A Sensor Localization and Orientation Method for OPM-MEG Based on Rigid Coil Structures and Magnetic Dipole Fitting Models

High-precision sensor co-registration is a critical prerequisite for achieving high-resolution imaging in Optically Pumped Magnetometer-Magnetoencephalography (OPM-MEG) systems. The conventional magnetic dipole fitting method, essentially a multipole expansion approximation of a finite-size coil, exhibits accuracy that strongly depends on spatial geometric factors such as coil-sensor distance, dipole orientation, and the projection angle of the sensor's sensitive axis. Moreover, the approximation error increases significantly when sensors are placed either too close to the coils or at an unfavorable angular coupling. To address this issue, we propose a sensor localization and orientation method that combines magnetic dipole-equivalent modeling with a rigid coil structure (RCS). The RCS provides stable geometric constraints and eliminates uncertainties introduced by scalp-attached coils. In addition, three objective functions (the standard Frobenius norm, a weighted Frobenius norm and the structural similarity index (SSIM)) are formulated to mitigate the imbalance caused by near-field strong signals and to improve stability under noise and error propagation. Simulation results demonstrate that both under ideal conditions and with assembly perturbations, the weighted Frobenius norm and SSIM methods consistently achieve position errors below 1 mm and orientation errors below 1°, which effectively suppress large outlier deviations and achieve better performance than the standard Frobenius norm. The results confirm the effectiveness of the proposed method in achieving both high accuracy and robustness. Beyond clarifying the primary factors influencing magnetic dipole approximation errors, this study provides a geometry-constrained and optimization-based framework, offering a feasible pathway toward the practical implementation of high-precision, multi-channel OPM-MEG systems.