Nonlinear propagation of ultrasonic signals : theoretical studies and potential applications

Abstract

Countless applications use the propagation and reflection of sound to gain better knowledge of the surrounding medium. This medium can, for instance, be made of a set of complex and heterogeneous biological tissues or of ships in the sea several kilometres away from the sound receiver. In all cases, the sound propagation is affected by some nonlinear effects. In many applications those effects are neglected, while in others they are exploited.<br><br>

In this thesis we investigate the possibility of using the nonlinear effects in fields where they are avoided, neglected, or overseen. We also try to establish faster or more accurate estimations of nonlinear sound fields. The two domains that were investigated are the domain of underwater acoustics with applications such as echo sounders or acoustic Doppler current profilers, and the domain of medical imaging.<br><br>

In underwater acoustics, we studied the combined use of the second harmonic and fundamental signals for imaging using a scientific echo sounders and for determining current velocities using acoustic Doppler current profilers. We show that the use of the second harmonic signal can improve the performance in these applications when the range is limited.<br><br>

In medical imaging, we investigated the use of the second harmonic signal with the multi-line transmission technique. In this case too, images produced by the second harmonic signal suffer from less perturbations than images produced by the fundamental signal.<br><br>

We have developed new models to estimate the nonlinear propagation of sound. One model intends to appropriately describes the attenuation and the dispersion observed in complex media. It derives a wave equation with a loss operator defined by fractional order derivatives. The model relies on variations of the constitutive equations that adequately describe the stress-strain relation and heat transfer. The other models based on the quasi-linear approximation intend to speed up or increase the flexibility of the implementation. They proved in one case to be faster than other state-of-the-art simulators, and in the other case, more flexible than alternative methods. Given that the conditions for quasi-linear propagation are satisfied, those simulators adequately describe the sound field for the fundamental and second harmonic signals.