Revisiting the Stokes relations in a time-reversal cavity: Suppression of intraplate echoes induced by a titanium plate

Abstract

When focusing through plates or tubes the presence of multiple interfaces induces reflected wavefronts that follow the main wavefront. Adaptive focusing techniques can be used to cancel the echoes. For that purpose, two linear arrays of transducers have been placed on each side of a titanium plate. Three propagation operators have been acquired: transmission from one array to the other, and two reflection operators acquired by each array. In this work, two adaptative focusing methods have been used to cancel the echoes: first, they have been suppressed with a time-reversal mirror, using the two arrays’ cavity surrounding the plate. Second, the echoes have been canceled by using the inverse filter technique, inverting the transmission operator. Thus, the inverse filter achieves echo cancellation by using only the transmitted fields, whereas time reversal also requires the reflected fields. It is shown how transmission and reflection operators are related by the Stokes relations in a matrix formalism. These relations clearly exhibit how the inverse filter takes advantage of the reflections in the medium. An iterative mathematical resolution of these equations yields a new way to invert the transmission operator.