Experimental confirmation of time reverse operator eigenvalues on target scattering moments

Abstract

Laboratory experiments confirm multiple distinct, scatterer dependent, eigenvalues of the time reverse operator (TRO) for a linear time reverse mirror (TRM). Prada and Fink [Wave Motion 20, 151–163 (1994)] discuss a one-to-one correspondence between the eigenvalues of the TRO and each scatterer. Chambers and Gautesen [J. Acoust. Soc. Am. 109, 2616–2624 (2001)] extend this theory to equate the TRO eigenstates to functions of the induced scattering moments of the target object. Each scatterer has a monopole moment associated with the compressibility contrast between the object and the surrounding medium. Likewise, a density contrast will induce multiple dipole moments. Each of these moments results in an eigenstate of the TRO. Experimentally the TRO was determined for two cylindrical scatters in two different media: glass and aluminum. Procedurally, in each case the eigenstates for the TRO were first determined. The DORT method was then applied and the focal point determined. An association between the scattering moment and an eigenstate is confirmed when more than one eigenstate focused the TRM to the same scatter. [This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-ENG—48.]