Marc Saillard

Special section: Testing inversion algorithms against experimental data

An introduction to the special section is given. The new database of experimental data used in this section is also introduced. This database can be accessed from this articles Multimedia Enhancements page.

Scattering from metallic and dielectric rough surfaces

Using a generalization of the integral theory of metallic and dielectric gratings developed in our laboratory 15 years ago, we propose a rigorous integral theory of scattering by metallic or dielectric nonperiodic rough surfaces leading to a single integral equation. The numerical implementation has been carried out despite strong difficulties for TM polarization and metallic surfaces because of propagation of surface plasmon waves outside the illuminated region of the rough surface. Numerical results show the influence of the statistical parameters of the asperities on the absorption phenomena for metallic surfaces. Then the influence of asperities on the total transmission around Brewster incidence is studied. Finally numerical results of enhanced backscattering from perfectly conducting, metallic, and dielectric random rough surfaces are given.

Decomposition of the Time Reversal Operator for Electromagnetic Scattering

The method of decomposition of the time reversal operator has been introduced with the aim of focusing acoustic waves on a selected target. It is based on the derivation of the invariants of the time reversal operator, which is linked to the transfer matrix of the array of transducers insonifying a time invariant scattering medium. The theoretical and numerical results concern independent point-like scatterers. Here, we apply numerically the same technique to electromagnetic waves, and all the interactions between the various scatterers are taken into account. This method may be very useful to detect and localize buried objects. With this goal, we have investigated the role of polarization and of the geometrical or electromagnetic parameters, as well as the ability of accurately focusing on a scatterer. The sensitivity of the results to the initial set of data, namely the number of measurements or the accuracy, is also studied.

Rigorous solutions for electromagnetic scattering from rough surfaces

Abstract First, the rough surface scattering problem is formulated from a statistical point of view. Then, different numerical schemes that permit one to solve Maxwell equations without approximation are presented for the three-dimensional scattering problem. Particular attention is paid to boundary integral methods and to the numerical techniques developed to handle large linear systems when short-range interactions dominate. Lastly, several important connected issues that require further numerical and theoretical improvements are discussed.

DORT method as applied to ultrawideband signals for detection of buried objects

The decomposition of the time reversal operator (DORT) method, originally developed in acoustics, allows detection of scatterers embedded in the probed domain and provides some very robust means for focusing an incident wave onto a given scatterer. Hence, this method is very helpful for clutter reduction. Here, it is applied to the detection of buried cylindrical objects with the help of electromagnetic ultrawideband signals. It is shown that when the set of antennas is located on a piece of line above an interface, the use of the DORT method remains simple, whatever the polarization, provided the contribution from the target can be separated from that of the interface. Using wideband signals also permits one to excite natural resonances of the buried scatterer, which can easily be extracted from the eigenvalues of the time reversal operator. Numerical examples based on a finite-difference time-domain algorithm are given.

Validation of 2d iNverse Scattering Algorithms From Multi-Frequency Experimental Data

Reconstructions of two dimensional dielectric or conducting objects from multi-frequency experimental data are considered in the present paper. Two different iterative methods are used for solving the inverse scattering problem. The first one is based on a boundary integral formalism and retrieves boundaries and complex permittivities of unknown homogeneous scatterers. For this method initial guesses are derived from method of decomposition of the time reversal operator (DORT) combined with a low frequency approximation. The second method is based on a domain integral formalism and retrieves the relative complex permittivity distribution inside some investigated domain. The data were carried out in a controlled environment (anechoic chamber) and the reconstructions have been performed using multifrequency approach, i.e., the scheme starts with the lowest available frequency and uses the final result as initial guess at higher frequency in order to enhance the resolution.

Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation

The sparse-matrix-flat-surface iterative approach has been implemented for perfectly conducting surfaces and modified to enhance convergence stability and speed for very rough surfaces. Monte Carlo simulations of backscattering enhancement using a beam decomposition technique are compared with millimeter-wave laboratory experimental data. Strong but finite conductivity for metals or thin skin depth for dielectrics is simulated by an impedance approximation. This gives rise to a nonhypersingular integral equation derived from the magnetic field integral equation. The effect of finite conductivity for a metal at visible wavelengths is shown.

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.

Doppler Spectra From a Two-Dimensional Ocean Surface at L-Band

An approximate time-harmonic three-dimensional electromagnetic boundary-integral method, the small-slope integral equation, is combined with a series expansion of the Creamer surface representation at second order with respect to the height, denoted by Creamer (2). The resulting model provides at low numerical cost simulations of the nonlinear ocean surface Doppler spectrum at L-band. As a result of approximations, the model is designed for a low-wind speed, typically up to 5 m/s. It is shown that applying directly a second-order model such as Creamer (2) to a semiempirical sea surface spectrum induces an unrealistic magnification of small-scale roughness that is involved in the scattering process at microwave frequencies. This paper thus proposes an undressed version of the Pierson-Moskowitz spectrum that corrects this artifact. Full-polarized Doppler simulations at L-band and 70deg incidence are presented. Effects of the surface nonlinearities are outlined, and the simulated Doppler spectra show correct variations with respect to wind speed and direction

Localization and characterization of two-dimensional targets buried in a cluttered environment

In the present paper, we consider a two-dimensional inverse scattering problem involving two semi-infinite media separated by an interface. The targets under test are assumed to be buried in one of the two media while the sources and the receivers are located in the other medium (limited-aspect data configuration). We present an iterative scheme to reconstruct the permittivity distribution of the unknown object. This method consists in building up a sequence of the parameter of interest by minimizing, at each iteration step, a cost functional representing the discrepancy between the data and those that would be obtained with the best available estimation of the parameter. In addition, when clutter is present, the decomposition of the time reversal operator method is used to improve the signal-to-clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer. The data associated with this incident field are included in the iterative minimization procedure.