Fundamental analysis of the remote-field eddy-current effect

The Remote-Field Eddy-Current (RPEC) technique is used to nondestructively inspect both ferrous and nonferrous metal tubes. It is especially helpful when both the inside and outside of the pipe need to be examined, but only the inside of the pipe can be accessed. This method can also be used to detect wall loss on the outer tube if two tubes are arranged so that one is enclosed by the other. In order to elucidate the physics of the RPEC measurement, the mutual impedance between two induction coils, placed inside a long metal (ferrous or nonferrous) pipe is examined in detail. Cases where the coils are placed inside the innermost of two metal pipes are also considered. The impedance is decomposed into terms that represent waveguide modes (associated with the poles of its Fourier transform) and a radiation term (associated with the branch point singularity of its Fourier transform). The terms associated with the pole and branch point singularity are computed separately and compared to the total mutual impedance. It is shown that RFEC measurements can be made when the branch cut term (also known as a lateral or a head wave) is dominant. For completeness, a comparison between theoretically computed results and experimental measurements is given. The measured and calculated data agree well given uncertainty in the values for the parameters of the pipe which need to be input to the theoretical model.