A diffraction tomographic algorithm for eddy current imaging from anomalous fields at fictitious imaginary frequencies
Résumé
One key question when extending wave imaging algorithms to strongly attenuating environments like a damaged metallic structure where eddy currents are generated, is how to deal with evanescent waves. A similar question arises when super-resolution of a scatterer is aimed at by using the evanescent spectrum of its near-field. Here we focus on imaging a 2D anomaly within a metal half-space probed by a low-frequency electromagnetic source in air above, from the anomalous field the anomaly is associated with. Assuming the eddy current phenomenon to be cast in a wave framework, it is possible to devise a diffraction tomographic procedure that partially matches the skin-effect in the metal. From the same starting point, continuation of the time-harmonic anomalous data onto a set of fictitious imaginary frequencies leads to a diffraction tomographic procedure which works somewhat like in a nonattenuating embedding and which is not impaired by the same drastic approximations as the attenuation-matched approach. Simulations from synthetic fields calculated in the case of simple geometries illustrate the derivation. Ways to proceed with the continuation when probing an effectively unknown defect are discussed and a model-based approach is outlined.