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Aiming at the high requirement for pulse-repetition frequency of the existing single-beam synchronous scanning circumferential detection, which is difficult to use practically. The method of single-beam expanding scanning laser circumferential detection is proposed. Based on the principle of single-beam expanding scanning laser circumferential detection, the mode of scanning has an inherent defect of periodic detection blind area in the detection field. The method of one-way spreading laser line beam into fan-shaped beam is proposed. The analytical expression of the lowest scanning frequency and the pulse frequency are derived. Echo characteristics of cylindrical target and the section attenuation coefficient are analyzed. Mathematic model of cylindrical target echo power of pulsed expanding laser beam is established. The mathematical model of section attenuation coefficient of cylindrical object is established, and the variation of the section attenuation coefficient when the center line and the edge of the beam have different positions relative to the cylindrical target is analyzed. The expression of the position having the smallest section attenuation coefficient and the expression of largest angle between the adjacent pulse laser beams are obtained, then the influence of system parameters on the section attenuation coefficient is also discussed. The emphasis is placed on the influence of pulse frequency, beam angle and incidence angle on the ability to detect different diameter targets. As the laser pulse frequency increases, the detectable target diameter is smaller and the detection ability is stronger. Increasing the beam angle and lowering the laser incident angle are beneficial to reducing the minimum laser pulse frequency required to discover the target. The methods of calculating maximum beam angle and minimum pulse frequency under typical conditions of the detection system are presented. When the incident angles are
${\text{π}}/3$ ,${\text{π}}/4$ and${\text{π}}/6$ , the maximum beam angle and the lowest pulse frequency are calculated for a cylindrical target with a diameter of 0.18 m at a detection distance of 6 m, the minimum pulse frequency decreases effectively after beam expansion. The results show that the pulse repetition frequency will be effectively reduced by slightly expanding the beam. This study may provide theoretical basis for designing and optimizing the single-beam pulsed laser circumferential detection.-
Keywords:
- single-beam expanding scanning laser circumferential detection /
- cylindrical target echo characteristics /
- laser expanding /
- pulse frequency
[1] 杨雨川, 谭碧涛, 龙超, 陈力子, 张己化, 陈军燕 2013 红外与激光工程 42 3228
Google Scholar
Yang Y C, Tan B T, Long C, Cen L Z, Zhang J H, Chen J Y 2013 Infrared and Laser Engineering 42 3228
Google Scholar
[2] 黄涛, 胡以华, 赵钢, 赵楠翔, 翟福琪, 吴永华 2011 红外与毫米波学报 30 179
Huang T, Hu Y H, Zhao G, Zhao N X, Zhai F Q, Wu Y H 2011 J. Infrared Millim. Waves 30 179
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Zhao N X, Hu Y H, Lei W H, He M 2009 Infrared and Laser Engineering 38 748
Google Scholar
[4] 徐效文 2004 博士学位论文 (长春: 中国科学院研究生院)
Xu X W 2004 Ph. D. Dissertation (Changchun: Graduate University of the Chinese Academy of Sciences)
[5] 李元, 李燕华, 李洛, 郭海超, 张彦梅, 温玉全 2015 兵工学报 36 2073
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Li Y, Li Y H, Li L, Guo H C, Zhang Y M, Wen Y Q 2015 Acta Armamentarii 36 2073
