Evaluating the permeability distribution of a layered conductor by inductance spectroscopy

This paper presents an inverse method for determining the permeability distribution of a flat, layered conductor by using a multifrequency electromagnetic sensor. It discusses the use of spectroscopic techniques to extract depth profiles and examine more fully the internal structure of the test piece. 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 the inverse solution, a modified Newton-Raphson method is used to adjust the permeability profile to fit a set of multifrequency inductances in a least-squared sense. The approximate Jacobian matrix (sensitivity matrix) is obtained by the perturbation method. The paper provides numerical results of the forward solution for cases of step and continuous permeability profiles. Inverse results based on experimental and simulated data verify the accuracy of this method, which yields good estimates for the permeability profile. Index Terms--Electromagnetic sensor, layered conductor, multifrequency, permeability distribution.