Several approaches are possible solve such problems in magnetic defectoscopy. For example, one may choose a certain analytical model find the solution of the direct problem and then compare the calculated values of the field with the measured ones.

We suggest to restore on a plane the scalar potential of magnetic field in air in a form of expansion series of harmonic polynomials and the parameters of a defect may be expressed in terms of the expansion coefficients.

In practice the magnetic field probes are disposed along a circumference above the manufactured article and the measured quantity is the magnetic field H component normal to the circumference. The expansion coefficients are found from Neumann's problem for a circle. If a defect has a complicated shape it is necessary to calculate quite a number of terms in the expansion series, but in the simple cases this number is less than ten. On the example of a surface defect we show that at such (sufficiently low) number of expansion series terms it is possible to determine the depth of a defect as well as its width.

The actual realization depends on the quality of magnetic field measurements: the field probes should be of very small sizes and should possess a high accuracy. We suggest the matrix transducers manufactured by the integral technology. They have magnetic field localization resolution upto 100 µm. The transducer 256 probes are disposed on 1 cm²area and allow to restore magnetic field in the immediate vicinity of the tested article surface.