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Beam arrangement with limited projections based on tunable diode laser absorption spectroscopy is the key to achieving a more accurate two-dimensional reconstruction of the combustion. Using fractional calculus theory, a beam optimization method based on fractional Tikhonov regularization is proposed. The beam arrangement function based on fractional Tikhonov regularization is established by extending the standard Tikhonov regularization to fractional modes. The genetic algorithm is used to analyze the calculation results of different orders in a range of (0, 1), and the beam arrangement is obtained. Using 20 laser beams to scan the characteristic absorption spectrum of H2O in the near-infrared band 7185.6 cm–1, modeling the calculations in a 10×10 element discrete tomography domain, and comparing the reconstruction results of the five beam arrangements for different Gaussian distribution models, the beam arrangement based on fractional Tikhonov regularization shows more obvious advantages. This design method proposed in this work is valuable for the theoretical study of the optimal design of two-dimensional measurement beams based on the tunable diode laser absorption spectroscopy technique, which can promote the application of this technique in the two-dimensional reconstruction of complex engine combustion and combustion efficiency improvement.
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Keywords:
- laser absorption spectroscopy /
- two-dimensional reconstruction /
- fractional Tikhonov regularization /
- beam arrangement optimization
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Song J L, Hong Y J, Wang G Y, Pan H 2014 Infrared Laser Eng. 43 2460
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图 1 TDLAS测量及重建示意图
Figure 1. Schematic diagram of TDLAS measurement and reconstruction.
图 2 遗传算法求解流程框图
Figure 2. Flow chart of genetic algorithm.
图 3 滤波函数随阶数α的变化
Figure 3. Variation of filter function with α order.
图 4 不同阶数下正则化参数取值对遗传算法结果的影响 (a) α = 0.2; (b) α = 0.4; (c) α = 0.5; (d) α = 0.6; (e) α = 0.8; (f) α = 1.0
Figure 4. Influences of regularization parameters on the genetic algorithm results under different orders: (a) α = 0.2; (b) α = 0.4; (c) α = 0.5; (d) α = 0.6; (e) α = 0.8; (f) α = 1.0
图 5 光路优化函数的遗传算法求解
Figure 5. Genetic algorithm solution for beam optimization function.
图 6 不同阶数取值下的光路优化函数求解
Figure 6. Solution of beam optimization function under different order values.
图 7 五种光路布置方式的空间分布图与投影点分布图 (a) 2×10正交光路布置方式; (b) 4×5扇形光路布置方式; (c) 交叉光路布置方式; (d) 基于标准Tikhonov正则化设计的光路布置方式; (e) 基于分数阶Tikhonov正则化设计的光路布置方式
Figure 7. Spatial distribution and projection point distribution diagram of five beam arrangements: (a) 2×10 orthogonal optical path arrangement; (b) 4×5 fan-shaped optical path arrangement; (c) cross optical path arrangement; (d) beam arrangement based on standard Tikhonov regularization design; (e) beam arrangement based on fractional Tikhonov regularization design.
图 8 单峰分布模型与不同光路布置方式的重建结果图 (a) 重建模型; (b) 2×10正交光路布置方式; (c) 4×5扇形光路布置方式; (d) 交叉光路布置方式; (e) 基于标准Tikhonov正则化设计的光路布置方式; (f) 基于分数阶Tikhonov正则化设计的光路布置方式
Figure 8. Reconstruction results of unimodal distribution model and different beam arrangements: (a) reconstruction model; (b) 2×10 orthogonal beam arrangement; (c) 4×5 fan-shaped beam arrangement; (d) cross beam arrangement (e) beam arrangement based on standard Tikhonov regularization design; (f) beam arrangement based on fractional Tikhonov regularization design.
图 9 双峰分布模型与不同光路布置方式的重建结果图 (a) 重建模型; (b) 2×10正交光路布置方式; (c) 4×5扇形光路布置方式; (d) 交叉光路布置方式; (e) 基于标准Tikhonov正则化设计的光路布置方式; (f) 基于分数阶Tikhonov正则化设计的光路布置方式
Figure 9. Reconstruction results of bimodal distribution model and different beam arrangements: (a) Reconstruction model; (b) 2×10 orthogonal beam arrangement; (c) 4×5 fan-shaped beam arrangement; (d) cross beam arrangement; (e) beam arrangement based on standard Tikhonov regularization design; (f) beam arrangement based on fractional Tikhonov regularization design.
