Hervé Tortel

A Two-Step Procedure for Characterizing Obstacles Under a Rough Surface From Bistatic Measurements

A two-step electromagnetic detection procedure is proposed to characterize a dielectric obstacle buried at low depth under a rough surface from single-frequency and multistatic data. First, we have developed, in the framework of the small perturbation theory, a correlation procedure of the scattered field, which enables us to recover an estimation of the roughness profile. This method is tested for various cases with synthetic data provided by a rigorous boundary integral solver. Second, the obtained surface profile is introduced into the numerical simulation due to a finite-element code. An iterative process is then used, based on a level-set formulation, to obtain the shape of the buried target. The influence of the prior step on the accuracy of the reconstruction of the target is studied via various criteria and for different configurations.

On the Calibration of a Multistatic Scattering Matrix Measured by a Fixed Circular Array of Antennas

The calibration of the multistatic scattering matrix plays an important part in the construction of a quantitative microwave imaging system. For scattering measurement applications, the calibration must be performed on the amplitude and on the phase of the flelds of interest. When the antennas are not completely identical, as for example with a multiplexed antennas array, a speciflc calibration procedure must be constructed. In the present work, we explain how a complex calibration matrix can be deflned which takes advantage of the geometrical organization of the antennas. Indeed, for arrays of antennas positioned on a circle, the inherent symmetries of the conflguration can be fully exploited by means of an adequate reorganization of the multistatic scattering matrix. In addition, the reorganization permits to detect antenna pairs which are not properly functioning and to estimate the signal-to-noise ratio. Experimental results obtained within a cylindrical cavity enclosed by a metallic casing are provided to assess the performance of the proposed calibration procedure.This calibration protocol, which is described here in detail, has already been applied to provide quantitative images of dielectric targets (1,2).

Microwave Imaging of Soil Water Diffusion Using the Linear Sampling Method

This letter deals with the monitoring of the volumetric water content of a soil column in a fully controlled environment by means of a noninvasive microwave imaging system. Indeed, soil moisture is an important piece of information to improve fluid flow modeling or to better understand the water uptake by plant roots. In this letter, we address the problem of recovering the footprint of soil moisture evolution with respect to time using a built-in laboratory microwave setup coupled to a robust qualitative microwave imaging method: the linear sampling method (LSM). The evolution of the water content in the soil is ruled by the Richards equations and stored at different time steps. The associated maps of soil water content are converted into permittivity maps using the Dobson model. Electromagnetic scattered fields are then computed with finite-element software. We have tested the LSM in a situation that can be encountered in agricultural soils where the water content is not homogeneous. We show that the evolution of the soil water content can be qualitatively monitored with the LSM. We also point out that the source is more precisely located by considering the evolution in time of the singular system of the multistatic matrix (multiple signal classification method).

Measurement strategies for a confined microwave circular scanner

This article deals with the inverse scattering problem from scattered field data measured inside a closed microwave scanner. This system is presently being developed to demonstrate the potentiality of a non-invasive microwave imaging system for volumetric water content monitoring. The final goal is to retrieve soil moisture information as it is an important parameter for understanding fluid flow modelling, as well as water uptake by plants roots. Based on the actual state of the setup, we are proposing appropriate numerical tools, in particular a finite element formalism combined with a Lagrangian minimization scheme to provide a fast and accurate imaging tool. We will also show how we can improve the reconstruction algorithms by changing in a very simpler manner the measurement configuration, using either off-centred information or impedance boundary matching environment.

Complex Permittivity Determination From Far-Field Scattering Patterns

An accurate knowledge of the complex permittivity value of materials is compulsory when performing experimental electromagnetic applications. Unfortunately, these values are not so obvious to determine in practice. In this letter, we propose a novel approach for determining the complex dielectric constant of materials. This method combines free-space far-field scattering pattern measurements with a Bayesian procedure, which fully exploits the measurement uncertainties. Therefore, the measured values weighted according to their experimental accuracy are incorporated in the permittivity determination algorithm. In this letter, the samples are all shaped as spheres in order to benefit from efficient Mie scattered field computations. The dielectric properties of typical plastic samples are first determined and compared to values found in the literature in order to assess the validity and the accuracy of the proposed methodology. A more “exotic” sample extracted from a microwave absorber, which is a polyurethane foam charged with carbon particles, is also analyzed.

Spatial depolarization of light from the bulks: electromagnetic prediction.

The spatial depolarization of light emitted by heterogeneous bulks is predicted with exact electromagnetic theories. The sample microstructure and geometry is connected with partial polarization.

Near-subsurface imaging in an absorbing embedding medium with a multistatic/single frequency scanner

Probing the near-subsurface in the presence of absorbing media is a very challenging problem. Within that framework, we analyse the capabilities of a mono-frequency/multistatic set-up for detecting shallowly buried targets. As the antennas constitute an important part of the probing device, an accurate method for modelling the antennas behaviour is proposed. This modelling, performed thanks to a correct balanced set of elementary sources, is then incorporated in the calculation of the scattered field, performed with a home-made Finite Element Method software. Efforts have also been put into the measurement procedure. The measured fields are thus post-processed with an efficient method which takes profit of the spectral bandwidth properties of the scattered field. These fields serve as input data for the inversion algorithm, an extension of the DORT method to elongated targets. This qualitative and fast imaging procedure, which exploits the spectral properties of the multistatic scattering matrix, has been adapted to the present stratified configuration. Imaging results of shallowly buried targets embedded in a high losses medium are presented to assess the well-behaviour of the proposed methodology.

An extended-DORT method and its application in a cavity configuration

In this work, we present an extension of the classical DORT method for time-harmonic inverse medium scattering problems. This tool enables one to estimate the shape of the unknown scatterers even if they are not necessarily point-like scatterers. This method is described and compared with existing sampling methods. Moreover, a mathematical derivation is provided for its validation, either in a free-space environment or in a metallic enclosure setup. Two-dimensional examples, based on measured data sets acquired in the circular microwave scanner developed at Institut Fresnel, are presented, which show that the method is computationally efficient and robust to noise.

A microwave imaging circular setup for soil moisture information

Soil moisture is an important parameter for understanding fluid flow modelling as well as the water uptake by plants roots. A microwave scanner is presently being designed to demonstrate the potentiality of a non-invasive microwave imaging system for volumetric water content monitoring. After briefly describing the setup, the numerical tools which are needed for the modelling and the inversion of the electromagnetic fields are introduced. In particular, a finite element method has been adapted to the specific setup geometry. An iterative inversion scheme, based on a Lagrangian formalism has been implemented to provide dielectric permittivity maps of the domain under investigation.

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.