A robust method that uses eddy current measurements to determine the conductivity and thickness of uniform conductive layers is described. The method was tested by estimating the conductivity and thickness of aluminum and copper layers on various substrate metals, and the thickness and conductivity of free-standing foils of aluminum. The electrical impedance was measured for air-core and ferrite-core coils in the presence and absence of the layer for frequencies ranging from 1 kHz to 1 MHz. The thickness and conductivity of the metal layers were inferred by comparing the data taken with air-core coils to the exact theoretical solution of Dodd and Deeds [J. Appl. Phys. 39, 2829 (1968)] using a least-squares norm. The inferences were absolute in the sense that no calibration was used. We report experimental tests for eight different thicknesses of aluminum (20–500 μm) in free space and on four different substrates: Ti-6Al-4V, 304 stainless steel, copper, and 7075 aluminum, and for five different thicknesses of copper (100–500 μm) on 304 stainless steel. Both the thickness and conductivity could be determined accurately (typically within 10%) and simultaneously if the ratio of the layer thickness to the coil radius was between 0.20 and 0.50. For thinner samples either the thickness could be found if the conductivity were known, or vice versa.

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We describe a time-domain (pulsed) eddy-current technique for determining the thickness and conductivity of conductive coatings on metal plates. The pulsed eddy-current instrument records the transient current induced in an absolute, air-cored coil placed next to a layered sample and excited with a step-function change in voltage. Signals are digitized with 16-bit resolution at a sampling rate of 1 megasamples per second, and the excitation is repeated at a rate of 1 kHz. The instrument displays the difference in the transient current measured on the substrate and on the substrate plus coating. We measured pulsed eddy-current signals for a series of metal foils of varying thickness placed over 1 cm thick metal plates. Seven combinations of foil and substrate metals were studied including pure aluminum, copper, and titanium foils over substrates of aluminum, titanium alloy, and stainless steel. We report results for three types of samples: aluminum foils on Ti–6Al–4V substrate, titanium foils on 7075 aluminum alloys, and aluminum foils on AISI 304 stainless steel. Foil thickness ranged from 0.04–1.00 mm. We found that three features of the signal—the peak height, the time of occurrence of the first peak, and a characteristic zero-crossing time—depend sensitively upon the thickness of the layers and the relative electrical conductivity of coating and substrate. Theoretical calculations were compared to the measurements. Absolute agreement between calculated and measured signals was, in most cases, within 3%. No calibration with respect to artifact standards was used. Finally, a feature-based rapid inversion method was developed and used to infer the thickness and conductivity of the layers. The accuracy of the inversion depends upon the thickness of the layer and the contrast in conductivity between layer and substrate. For the materials studied the thickness could be determined within 13%, while the error in determining conductivity was 20%–30%. The time-domain method is much simpler and hundreds of times faster than the frequency-domain method previously reported by Moulder et al. [Rev. Sci. Instrum. 63, 3455 (1992)].

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The frequency-dependent impedance of right-cylindrical air-core eddy-current probes over thick metal plates whose conductivity and permeability vary as a function of depth in the near-surface region have been studied both experimentally and theoretically. Measurements of probe impedance were made from 1 kHz to 1 MHz using an impedance analyzer. Precision-wound air-core coils were used for testing the theory, and commercial eddy-current probes were used to connect with industrial practice. The samples were of two types. First, to model a continuous profile, otherwise uniform plates of metal covered with many thin, discrete layers of other metals were considered. Second, as a practical example, case-hardened titanium plates, whose near-surface conductivity varies smoothly and continuously as a function of depth, were considered. Two theoretical results are presented for continuously varying profiles. First, an exact closed-form solution (within the quasistatic approximation) is reported for the impedance of a right-cylindrical air-core probe above a nonmagnetic metal whose near-surface conductivity difference varies as a hyperbolic tangent as a function of depth. Second, a new numerical technique is reported for determining the impedance of an air-core probe above a layered material whose conductivity and permeability vary arbitrarily. It is shown that the numerical technique converges and that for a hyperbolic tangent profile it agrees with the closed-form analytic solution and experiment. In general, it was found that continuous profiles can be experimentally (and theoretically) simulated by stacking many thin layers with differing conductivities, and that the probe’s impedance change is larger if the conductivity change is localized at the surface, and is smaller for more diffuse profiles.

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