Inversion calculation of two dimensional current distributions from their magnetic field

For nondestructive evaluation and geophysical explorations, e.g., with superconducting quantum interference devices, efficient inversion calculations are needed. A program has been developed to compute the current distribution in a plane from the magnetic field sampled in a parallel plane. The process uses an iterative matrix inversion for the relation between current and magnetic field (the Biot-Savart law). Examples of the determination of up to 100*100 current dipoles out of magnetic field components with different signal-to-noise ratios as a function of distance are presented. The efficient indirect inversion procedure for calculating currents of up to 100*100 dipoles requires about 1 h on a VAX 3100 workstation, even if all three components of the magnetic field are disturbed by noise and the distance between the field and current plane is large, corresponding to a normalized distance g=10.<>