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[6] 林永兵, 张国雄, 李真, 李杏华 2002 中国激光 11 1000
Google Scholar
Lin Y B, Zhang G X, Li Z, Li X H 2002 Chin. J. Lasers 11 1000
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[7] 张伟, 张合, 陈勇, 张祥金, 徐孝彬 2017 物理学报 66 012901
Google Scholar
Zhang W, Zhang H, Chen Y, Zhang X J, Xu X B 2017 Acta Phys. Sin. 66 012901
Google Scholar
[8] 张磊, 郭劲 2012 光学精密工程 20 789
Zhang L, Guo J 2012 Optics Precis Eng. 20 789
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Zhao Y Z, Song F H, Sun H Y 2007 Infrared and Laser Engineering 36 891
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[10] 甘霖, 张合, 张祥金, 冯颖 2013 红外与激光工程 42 84
Google Scholar
Gan L, Zhang H, Zhang X J, Feng Y 2013 Infrared and Laser Engineering 42 84
Google Scholar
[11] 谭亚运, 张合, 查冰婷 2015 强激光与粒子束 27 73
Tan Y Y, Zhang H, Zha B T 2015 High Pow. Las. Part. Beams 27 73
[12] 查冰婷, 张合 2014 红外与激光工程 43 2081
Google Scholar
Zha B T, Zhang H 2014 Infrared and Laser Engineering 43 2081
Google Scholar
[13] 徐孝彬, 张合 2016 中国激光 43 201
Xu X B, Zhang H 2016 Chin. J. Lasers 43 201
[14] 寇添, 王海晏, 王芳, 陈闽, 徐强 2015 光学学报 35 211
Kou T, Wang H Y, Wang F, Chen M, Xu Q 2015 Acta Opt. Sin. 35 211
[15] 张旭升, 郭亮, 黄勇, 罗志涛 2015 中国激光 42 20
Zhang X S, Guo L, Huang Y, Luo Z T 2015 Chin. J. Lasers 42 20
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[17] Steinvall O 2000 Appl. Opt. 39 4381
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[18] Cao T, Xiao A C, Wu L, Mao L G 2017 Comput. Geosci. 106 209
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[19] Krása J, Delle S D, Giuffreda E, Nassisi V 2015 Laser Part. Beams 33 601
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[20] 马圆 2015 硕士学位论文 (南京: 南京理工大学)
Ma Y 2015 M. S. Thesis (Nanjing: Nanjing University of Science and Technology)
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图 1 单光束扩束扫描激光周视探测系统结构
Figure 1. The structure of a single beam expanding beam scanning laser periscope detection system.
图 2 单光束脉冲激光周向扫描探测系统探测目标示意图[11]
Figure 2. Schematic diagram of detection target of single-beam pulsed laser circumferential scan detection system.
图 3 沿x轴正方向脉冲光束视图
Figure 3. Pulse beam view in the positive direction of the x-axis.
图 4 相邻脉冲激光束在面M上的投影
Figure 4. Projection of adjacent pulsed laser beam on plane M.
图 5 发射激光束与投影图像几何关系
Figure 5. Geometrical relationship between the laser beam and the projected image.
图 6 回波功率Pr与K(R), R,
$\alpha$ 之间的关系 (a)${\alpha _{\rm{t}}}={\text{π}}/6$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/3$ Figure 6. The echo power with different K(R), R and
$\alpha$ : (a)${\alpha _{\rm{t}}}={\text{π}}/6$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/3$ 
图 7 K(R)数学模型 (a)光束中心线位置示意图; (b)光束左边沿线与目标相交时K(R)模型; (c)光束左边沿线与目标相离时K(R)模型
Figure 7. Mathematical model of K(R): (a) The position of the center line of the beam; (b) the K(R) model when the left side of the beam intersects the target; (c) the K(R) model when the left side of the beam is separated from the target.
图 8 K(R)与
${\alpha _{\rm{t}}}$ ,${\xi _1}$ 和$\theta_{\rm{d}}$ 之间的关系 (a)${\alpha _{\rm{t}}}$ ,$\theta_{\rm{d}}$ 与K(R)的关系; (b)${\alpha _{\rm{t}}}$ ,${\xi _1}$ 和$\theta_{\rm{d}}$ 对K(R)的影响曲线Figure 8. The relationship between K(R) and
${\alpha _{\rm{t}}}$ ,${\xi _1}$ and$\theta_{\rm{d}}$ : (a) The relationship between K(R) and${\alpha _{\rm{t}}}$ ,$\theta_{\rm{d}}$ ; (b) the influence curve of${\alpha _{\rm{t}}}$ ,${\xi _1}$ and$\theta_{\rm{d}}$ on K(R).
