriques dans les structures de filtres a coefficients fixes : application a l'arithmetique classique et a l'arithmetique distribuee

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A physical model of differential Mueller matrix for depolarizing uniform media

Based on a layered-medium interpretation, Jones introduced the concept of “N-matrices ” in the seventh paper of his series [1]. He also derived a differential equation governing the evolution of the state of polarization for a totally polarized light beam propagating through a linear and non depolarizing medium: d

Geodesic distance on non-singular coherency matrix space in polarization optics

International audienceWe define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of this geodesic distance and the classical Euclidean one and their appropriateness for interpixel comparisons in a context of imaging polarimetry. Finally, results are presented for a geodesic version of the classical K-means clustering algorithm with simulated data and real data. The results demonstrate the advantages of the geodesic approach

Definition of a parametric form of nonsingular Mueller matrices

International audienceThe goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of degrees of freedom and explain why subsets of O 5,1 , the orthogonal group associated with six-dimensional Minkowski space, is a physically admissible solution to this question. Generators of this group are used to define possible expressions of an arbitrary nonsingular Mueller matrix. Ultimately, the problem of decomposition of these matrices is addressed, and we point out that the "reverse" and "forward" decomposition concepts recently introduced may be inferred from the formalism we propose