In-situ and synchronous calibration of coil constants and non-orthogonal angles based on electron resonance

A novel method for in-situ calibration of magnetic coil constants and non-orthogonal angles based on electron resonance is proposed. We study the evolution process of the atomic ensemble polarization vector under the influence of bias magnetic fields and radio frequency magnetic fields. By analyzing the resonance curves under different magnetic fields, a calibration model for coil constants and non-orthogonal angles is established. Calibration is conducted both in the magnetic shield and in the geomagnetic field environment. We compare the proposed method with the conventional fluxgate method, and the experimental results show good consistency in both environments, with relative errors of less than 1.39% for coil constant measurements and absolute errors of less than 2.55° for non-orthogonal angle measurements. The method is suitable for calibrating the magnetic coils of miniaturized single-beam optically pumped atomic magnetometers, enabling in-situ calibration without the need for additional auxiliary devices.