A corrected image method for uniform coil design with size adaptability in magnetic shielding rooms

Achieving a highly uniform magnetic field in magnetic shielding rooms (MSRs) is essential for the stable operation of optically pumped magnetometer (OPM) arrays in biomagnetic sensing and magnetoencephalography. However, the magnetic field generated by the coils inside the MSR is easily distorted by adjacent ferromagnetic materials, and traditional coil designs often struggle to maintain consistent performance in different MSRs of various sizes. This study proposes a design method for square uniform coils (SUCs) based on a corrected image method (CIM), which explicitly incorporates the finite thickness and permeability of shielding layers into the coil-field analytical model. The proposed CIM establishes a direct coupling relationship among shielding parameters, coil geometry, current distribution, and magnetic field, enabling shielding-aware coil optimization. A current adjustment method is also introduced, which allows the same coil structure to operate effectively in MSRs of different sizes by recalculating only the excitation currents. Simulation and experimental results demonstrate that the proposed SUC design achieves a uniform magnetic field volume fraction of 65.47% (error < 1%) within a 400 mm cubic region inside an MSR with a side length of 590 mm. Furthermore, the uniform-field performance remains stable for MSR side lengths ranging from 530 mm to 620 mm using the same coil structure. The proposed method outperforms conventional coil designs and provides a practical solution for precision magnetic field generation in biomagnetic sensing and quantum measurement systems.