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[1] Strand C L, Hanson R K 2015 AIAA J. 53 2978
Google Scholar
[2] Wang Z, Deguchi Y, Kamimoto T, Tainaka K, Tanno K 2020 Fuel 268 117370
Google Scholar
[3] Liu C, Xu L, Chen J, Cao Z, Lin Y, Cai W 2015 Opt. Express 23 22494
Google Scholar
[4] Jatana G S, Perfetto A K, Geckler S C, Partridge W P 2019 Sens. Actuators, B 293 173
Google Scholar
[5] Peng W Y, Strand C L, Hanson R K 2020 Appl. Phys. B 126 1
Google Scholar
[6] Tsekenis S, Wilson D, Lengden M, Hyvönen J, Leinonen J, Shah A, Andersson Ö, McCann H 2017 Flow Meas. Instrum. 53 116
Google Scholar
[7] Liu C, Tsekenis S-A, Polydorides N, McCann H 2018 IEEE Sens. J. 19 1748
Google Scholar
[8] Shui C, Wang Y, Cai W, Zhou B 2021 Opt. Express 29 20889
Google Scholar
[9] Brown M, Herring G, Cabell K, Hass N, Barhorst T, Gruber M 2012 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition Nashville, Tennessee, January 9–12, 2012 p857
[10] [11] Wang F, Wu Q, Huang Q, Zhang H, Yan J, Cen K 2015 Opt. Commun. 346 53
Google Scholar
[12] Song J, Hong Y, Wang G, Pan H 2013 Appl. Phys. B 112 529
Google Scholar
[13] 王兴平, 彭冬, 李佳胜, 金熠, 翟超 2021 中国激光 48 0711002
Google Scholar
Wang X P, Peng D, Li J S, JinY, Zhai C 2021 Chin. J. Lasers 48 0711002
Google Scholar
[14] 李金义 2008 博士学位论文 (天津: 天津大学)
Li J Y 2013 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese)
[15] Terzija N, Davidson J, Garcia-Stewart C, Wright P, Ozanyan K, Pegrum S, Litt T, McCann H 2008 Meas. Sci. Technol. 19 094007
Google Scholar
[16] Sun P, Zhang Z, Li Z, Guo Q, Dong F 2017 Appl. Sci. 7 990
Google Scholar
[17] Xu L, Liu C, Jing W, Cao Z, Xue X, Lin Y 2016 Rev. Sci. Instrum. 87 013101
Google Scholar
[18] 房鹏飞, 贾兆丽, 陈东, 王尹秀 2016 激光与光电子学进展 53 071001
Google Scholar
Fang P F, Jia Z L, Chen D, Wang Y X 2016 Laser Optoelectron. Prog. 53 071001
Google Scholar
[19] 宋俊玲, 洪延姬, 王广宇 2013 光学学报 33 0430001
Google Scholar
Song J L, Hong Y J, Wang G Y 2013 Acta Opt. Sin. 33 0430001
Google Scholar
[20] Tsekenis S, Tait N, McCann H 2015 Rev. Sci. Instrum. 86 035104
Google Scholar
[21] Yu T, Tian B, Cai W 2017 Opt. express 25 5982
Google Scholar
[22] 宋俊玲, 洪延姬, 王广宇, 潘虎 2014 红外与激光工程 43 2460
Song J L, Hong Y J, Wang G Y, Pan H 2014 Infrared Laser Eng. 43 2460
[23] 那奕君, 李宁, 黄孝龙, 翁春生 2020 光谱学与光谱分析 40 3686
Na Y J, Li N, Huang X L, Weng C S 2020 Spectrosc. Spectral Anal. 40 3686
[24] Grauer S J, Hadwin P J, Daun K J 2016 Appl. Opt. 55 5772
Google Scholar
[25] Twynstra M G, Daun K J 2012 Appl. Opt. 51 7059
Google Scholar
[26] 李宁, Tu Xin, 黄孝龙, 翁春生 2020 69 227801
Google Scholar
Li N, Tu X, Huang X L, Weng C S 2020 Acta Phys. Sin. 69 227801
Google Scholar
[27] Morigi S, Reichel L, Sgallari F 2017 J. Comput. Appl. Math. 324 142
Google Scholar
[28] Hochstenbach M E, Reichel L 2011 BIT Numer. Math. 51 197
Google Scholar
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