Target detection and characterization from electromagnetic induction data |
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| Authors: | Habib Ammari Junqing Chen Zhiming Chen Josselin Garnier Darko Volkov |
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| Affiliation: | 1. Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d?Ulm, 75005 Paris, France;2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;3. LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100190, China;4. Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13, France;5. Department of Mathematical Sciences, Stratton Hall, 100 Institute Road, Worcester, MA 01609-2280, USA |
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| Abstract: | The goal of this paper is to contribute to the field of nondestructive testing by eddy currents. We provide a mathematical analysis and a numerical framework for simulating the imaging of arbitrarily shaped small-volume conductive inclusions from electromagnetic induction data. We derive, with proof, a small-volume expansion of the eddy current data measured away from the conductive inclusion. The formula involves two polarization tensors: one associated with the magnetic contrast and the second with the conductivity of the inclusion. Based on this new formula, we design a location search algorithm. We include in this paper a discussion on data sampling, noise reduction, and probability of detection. We provide numerical examples that support our findings. |
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| Keywords: | 35R30 35B30 |
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