Imaging the continuous conductivity profile within layered metal structures using inductance spectroscopy

This paper presents an inverse method for determining the conductivity distribution of a flat, layered conductor using a multifrequency electromagnetic sensor. Eddy-current sensors are used in a wide range of nondestructive testing applications. Single-frequency sensors are very common; however, the potential of an eddy-current sensor with spectroscopic techniques offers the ability to extract depth profiles and examine more fully the internal structure of the test piece. In this paper, the forward solution for a small right-cylindrical air-cored coil placed next to a layered conductor is based on the analytic solution provided by the transfer matrix approach. For an inverse solution, a modified Newton-Raphson method was used to adjust the conductivity profile to fit a set of multifrequency inductances in a least-squared sense. The approximate Jacobian matrix (sensitivity matrix) was obtained by the perturbation method. Numerical results of the forward solution are provided for cases of step, continuous conductivity profiles. Good estimates for the conductivity profile were obtained. Experimental eddy-current tests are performed by taking the difference in inductance of the coil when placed next to a reference conductor and next to a layered conductor over the range 100 kHz - 1 MHz. Inverse results based on experimental and simulated data verified this method.