超极化³He气体在中子极化、基础物理和诊断医学等领域广泛应用．测量其极化率对于³He极化系统至关重要．通常使用自由感应衰减核磁共振（FID NMR）线圈来检测³He原子的FID信号．线圈的测量信噪比与直径、匝数、以及其与气室的相对位置等因素相关．关于FID NMR线圈的优化分析，目前仅有少量的文献提及且缺乏详细的实验验证．本文通过对FID信号和线圈噪声的理论分析，建立了线圈测量信噪比模型，并且在基于亚稳态交换光泵（Metastability-Exchange Optical Pumping，MEOP）极化技术的³He极化系统中对FID NMR线圈进行了实验验证．实验结果显示，在半径和高度均为r_cell的柱形气室中，线圈的测量信噪比在半径为r_cell/2时达到最优值，此结论与理论分析结果相符．该信噪比模型的相对误差不超过10%，证明了理论模型的有效性．这些研究结果对于优化设计³He极化系统具有重要的指导意义．

The application of hyperpolarized ³He gas is extensive in fields such as neutron polarimetry, fundamental physics, and diagnostic medicine. The polarimetry measurement is crucial for ³He polarization systems. Typically, a free induction decay nuclear magnetic resonance (FID NMR) coil is used to detect the FID signal of ³He atoms. The measurement signal-to-noise ratio (SNR) of the coil is correlated with factors such as diameter, number of turns, and relative position to the cell. There is limited literature and insufficient experimental verification on the optimization analysis of FID NMR coils. In this study, an SNR model for the coil was established through theoretical analysis of the FID signal and coil noise. The FID NMR coil was experimentally validated in a ³He polarization system based on the metastability-exchange optical pumping (MEOP) technique, which is known for its high polarization efficiency. The experimental results indicated that for a cylindrical cell with both radius and height of r_cell, the optimal SNR of the coil was achieved at a radius of r_cell/2, which was consistent with the theoretical analysis. The relative error of the fitted SNR model was less than 10%, demonstrating its effectiveness. These research findings hold significant practical implications for optimizing the design of ³He polarization systems.