TIME-REVERSAL OF ULTRASONIC FIELDS .3. THEORY OF THE CLOSED TIME-REVERSAL CAVITY

A theoretical model for time-reversal cavities to optimize focusing in homogeneous and inhomogeneous media is described. The concept of the cavity can be understood as the most realistic approximation to an exact three-dimensional (3-D) time-reversal of ultrasonic fields; it is also a generalization of the time-reversal mirrors realized experimentally in our laboratory. The proposed method is based on an approach in the transient regime, that is more general than the monochromatic formalism used in optics to analyze the phase conjugation mirrors efficiency. This method uses impulse diffraction theory to obtain the impulse response of the cavity in any inhomogeneous medium. It is also proposed an original interpretation of the limitations due to diffraction observed in wave field propagation in terms of the different waves generated inside the cavity. The time-reversal focusing process using a closed cavity in a weakly inhomogeneous medium is finally compared with more classical techniques to compensate wavefront distortions, thus illustrating the focusing improvement due to the time-reversal method.