Uncertainties of a Spherical Magnetic Field Camera

Abstract

Spherical harmonic expansions are well-established tools for estimating magnetic fields from surface measurements and are widely used in applications such as tomographic imaging, geomagnetism, and biomagnetism. Although the mathematical foundations of these expansions are well understood, the impact of real-world imperfections, on the uncertainty of the field model has received little attention. In this work, we present a systematic uncertainty propagation analysis for a magnetic field camera that estimates the field from surface measurements using a spherical array of Hall magnetometers arranged in a spherical t-design. A Monte Carlo-based approach is employed to quantify how sensor-related uncertainties, such as calibration errors and positioning inaccuracies, affect the spatial distribution of the estimated field's uncertainty. The results offer insights into the robustness of spherical harmonic methods and help identify the dominant sources of uncertainty in practical implementations.