The magnetic inverse problem for two stacked layers of sources

TL;DR

This paper introduces a method to reconstruct electronic current densities in two stacked layers using magnetic field measurements at two planes, with potential applications in non-destructive testing of layered electronic devices.

Contribution

The paper develops a novel inverse problem solution for two-layer current density reconstruction from magnetic field data, validated through numerical simulation.

Findings

Accurate current density reconstruction demonstrated in simulations.

Method applicable to non-destructive testing of layered electronic devices.

Framework extendable to more than two layers in future work.

Abstract

We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both current layers, one below -- corresponding to non-invasive measurements of the field. We corroborate the accuracy of current density reconstruction from the resulting system of equations using a numerical simulation. This method is anticipated to be applicable to non-destructive current imaging for quality assurance in a range of applications featuring two-layer geometries, including printed circuit boards, capacitors, fuel cells, and battery cells; we focus particularly here on battery cells, due to their rapidly increasing relevance for automotive applications. This method also offers a framework for generalising the model to more than two layers in future work.