Investigations in ultrasonic tomography

Abstract

Ultrasonic tomography (UT) is a technique to reconstruct the spatial distribution of some physical parameter of an object from measurements of the scattered field. The measurements are made for more or less dense sets of emitter and receiver positions and of frequencies of the interrogating wave. This inverse scattering problem was solved by using a Born approximation that leads to a particularly simple and attractive linear relation between the object function (OF) and the scattered field, particularly in the far-field (2-D or 3-D Fourier transform), making it possible, in principle, to reconstruct the OF in near real time for a sufficiently large set of scattering data. Ultrasonic tomography was investigated numerically and experimentally. Numerical simulations, using ideal measures with ideal objects, allow the examination in detail of the influence of various parameters such as the object’s dimension and contrast, transducers bandwidth, etc. It allows one to analyze what happens when the Born approximation is no longer valid (high frequencies, high contrasts), to find limits of quantitative and qualitative imagery, and to imagine various improvement procedures (e.g., superresolution procedures leading to high resolution with low frequencies). Experimentations (with a mechanical and an antenna-based system) show the applicability of the method for medical and materials applications.