1. 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

2. Eddy Current Tomography
Anomaly
Probe
Conducting specimen

3. 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)

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

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

6. 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 , 2006.

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

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

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The test for k is no longer valid !

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

11. 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

12. Results Reconstructed Map Region under test measurements Test domain

13. Results
Reconstructed Map

14. 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

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

16. 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.

17. 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 , 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 ,