Application of a diffusion-to-wave transformation for inverting eddy current nondestructive evaluation data

A transformation from diffusion fields to wave fields is examined as an approach to inverting eddy current nondestructive evaluation (NDE) data. An analytic inversion to the transformation is used as a means to gain insight into robustness issues associated with the method. A discretized version of the transformation is utilized to solve a 1-D inverse problem with a direct "wave-based" approach. Because the transformation lacks robustness, two regularization schemes are used to stabilize the inversion, which are themselves enhanced by an averaging algorithm. The technique is shown to be unstable when applied to sources which are not ideal impulse functions, in which case the transformation can be stabilized via low-pass filtering. The transformation is not useful with time-harmonic sources and is therefore limited to pulsed eddy current inspections.