surrey GU2 5XH, United Kingdom.

In eddy-current reconstruction the aim is to approach a full characterisation of defects using either probe responses or electromagnetic field data to infer the flaw geometry. The process of inverting the data is inherently ill-conditioned therefore a good deal of care is needed in designing an algorithm giving stable results in the presence of noise(!]. We have developed a new general purpose numer ical inversion method, applicable to a wide range of problems in nondestructive evaluation and to eddy-current flaw reconstruction in particular. Here we shall apply the procedure to solve an inverse source problem in eddy-current testing, using limited a priori knowledge of the flaw to ensure that the source distribution is uniquely defined. Suppose we know the magnetic field above the plane surface of a conductor resulting from the scattering of eddy currents by a subsurface crack. If the crack has a negligible opening and acts as a surface barrier to eddy-currents, its effect on the field is the equivalent of a surface layer of current dipoles (2]. Because the dipole moment extends over the whole crack surface and is zero elsewhere, finding the dipole distribution from the scattered r.1agnetic field reveals the size, shape and orientation of the flaw. In general the dipole density associated with a given magnetic field outside the conductor is not unique, therefore one cannot in general, determine the crack geometry from the external magnetic field at a particular frequency, without additional information. However by assuming the crack lies in a known plane, the extent of the dipole distribution in the plane may be found and hence the flaw geometry inferred. SCALAR POTENTIAL In formulating the inverse problem we neglect displacement current. The magnetic field in air ( z>O) scattered by a flaw in the conductor ( z<O) is expressed in terms "'f the transverse electric ( TE) Hertz potential W(r) as [3