Cross-Axis Dynamic Field Compensation of Optically Pumped Magnetometer Arrays for MEG

We present dynamic field compensation (DFC), whereby three-axis field measurements from reference magnetometers are used to dynamically maintain null at the alkali vapor cells of an array of primary sensors that are proximal to a subject's scalp. Precision measurement of the magnetoencephalogram (MEG) by zero-field optically pumped magnetometer (OPM) sensors requires that sensor response is linear and sensor gain is constant over time. OPMs can be operated in open-loop mode, where the measured field is proportional to the output at the demodulated photodiode output, or in closed-loop, where on-board coils are dynamically driven to maintain the internal cell at zero field in the measurement direction. While OPMs can be operated in closed-loop mode along all three axes, this can increase sensor noise and poses engineering challenges. Uncompensated fluctuations in the ambient field along any statically nulled axes perturb the measured field by tipping the measurement axis and altering effective sensor gain - a phenomenon recently referred to as cross-axis projection error (CAPE). These errors are particularly problematic when OPMs are allowed to move in the remnant background field. Sensor gain-errors, if not mitigated, preclude precision measurements with OPMs operating in the presence of ambient field fluctuations within a typical MEG laboratory. In this manuscript, we present the cross-axis dynamic field compensation (DFC) method for maintaining zero field dynamically on all three axes of each sensor in an array of OPMs. Together, DFC and closed-loop operation strongly attenuate errors introduced by CAPE. This method was implemented by using three orthogonal reference sensors together with OPM electronics that permit driving each sensor's transverse field coils dynamically to maintain null field across its OPM measurement cell. These reference sensors can also be used for synthesizing 1^st-gradient response to further reduce the effects of fluctuating ambient fields on measured brain activity and compensate for movement within a uniform field. We demonstrate that, using the DFC method, magnetic field measurement errors of less than 0.7% are easily achieved for an array of OPM sensors in the presence of ambient field perturbations of several nT.