Imaging and Inverse Scattering in Nondestructive Evaluation with Acoustic and Elastic Waves

Abstract

Ultrasonic nondestructive testing of solid materials requires the assessment of location, shape and size of defects. If appropriate scattering data are received within a synthetic aperture as function of time in — for instance — a pulse-echo mode, defect imaging in terms of B-or C-scan display of the data is available. In contrast to that, heuristic imaging algorithms like SAFT (Synthetic Aperture Focusing Technique) try to invert the scattering process in order to reconstruct the defect geometry via an image. As a matter of fact, such heuristic imaging concepts cannot answer — apart from performing a large number of test experiments — the question whether their image output is a quantitative reconstruction of the defect or not: An inverse scattering theory is required. One particularly successful approach is based on a linearization of inverse scattering in terms of either the Born or Kirchhoff approximation and results in a generalized diffraction tomography, which contains SAFT as a special approximation (Langenberg, 1987; Langenberg, 1989; Mayer et al., 1990). Unfortunately, the linearization can often not be tolerated, and, hence, apart from developing algorithms without relying on this approximation, numerical techniques to model ultrasonic acoustic and elastic wave scattering should be available for the computation of synthetic data to be utilized as input to imaging procedures. This interactive imaging approach — combining modeling and imaging — is called CAI for Computer Aided Inspection.