Research on Gas Concentration Measurement Method Based on Gradient Descent Method to Fit Spectral Absorption Signal Directly

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Fig. 1. Fitting flowchart

Fig. 2. Experimental system diagram

Fig. 3. Point selection for initial value calculation of incident laser intensity parameters

Fig. 4. Convergence speed of five step factors

Fig. 5. Fitting results at different concentrations
(a): 10%; (b): 12%; (c): 14%; (d): 16%; (e): 18%; (f): 20%

Fig. 6. Absorbance at different concentrations obtained by routine baseline fitting

Line	Wavelength /nm	Linestrength S [cm^-1·(molecule·cm^-2)^-1]	Self-broadening γ_self/(cm^-1·atm^-1)	Air-broadening γ_air/(cm^-1·atm^-1)
Line1	1 580.512 7	1.301×10^-23	0.096	0.071 6
Line2	1 580.039 5	1.431×10^-23	0.098	0.072 7

Table 1. Spectral parameters of two absorption lines of CO₂ around 1 580 nm (296 K)

实际浓度	直接拟合法拟合浓度	相对误差1	拟合方差	积分面积法计算浓度	相对误差2
10%	10.37%	3.70%	9.27×10^-5	9.07%	-9.30%
12%	12.53%	4.40%	3.29×10^-5	11.49%	-4.25%
14%	14.57%	4.07%	6.39×10^-5	12.96%	-7.43%
16%	16.14%	0.90%	1.85×10^-5	15.29%	-4.44%
18%	17.70%	-1.65%	8.32×10^-5	17.11%	-4.94%
20%	19.79%	-1.03%	6.92×10^-5	19.18%	-4.10%

Table 2. Analyze the results of direct fitting method and integral area method

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