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| A Study of Gas Absorption Spectral Inversion Method Based on K-MLE With Wide Concentration Range |
| YU Qin-yi1, 2, FAN Bo-qiang1, YOU Kun1, HE Ying1, ZHANG Shi-qi1, 2, CAI Ao-xue1, 2, HAN Ling-ran1, 2, ZHANG Yu-jun1* |
1. Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
2. University of Science and Technology of China, Hefei 230026, China
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Abstract The gas absorption spectroscopy technique, based on the Lambert-Beer Law, is extensively employed for the detection of various pollutant gases. However, challenges arise due to the limitations of devices, the saturation absorption of gases, and other interfering factors. When measuring gases at high concentrations, these issues create a nonlinear relationship between absorbance and concentration, resulting in significant deviations in gas detection across a wide concentration range.In this paper, we leverage the linear signal correlation between the measured spectra and reference spectra to reflect the relationship between the concentrations of the two. We propose employing Maximum Likelihood Estimation (MLE) to determine the linear correlation coefficient K between spectra signals, facilitating the inversion of gas concentrationsover a wide concentration range.To determine the linear correlation coefficients across variable spectral intervals in the gas absorption band, we implement a moving internal algorithm with adjustable parameters. The interval-wise statistical inference is carried out on the set of correlation coefficients, and optimal parameter estimators, K-values, are derived by constructing a piecewise likelihood function. This approach effectively mitigates fluctuations in measurement results caused by signal perturbation.Ultimately, gas concentration inversion across a wide concentration range is achieved through a combination of concentration threshold and compensation equation. Using sulfur dioxide (SO2) gas concentration detection as a case study, we process thirty sets of spectral datasets acquired under each predetermined concentration condition. The accuracy of the concentration inversion methodologywas quantified through the relative error of the mean concentrations calculated from thirty replicate measurements. At the same time,its stability wasevaluatedusing the standard deviation of the concentration values. Under identical low-concentration conditions, the broadband method, narrowband method, and K-MLE algorithm demonstrated mean retrieved concentration errors of 6.14%, 22.13%, and 0.11% respectively. Under the premise of ensuring the stability of the results, the K-MLE algorithm achieved superior measurement accuracy. Furthermore, across a wide concentration range of 0~508 μL·L-1, the maximum mean error for concentration inversion of the K-MLE method is only 0.98%, with a maximum standard deviation of 1.25, outperforming the other two conventional methods. The results demonstrate that the K-MLE method offers an effective approach for nonlinear offset compensation, enabling accurate and stable gas concentration inversion across a wide range of concentrations.
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Received: 2024-10-21
Accepted: 2025-04-22
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Corresponding Authors:
ZHANG Yu-jun
E-mail: yjzhang@aiofm.ac.cn
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