差分吸收光谱FFT+FT频谱细化方法研究

利用差分吸收光谱法（DOAS）可以实现污染气体的在线监测。为了提高监测精度，通常利用傅里叶变换滤波法（FFT）处理差分吸收光谱数据，但是因其频率分辨率的限制，影响其幅值精度，导致气体浓度的测量误差较大。提出了一种将FFT和FT相结合的差分光谱数据处理方法（FFT+FT），首先对差分吸收光谱数据做FFT变换，得到其全景谱，再对峰值点附近的频谱用改进的连续FT进行细化，提高特征吸收频段的分辨率，对幅值误差进行补偿，从而提高气体浓度在线监测的精度。实验配制了不同浓度的SO₂和NO₂气体，当细化倍数为15时，SO₂和NO₂气体的最大测量误差不超过3.68%和3.17%，相对于FFT法，平均误差分别降低了1.82%和1.45%；相对于传统的多项式拟合法，平均误差分别降低了14.9%和1.80%；对恒定浓度的SO₂和NO₂气体分别进行了多次测量，验证了FFT+FT方法的稳定性。分析了细化倍数对测量精度的影响，当细化倍数小于15时，浓度测量误差随着细化倍数的增加而降低；当细化倍数从15增加到20时，误差反而逐渐变大，在大于20以后，误差出现波动，且都大于细化倍数为15时的测量误差。由于细化倍数太大，使谱线过于密集，找到频谱序列最大值的概率降低了，因此在有噪声的情况下采用该法进行频谱校正时，会出现细化倍数加大而测量精度反而降低的现象。确定了最优细化倍数，在确保测量精度前提下，使频谱细化的计算量最小，满足DOAS法实时在线监测气体浓度的要求。

Research on FFT+FT Spectrum Zooming Method for Differential Optical Absorption Spectroscopy

Differential Optical Absorption Spectroscopy (DOAS) can be used to achieve online monitoring of polluted gas. To improve the monitoring accuracy, the Fourier Transform Filtering Method (FFT) is usually used to process differential absorption spectral data. However, due to the limitation of frequency resolution, its amplitude accuracy is affected, which leads to a large inversion error of gas concentration. A spectral data processing method that combining FFT and FT (FFT+FT) is proposed. First, the panoramic spectrum of differential absorption spectrum data is obtained by FFT filtering，then the spectrum near the peak point is refined by using the improved continuous FT, which can improve the resolution of the characteristic absorption frequency band, the amplitude error is compensated, and the accuracy of gas concentration on-line monitoring is improved. Many SO₂ and NO₂ gases with different concentrations were measured. When the zoom multiple is 15, the maximum measurement error of SO₂ and NO₂ gas is not greater than 3.68% and 3.17%. Compared with the FFT method, the average error decreases by 1.82% and 1.45%, respectively. Compared with the traditional polynomial fitting method, the average error is reduced by 14.9% and 1.80%, respectively. SO₂ and NO₂ gas with the same concentration were measured many times, which verified the stability of the algorithm. The influence of the zoom multiple on the measurement accuracy is analyzed. When the zoom multiple is less than 15, the concentration inversion error decreases with the increase of the zoom multiple. When the refinement multiple increases from 15 to 20, the error increases gradually. When the refining multiple is greater than 20, the errors fluctuate, and all of them are greater than the measurement errors when the multiple is 15. This is because the spectrum lines are too dense due to the large refinement multiples, and the probability of finding the maximum value of the spectrum sequence is reduced. Therefore, when the spectrum with noise is corrected by this method, the measurement accuracy will decrease with the increase of zoom multiple. To reduce the calculation amount of frequency spectrum zooming, the optimal zoom multiple is determined, which satisfies the requirements of measurement accuracy and meets the requirements of DOAS method for real-time online monitoring of pollution gas.