Self Focusing with “Time Reversal” Acoustic Mirrors

Abstract

The focusing of an ultrasonic wave on a fixed or moving target, in an inhomogeneous medium is usually degraded. Such a problem occurs in different medical applications, such as hyperthermia or lithotripsy. Even when the target to be insonified is localized with high precision (absolute position determined by X-ray imaging for instance), it is difficult to know which wavefront to transmit through the surrounding medium in order to obtain a good focusing. Ultrasonic imaging techniques also suffer from wavefront distortions through the abdominal layer. Dynamical focusing techniques suppose a constant sound velocity in the medium and neglect the wavefront distortions due to fat, muscles and collagen. The ultrasound velocity is usually taken equal to 1540 m/s, though it is 1410 m/s in fat and 1675 m/s in collagen. Previous publications [1][2] show that the detectability of low contrast tumors can be degraded by these distortions, and propose methods for distortion correction. The same kind of problems occurs in optics: wavefront distortions may be due to the aberrations of an optical system or to inhomogeneities of the refractive index in the transmitting medium (e.g. the atmosphere). Different methods allowing phase distortion compensation have been developed, among them the optical phase conjugation which has been studied since 1970 led to very impressive results. This technique applies to monochromatic fields and is performed with a phase conjugate mirror (PCM). An incident monochromatic wave distorted by an inhomogeneous medium impinges on the PCM, a new wave is generated by reversing the phase of the incident one on the mirror. The distortions of the wave are cancelled after the back propagation through the medium. Such phase conjugation can be physically realized in optics through non linear interactions that involve, for example, stimulated Brillouin scattering, three-wave mixing or the so-called degenerated four-wave mixing [3]. All these techniques require the incidence of several reference fields and only work with quasi-monochromatic waves as those produced by lasers. Methods of phase conjugation have also been developed in acoustics, but non linear effects in acoustics need high amplitude fields [4].