A Multispectrum Fitting Program Based on Non-Linear Least-Squares Method for Line Parameters: Application to <sup>12</sup>CH<sub>4</sub>

Hong-liang MA; Jian-jie ZHENG; Qiang LIU; Xian-mei QIAN; Wen-yue ZHU

doi:10.3964/j.issn.1000-0593(2021)12-3887-05

Spectroscopy and Spectral Analysis, Volume. 41, Issue 12, 3887(2021)

A Multispectrum Fitting Program Based on Non-Linear Least-Squares Method for Line Parameters: Application to ¹²CH₄

Hong-liang MA^*, Jian-jie ZHENG^{1; 3; 4;}, Qiang LIU^{1; 3; *;}, Xian-mei QIAN^{1; 3;}, and Wen-yue ZHU^{1; 3;}

1. Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China

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Figures & Tables(6)

Fig. 1. Simplified flow diagram of the multispectrum fitting program

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Fig. 2. Example of multispectrum fitting program operation of with four spectra
(a): The measured (in scatter line) and calculated (in solid line)line profiles with a multi-peak fitting program; (b): The corresponding fitting residuals

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Table 1. The initial parameter names and meanings of the model

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Table 1. The initial parameter names and meanings of the model

输入参数	意义
Ω₂₉₆	296 K下分子的总配分函数
P	实验压强
T	实验温度
Ω_T	实验温度下的配分函数
BASE₀, BASE₁, BASE₂	二次多项式作为光谱基线时, 各次项的初始参数
IFLG	判断是否拟合该基线参数, 0表示固定, 1表示拟合
f	实验噪声水平
THE NUMBER OF TRANSITION	拟合的每张光谱中包含的跃迁谱线条数
ν₀	平移后的谱线中心位置初始值
γ_D	跃迁谱线的多普勒展宽半高半宽初始值
γ_P	跃迁谱线的压力展宽半高半宽初始值
A	跃迁谱线的面积初始值
S_H	数据库中相应谱线的强度
E	跃迁谱线的下能级值

Table 2. The data processing and significance of the main program

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Table 2. The data processing and significance of the main program

名称	意义
读取实验数据和文件名	将方框1中两列ASCII原始实验数据和方框2中与实验数据对应的TXT文件名称读取到主程序相应的内存中
读取模型参数	将方框3之前存储的拟合参数的初始值和实验条件读取到主程序中
寻找极值	搜索实验数据数组的最小值和最大值, 利用最小二乘拟合确定谱线中心位置
计算频率谱	利用当前参数计算频率谱
拟合光谱	对具有给定初始参数的数据执行最小二乘拟合, 并返回一组最佳拟合参数
输出参数	存储拟合之后的光谱数据及相应的谱线参数

Table 3. The execution steps and significance of the main program

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Table 3. The execution steps and significance of the main program

操作步骤名称	意义
HOW MANY SPECTRA DO YOU WANT TO SIMULATE	输入需要拟合几张光谱(即方框1中文件数量)
PLEASE INPUT THE ZERO FREQUENCY	输入谱线的中心频率平移值
ABSORPTION SPECTRUM: 2; TRANSMISSION SPECTRUM: 1	选择拟合光谱数据是发射谱还是吸收谱
SPECTRUM RECORDED AT THE SAME EXPERIMENTAL CONDITION? YES: 1; NO: 0	选择拟合光谱文件是否在同一实验条件下获得
DO YOU WANT TO PROCESS THE GLOBAL FITTING? YES: 1; NO: 0	是否需要进行全局拟合

Table 4. The air-broadening coefficients of ¹²CH₄ derived from the multispectrum fitting program and the difference between them and those from Ref. [7]

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Table 4. The air-broadening coefficients of ¹²CH₄ derived from the multispectrum fitting program and the difference between them and those from Ref. [7]

$ν_{0}^{b}$ /cm^-1	T/K	空气展宽系数/(cm^-1·atm^-1)
$ν_{0}^{b}$ /cm^-1	T/K	$γ_{ref}^{air}$	$γ_{TW}^{air}$	$(\frac{γ_{ref}^{air} - γ_{TW}^{air}}{γ_{TW}^{air}})$ /%
2 958.017 3	296.0±0.3	0.057 6(4)	0.057 7(3)	-0.17
	251.0±0.2	0.065 1(4)	0.065 3(3)	-0.31
	223.0±0.2	0.071 7(12)	0.071 9(3)	-0.28
	198.0±0.2	0.077 8(1)	0.078 2(4)	-0.51
	173.0±0.3	0.086 9(16)	0.088 4(8)	-1.7
2 958.120 0	296.0±0.3	0.064 9(3)	0.065 5(2)	-0.92
	251.0±0.2	0.075 2(3)	0.075 3(1)	-0.13
	223.0±0.2	0.083 6(3)	0.082 3(3)	1.58
	198.0±0.2	0.092 1(1)	0.092 1(2)	0
	173.0±0.3	0.104 2(6)	0.104 4(3)	-0.19
2 958.2329	296.0±0.3	0.064 1(10)	0.066 3(7)	-3.32
	251.0±0.2	0.074 0(3)	0.075 7(2)	-2.24
	223.0±0.2	0.082 1(7)	0.083 5(4)	-1.68
	198.0±0.2	0.089 7(9)	0.092 5(3)	-3.03
	173.0±0.3	0.100 2(16)	0.103 9(10)	-3.56
2 958.5364	296.0±0.3	0.060 1(7)	0.061 0(4)	-1.48
	251.0±0.2	0.069 3(5)	0.070 9(5)	-2.26
	223.0±0.2	0.076 1(10)	0.077 7(7)	-2.06
	198.0±0.2	0.083 2(2)	0.086 1(3)	-3.37
	173.0±0.3	0.092 2(12)	0.095 9(8)	-3.86
2 958.650 8	296.0±0.3	0.061 5(1)	0.063 6(6)	-3.30
	251.0±0.2	0.070 1(6)	0.071 0(5)	-1.27
	223.0±0.2	0.076 5(9)	0.080 5(8)	-4.97
	198.0±0.2	0.083 4(9)	0.085 2(8)	-2.11
	173.0±0.3	0.092 5(15)	0.097 1(14)	-4.74
2 958.682 5	296.0±0.3	0.055 8(18)	0.056 9(10)	-1.93
	251.0±0.2	0.063 9(4)	0.065 8(3)	-2.89
	223.0±0.2	0.070 0(6)	0.071 3(5)	-1.82
	198.0±0.2	0.077 4(8)	0.081 4(3)	-4.91
	173.0±0.3	0.086 4(21)	0.089 9(18)	-3.89

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Hong-liang MA, Jian-jie ZHENG, Qiang LIU, Xian-mei QIAN, Wen-yue ZHU. A Multispectrum Fitting Program Based on Non-Linear Least-Squares Method for Line Parameters: Application to ¹²CH₄[J]. Spectroscopy and Spectral Analysis, 2021, 41(12): 3887

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