RECONSTRUCTION OF 3-DIMENSIONAL CONDUCTIVITY VARIATIONS FROM EDDY-CURRENT (ELECTROMAGNETIC INDUCTION) DATA

A direct linear inverse method for eddy current non-destructive evaluation is presented in this paper. The method is based on inverting the impedance change measured in an eddy current probe, placed above a conducting half-space containing a three-dimensional (3D) conductivity anomaly. The eddy current probe used for this purpose consists of a spatially periodic, time-harmonic current sheet. The Born approximation is used to linearize the relevant integral equations used for inversion. It is found that a coupled Fourier-Laplace transform has to be inverted to provide a 3D reconstruction of the inhomogeneity in the conventional frequency domain; however, the transforms decouple in the time domain. The 3D inversion procedure is specialized to the 1D case of a uniform-current sheet. The conductivity variation with depth is now recovered by inverting a single Laplace transform. Numerical algorithms to invert Laplace transforms and similar Fredholm integral equations of the first kind are developed and used to implement the 1D inversion procedure. The algorithms are tested by the reconstruction of surface coatings of a constant, but different, conductivity from that of the underlying half-space. Surprisingly, certain features of the inversion algorithm are found to be exact for a layered half-space and independent of the Born approximation. These features enable us to reconstruct the depth and conductivity of the coatings exactly from the inverse Born profiles.