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We construct a nonlinear equation between the return signal and the boundary value of extinction coefficient according to the lidar equation. And according to the nonlinear equation, we put forward a new method to solve the nonlinear equation by using Broyden algorithm. The Broyden algorithm is a concrete application of the quasi-Newton method. It has faster convergence and less iteration times, and does not need to calculate the derivative value. After choosing a suitable initial value, the boundary value can be obtained through the algorithm. A 532 nm single-band Mie scattering imaging lidar system is developed in Hefei, Southern China, for real-time atmospheric aerosol/particle remote sensing. Atmospheric measurement has been performed in Science Island during night time, and the time-range distribution of atmospheric backscattering signal was recorded on April 6, 2017, by employing the imaging lidar system. Then, the boundary values are achieved based on the Broyden algorithm and the least square algorithm. It adopts the Klett backward integration method to retrieve the horizontal distribution of extinction coefficients in a range of 1 km after the acquisition of the signal by changing the distance, then the horizontal atmospheric transmittance can be achieved based on the path integral. We also conduct a contrast experiment with the one-way transmission of the horizontal light near the ground within the range of 1 km at the same time. The initial site is situated in the experimental room besides the Dongpu reservoir and the end site is located on the second floor of our office building. The important things in this experiment are that the light reaching the target surface must be fully received and the laser power should be monitored at the double-end. Then we can obtain the transmittance by the direct method. By comparing the transmittance from the direct method with the transmittance from imaging lidar between the two different ways, i.e., Broyden algorithm and least square algorithm, then the correlation coefficients are obtained to be both over 0.95 in the period. And the method introduced in this paper is a little better than the least square algorithm with a value of 0.968. Besides, the average relative errors between the two inverse methods and the direct method are 4.66% and 9.10%, respectively. The average relative errors obtained by using the least square algorithm is about twice that by using the Broyden algorithm. It can be concluded that the algorithm introduced in this paper is effective and has certain advantages for the inverse problem.
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Keywords:
- lidar /
- Broyden algorithm /
- boundary value /
- atmospheric transmittance
[1] Man S W, Kai Q, Hong L, James R C, Kwon H L 2017 Atmos. Environ. 154 189
[2] Zhao G Y, Liang M, Li Y Y, Duan Z, Zhu S M, Liang M, Sune S 2017 Appl. Opt. 56 1506
[3] John E B, Sebastian B, Robert B, Parikh N C 2003 Appl. Opt. 42 2647
[4] Liang M, Mikkel B 2015 Opt. Express 23 A1613
[5] James D K 1985 Appl. Opt. 24 1638
[6] James D K 1981 Appl. Opt. 20 211
[7] Liang M, Peng G, Yang Y, Zheng K 2017 Opt. Express 25 A628
[8] Cao N W 2015 Optik 126 2053
[9] Masap M, Nobuo T 1994 Appl. Opt. 33 6451
[10] Zhou J, Yue G M, Qi F D 1998 Chin. J. Quant. Elect. 15 140 (in Chinese) [周军, 岳古明, 戚福第 1998 量子电子学报 15 140]
[11] Kovalev V A 1993 Appl. Opt. 32 6053
