A Novel Efficient Algorithm for Magnetic Biplanar Coils

Optically pumped magnetometers (OPMs) with ultrahigh sensitivity offer the potential for a significant advancement in magnetoencephalography (MEG), enabling wearable systems that benefit from their compact size and flexibility. OPM requires operating near-zero magnetic field. To compensate the residual magnetic field within the magnetic shielding room, external compensation coils are necessary. Biplanar coils are widely applied for magnetic compensation due to their simplicity and practicality. We introduce a novel convolution-type Gauss fast Fourier transform (CGFT) algorithm for accurate and efficient computation of convolution-type integrals, which plays an essential role in the forward and inverse modeling of biplanar coils. We prove that the traditional discrete/fast Fourier transform (DFT/FFT)-based algorithm should be used with caution. An insufficient value of grid expansion would bring significant errors into the forward process, which will further lead to an inadequately compensated target magnetic field. Numerical tests show that the CGFT algorithm is superior both in accuracy and efficiency comparing with the DFT/FFT algorithm and, thus, is always recommended in forward and inverse calculations. The CGFT method can be applied to the coil design of magnetic resonance imaging or the development of quantum precision measurement instruments, such as atomic gyroscopes and atomic magnetometers.