Simulation of Tomographic Reconstruction Algorithms for Open-Path Fourier Transform Infrared Spectroscopy

Chuling Deng; Jingjing Tong; Minguang Gao; Xiangxian Li; Yan Li; Xin Han; Wenqing Liu

doi:10.3788/AOS201939.0707001

Acta Optica Sinica, Volume. 39, Issue 7, 0707001(2019)

Simulation of Tomographic Reconstruction Algorithms for Open-Path Fourier Transform Infrared Spectroscopy

Chuling Deng^1,2, Jingjing Tong^1、*, Minguang Gao¹, Xiangxian Li¹, Yan Li¹, Xin Han¹, and Wenqing Liu¹

¹ Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, Anhui 230031, China

² University of Science and Technology of China, Hefei, Anhui 230026, China

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Figures & Tables(13)

Fig. 1. Reconstruction model

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Fig. 2. (a) Light path arrangement and (b) single-peak gas concentration field

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Fig. 3. Effect of relaxation factors α on reconstruction results. (a) Effect on nearness A; (b) effect on correlation coefficient R

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Fig. 4. Reconstruction results under different grid resolutions. (a)-(c) ART; (d)-(f) MLEM

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Fig. 5. Reconstruction results under different concentration fields. (a) Original concentration field of single peak; (b) original concentration field of double peak; (c) single peak, ART algorithm; (d) double peak, ART algorithm; (e) single peak, MLEM algorithm; (f) double peak, MLEM algorithm

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Fig. 6. Error analysis under different noise levels. (a) A; (b) R

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Table 1. Overall reconstruction accuracy under different grid resolutions
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Table 1. Overall reconstruction accuracy under different grid resolutions
Resolution Nearness A Correlation coefficient R Running time T /s
ART MLEM ART MLEM ART MLEM
5×5 0.236 0.073 0.972 0.998 0.153 0.061
7×7 0.227 0.056 0.978 0.999 0.185 0.064
10×10 0.197 0.055 0.981 0.999 0.236 0.066

Table 2. Detail reconstruction accuracy under different grid resolutions
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Table 2. Detail reconstruction accuracy under different grid resolutions
Resolution Peak value /(mg·m^-3) Peak error /% Peak location error /m
ART MLEM ART MLEM ART MLEM
5×5 39.7 45.3 20.60 9.40 4 4
7×7 38.7 44.6 22.60 10.80 5 5
10×10 39.1 45.6 21.80 8.80 4 4

Table 3. Overall reconstruction accuracy of different source locations

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Table 3. Overall reconstruction accuracy of different source locations

Source location	Nearness A		Correlation coefficient R		Running time T /s
Source location	ART	MLEM	ART	MLEM	ART	MLEM
(75,25)	0.167			0.044			0.986	0.999	0.219	0.063
(53,53)	0.200			0.057			0.980	0.998	0.218	0.064
(30,70)	0.180			0.051			0.983	0.999	0.217	0.067
Mean	0.182			0.049			0.983	0.999	0.218	0.065

Table 4. Detail reconstruction accuracy of different source locations

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Table 4. Detail reconstruction accuracy of different source locations

Source location	Peak value /(mg·m^-3)		Peak error /%		Peak location error /m
Source location	ART	MLEM	ART	MLEM	ART	MLEM
(75,25)	41.3			47.4			17.40	5.20	0	0
(53,53)	38.5			45.9			23.00	8.20	3.0	3.0
(30,70)	37.7			42.2			24.60	15.60	7.0	7.0
Mean	39.2			45.2			21.67	9.67	3.3	3.3

Table 5. Overall reconstruction accuracy of different concentration fields
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Table 5. Overall reconstruction accuracy of different concentration fields
Source location Nearness A Correlation coefficient R Running time T /s
ART MLEM ART MLEM ART MLEM
(55,75) 0.177 0.044 0.984 0.999 0.233 0.063
(35,55),(75,55) 0.263 0.069 0.964 0.998 0.228 0.065

Table 6. Detail reconstruction accuracy under different concentration fields

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Table 6. Detail reconstruction accuracy under different concentration fields

Source location	Peak value /(mg·m^-3)		Mean peak error /%			Peak location
Source location	ART	MLEM	ART	MLEM		ART	MLEM
(55,75)	64.90				75.40			17.40	5.20	(55,75)	(55,75)
(35,55),(75,55)	49.40,72.30				50.30,91.10			14.45	4.75	(35,55),(75,55)	(35,55),(75,55)

Table 7. Evaluation indexes of reconstruction under different noise levels
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Table 7. Evaluation indexes of reconstruction under different noise levels
Noise level Nearness A Correlation coefficient R
ART MLEM ART MLEM
0.3 0.402 0.352 0.929 0.936
0.5 0.656 0.527 0.872 0.885
0.7 1.134 1.498 0.706 0.585

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Chuling Deng, Jingjing Tong, Minguang Gao, Xiangxian Li, Yan Li, Xin Han, Wenqing Liu. Simulation of Tomographic Reconstruction Algorithms for Open-Path Fourier Transform Infrared Spectroscopy[J]. Acta Optica Sinica, 2019, 39(7): 0707001

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