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Removal of the numerous centimeter-level space debris in low Earth orbit by using high-power lasers is always a hot topic of international academic research. Specifically, the precise positioning of space debris and high-precision measurement of barycenter range of debris are the key points and worldwide problems that need to be promptly solved. As a new remote high-resolution imaging method, laser reflective tomography is an effective approach to detecting the dark targets in remote space with its imaging resolution independent of the detection range. Hence, a centimeter-level space debris barycenter model is established according to the principle of laser reflective tomography in order to analyze the relative movement of debris and detector. On this basis, an approach to estimating the barycenter range of centimeter-level space debris is proposed to carry out the experimental verification of 1km detection range laser reflective tomography. The experimental results show that this method can improve the accuracy of barycenter detection from 1.50 cm to 0.34 cm, which is an effective measure for realizing high-precision measurement of barycenter ranges of centimeter-level space debris. Furthermore, this study achieves a breakthrough in kilometer-level laser reflective tomography experiments and theory of validation, and the kilometer-level laser reflective tomography has a great application prospect and technical potential.
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Keywords:
- lidar /
- reflective tomography /
- barycenter estimation /
- kilometer-level experiment
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图 1 LRT示意图 (a) 目标投影; (b) 数据反投影
Figure 1. Schematic diagram of LRT: (a) Target projection; (b) data back-projection.
图 2 LRT雷达样机原理图, 其中 R表示反射镜, NPBS表示消偏振分光棱镜, APD表示雪崩光电二极管, Pin表示光电二极管, SMF表示单模光纤, MC laser表示微片激光器
Figure 2. Schematic diagram of LRT radar prototype, where R is reflector, NPBS is non-polarizing beam splitter, APD is avalanche photodiode, Pin is positive intrinsic negative, SMF is single mode fiber, and MC laser is microchip laser.
图 3 典型空间碎片模型 (a)结构示意图; (b)遮挡效应示意图
Figure 3. Typical space debris model: (a) Structure diagram; (b) diagram of shielding effect.
图 4 (a) 实验装置图; (b) 1 km实验验证示意图
Figure 4. (a) Diagram of the experimental set-up; (b) diagram of 1 km experiment verification.
图 5 多角度激光回波和峰值点距离确定转动周期
Figure 5. Multi-angle laser echoes and the peak point range determined the period of rotation.
图 6 补全后的多角度激光回波和目标重构图像 (a) 凹面对应回波数据的FBP重构图像; (b) 凸面对应回波数据的FBP重构图像
Figure 6. Multi-angle laser echoes after completion and reconstructed image of target: (a) Image reconstruction by FBP based on the echo data of concave surface; (b) image reconstruction by FBP based on the echo data of convex surface.
图 7 采样间隔1°的目标重构图像与质心确定结果. FBP重构图像 (a) 质心距离校正前; (b) 质心距离校正后. 阈值分割图像 (c) 质心距离校正前; (d) 质心距离校正后
Figure 7. Target reconstruction image with sampling interval of 1° and barycenter determination results. Image reconstruction by FBP: (a) Barycenter range before correction; (b) barycenter range after corrected. Threshold segmentation image: (c) Barycenter range before correction; (d) barycenter range after corrected.
图 8 采样间隔7°的目标重构图像与质心确定结果. FBP重构图像 (a) 质心距离校正前; (b) 质心距离第一次校正后; (c) 质心距离第二次校正后. 阈值分割图像与质心确定结果 (d) 质心距离校正前; (e) 质心距离第一次校正后; (f) 质心距离第二次校正后
Figure 8. Target reconstruction image with sampling interval of 7° and barycenter determination results. Image reconstruction by FBP: (a) Barycenter range before correction; (b) barycenter range after first corrected; (c) barycenter range after second corrected. Threshold segmentation image and barycenter determination results: (d) Barycenter range before correction; (e) barycenter range after first corrected; (f) barycenter range after second corrected.
图 9 采样间隔20°的目标重构图像与质心确定结果. FBP重构图像 (a) 质心距离校正前; (b) 质心距离校正后. 阈值分割图像; (c) 质心距离校正前; (d) 质心距离校正后
Figure 9. Target reconstruction image with sampling interval of 20° and barycenter determination results. Image reconstruction by FBP: (a) Barycenter range before correction; (b) barycenter range after corrected. Threshold segmentation image: (c) Barycenter range before correction; (d) barycenter range after corrected.
