Measurement models for ultrasonic nondestructive evaluation

The article reviews ways to use the electromechanical reciprocity relation to construct theoretical models of measurement processes in ultrasonic nondestructive evaluation. This relationship is important because it connects the change in the voltages measured at the electrical terminal of the transducer to the perturbation in the mechanical wavefield caused by the change in the propagation environment. It does so by mixing an unperturbed reference wavefield with one containing the perturbed wavefield. Two problems of progressive difficulty are explored. We begin by investigating the imaging of a one-dimensional sinusoidal fluid-solid interface using a cylindrically focused beam and continue by developing a model of the imaging of the mechanical properties of a two-dimensional, thin solid film using a confocal arrangement of point-focused transducers. This last problem uses an approximation to the thin solid film, which reduces its mechanical response to one similar to that of a membrane. Integral relations are given that can be used to form integral equations or to generate asymptotic approximations to the particle displacements and stresses in the film.