Analytical Approximations for the Expression of Absorption Current by Ferromagnetic Boundary Inside the MINI-Magnetically Shielded Cabin

The MINI-magnetically shielded cabin (MINI-MSC) offers a near-zero magnetic environment for optically pumped atomic magnetometers (OPMs) to measure the magnetocardiography (MCG) and magnetoencephalography (MEG). However, the MINI-MSC's confined interior and restricted uniform area make it challenging to capture high-quality bodily signals. Once the external interference surpasses the passive magnetic shielding capacity of the MINI-MSC, the volume and the homogeneity of the uniform region are reduced significantly, leading to the poor quality of the signal collected by OPMs. Therefore, an uniform active magnetic compensation system (UAMCS) composed of bi-planar coils (BCs) is introduced to suppress interference for enlarging the uniform region. The performance of the UAMCS depends on the BCs, but under finite-size ferromagnetic boundaries, approximate magnetic field values that deviate from reality are usually provided by the image method with the inaccurate calculation. To overcome these limitations, an analytical expression of the absorption current is derived to accurately characterize the coupling effect, thereby maintaining the high uniformity performance effectively. A forward analytical model is proposed to characterize magnetic fields, and the equivalent current could be analytically determined, which are put into the target field method (TFM) to express the superimposed the magnetic field. The inhomogeneity errors of BCs using the forward analytical model are 0.39 times of the image method. After the magnetic compensation, the signal-to-noise ratio at 0.1 Hz, 1 Hz and 10 Hz were improved by 39.5 dB, 34.3 dB, and 6.7 dB, respectively, verifying the magnetic noise can be well compensated in the whole target region. Note to Practitioners -The challenge of ensuring high signal quality in MINI-MSC for OPMs is critical in biomedical imaging applications. An forward analytical method is introduced to character the absorbed magnetic field of shielding layers, and an advanced UAMCS utilizing BCs is used for the precise magnetic field compensation to significantly enhance the signal-to-noise ratio. This approach addresses the limitations of traditional image methods, offering improved accuracy in magnetic compensation and enhance the reliability of MEG and MCG tests.