Profiling a surface using its echoes

Abstract

The electromechanical reciprocity relation is used to construct a theoretical model of the imaging of a sinusoidal fluid–solid interface using a cylindrically focused acoustic beam. The electromechanical reciprocity relation is used to connect the change in the voltage measured at the electrical terminal of the transducer to the perturbation in the mechanical wave field caused by a change in the profile of the interface. It does so by mixing an unperturbed reference wave field with one containing the perturbed wave field. We use a regular boundary perturbation expansion to obtain an approximate boundary condition that fits directly into the reciprocity relation. This perturbation assumes both the amplitude and the slope of the profile are small. We limit our discussion to imaging a sinusoidal interface with the understanding that resolution of this profile is central to understanding that of more general profiles. We find that depending on the choice of parameter values the measured profile is not simply a replication of the original sinusoidal profile. Time permitting, we briefly indicate preliminary work on a related model of the imaging of the mechanical properties of a thin solid film using a confocal arrangement of point-focused transducers. [Work supported by NSF.]