Modeling Scanned Acoustic Imaging of Defects at Solid Interfaces
This is an expository summary of my and my collaborators work building mathematical models of scanned acoustic imaging of defects such as cracks or voids that break the surface of a solid or form along solid-solid interfaces. We construct explicit models both of a high frequency, scanned acoustic microscope operating in a reflection mode, and of a lower frequency, scanned confocal acoustic imaging system operating in a transmission mode. The acoustic microscope can operate from 100 megahertz to several gigahertz. One of its most interesting imaging modes is the detection of small surface- breaking cracks, whose traces at the surface of a solid are smaller than an acoustic wavelength, even at high megahertz frequencies. It does so by using a leaky Rayleigh wave as part of its imaging mechanism. The confocal imaging system operates in a neighborhood of 10 megahertz, a lower frequency. It is used to image complicated solid- solid interfaces comprised of scatterers at numerous length scales, many of which are less than a wavelength. For both cases, we explain how the sound scattered from the defects is mapped into the sound collected by the transducers and hence into the voltages they produce. The models are approximate, make use of reciprocity relations and depend upon asymptotic evaluations of Fourier integrals.
KeywordsFatigue Quartz Anisotropy Attenuation Nitride
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