Design for Biplane Self-Compensating Leakage Magnetic Coils Based on MOPSO-TFM

High-density arrays of optically pumped magnetometers (OPMs) suffer from severe sensor-to-sensor crosstalk and boundary coupling effects. Conventional biplanar coils often fail to limit leakage fields while maintaining internal uniformity without introducing complex active shielding layers. This work presents a design and optimization method for biplanar self-compensating leakage magnetic coils (SCLMCs) capable of producing spatially uniform magnetic fields while exhibiting rapid off-axis field decay. The approach begins with the target-field method (TFM), in which the prescribed magnetic-field distribution is imposed at discrete spatial nodes, and the associated current stream function is recovered through a Fourier-series representation regularized by the Tikhonov scheme to yield smooth and fabricable coil windings. To further enhance performance, a multi-objective particle swarm optimizer (MOPSO) is employed to directly refine the stream-function coefficients, simultaneously improving in-volume uniformity and out-of-volume attenuation without repeated field-model reconstruction. The resulting coil geometries exhibit improved field quality compared with conventional target-field designs. Finite element analysis confirms that the optimized coils achieve approximately 1.5% uniformity error within the target region, while the field attenuation capability outside the coil improves by 28.1% compared to conventional target-field designs. Scaled prototypes fabricated on printed circuit boards validate the simulation results. It is anticipated that this method will suppress magnetic field crosstalk in densely arranged optically pumped magnetometers-magnetoencephalography (OPM-MEG) and mitigate coupling between large compensation coils and ferromagnetic boundaries within magnetically shielded rooms.