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Experimental validation of a fast non-iterative imaging algorithm for eddy current tomography Flavio Calvano1, Guglielmo Rubinacci1, Antonello Tamburrino2 and Salvatore Ventre2 1 Ass. EURATOM/ENEA/CREATE, DIEL, Università di Napoli Federico II, Italy 2 Ass. EURATOM/ENEA/CREATE, DAEIMI, Università di Cassino, Italy

Eddy Current Tomography Anomaly Probe Conducting specimen

Problem Definition i>b Impedance Analyzer Personal Computer PC (auto and mutual impedances) Personal Computer (imaging algorithm) PC Impedance ( Inversion Analizer Algorithm ) ECT coils i2 iM i1 V c c V i>b Anomaly (=i) Conductor (=b)

Eddy Current Data Phase 1 Vc # l # k Phase 2 V

Low frequency expansions Key quantity for the inversion method Matrix of the mutual impedances between coils

Monotonicity Phase 1 Phase 2 Vc D Phase 1 Phase 2 Vc D A. Tamburrino and G. Rubinacci, “Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials”, IEEE Trans. Magn., vol. 42, no. 8, pp. 2017-2028, 2006.

Inversion: underlying idea Phase 1 Phase 2 Vc V Phase 1 Phase 2 Vc k

Inversion: underlying idea Basic inversion algorithm: Take as estimate of V the union of those k such that V

The Noise   The test for k is no longer valid !

The Sign Index At each k we associate is the j-th eigenvalue of

Experimental setup Benckmark: printed circuit board External Coil Internal diameter=5mm, external diameter=10.5mm, height=6.5mm, number of turns=700. Internal Coil internal diameter=1mm, external diameter=4mm, height=3mm, number of turns=180. The excitation frequency is 20kHz

Results Reconstructed Map Region under test measurements Test domain

Results Reconstructed Map

Results Top view Bottom view (scanned from the top view) Top Bottom Estimated Noise level : 50 mW Reconstructed Map with top test domains Reconstructed Map with the bottom test domains

Results Top view Bottom view (scanned from the top view) Reconstructed Map with top test domains Reconstructed Map with the bottom test domains

CONCLUSIONS A fast inversion method for inverting eddy-current testing data has been applied to the identification of the shape of inclusions in a conductor by eddy current tomography. The eddy-current data consists of the variation of the impedance matrix using an a-priori designed with numerical simulation array of coils to scan the specimen under test. The second-order moment P(2) accounts for the resistive contribution to the changes of the impedance matrix occurring at relatively low frequencies. A direct imaging algorithm based on monotonicity principle is available that allows real-time imaging on directly measured experimental data.

REFERENCES A. Tamburrino and G. Rubinacci, “A new non-iterative inversion method for electrical impedance tomography”, Inverse Problems, pp. 1809–1829, 2002. A. Tamburrino and G. Rubinacci, “Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials”, IEEE Trans. Magn., vol. 42, no. 8, pp. 2017-2028, 2006. A. Tamburrino, S. Ventre, G. Rubinacci, “Recent developments of a Monotonicity Imaging Method for Magnetic Induction Tomography” accepted for publication on Inverse Problems. G. Rubinacci, A. Tamburrino, S. Ventre, “Eddy current imaging of surface breaking defects by using monotonicity based methods”, ACES Journal, vol.23, no. 1, pp. 46-52, 2008.