表 1 LRT雷达样机关键参数
Table 1. Key parameters of the LRT radar prototype.
参数/单位 数值 参数/单位 数值 工作波长$\lambda $/nm 1064 APD模块带宽$B{W_1}$/GHz 7.5 脉冲宽度$\tau $/ps 93 APD模块灵敏度${S_1}$/dBm –25.5 单脉冲能量$E$/μJ 10 Pin模块带宽$B{W_2}$/GHz 15 重复频率$f$/Hz 10 Pin模块灵敏度${S_2}$/dBm –27 激光发射发散角$\theta $/mrad 0.22 高速采集器带宽$B{W_3}$/GHz 4.25 望远系统口径D/m 0.1 高速采集器采样率fs/GSPS 50 望远系统视场角$\omega $/mrad 0.3 高速采集器触发延时t/μs 6.546 
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表 2 采样间隔1°的目标重构图像校正前后质心距离和质心确定误差结果比较
Table 2. Comparison of barycenter range and determination error before or after target reconstruction image correction with sampling interval of 1°.
类型 质心距离 质心确定误差 R/m 确定值E0/cm 实际值E/cm 质心距离校正前 2.2246 1.29 1.54 质心距离校正后 2.2366 0.14 0.34
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表 3 采样间隔7°的目标重构图像校正前后的质心距离和质心确定误差结果比较
Table 3. Comparison of barycenter range and determination error before or after target reconstruction image correction with sampling interval of 7°.
类型 质心距离 质心确定误差 R/m 确定值E0/cm 实际值E/cm 质心距离校正前 2.2021 2.43 1.79 质心距离第一次校正后 2.2320 0.39 0.80 质心距离第二次校正后 2.2350 0.22 0.50
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表 4 采样间隔20°的目标重构图像校正前后质心距离和质心确定误差结果比较
Table 4. Comparison of barycenter range and determination error before or after target reconstruction image correction with sampling interval of 20°.
类型 质心距离 质心确定误差 R/m 确定值E0/cm 实际值E/cm 质心距离校正前 2.2170 0.70 2.30 质心距离校正后 2.2230 0.15 1.70
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[1] Bonnal C, Ruault J M, Desjean M C 2013 Acta Astronaut. 85 51
Google Scholar
[2] Esmiller B, Jacquelard C, Eckel H A, Wnuk E 2014 Appl. Opt. 53 45
Google Scholar
[3] Phipps C, Birkan M, Bohn W, Eckel H A, Horisawa H, Lippert T, Michaelis M, Rezunkov Y, Sasoh A, Schall W, Scharring S, Sinko J J 2010 Propul. Power 26 609
Google Scholar
[4] 金星, 洪延姬, 李修乾 2012 强激光与粒子束 24 281
Google Scholar
Jin X, Hong Y J, Li X Q 2012 High Power Part. Beam 24 281
Google Scholar
[5] 洪延姬, 金星, 常浩 2016 红外与激光工程 45 9
Google Scholar
Hong Y J, Jin X, Chang H 2016 Infrared Laser Eng. 45 9
Google Scholar
[6] 扈荆夫, 杨福民, 张忠萍, Hamal K, Prochazka I, Blazej J 2004 中国科学G辑: 物理学 力学 天文学 34 711
Hu Y F, Yang F M, Zhang Z P, Hamal K, Prochazka I, Blazej 2004 Sci. China Ser. G 34 711
[7] Li H, Chen S J, You L X, Meng W D, Wu Z B, Zhang Z P, Tang K, Zhang L, Zhang W J, Yang X Y 2016 Opt. Express 24 3535
Google Scholar
[8] 杨福民, 陈婉珍, 张忠萍, 陈菊平, 扈荆夫, 李鑫, Prochazka I, Hamal K 2002 中国科学(A辑) 32 935
Google Scholar
Yang F M, Chen W Z, Zhang Z P, Chen J P, Hu J F, Li X, Prochazka I, Hamal K 2002 Sci. China Ser. A 32 935
Google Scholar
[9] 孟文东, 张海峰, 邓华荣, 汤凯, 吴志波, 王煜蓉, 吴光, 张忠萍, 陈欣扬 2020 物理学报 69 019502
Google Scholar
Meng W D, Zhang H F, Deng H R, Tang K, Wu Z B, Wang Y R, Wu G, Zhang Z P, Chen X Y 2020 Acta Phys. Sin. 69 019502
