Bernard Duchêne

Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics

After a brief presentation of the principles of diffraction tomography, the authors focus on the applications they have investigated in the biomedical and non-destructive testing domains. Typical numerical and experimental results are presented and in their comments they state what they think are the current limitations of this approach and the possible opportunities for future work with this imaging technique.

Modified gradient approach to inverse scattering for binary objects in stratified media

We are concerned herein with inverse scattering problems in stratified media and aspect-limited data configurations. In such configurations, the sources and receivers of the probing waves are located in a medium different from the one which contains the object under test. This results in a lack of information which enhances the inherent ill-posedness of the inverse problem. To make the problem more tractable, we assume that the test object is homogeneous with known constitutive parameters so that the inverse problem consists of reconstructing its shape and location. This non-linear inverse problem is solved using the modified gradient method in which the a priori information is introduced as a binary constraint. A cooling parameter is introduced at the same time, which allows us to control the evolution of the iterative process. The effectiveness of this algorithm is studied for three different physical applications.

Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data

We deal with an electromagnetic inverse scattering problem where the goal is to characterize unknown objects from measurements of the scattered fields that result from their interaction with a known interrogating wave in the microwave frequency range. This nonlinear and ill-posed inverse problem is tackled from experimental data collected in a laboratory-controlled experiment led at the Institut Fresnel (Marseille, France), which consist of the time-harmonic scattered electric field values measured at several discrete frequencies. The modelling of the wave–object interaction is carried out through a domain integral representation of the fields in a 2D-TM configuration. The inverse scattering problem is solved by means of an iterative algorithm tailored for objects made of a finite number of different homogeneous dielectric and/or conductive materials. The latter a priori information is introduced via a Gauss–Markov field for the distribution of the contrast with a hidden Potts–Markov field for the class of materials in the Bayesian estimation framework. In this framework, we first derive the posterior distributions of all the unknowns and, then, an appropriate Gibbs sampling algorithm is used to generate samples and estimate them. The proposed Bayesian inversion method is applied to both a linear case derived from diffraction tomography and the full nonlinear problem.

Eddy current testing of anomalies in conductive materials. I. Qualitative imaging via diffraction tomography techniques

The authors consider the analysis of eddy current testing of defects in conductive materials. The authors investigate the application of reflection-mode diffraction tomography (DT) imaging techniques. First, exact synthetic data are calculated for various canonical configurations using a method of moments, and they are compared with those calculated by a finite-element code and with experimental data. Analysis of these data in particular evidences interest and some limitations of the Born approximation. Second, two imaging algorithms are proposed and investigated from numerical simulations; the first directly originates from ultrasonic DT where most of the attenuation is neglected, and the other approximately accounts for the skin effect. >

Eddy current testing of anomalies in conductive materials. II. Quantitative imaging via deterministic and stochastic inversion techniques

For pt.I, see ibid., vol.27, no.6, p.4416-37 (1991). Application of deterministic and stochastic quantitative inversion techniques to configurations similar to those treated in Pt.I by tomographic techniques is discussed. The defects are modeled as cylindrical inhomogeneities concealed within a homogeneous nonmagnetic metallic half-space. Values of the conductivity within the anomaly cross section have to be retrieved from multifrequency anomalous fields observed on a line above and parallel with the surface on the damaged block when a known time-harmonic source illuminates the block. Such quantitative imaging involves the ill-posed inversion of a Fredholm first-kind integral equation with exponentially damped kernel and requires some kind of regularization. In a deterministic context, an iterative algorithm provides a regularized generalized inverse, with the inconvenience that the stopping parameter should be appropriately chosen. In a stochastic context. Kalman filtering rapidly yields a good estimate of the conductivities, which could lead to a more precise but costlier solution. >

Breast Phantoms for Microwave Imaging

Herein, we study the dielectric properties of various mixtures susceptible to be used in manufacturing of reference inhomogeneous breast phantoms dedicated to the experimental validation of microwave breast imaging systems in the 0.5-6-GHz frequency range. Particularly, we investigate the stability over time and temperature of these properties and their reproducibility for a given mixture, as well as the ability of some mixtures to mimic the various breast tissues, i.e., to show dielectric properties close to that given by one-pole Debye models that describe the mean relative dielectric permittivity of various tissue types.

Bayesian inversion for optical diffraction tomography

In this paper, optical diffraction tomography is considered as a non-linear inverse scattering problem and tackled within the Bayesian estimation framework. The object under test is a man-made object known to be composed of compact regions made of a finite number of different homogeneous materials. This a priori knowledge is appropriately translated by a Gauss–Markov–Potts prior. Hence, a Gauss–Markov random field is used to model the contrast distribution whereas a hidden Potts–Markov field accounts for the compactness of the regions. First, we express the a posteriori distributions of all the unknowns and then a Gibbs sampling algorithm is used to generate samples and estimate the posterior mean of the unknowns. Some preliminary results, obtained by applying the inversion algorithm to laboratory controlled data, are presented.

Electromagnetic Modeling of a Damaged Ferromagnetic Metal Tube by a Volume Integral Equation Formulation

We propose a volume integral equation formulation for eddy-current nondestructive evaluation of ferromagnetic tubes affected by volumetric defects. We solve the system of integral equations (introduced into the model by application of Greens theorem) by the method of moments for both fictitious electric and magnetic currents within the defects, and calculate variations of impedance of the probes by the reciprocity theorem. We have made thorough comparisons of our results with finite-element-method simulations and with experimental data as well.

High Tc SQUIDs and eddy-current NDE: a comprehensive investigation from real data to modelling

The interest in magnetometry for eddy-current non-destructive testing, e.g. of planar conductive structures encountered in the aircraft industry, using high-temperature superconducting quantum interference devices (SQUIDs) is primarily due to their high sensitivity to magnetic flux even at very low frequencies. Here it is shown how theoretical, numerical and measurement machineries are combined to get reasonable synthetic and experimental data and to reach a good understanding of the interaction of diffusive wavefields with a damaged non-magnetic metal plate (as a first step towards the retrieval of pertinent features of the defects). The measurement modalities are considered first. It is illustrated in some detail how laboratory-controlled experiments are performed by a SQUID-based probe displaced above artificially damaged plates. Experimental data are then confronted with simulation results in order to evaluate the accuracy and reliability of this measurement system. Simulations are carried out by a computationally fast vector volume integral method dedicated to a planar layering affected by a volumetric defect, which involves the construction of the dyadic Green system of the layering.

Experimental investigation of a diffraction tomography technique in fluid ultrasonics

Qualitative ultrasonic imaging of cylindrical fluid targets is investigated by a diffraction tomography technique applied to experimental data. The principles of the image formulation are stated and an experimental setup is described. Experimental difficulties related to the short wavelength used and respective advantages in collecting the data, either with a mechanically scanned single transducer or with an electronically scanned array of transducers, are emphasized. Representative images of simply structured phantoms and of real biological bodies are obtained in spite of the small number of views available.<<ETX>>