Interrogating a Thin Layer of Heterogeneity with Confocal Transducers

This is an expository summary of our work [1] building a mathematical model of scanned acoustic imaging of complicated solid-solid interfaces comprised of scatterers at several length scales, many of which are less than a wavelength. We construct an approximate two dimensional model of a scanned confocal acoustic imaging arrangement operating in a transmission or reflection mode using anti-plane shear or SH waves. Further, we suggest how the sound scattered from the interface is mapped into the sound collected by the transducers. The scalar approximation, while restrictive, still captures many of the basic ideas, ideas that we are at present extending to a three dimensional calculation.