Google Scholar
[10] 李语强, 李祝莲, 伏红林, 郑向明, 何少辉, 翟东升, 熊耀恒 2011 中国激光 38 160
Google Scholar
Li Y Q, Li Z L, Fu H L, Zheng X M, He S H, Zhai D S, Xiong Y H 2011 Chin. J. Lasers 38 160
Google Scholar
[11] Zhang H F, Long M L, Deng H R, Cheng S Y, Wu Z B, Zhang Z P, Zhang A L, Sun J T 2021 Appl. Sci. 11 10080
Google Scholar
[12] Bai X R, Xing M D, Zhou F, Bao Z 2009 IEEE Trans. Geosci. Remote Sens. 47 2352
Google Scholar
[13] Sun T, Shan X M, Chen J 2014 IEEE Geosci. Remote S. 11 1041
Google Scholar
[14] Morselli A, Lizia P D, Armellin R, Bianchi G, Bortolotti C, Montebugnoli S, Naldi G, Perini F, Pupillo G, Roma M, Schiaffino M, Mattana A, Salerno E, Sergiusti A L, Magro A, Adami K Z, Villadei W, Dolce F, Reali M, Paoli J IEEE Metrology for Aerospace Italy, Benevento, June 4–5, 2015 p562
[15] Xi J B, Wen D S, Ersoy O K, Yi H W, Yao D L, Song Z X, Xi S B 2016 Appl. Opt. 55 7929
Google Scholar
[16] 胡以华, 张鑫源, 徐世龙, 赵楠翔, 石亮 2021 中国激光 48 13
Google Scholar
Hu Y H, Zhang X Y, Xu S L, Zhao N X, Shi L 2021 Chin. J. Lasers 48 13
Google Scholar
[17] Parker J K, Craig E B, Klick D I, Knight F K, Kulkarni S R, Marino R M, Senning J R, Tussey B K 1988 Appl. Opt. 27 2642
Google Scholar
[18] Matson C L, Mosley D E 2001 Appl. Opt. 40 2290
Google Scholar
[19] Murray J, Triscari J, Fetzer G, Epstein R, Plath J, Ryder W, Van L N Applications of Lasers for Sensing and Free Space Communications San Diego, CA, United states, January 31–February 3, 2010 pLSWA1
[20] Jin X F, Sun J F, Yan Y, Zhou Y, Liu L R 2010 Opt. Commun. 283 3472
Google Scholar
[21] Lin F, Wang J C, Lei W H, Hu Y H 2017 Opt. Commun. 402 540
Google Scholar
[22] 金鑫, 李亮, 陈志强, 徐荣栏, 黄娅, 张丽 2011 地球物理学报 54 1691
Google Scholar
Jin X, Li L, Chen Z Q, Xu R L, Huang Y, Zhang L 2011 Acta Petpol. Sin. 54 1691
Google Scholar
[23] Chen J B, Sun H Y 2020 Opt. Commun. 455 124548
Google Scholar
[24] 谷雨, 胡以华, 郝士琦, 王金诚, 王迪 2011 光学学报 54 1691
Google Scholar
Gu Y, Hu Y H, Hao S Q, Wang J C, Wang D 2011 Acta Opt. Sin. 54 1691
Google Scholar
[25] Natter F, Wang G 2002 Med. Phys. 29 107
Google Scholar
[26] 宋大伟, 尚社, 李小军, 罗熹, 孙文锋, 范晓彦, 李栋 2016 红外与激光工程 45 76
Google Scholar
Song D W, Shang S, Li X J, Luo X, Sun W F, Fan X Y, Li D 2016 Infrared Laser Eng. 45 76
Google Scholar
[27] 金晓峰, 孙建锋, 严毅, 周煜, 刘立人 2010 光学学报 30 747
Google Scholar
Jin X F, Sun J F, Yan Y, Zhou Y, Liu L R 2010 Acta Opt. Sin. 30 747
Google Scholar
[28] Candes E J, Romberg J K, Tao T 2006 Commun. Pur. Appl. Math. 59 1207
Google Scholar
[29] Romberg J 2008 IEEE Signal Proc. Mag. 25 14
Google Scholar
[30] Sidky E Y, Chartrand R, Pan X C IEEE Nuclear Science Symposium and Medical Imaging Conference Honolulu, HI, United states, October 27–November 3, 2007, p3526
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