A measurement method for coil non-orthogonal angles based on electron paramagnetic resonance in NMR gyroscopes

Non-orthogonal angles between pairs of three-axis coils can lead to magnetic field bias and measurement errors, affecting the final angular velocity accuracy in Nuclear Magnetic Resonance Gyroscopes (NMRG). We analyzed the precession model of polarized Rb spin and the measurement model of non-orthogonal angles, and proposed a method to measure the non-orthogonal angle in NMRG after transverse magnetic compensation, which can simultaneously measure the coil constants. We also provided transformation matrix for coil magnetic field unit direction vector to the detection orthogonal coordinate system. The effectiveness of this method was demonstrated both theoretically and experimentally. The experimental results with uncertainty show that the non-orthogonal angles between the x - z , y - z , and x - y coils are ( 90.44 ± 0.03 ) ∘ , ( 90.30 ± 0.05 ) ∘ and ( 90.75 ± 0.05 ) ∘ , respectively. The coil constants along the x , y , and z axes are ( 372.9 ± 2.1 ) nT / mA , ( 413.4 ± 3.2 ) nT / mA , and ( 1648 ± 3.9 ) nT / mA , respectively. The proposed method can be applied to precise measurements using EPR VAM with other alkali metal atoms, especially for miniaturized atomic magnetometers and gyroscopes. In future work, the model established in this study can be used to suppress the magnetic field non-orthogonal coupling errors, enhancing the performance of atom magnetometers and NMR gyroscopes. • All non-orthogonal angles of the coil magnetic fields are measured. • Numerical solution of coil magnetic field direction vector. • In-situ residual magnetic field compensation. • Synchronous measurement of coil constants.