Christopher Miller (MITRE)

Title:

Abstract:

The reconstruction of current distributions from samples of their induced magnetic field is a challenging problem due to multiple factors. First, the problem of reconstructing general three dimensional current distributions is inherently ill-posed. Second, the current-to-field operator performs a low-pass filter that dampens high spatial frequency information. Most contemporary methods for reconstructing current distributions in two dimensions are based on Fourier techniques and apply a low pass filter to the reconstructed field, which prevents excessive noise amplification during reconstruction at the cost of admitting blurring in the reconstructed solution. Meanwhile all methods that attempt to recover three dimensional distributions rely on constraining the distribution so that the problem is well posed. In this report we present a method of current recovery based on regularizing the $L1$ norm of the $curl$ of the current distribution. The utility of this method is based on the observation that in microelectronics settings, the conductivity is piecewise constant. We demonstrate both high resolution recovery of two-dimensional current distributions and stacked multi-layer distributions under challenging noise and standoff distance conditions.