Localization and characterization of simple defects in finite-size photonic crystals

Structured materials like photonic crystals require for optimal use a high precision both on position and optical characteristics of the components which they are made of. Here, we present a simple tomographic algorithm, based on a specific Green's function together with a first-order Born approximation, which enables us to localize and characterize identical defects in finite-size photonic crystals. This algorithm is proposed as a first step to the monitoring of such materials. Illustrative numerical results show in particular some possibility of focalization beyond the Rayleigh criterion.Comment: submitted to Journal of the Optical Society of America

Bases de données séquentielles et méthodes inverses appliquées au CND par courants de Foucault.

1pLe but de cette étude est de développer une méthode d'optimisation capable, en temps réel, de donner un résultat fiable de Contrôle Non Destructif par Courants de Foucault (CND-CF). On utilise des bases de données séquentielles à partir desquelles il est possible de générer des données par interpolation tout en maîtrisant l'erreur maximale d'interpolation. Ces bases de données sont ensuite utilisées avec des méthodes d'optimisation afin de résoudre le problème de CND. D'une part, elles servent à générer rapidement des signaux utilisés par des méthodes d'optimisation particulaires, ici le PSO (Particle Swarm Optimizer). Cela permet d'accélérer considérablement la méthode PSO avec en contrepartie une perte en précision due à l'interpolation. D'autre part, elles sont utilisées comme bases d'apprentissage pour une méthode d'inversion par SVM (Support Vectors Machines). On obtient ainsi deux méthodes rapides, l'une particulaire et l'autre par apprentissage, permettant de mesurer les dimensions des défauts que l'on désire retrouver. Des premiers résultats sont exposés et les deux méthodes d'inversion sont comparées

Particle optimization with metamodel for crack characterization

International audienceA new inverse method for real time eddy current testing is introduced. It is based on particle swarm optimization coupled with a metamodel. This metamodel is generated by interpolating data from an adaptive database. Linear and radial basis function interpolations are compared as means to generate the metamodel. The inverse method gives a result combined with an approximation of the likelihood function to help for decision analysis. It is finally compared to a state-of-art inverse method using support vector machine on a 3D case on simulated data with very promising results

Low-frequency dipolar excitation of a perfect ellipsoidal conductor

International audienceThis paper deals with the scattering by a perfectly conductive ellipsoid under magnetic dipolar excitation at low frequency. The source and the ellipsoid are embedded in an infinite homogeneous conducting ground. The main idea is to obtain an analytical solution of this scattering problem in order to have a fast numerical estimation of the scattered field that can be useful for real data inversion. Maxwell equations and boundary conditions, describing the problem, are firstly expanded using low-frequency expansion of the fields up to order three. It will be shown that fields have to be found incrementally. The static one (term of order zero) satisfies the Laplace equation. The next non-zero term (term of order two) is more complicated and satisfies the Poisson equation. The order-three term is independent of the previous ones and is described by the Laplace equation. They constitute three different scattering problems that are solved using the separated variables method in the ellipsoidal coordinate system. Solutions are written as expansions on the few analytically known scalar ellipsoidal harmonics. Details are given to explain how those solutions are achieved with an example of numerical results

Subspace-based optimization method for reconstructing 3-D scatterers in anisotropic laminates

International audienceThis paper investigates the subspace-based optimization method (SOM) for reconstructing defects in the anisotropic laminates. Reconstruction of defects in such media, like planar composite panels applied in aeronautic and automotive industry, is greatly challenging to execute, due to the complexity in the anisotropy of materials and multi-layered structure. The main advantage of SOM is to split the space of induced currents into mathematical deterministic and ambiguous subspaces, as opposed to physical radiating and non-radiating subspaces in the noise-free scenario and mathematically measurable and non-measurable in the noisy scenario. The deterministic subspace is determined from the spectrum analysis, whereas the ambiguous subspace is calculated by an optimization method. This feature makes SOM fast convergent, robust against noise and the selection of the regularization parameter L that is used to split the space of induced currents. This work extends the SOM to multi-layered anisotropic inverse scattering problems involving 3-D complex defects

Nondestructive testing of fiber array with multiple missing fibers

National audienceOur goal is to detect defects in composite materialscomposed by multilayer planar plates with a periodicset of circular cylindrical fibers embedded in each layer. As astarter, the work presented is electromagnetic (EM) modelingand imaging of missing fibers within a fiber array standingin air. The multiple scattering method is utilized to analyzethe electromagnetic behavior, and the corresponding imagingmodel is established directly from Lippman-Schwinger integralformulation. Standard MUltiple SIgnal Classification (MUSIC)and the proposed joint sparsity which borrows the idea ofsparse theory are applied to retrieve the locations of missingfibers. Numerical results are provided to confirm availabilityand accuracy of EM modeling and defect imaging

Electromagnetic small-scale modeling of composite panels

2 pagesWe are interested in non-destructive electromagnetic characterization of disorganized periodic composite materials composed of a multi-layer infinite plate with a periodic set of circular cylindrical fibers in each layer. The work presented is the preliminary analysis of the scattering of a single-layer plate. An approach based on the multipole method and plane-wave expansion is proposed for obtaining the field representations in all regions of space and forming the formulas for the calculation of reflection and transmission coefficients. To confirm applicability and accuracy of the proposed method, various numerical examples are given when the plate is illuminated by a plane wave

Multi-frequency imaging of perfectly conducting cracks via boundary measurements

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.Comment: 4 pages, 3 figure

An efficient interpolation for calculation of the response of composite layered material and its implementation in MUSIC imaging

2 pagesInternational audienceThere is always the need to calculate the response of a layered composite material to a source that is not close to the domain of interest when dealing with the imaging of an anomaly that might be affecting such a background medium. If this medium is anisotropic, the availability of an efficient and accurate method to calculate this response becomes essential. A novel interpolation and integration method that is taking care of fast oscillating spectral response due to a source that is not close to the domain of interest is proposed herein. The implementation of such a technique to the multiple signal classification (MUSIC) imaging method is presented also

Non-iterative electromagnetic imaging of perfectly conducting screens from limited range far-field data

Abstract We propose a non-iterative multi-frequency algorithm for the imaging of arbitrarily shaped perfectly conducting screens from limited range far-field data. Based on the factorization of the Multi-Static Response (MSR) matrix collected in the far-field at multiple frequencies in Transverse Magnetic (TM) mode, the imaging problem can be solved through the simple analysis of corresponding eigenvectors. Numerical examples illustrate how the proposed algorithm behaves