Gradient phase and amplitude errors in atomic magnetic gradiometers for biomagnetic imaging systems

The cross-axis projection error (CAPE) caused by residual magnetic fields has recently attracted widespread attention. In this study, we propose a more specific theoretical model and expand the CAPE in gradient measurements. We first report that differences in relaxation rate and residual magnetic field between optically pumped magnetometers (OPMs) introduce a significant error term in the output of OPM gradiometers, referred to as the gradient phase error. Furthermore, when the longitudinal field compensation is inadequate, the interaxial response interference of a single OPM is prominent, resulting in an amplitude distortion of the signal. This is further amplified in the gradiometer configuration, introducing the gradient amplitude error. Our experiments demonstrated that the efficacy of mitigating common-mode noise of OPM gradiometers was significantly impaired when existing the gradient errors. In addition, a simulation with a magnetoencephalography (MEG) system illustrated an induced source localization error of exceeding 2 cm, severely compromising the localization accuracy of OPM-MEG systems.