Applied Inversion in Nondestructive Testing

The explicit inverse problems in nondestructive testing range from material characterization to defect imaging, and, as such, they exhibit a large bandwidth of complexity: Material characterization should be quantitative, thus accounting for nonlinearities of the underlying physical phenomena as well as for the nonlinearity of the inverse problem, whereas defect imaging might already be sufficiently solved if the location, the size and the orientation of a defect has been determined. As a matter of fact, the latter task can be accomplished with rather simple inverse algorithms, which rely on the linearization of the elastic and/or electromagnetic wave inverse scattering problem. Nevertheless, in particular in safety relevant applications like nuclear power generation, aircraft and/or bridge testing, one is interested to extract the maximum amount of information from the data utilizing all a priori knowledge of the physical model under concern, for instance with regard to the propagation characteristics of the defect embedding medium or with regard to the polarization of the wave mode. In that sense, some recent fundamental improvements of linear diffraction tomographic inverse scattering have been made, which will be summarized and commented upon in the present article. In addition, a novel philosophy of computer aided nondestructive testing will be discussed, which comes under the alias ULIAS: Ultrasonic Inspection Applying Simulation. The key idea is to support the assessment of the output of existing imaging algorithms with simulations applying numerical techniques to compute wave propagation and scattering for the testing problem under concern; the resulting synthetic data supply a testbed for the inverse problem.