Born Ultrasonic Tomography: Some Limits and Improvements

Summary

The goal of Ultrasonic Tomography (UT) is to reconstruct the spatial distribution of some physical parameter of an object from scattered ultrasonic measures. The measurements are made for more or less dense sets of emitter and receiver positions and of frequencies of the interrogating wave.

We solved this inverse scattering problem by using a Born approximation which leads to a particularly simple and attractive linear relation between the object function (OF) and the scattered field, particularly in the far-field (2D or 3D Fourier transform), making it possible, in principle, to reconstruct the OF in near real time for a sufficiently large set of scattering data.

We investigated wide-band Born UT both numerically and experimentally. Numerical simulations, using ideal measures with ideal objects, allow to examine in detail the influence of various parameters as object’s dimension and contrast, transducers bandwidth, etc. It allows to analyse what happens when the Born approximation is no more valid (high frequencies, high contrasts), to find limits of quantitative and qualitative imagery, to imagine various improvement procedures (artefacts elimination, superresolution procedures leading to high resolution with low frequencies). Experiments (with a mechanical and an antenna-based system) show the applicability of the basic method and of its various improvements for medical and materials applications.