Error analysis and vapor cell temperature optimization for NMR sensor

Nuclear magnetic resonance (NMR) sensors hold great potential for research advancements. The precision of NMR sensors depends on the frequency stability of Xe isotopes. However, the measurement noise of the embedded Rb magnetometer exerts a significant nonlinear influence on the Xe frequency via the phase detector and phase-locked loop, thereby rendering the error propagation process highly complex and intractable. Existing research lacks corresponding modeling analysis. Therefore, a novel temperature optimization method is proposed to reduce NMR sensor root mean square error (RMSE) based on the temperature-dependent RMSE model. First, the error propagation of the NMR sensor is analyzed based on error amplitude spectral density, demonstrating that the temperature-related Xe signal amplitude and relaxation rate are key factors influencing error propagation. Then, a temperature-dependent RMSE model of the NMR sensor is developed to accurately determine the vapor cell temperature. Finally, the NMR sensor RMSE is reduced by optimizing vapor cell temperature. The experiment verifies the effectiveness of the model, with a goodness of fit of 96.2%, and reduces the sensor RMSE by 22.8%. Compared to traditional methods, the proposed method significantly improves the accuracy of NMR sensors without incurring additional data lag and hardware costs.