Fast methods for quantitative eddy-current tomography of conductive materials

In this paper, we address the imaging of the spatial distribution of the resistivity of conductive materials by using data from eddy-current nondestructive testing. Specifically, the data consists of measurements of the impedance matrix at several frequencies acquired using a coil array. The imaging method processes the second-order term (estimated from the measured data) of the power series expansion, with respect to frequency, of the impedance matrix. This term accounts for the resistive contribution to changes of the impedance matrix, due to the presence of anomalies in the conductor under test, occurring at relatively low frequencies. The operator mapping a given resistivity distribution inside the conductor into the second-order term satisfies a proper monotonicity property. The monotonicity makes it possible to apply a fast noniterative imaging method initially developed by the authors for elliptic problems such as electrical resistance tomography. Numerical examples show the main features of the proposed method, and demonstrate the possibility of real-time imaging.