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Light field camera can solve the problems of complex optical path and difficult synchronous trigger of radiation temperature measurement multi camera system, which has some unique advantages in three-dimensional temperature reconstruction of radiation imaging. The LSQR is a classical algorithm for solving the least square problem based on large sparse matrix. When the algorithm is used to reconstruct three-dimensional temperature field, it depends on the initial value of temperature, and the reconstruction accuracy is not ideal when the signal-to-noise ratio is low. In this paper, a damped LSQR-LMBC reconstruction algorithm is proposed. By adding a damped regularization term into the LSQR method, the anti noise performance of flame three-dimensional temperature field reconstruction is improved. By combining the LMBC algorithm, the absorption coefficient and three-dimensional temperature field are solved at the same time. In the numerical simulation part, with the gradual reduction of signal-to-noise ratio, the reconstruction effect of Damped LSQR turns more stable than LSQR. When the signal-to-noise ratio reaches 13.86 dB, the reconstruction accuracy is improved by about 30%. The average reconstruction error of damped LSQR-LMBC is 6.63%. The three-dimensional temperature field distribution of butane flame is consistent with the characteristic of radiation flame combustion. Compared with the temperature measurement data of thermocouple, the relative error is about 6.8%.
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Keywords:
- light field camera /
- flame /
- 3 D temperature field /
- damped LSQR-LMBC reconstruction algorithm
[1] 孙晓刚, 戴景民, 丛大成, 褚载祥 2003 清华大学学报: 自然科学版 43 916
Sun X G, Dai J M, Cong D C, Chu Z X 2003 J. Tsinghua Univ., Sci. Technol. 43 916
[2] 黄苏春 2004 硕士学位论文(上海: 同济大学)
Huang S C 2004 M. S. Thesis (Shanghai: Tongji University) (in Chinese)
[3] Zhou B, Zhang J Y, Wang S H 2011 IET Image Process 5 382
Google Scholar
[4] 黄群星, 刘冬, 王飞, 严建华, 池涌, 岑可法 2007 56 6472
Google Scholar
Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6472
Google Scholar
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Google Scholar
[6] Hossain M M, Lu G, Sun D, Yan Y 2013 Meas. Sci. Technol. 24 074010
Google Scholar
[7] 陆永刚, 王式民, 朱震, 徐益谦 2000 光学学报 20 570
Lu Y G, Wang S M, Zhu Z, Lu Y, Xu Y Q 2000 Acta Opt. Sin. 20 570
[8] Zhu H, Wang Q, Yu J Y 2017 Front. Inf. Technol. Electron. Eng. 18 1236
Google Scholar
[9] Apelt F, Breuer D, Nikoloski Z, Stitt M, Kragler F 2015 Plant J. 82 693
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Google Scholar
[12] 肖相国, 王忠厚, 孙传东, 白加光 2008 光学学报 37 2539
Xiao X G, Wang Z H, Sun C D, Bai J G 2008 Acta Photonica Sin. 37 2539
[13] Su L J, Zhou Z L, Yuan Y, Hu L, Zhang S Y 2015 Optik 126 877
Google Scholar
[14] Tian L, Waller L 2015 2015 Optica 2 104
Google Scholar
[15] Fahringer T W, Lynch K P, Thurow B S 2015 Meas. Sci. Technol. 26 115201
Google Scholar
[16] Horstmeyer R, Euliss G, Athale R 2009 IEEE International Conference on Computational Photography (ICCP) San Francisco, CA USA, April 16–17, 2009 p1
[17] Prevedel R, Yoon Y G, Hoffmann M, Pak N, Wetzstein G, Kato S, Schrödel T, Raskar R, Zimmer M, Boyden E S, Vaziri A 2014 Nat. Methods 11 727
Google Scholar
[18] 聂云峰, 相里斌, 周志良 2011 中国科学院大学学报 28 563
