Uncertainties of a Spherical Magnetic Field Camera

TL;DR

This paper analyzes how real-world sensor uncertainties impact the accuracy of magnetic field estimations using spherical harmonic expansions in a spherical magnetic field camera, providing a systematic uncertainty propagation approach.

Contribution

It introduces a Monte Carlo-based method to quantify the effects of sensor errors on magnetic field estimates in spherical harmonic models.

Findings

Sensor calibration errors significantly affect field accuracy

Positioning inaccuracies contribute to uncertainty distribution

The approach helps identify dominant uncertainty sources

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.