图 9 脉冲频率f、光束角
$\theta$ 和光束入射角${\alpha _{\rm{t}}}$ 对不同目标直径的影响 (a)${\alpha _{\rm{t}}}={\text{π}}/6$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/3$ Figure 9. Effects of pulse frequency f, beam angle
$\theta$ , and beam incidence angle${\alpha _{\rm{t}}}$ on targets with different diameters: (a)${\alpha _{\rm{t}}}={\text{π}}/6$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/3$ .
图 10 最大相邻脉冲光束夹角
${\xi _{\max}}$ (a) f1与目标圆位置关系曲线; (b)$\theta_{\rm{d1}}$ 与$\theta_{\rm{d2}}$ 取值计算Figure 10. Maximum angle
${\xi _{\max}}$ between adjacent pulse beams: (a) The relation curve between f1 and the position of the target circle; (b) value of$\theta_{\rm{d1}}$ and$\theta_{\rm{d2}}$ .
图 11
${\xi _1}$ 和$\theta_{\rm{d}}$ 对系统回波功率的影响 (a)${\alpha _{\rm{t}}}={\text{π}}/3$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/6$ Figure 11. Influence of
${\xi _1}$ and$\theta_{\rm{d}}$ on echo power. (a)${\alpha _{\rm{t}}}={\text{π}}/3$ ; (b)${\alpha _{\rm{t}}}={\text{π}}/4$ ; (c)${\alpha _{\rm{t}}}={\text{π}}/6$ .表 1 探测系统仿真参数
Table 1. Simulation parameters of the detection system.
Parameter Value Parameter Value Pt/W 70 Pmin/${\text{μ}}$W 5 vm/m·s–1 700 vt/m·s–1 200 Lt/m 3 $\eta$ 0.9 Ar/m2 0.00031 $\sigma$/m–1 0.00054 $\theta_{\simfont\text{边界}}$/rad 0.26 $\xi_{\simfont\text{边界}}$/rad ${\text{π}}/2$ 
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表 2 计算最低脉冲频率及光束角系统参数
Table 2. Calculate the minimum pulse frequency and beam angle system parameters
Parameter Value Parameter Value Pt/W 70 Dt/m 0.18 R/m 6 ${\alpha _{\rm{t}}}$ ${\text{π}}/3$, ${\text{π}}/4$, ${\text{π}}/6$
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表 3 不同入射角
${\alpha _{\rm{t}}}$ 下的nmin,${\xi _{\max}}$ ,${\theta _{\max }}$ 以及fminTable 3. nmin,
${\xi _{\max}}$ ,${\theta _{\max }}$ and fmin at different incident angles${\alpha _{\rm{t}}}$ .入射角 扩束前 扩束后 ${\alpha _{\rm{t}}}$/rad $\xi$/rad $\theta$/rad k f/Hz ${\xi _{\max}}$/rad ${\theta _{\max }}$/rad kmin fmin/Hz ${\text{π}}/3$ 0.0345 0.0025 182 54411 0.2417 0.2417 26 7798.74 ${\text{π}}/4$ 0.0422 0.0025 149 44425 0.2513 0.2513 25 7500.82 ${\text{π}}/6$ 0.0598 0.0025 105 31411 0.2513 0.2513 25 7500.82
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[1] 杨雨川, 谭碧涛, 龙超, 陈力子, 张己化, 陈军燕 2013 红外与激光工程 42 3228
Google Scholar
Yang Y C, Tan B T, Long C, Cen L Z, Zhang J H, Chen J Y 2013 Infrared and Laser Engineering 42 3228
