Inverse Methods and Imaging

Abstract

Ultrasonic nondestructive testing (NDT) of solid materials exploits the scattering of elastic waves by defects such as cracks, voids, inclusions, and other inhomogeneities. The scattered waves carry information about location, size, shape, and orientation of these defects which has to be extracted appropriately from measurements [1, 2]. The ultimate goal is to produce threedi-mensional images of the interior of the material. In principal, this can be achieved “inverting” the scattering of ultrasound with the aid of inverse scattering theories. Particularly, in three spatial dimensions this turns out to be a complicated and ill-conditioned task even for the much simpler case of scalar acoustic waves. Therefore, approximations and simplifying assumptions are introduced as a trade-off between complexity of algorithms and proper assessment of the integrity of the material [6]. In addition, for practical applications, data recording and processing has to be fast and cheap, which is only available if the algorithms are simple enough; this essentially means, that they are capable of producing images — even in three dimensions — but, due to the fact, that they are not exact inverse scattering solutions, these images have to be properly assessed and understood. For that reason, apart from making many test experiments, numerical modeling of the radiation, propagation, and scattering of elastic waves for given NDT situations and using the computed data as input for the available imaging schemes seems to be a powerful tool to understand the images better, particularly, if elastic waves are under concern in those imaging algorithms which have been designed for scalar acoustic waves only.