Resolution of two-dimensional currents in superconductors from a two-dimensional magnetic field measurement by the method of regularization

The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of regularization. Regularization directly addresses the inherent instability of this inversion problem for nonexact (noisy) data. Performance of the technique is evaluated for different current distributions and for data with varying amounts of added noise. Comparisons are made to other methods, and the present method is demonstrated to achieve a better regularizing (noise filtering) effect while also employing the generalized-cross validation (GCV) method to choose the optimal regularization parameter from the data, without detailed knowledge of the true (and generally unknown) solution. It is also shown that clean, noiseless data is an ineffective test of an inversion algorithm.