Accuracy of numerical analysis for Hall sensor magnetometer measurements

The Hall sensor magnetometer is a widely used tool to characterize the homogeneity of high temperature superconducting tapes. However, it is well known that the current density distribution inside the sample, J, cannot be uniquely solved from the measured magnetic flux density, B. By discretising the Biot-Savart law the problem can be reduced to a solvable set of linear equations. Inaccurate assumptions about the sample geometry, noise in the measured data, and numerical errors can cause considerable error in the computed J. In this paper, a statistical approach to compare different inversion methods is presented. Example runs are carried out in order to find optimal locations for the measurement points. The results show that the relative error can be reduced by several orders of magnitude with the proper choice of measurement points, but the problem always remains ill-conditioned.