Nie Y F, Xiang L B, Zhou Z L 2011 J. Grad. Univ. Chin. Acad. Sci. 28 563
[19] 周志良 2012 博士学位论文 (合肥: 中国科学技术大学)
Zhou Z L 2012 Ph. D. Dissertation(Hefei: University of Science and Technology of China) (in Chinese)
[20] Yuan Y, Liu B, Li S, Tan H P 2016 Int. J. Heat Mass Tran. 102 518
Google Scholar
[21] Li T J, Li S, Yuan Y, Liu Y D, Xu C L, Shuai Y, Tan H P 2017 Opt. Express 25 8274
Google Scholar
[22] Sun J, Xu C L, Zhang B, Hossain M M, Wang S M, Qi H, Tan H P 2016 Opt. Express 24 1118
Google Scholar
[23] Xu C L, Zhao W C, Hu J H, Zhang B, Wang S M 2017 Fuel 196 550
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[24] Sun J, Hossain M M, Xu C L, Zhang B, Wang S M 2017 Opt. Commun. 390 7
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[25] Sun J, Hossain M M, Xu C L, Zhang B 2018 Int. J. Heat Mass Transfer 121 1281
Google Scholar
[26] Zhao W C, Zhang B, Xu C L, Duan L B, Wang S M 2017 IEEE Sens. J. 18 528
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[27] Adelson E H, Wang J Y 1992 IEEE Trans. Pattern Anal. Mach. Intell. 14 99
Google Scholar
[28] 程万胜, 赵杰, 蔡鹤皋 2008 光学精密工程 16 314
Cheng W S, Zhao J, Cai H G 2008 Opt. Precis. Eng. 16 314
[29] 孙俊 2018 博士学位论文 (南京: 东南大学)
Sun J 2018 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)
[30] 孙俊阳 2018 硕士学位论文 (南京: 东南大学)
Sun J Y 2018 M. S. Thesis Dissertation (Nanjing: Southeast University) (in Chinese)
[31] 杨薇, 刘四新, 冯彦谦 2008 物探与化探 32 199
Yang W, Liu S X, Feng Y Q 2008 Geophys. Geochem. Explor. 32 199
[32] 孟祥宁 2012 硕士学位论文 (成都: 成都理工大学)
Meng X N 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)
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Google Scholar
Meng X N, Zhong Z, Wang Y F 2012 Sci. Techno. of West Chin. 11 33
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Google Scholar
[35] Zhou P, Zhang Y T, Yu Y L, Cai W J, Zhou G Q 2020 Math. Biosci. Eng. 17 654
Google Scholar
[36] 牛春洋 2016 博士学位论文 (哈尔滨: 哈尔滨工业大学)]
Niu C Y 2016 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)
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图 1 光场相机结构示意图
Figure 1. Structure diagram of light field camera.
图 2 模拟火焰中心切片温度分布
Figure 2. Temperature distribution of simulated flame center slice.
图 3 模拟火焰光场辐射图像
Figure 3. Simulated flame light field radiation image.
图 4 QR和阻尼LSQR算法的火焰温度场重建结果
Figure 4. Flame temperature field reconstruction results of LSQR and damped LSQR algorithms.
图 5 不同噪声水平下, LSQR与阻尼LSQR算法重建误差对比 (a)初值叠加1%噪声; (b) 初值叠加5%噪声; (c) 初值叠加10%噪声; (d) 初值叠加15%噪声; (e) 初值叠加20%噪声
Figure 5. Comparison of reconstruction errors between LSQR and Damped LSQR algorithm under different noise levels: (a) Initial value superimposed 1% noise; (b) initial value superimposed 5% noise; (c) initial value superimposed 10% noise; (d) initial value superimposed 15% noise; (e) initial value superimposed 20% noise.
图 6 阻尼LSQR-LMBC算法下重建的火焰温度分布图
Figure 6. Flame temperature distribution reconstructed by Damped LSQR-LMBC algorithm.
图 7 阻尼LSQR-LMBC算法重建的火焰温度的相对误差 (a) –16 mm位置; (b) 火焰–12 mm位置; (c) –8 mm位置; (d) –4 mm位置; (e) 0 mm位置
Figure 7. Relative errors of flame temperature reconstructed by Damped LSQR－LMBC algorithm: (a) –16 mm position; (b) –12 mm position; (c) –8 mm position; (d) –4 mm position; (e) 0 mm position.
图 8 光场相机辐射强度标定实验装置图
Figure 8. Experimental deviceofradiation intensity calibration of light field camera.
