Perturbation Theory Approach for the Impedance of an Air-core Coil Over a Surface-Breaking Flaw

Eddy-current air-core coils are widely used to detect surface flaws and to measure properties of the surface layers. The technique consists of measuring the impedance of the coil over a homogeneous half-space and then over a half-space with the flaw or the surface layer at various frequencies and for positions of the coil, and then inferring the properties of the flaw or the surface layer from the difference in the impedance. A crucial part of this process is the ability to solve the forward problem, i.e., computing the impedance when the properties of the flaw or the layer are given