Walid Tabbara

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.

An interferometric coherence optimization method in radar polarimetry for high-resolution imagery

This paper investigates to what extent a new interferometric coherence optimization in radar polarimetry allows the separation of point scatterers located in the same resolution cell according to their interferometric phases. An interferometric coherence definition called the single-mechanism coherence is introduced, and the corresponding optimization method is briefly discussed. This method was first validated theoretically when no volume decorrelation occurs. Then, it has been applied to simple target measurements acquired in an anechoic chamber, and to an X-band polarimetric and interferometric synthetic aperture radar image containing man-made targets. In both cases, the single-mechanism coherence optimization enables to resolve the interferometric phases of several scattering centers inside the same resolution cell.

Spectral and time domain approaches to some inverse scattering problems

Four methods of electromagnetic probing of an inhomogeneous plane stratified medium are presented. They differ by the nature of the incident wave used in the diagnostic. In the first method, the medium is considered as a structure propagating guided modes, and permittivity profiles are determined from the knowledge of one of the guided modes. In the next three, the medium is considered as a scatterer illuminated by a plane wave. Two of them are devoted to reconstruction of conductivity or permittivity profiles from time domain analysis of the reflected field. The last one allows one to obtain permittivity profiles from spectral domain analysis of the reflection coefficient. In spite of their apparent diversity, all these methods are issued from integral representations of the electromagnetic fields. These representations provides the simulated experimental data for the inverse problems. The behavior of these processes has been examined when parameters of practical interest are varied.

A coherent model of forest scattering and SAR imaging in the VHF and UHF-band

We present a coherent scattering model to determine the forest response to an illuminating plane wave in the frequency band 20-300 MHz. In this frequency band, at low frequencies, it is well-known that the waves penetrate the canopy and allow the detection of a hidden target. We have developed a model based on a domain integral representation of the electric field. A decoupling hypothesis is stated and validated, allowing to significantly reduce the numerical complexity of the problem inherent to integral representations. The simulated scattered field is used in a standard synthetic aperture radar (SAR) imaging algorithm to build horizontal and vertical SAR images of a set of trunks and a concealed target.

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>>

Acoustical Imaging of 2D Fluid Targets Buried in a Half-Space: A Diffraction Tomography Approach

The imaging of inhomogeneous cylindrical fluid targets buried in a stratified medium is investigated by means of a diffraction tomography approach. The fundamental equations are briefly stated and then illustrated by a number of characteristic examples. The qual- ity of the image is discussed when changes occur in the geometry of the target, its contrast with the embedding medium, and in the number of views. It is shown that this approach performs in an acceptable manner as long as qualitative results are sought.

Diffraction tomography approach to acoustical imaging and media characterization

An ultrasonics diffraction tomography method is discussed that images cylindrical inhomogeneous fluid targets located in a fluid environment. This method is based on an exact model of the interaction between a compressional plane wave and the target (multiple scattering is not neglected). First the theoretical background is summarized. Then numerical simulations illustrate the behavior of the imaging procedure. These simulations are conducted under conditions close to those of experiments that we perform concurrently. Emphasis is put on the retrieval of large but weakly refractive two-layer circular shells, into which can be inserted a high-speed core. The influence of the conditions of the image formation and the discrepancy between images derived from exact scattered pressures and Born’s approximated ones are especially investigated. Finally, procedures of reconstruction of the target’s sound velocity and attenuation are presented and discussed using synthetically generated data.

Iterative Solution of Some Direct and Inverse Problems in Electromagnetics and Acoustics

ABSTRACT Five radiation and scattering problems in electromagnetics and acoustics are successively investigated to illustrate the interest and drawbacks of iterative solutions with respect to conventional direct ones, if they exist. All these solutions are based upon integral formulations of the fields. The iterative ones are in general developed from two conjugate-gradient algorithms whose main properties are recalled herein from the viewpoint of linear operator equations in Hilbert space. The first two problems concern radiation by rotational thick antennas and by large wire-structures. Methods of moments are applied as usual and the linear systems deduced from are directly or iteratively solved; conditioning is confirmed to be the main reason of either choice. The next two concern scattering by inhomogeneous cylindrical targets: fluid ones illuminated by a compressional plane-wave in acoustics, and lossy dielectric ones illuminated by a wave whose field is parallel with the target cross-section In elec...

Characterization of a buried cylindrical object from its scattered field

The field scattered by a buried object is investigated as a function of various parameters of the object. An exact method based on an integral representation of the field is used to show the strong dependence of the field on the parameters. The possibility of characterizing the target from the knowledge of its scattered field is examined. An approximate method basedo n geometrical optics is introduced and its results are compared with those of the exact one. A simple representation of the field is provided by this method, which also allows the reconstruction of someo f the object parameters. Numerical results are given for objects with weak interactions, which are of interest in biomedical applications.

A Geometrical Optics Method for Assessing an Inverse Scattering Problem for Blood Vessels - Part I: A Multistatic Single Frequency Approach

Ahrracr-We investigate the acoustic characterization of infinite cylindrical fluid shells and its application to ultrasonic diagnostic of blood vessels. The rigorous solution of the direct problem, i.e., a cylindrical shell, whose parameters are known, illuminated by an incident plane wave, is studied first. Then it is extended to the case where the incident wave is limited and characterized by a Gaussian profile. The rigorous solution is compared to an approximate one whose analytical exy :ession is very simple while describing accurately the field. The approximate solution will permit very simple relations to be obtained between the scattered field and the shell parameters and thus to assess some of these from the multistatic study of the backscattered field in a limited space.