Time reversal through a solid–liquid interface and super-resolution

Abstract

We present numerical computations that reproduce the time-reversal experimentsof Draeger et al (Draeger C, Cassereau D and Fink M 1998 Appl. Phys. Lett. 721567–9), where ultrasound elastic waves are time-reversed back to their sourcewith a time-reversal mirror in a fluid adjacent to the solid. We also shownumerically that multipathing caused by random inhomogeneities improves thefocusing of the back-propagated elastic waves beyond the diffraction limitseen previously in acoustic wave propagation (Dowling D R and JacksonD R 1990 J. Acoust. Soc. Am. 89 171–81, Dowling D R and Jackson DR 1992 J. Acoust. Soc. Am. 91 3257–77, Fink M 1999 Sci. Am. 91–7,Kuperman W A, Hodgkiss W S, Song H C, Akal T, Ferla C and Jackson D R1997 J. Acoust. Soc. Am. 103 25–40, Derode A, Roux P and Fink M1995 Phys. Rev. Lett. 75 4206–9), which is called super-resolution. Atheoretical explanation of the robustness of super-resolution is given,along with several numerical computations that support this explanation(Blomgren P, Papanicolaou G and Zhao H 2002 J. Acoust. Soc. Am. 111238–48). Time reversal with super-resolution can be used in non-destructivetesting and, in a different way, in imaging with active arrays (Borcea L,Papanicolaou G, Tsogka C and Berryman J 2002 Inverse Problems 18 1247–79).