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Uniqueness of Current Reconstructions for Magnetic Tomography in Multilayer Devices

Magnetic tomography is an important emerging technique for the nondestructive investigation and monitoring of electrical devices. Measurements of the magnetic field of the currents in a device are used to reconstruct the current distribution. Here we investigate the uniqueness problem for current reconstructions from multilayer devices. The general magnetic tomography problem is well known to be highly nonunique and unstable. Here, as a new result for the single-layer and multilayer device case we will study the splitting procedure and equivalence of the full nullspace to the nullspaces of operators supported on lower-dimensional subsets of the device. We will base our results on the uniqueness of wave source splitting combined with tools from potential theory and explicit estimates for particular surface integrals involving the Biot–Savart integral operator.