Reconstruction of crack shape by optimization using eddy current field measurement

The eddy current field perturbation due to a thin crack may be described as the field generated by a current dipole layer located on the surface of the crack. In this paper the Fourier-transform of the eddy current field by a known dipole layer is evaluated analytically if the dipole layer density function is given as, for example, a Taylor´s or Fourier series. This result is used for the calculation of the impedance change of the exciting coil due to a crack by solving an integral equation. In the case of an unknown crack the measured impedance is used for reconstruction. By zeroth order optimization the shape of the crack is varied to fit the calculated impedance data to the measured ones. Several local minima of the objective function are found and statistically processed to give reliable approximation of the crack shape even in the case of sparse and noisy data