Sampling and Layout of OPM Arrays for MCG Based on the Sampling Theorem

Given that the sampling and arrangement of the array need a reasonable standard to guide in high-precision magnetocardiography (MCG) imaging, the sampling range required for robust topography reconstruction is determined analytically by utilizing the frequency-domain analysis method according to the spatial Nyquist sampling theorem, and the layout with the highest sampling efficiency in uniform arrangement is found based on multidimensional sampling theorem. The results show that the upper limit of sampling distance required to reliably reconstruct the normal component is 0.71 times linearly related to the distance between the detection plane and source, and the minimum sampling period is also quantitatively associated with the distance and the noise level. When sampling the 2-D signal with the isotropic spectrum, among all uniform layouts without aliasing, the hexagonal lattice exhibits the highest sampling efficiency, surpassing that of the conventional rectangular lattice by approximately 12.15%. Finally, the necessity of sampling range and the effectiveness of hexagonal lattice are verified through simulation and experiment. This article provides the constraint and reference for the design of MCG array and the selection of sensor in various scenarios, while also indicating the sensor direction for further development.