Google Scholar
[2] 黄涛, 胡以华, 赵钢, 赵楠翔, 翟福琪, 吴永华 2011 红外与毫米波学报 30 179
Huang T, Hu Y H, Zhao G, Zhao N X, Zhai F Q, Wu Y H 2011 J. Infrared Millim. Waves 30 179
[3] 赵楠翔, 胡以华, 雷武虎, 贺敏 2009 红外与激光工程 38 748
Google Scholar
Zhao N X, Hu Y H, Lei W H, He M 2009 Infrared and Laser Engineering 38 748
Google Scholar
[4] 徐效文 2004 博士学位论文 (长春: 中国科学院研究生院)
Xu X W 2004 Ph. D. Dissertation (Changchun: Graduate University of the Chinese Academy of Sciences)
[5] 李元, 李燕华, 李洛, 郭海超, 张彦梅, 温玉全 2015 兵工学报 36 2073
Google Scholar
Li Y, Li Y H, Li L, Guo H C, Zhang Y M, Wen Y Q 2015 Acta Armamentarii 36 2073
Google Scholar
[6] 林永兵, 张国雄, 李真, 李杏华 2002 中国激光 11 1000
Google Scholar
Lin Y B, Zhang G X, Li Z, Li X H 2002 Chin. J. Lasers 11 1000
Google Scholar
[7] 张伟, 张合, 陈勇, 张祥金, 徐孝彬 2017 物理学报 66 012901
Google Scholar
Zhang W, Zhang H, Chen Y, Zhang X J, Xu X B 2017 Acta Phys. Sin. 66 012901
Google Scholar
[8] 张磊, 郭劲 2012 光学精密工程 20 789
Zhang L, Guo J 2012 Optics Precis Eng. 20 789
[9] 赵延仲, 宋丰华, 孙华燕 2007 红外与激光工程 36 891
Google Scholar
Zhao Y Z, Song F H, Sun H Y 2007 Infrared and Laser Engineering 36 891
Google Scholar
[10] 甘霖, 张合, 张祥金, 冯颖 2013 红外与激光工程 42 84
Google Scholar
Gan L, Zhang H, Zhang X J, Feng Y 2013 Infrared and Laser Engineering 42 84
Google Scholar
[11] 谭亚运, 张合, 查冰婷 2015 强激光与粒子束 27 73
Tan Y Y, Zhang H, Zha B T 2015 High Pow. Las. Part. Beams 27 73
[12] 查冰婷, 张合 2014 红外与激光工程 43 2081
Google Scholar
Zha B T, Zhang H 2014 Infrared and Laser Engineering 43 2081
Google Scholar
[13] 徐孝彬, 张合 2016 中国激光 43 201
Xu X B, Zhang H 2016 Chin. J. Lasers 43 201
[14] 寇添, 王海晏, 王芳, 陈闽, 徐强 2015 光学学报 35 211
Kou T, Wang H Y, Wang F, Chen M, Xu Q 2015 Acta Opt. Sin. 35 211
[15] 张旭升, 郭亮, 黄勇, 罗志涛 2015 中国激光 42 20
Zhang X S, Guo L, Huang Y, Luo Z T 2015 Chin. J. Lasers 42 20
[16] Xu G, Zhang X Y, Su J, Li X T, Zheng A Q 2016 Appl. Opt. 55 2653
Google Scholar
[17] Steinvall O 2000 Appl. Opt. 39 4381
Google Scholar
[18] Cao T, Xiao A C, Wu L, Mao L G 2017 Comput. Geosci. 106 209
Google Scholar
[19] Krása J, Delle S D, Giuffreda E, Nassisi V 2015 Laser Part. Beams 33 601
Google Scholar
[20] 马圆 2015 硕士学位论文 (南京: 南京理工大学)
Ma Y 2015 M. S. Thesis (Nanjing: Nanjing University of Science and Technology)
[21] Louis E 1964 Appl. Opt. 3 745
Google Scholar
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