Regional magnetic field prediction method in magnetic shielding room based on spherical harmonic function

Abstract This study addresses the challenge of predicting magnetic fields within magnetically shielded room for magnetocardiography (MCG) and magnetoencephalography (MEG). Traditional dense sensor arrays are prohibitively expensive, while single-point scanning introduces systematic errors. We propose a method utilizing a second-order spherical harmonic function to reconstruct the magnetic field. Six fluxgate sensors are symmetrically positioned around the target area, enabling the computation of spherical harmonic coefficients via regularized least-squares fitting to capture dipole and quadrupole modes. Experimental results demonstrate average prediction errors of 0.49 nT (5.23%), 0.33 nT (6.17%), and 0.15 nT (4.89%) for the X-, Y -, and Z -axis components, respectively. Compared to traditional methods, this method reduces the required sensor count by 77% and measurement time by 96% when predicting the magnetic field of 27 points in the target area. The key innovation lies in enabling high-precision field prediction with sparse measurements, thereby overcoming the limitations of point measurements. This technique surpasses prior art by achieving sub-nano Tesla accuracy while significantly reducing both cost and measurement time, providing an efficient solution for MCG and MEG systems.