图 9 不同炉温下的黑体辐射光场图像 (a) 1098.15 K; (b) 1123.15 K; (c) 1148.15 K; (d) 1173.15 K; (e) 1198.15 K; (f) 1123.15 K; (g) 1248.15 K; (h) 1273.15 K
Figure 9. Blackbody radiation light field images at different furnace temperatures: (a) 1098.15 K; (b) 1123.15 K; (c) 1148.15 K; (d) 1173.15 K; (e) 1198.15 K; (f) 1123.15 K; (g) 1248.15 K; (h) 1273.15 K.
图 10 光场图像灰度值与辐射强度的标定拟合曲线图
Figure 10. Calibration fitting curve of gray value and radiation intensity of light field image.
图 11 燃烧火焰实验图 (a) 实验装置; (b) 丁烷火焰辐射光场
Figure 11. Experimental diagram of combustion flame: (a) Experimental device; (b) light field of butane flame radiation.
图 12 丁烷火焰三维温度重建后的不同层温度分布图
Figure 12. Temperature distributions of different layers after three-dimensional temperature reconstruction of butane flame.
图 13 使用热电偶测量丁烷火焰温度 (a) 热电偶测温实验图; (b) 热电偶定点测温位置图
Figure 13. Measurement of butane flame temperature using thermocouples: (a) Thermocouple temperature measurement experiment diagram; (b) location diagram of thermocouple fixed-point temperature measurement.
表 1 LSQR与阻尼LSQR温度重建结果相对误差对比表
Table 1. Comparison of relative errors of temperature reconstruction results of LSQR and Damped LSQR.
噪声 信噪比/dB LSQR 阻尼LSQR 1% 45.95 0.43% 0.41% 5% 29.44 2.85% 2.15% 10% 21.97 6.66% 5.10% 15% 17.35 10.26% 7.67% 20% 13.86 14.58% 10.99% 
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表 2 阻尼LSQR-LMBC重建温度与热电偶修正温度对比表
Table 2. Comparison of DampedLSQR-LMBC reconstruction temperature and thermocouple correction temperature.
测量方法 A B C D T/ K T/ K T/ K T/ K 阻尼LSQR-LMBC 1121.78 1396.73 1351.81 1077.74 热电偶 1044.35 1307.5 1295.36 997.61
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[1] 孙晓刚, 戴景民, 丛大成, 褚载祥 2003 清华大学学报: 自然科学版 43 916
Sun X G, Dai J M, Cong D C, Chu Z X 2003 J. Tsinghua Univ., Sci. Technol. 43 916
[2] 黄苏春 2004 硕士学位论文(上海: 同济大学)
Huang S C 2004 M. S. Thesis (Shanghai: Tongji University) (in Chinese)
[3] Zhou B, Zhang J Y, Wang S H 2011 IET Image Process 5 382
Google Scholar
[4] 黄群星, 刘冬, 王飞, 严建华, 池涌, 岑可法 2007 56 6472
Google Scholar
Huang Q X, Liu D, Wang F, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 6472
Google Scholar
[5] Gilabert G, Lu G, Yan Y 2007 IEEE Trans. Instrum. Meas. 56 1300
Google Scholar
[6] Hossain M M, Lu G, Sun D, Yan Y 2013 Meas. Sci. Technol. 24 074010
Google Scholar
[7] 陆永刚, 王式民, 朱震, 徐益谦 2000 光学学报 20 570
Lu Y G, Wang S M, Zhu Z, Lu Y, Xu Y Q 2000 Acta Opt. Sin. 20 570
[8] Zhu H, Wang Q, Yu J Y 2017 Front. Inf. Technol. Electron. Eng. 18 1236
Google Scholar
[9] Apelt F, Breuer D, Nikoloski Z, Stitt M, Kragler F 2015 Plant J. 82 693
Google Scholar
[10] Fu W X, Yan F, Chen K, Ren Z J 2015 Appl. Opt. 54 6237
Google Scholar
[11] Kazemzadeh F, Jin C, Molladavoodi S, Mei Y, Emelko M B, Gorbet M B, Wong A 2015 Opt. Lett. 40 3862
