High-precision in-situ triaxial coils calibration using NMOR atomic magnetometer with genetic algorithm assistance

We present an in-situ calibration method for triaxial magnetic coils that leverages a heading-error-free NMOR atomic magnetometer on the ⁸⁷Rb atoms F=1→F^′=1 transition. We derive an analytical expression for the NMOR response that holds for arbitrary field directions. Using it, we jointly identify the coil constants, non-orthogonal angles, and ambient field components from 27 triplets of three-axis currents under unshielded geomagnetic conditions. The method demonstrates robust performance, with measured and reconstructed resonance frequencies agreeing within a maximum relative error of 0.02%. The coil constant standard deviation does not exceed 0.09 nT/mA, and the non-orthogonal angle standard deviation does not exceed 0.02 °. An independent fluxgate calibration corroborates the results, with a maximum absolute difference of 0.44 nT/mA in coil constant and less than 0.19 degrees in angles. NMOR atomic magnetometer traces the measurements back to frequency through Zeeman splitting, and the ⁸⁷Rb atoms F=1→F^′=1 transition exhibits minimal nonlinear splitting which improves precision. As an in-situ method, it can calibrate triaxial coils integrated into miniaturized NMOR atomic magnetometers and is suited to magnetic metrology, compensation systems, and vector NMOR atomic magnetometers that require precise reference frame definition.