[12] Wang Z H, Wang H B, He J, Zheng Y C, Yang J G, Li Y Q, Zhao X B 2008 Laser J. 29 36 (in Chinese) [王治华, 王宏波, 何捷, 郑玉臣, 杨经国, 李跃清, 赵兴炳 2008 激光杂志 29 36]
[13] Chen T, Wu D C, Liu B, Cao K F, Wang Z Z, Bo G Y, Yuan L, Zhou J 2010 Acta Opt. Sin. 30 1531 (in Chinese) [陈涛, 吴德成, 刘博, 曹开法, 王珍珠, 伯广宇, 袁林, 周军 2010 光学学报 30 1531]
[14] George L, John P (translated by Li J, Ren M M) 2016 Numerical Methods Using MATLAB (Beijing: China Machine Press) pp116-117 (in Chinese) [乔治 L, 约翰 P 著 (李君, 任明明 译)2016 数值方法-MATLAB版(北京: 机械工业出版社)第116–117页]
[15] Ma X M, Tao Z M, Ma M J, Li C J, Wang Z Z, Liu D, Xie C B, Wang Y J 2014 Acta Opt. Sin. 34 0201001 (in Chinese) [麻晓敏, 陶宗明, 马明俊, 李成军, 王珍珠, 刘东, 谢晨波, 王英俭 2014 光学学报 34 0201001]
[16] Anne G, Timothy P C (translated by Wu Z J, Wang G Y, Fan H J) 2016 Numerical Methods (Beijing: China Machine Press) p63 (in Chinese) [安妮 G, 蒂莫西 P C著(吴兆金, 王国英, 范红军 译) 2016 数值方法(北京: 机械工业出版社)第63页]
[17] Xiong X L, Jiang L H, Feng S, Zhuang Z B, Zhao J Y 2012 Infrar. Laser Eng. 41 1744 (in Chinese) [熊兴隆, 蒋立辉, 冯帅, 庄子波, 赵俊媛 2012 红外与激光工程 41 1744]
[18] Sun G D, Qin L A, Cheng Z, Hou Z H 2017 Laser Optoelect. Prog. 54 090102 (in Chinese) [孙国栋, 秦来安, 程知, 侯再红 2017 激光与光电子学进展 54 090102]
[19] Yang C P 2011 M. S. Dissertation (Dalian: Dalian Maritime University) (in Chinese) [杨成鹏 2011 硕士学位论文 (大连: 大连海事大学)]
[20] John E B, Parikh S, Trevor B K 2007 Appl. Opt. 46 2922
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[1] Man S W, Kai Q, Hong L, James R C, Kwon H L 2017 Atmos. Environ. 154 189
[2] Zhao G Y, Liang M, Li Y Y, Duan Z, Zhu S M, Liang M, Sune S 2017 Appl. Opt. 56 1506
[3] John E B, Sebastian B, Robert B, Parikh N C 2003 Appl. Opt. 42 2647
[4] Liang M, Mikkel B 2015 Opt. Express 23 A1613
[5] James D K 1985 Appl. Opt. 24 1638
[6] James D K 1981 Appl. Opt. 20 211
[7] Liang M, Peng G, Yang Y, Zheng K 2017 Opt. Express 25 A628
[8] Cao N W 2015 Optik 126 2053
[9] Masap M, Nobuo T 1994 Appl. Opt. 33 6451
[10] Zhou J, Yue G M, Qi F D 1998 Chin. J. Quant. Elect. 15 140 (in Chinese) [周军, 岳古明, 戚福第 1998 量子电子学报 15 140]
[11] Kovalev V A 1993 Appl. Opt. 32 6053
[12] Wang Z H, Wang H B, He J, Zheng Y C, Yang J G, Li Y Q, Zhao X B 2008 Laser J. 29 36 (in Chinese) [王治华, 王宏波, 何捷, 郑玉臣, 杨经国, 李跃清, 赵兴炳 2008 激光杂志 29 36]
[13] Chen T, Wu D C, Liu B, Cao K F, Wang Z Z, Bo G Y, Yuan L, Zhou J 2010 Acta Opt. Sin. 30 1531 (in Chinese) [陈涛, 吴德成, 刘博, 曹开法, 王珍珠, 伯广宇, 袁林, 周军 2010 光学学报 30 1531]
[14] George L, John P (translated by Li J, Ren M M) 2016 Numerical Methods Using MATLAB (Beijing: China Machine Press) pp116-117 (in Chinese) [乔治 L, 约翰 P 著 (李君, 任明明 译)2016 数值方法-MATLAB版(北京: 机械工业出版社)第116–117页]
[15] Ma X M, Tao Z M, Ma M J, Li C J, Wang Z Z, Liu D, Xie C B, Wang Y J 2014 Acta Opt. Sin. 34 0201001 (in Chinese) [麻晓敏, 陶宗明, 马明俊, 李成军, 王珍珠, 刘东, 谢晨波, 王英俭 2014 光学学报 34 0201001]
[16] Anne G, Timothy P C (translated by Wu Z J, Wang G Y, Fan H J) 2016 Numerical Methods (Beijing: China Machine Press) p63 (in Chinese) [安妮 G, 蒂莫西 P C著(吴兆金, 王国英, 范红军 译) 2016 数值方法(北京: 机械工业出版社)第63页]
[17] Xiong X L, Jiang L H, Feng S, Zhuang Z B, Zhao J Y 2012 Infrar. Laser Eng. 41 1744 (in Chinese) [熊兴隆, 蒋立辉, 冯帅, 庄子波, 赵俊媛 2012 红外与激光工程 41 1744]
[18] Sun G D, Qin L A, Cheng Z, Hou Z H 2017 Laser Optoelect. Prog. 54 090102 (in Chinese) [孙国栋, 秦来安, 程知, 侯再红 2017 激光与光电子学进展 54 090102]
[19] Yang C P 2011 M. S. Dissertation (Dalian: Dalian Maritime University) (in Chinese) [杨成鹏 2011 硕士学位论文 (大连: 大连海事大学)]
[20] John E B, Parikh S, Trevor B K 2007 Appl. Opt. 46 2922
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