Google Scholar
[12] 肖相国, 王忠厚, 孙传东, 白加光 2008 光学学报 37 2539
Xiao X G, Wang Z H, Sun C D, Bai J G 2008 Acta Photonica Sin. 37 2539
[13] Su L J, Zhou Z L, Yuan Y, Hu L, Zhang S Y 2015 Optik 126 877
Google Scholar
[14] Tian L, Waller L 2015 2015 Optica 2 104
Google Scholar
[15] Fahringer T W, Lynch K P, Thurow B S 2015 Meas. Sci. Technol. 26 115201
Google Scholar
[16] Horstmeyer R, Euliss G, Athale R 2009 IEEE International Conference on Computational Photography (ICCP) San Francisco, CA USA, April 16–17, 2009 p1
[17] Prevedel R, Yoon Y G, Hoffmann M, Pak N, Wetzstein G, Kato S, Schrödel T, Raskar R, Zimmer M, Boyden E S, Vaziri A 2014 Nat. Methods 11 727
Google Scholar
[18] 聂云峰, 相里斌, 周志良 2011 中国科学院大学学报 28 563
Nie Y F, Xiang L B, Zhou Z L 2011 J. Grad. Univ. Chin. Acad. Sci. 28 563
[19] 周志良 2012 博士学位论文 (合肥: 中国科学技术大学)
Zhou Z L 2012 Ph. D. Dissertation(Hefei: University of Science and Technology of China) (in Chinese)
[20] Yuan Y, Liu B, Li S, Tan H P 2016 Int. J. Heat Mass Tran. 102 518
Google Scholar
[21] Li T J, Li S, Yuan Y, Liu Y D, Xu C L, Shuai Y, Tan H P 2017 Opt. Express 25 8274
Google Scholar
[22] Sun J, Xu C L, Zhang B, Hossain M M, Wang S M, Qi H, Tan H P 2016 Opt. Express 24 1118
Google Scholar
[23] Xu C L, Zhao W C, Hu J H, Zhang B, Wang S M 2017 Fuel 196 550
Google Scholar
[24] Sun J, Hossain M M, Xu C L, Zhang B, Wang S M 2017 Opt. Commun. 390 7
Google Scholar
[25] Sun J, Hossain M M, Xu C L, Zhang B 2018 Int. J. Heat Mass Transfer 121 1281
Google Scholar
[26] Zhao W C, Zhang B, Xu C L, Duan L B, Wang S M 2017 IEEE Sens. J. 18 528
Google Scholar
[27] Adelson E H, Wang J Y 1992 IEEE Trans. Pattern Anal. Mach. Intell. 14 99
Google Scholar
[28] 程万胜, 赵杰, 蔡鹤皋 2008 光学精密工程 16 314
Cheng W S, Zhao J, Cai H G 2008 Opt. Precis. Eng. 16 314
[29] 孙俊 2018 博士学位论文 (南京: 东南大学)
Sun J 2018 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese)
[30] 孙俊阳 2018 硕士学位论文 (南京: 东南大学)
Sun J Y 2018 M. S. Thesis Dissertation (Nanjing: Southeast University) (in Chinese)
[31] 杨薇, 刘四新, 冯彦谦 2008 物探与化探 32 199
Yang W, Liu S X, Feng Y Q 2008 Geophys. Geochem. Explor. 32 199
[32] 孟祥宁 2012 硕士学位论文 (成都: 成都理工大学)
Meng X N 2012 M. S. Thesis (Chengdu: Chengdu University of Technology) (in Chinese)
[33] 孟祥宁, 钟峙, 王玉凤 2012 中国西部科技 11 33
Google Scholar
Meng X N, Zhong Z, Wang Y F 2012 Sci. Techno. of West Chin. 11 33
Google Scholar
[34] Chen B, Pan B 2018 Exp. Mech. 58 831
Google Scholar
[35] Zhou P, Zhang Y T, Yu Y L, Cai W J, Zhou G Q 2020 Math. Biosci. Eng. 17 654
Google Scholar
[36] 牛春洋 2016 博士学位论文 (哈尔滨: 哈尔滨工业大学)]
Niu C Y 2016 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese)
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