基于激光非线性的谐波通项推导和nf/1f免标应用

Deduction of General Term for Harmonics and Application of Calibration-Free nf/1f Models Based on the Lazer Nonlinearity

摘要: 本文通过高精度标定实验分析了可调谐二极管激光吸收光谱(TDLAS)中波长调制时广泛存在的激光频率和光强的非线性现象，通过吸收光谱理论和谐波理论推导出了基于激光非线性的各次谐波通项表达式和nf/1f免标模型；基于实际测量中二倍频(二阶近似)即可较高精度描述激光频率和光强的特征，建立了实用的、简化的、高精度的nf/1f模型。实验以CO分子的4300.6999 cm−1谱线为例，利用建立的nf/1f二阶近似模型对强、弱两种吸收工况下的CO气体浓度进行了测量，并将其与忽略激光非线性效应的测量结果进行对比。实验结果表明，当充分考虑激光频率和光强非线性效应时，基于二阶近似的2f/1f、4f/1f和6f/1f模型均可实现CO浓度的高精度测量，各次谐波测得的相对误差不超过0.5%。

Abstract: The nonlinearity of the laser frequency and intensity response in the wavelength modulation spectroscopy (WMS) was analyzed through the high-accuracy experiments. By full consideration of the nonlinear effect, the nf harmonic, and thus the calibration-free nf/1f model were further deduced based on the absorption spectrum and harmonic theory. Moreover, a practical and sim-plified nf/1f calibration-free method was established based on the second-order approximation of the laser frequency and intensity. As a verification of the proposed method, the CO transition at 4300.699 cm−1 was investigated under both strong and weak absorption conditions. Meanwhile, the CO concentrations were measured with the proposed method and compared with those ignoring the nonlinear effect. The measurement result shows that the accuracy of the gas concentration measurement can be effectively improved with consideration of the nonlinearity of laser intensity and frequency. In addition, the CO concentration can be measured with high precision (relative error < 0.5%) by using the quadratic approximation 2f/1f, 4f/1f and 6f/1f methods.