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The monochromaticity of the laser and the characteristics of the natural image’s spectrum, including sparsity and concentrating in the low frequency range, make it possible to sample the image spectrum sparsely. Based on small-scale laser detectors and the introduced laser reference signals, a method of laser imaging with sparse sampling in frequency domain is proposed in this paper. The principle of frequency sparse sampling laser imaging and the imaging system structure are introduced. The simulation results of spectrum and complex images reconstructed are given. Both the effects of the signals’ parameters, such as the ratio of the reference laser signal amplitude to the laser echo spectrum amplitude and the initial phase of the laser reference signal, on reconstruction results are investigated. The reconstruction results are evaluated by correlation coefficient, mean square error (MSE), and structural similarity index (SSIM). For the strong correlation between phase and amplitude of the laser echo complex image, the amplitude image and the phase image are both set to be 256 × 256 diagram. The sparse laser detector plane array consists of 5 64 × 64 frequency domain laser detector arrays, which form a cross and make a sparsity rate of 31.25%(5/16). The simulation results show that the correlation coefficient, MSE and SSIM of the spectrum reconstructed are 0.96, 22.14, 1.00 and those of the complex image reconstructed are 0.96, 1857.25 and 0.67 respectively. The simulation results indicate that the method proposed is effective. However, the method requires the laser reference signal amplitude to be about 30 times the mean value of the laser echo spectrum amplitude, which reduces the dynamic range of the detectors. The initial phase of the laser reference signal has no obvious effect on the reconstruction results.
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Keywords:
- laser imaging /
- sparse sampling in the frequency domain /
- laser detector /
- image reconstruction
[1] 吕乃光 2013 傅里叶光学 (2版) (北京: 机械工业出版社) 第297—312页
Lü N G 2013 Fourier Optics (Second Edition) (Beijing: China Machine Press) pp297–312 (in Chinese)
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图 1 基于直接探测器的频域稀疏采样成像系统结构
Figure 1. Structure of the frequency-domain sparse sampling imaging system based on direct detector.
图 2 激光回波复图像幅度图
Figure 2. Laser echo complex image amplitude diagram.
图 3 面阵探测器频谱实部重构 (a)频谱幅度; (b)频谱相位; (c)图像
Figure 3. Reconstruction of the real part of the plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 4 面阵探测器频谱虚部重构 (a)频谱幅度; (b)频谱相位; (c)图像
Figure 4. Reconstruction of the imaginary part of the plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 5 面阵探测器频谱重构 (a)频谱幅度; (b)频谱相位; (c)图像
Figure 5. Reconstruction of the plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 6 5个1/4 × 1/4规模频域探测器拼接构成十字型探测范围
Figure 6. Cross detection range constituted by five 1/4 × 1/4 scale frequency domain detectors.
图 7 稀疏面阵探测器频谱实部重构 (a)频谱幅度; (b)频谱相位; (c) 图像
Figure 7. Reconstruction of the real part of the sparse plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 8 稀疏面阵探测器频谱虚部重构 (a)频谱幅度; (b)频谱相位; (c)图像
Figure 8. Reconstruction of the imaginary part of the sparse plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 9 稀疏面阵探测器频谱重构 (a)频谱幅度; (b)频谱相位; (c)图像
Figure 9. Reconstruction of the sparse plane array detector signals’ spectrum: (a) Amplitude of the spectrum; (b) phase of the spectrum; (c) image.
图 10 R与稀疏面阵探测器重构复图像相干系数的变化曲线
Figure 10. Change curves of the relationship between R and correlation coefficient of the reconstructed complex image of the sparse plane array detectors.
图 11
$ {\varphi _2}\left( {x, y} \right) $ 与稀疏面阵探测器重构复图像相干系数的变化曲线Figure 11. Change curves of the relationship between
$ {\varphi _2}\left( {x, y} \right) $ and correlation coefficient of the reconstructed complex image of the sparse plane array detectors .表 1 面阵探测器和稀疏面阵探测器频谱与复图像重构效果
Table 1. Spectrum and complex image reconstruction effect of the plane array detectors and the sparse plane array detectors.
重构结果 相干
系数均方
误差结构
相似度面阵探测器重构频谱 1.00 2.51 1.00 面阵探测器重构复图像 1.00 0.01 1.00 稀疏面阵探测器重构频谱 0.96 22.14 1.00 稀疏面阵探测器重构复图像 0.96 1857.25 0.67 
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[1] 吕乃光 2013 傅里叶光学 (2版) (北京: 机械工业出版社) 第297—312页
Lü N G 2013 Fourier Optics (Second Edition) (Beijing: China Machine Press) pp297–312 (in Chinese)
[2] 韩亮, 田逢春, 徐鑫, 刘伟, 王宇 2008 重庆大学学报 31 426
Google Scholar
Han L, Tian F C, Xü X, Liu W, Wang Y 2008 J. Chongqing Univ. 31 426
Google Scholar
[3] Zheng G, Horstmeyer R, Yang C 2013 Nature Photon. 7 739
Google Scholar
[4] 孙佳嵩, 张玉珍, 陈钱, 左超 2016 光学学报 36 327
Google Scholar
Sun J S, Zhang Y Z, Chen Q, Zuo C 2016 Acta Opt. Sin. 36 327
Google Scholar
[5] 邵晓鹏, 苏云, 刘金鹏, 刘飞, 李伟, 席特立 2021 光子学报 50 931
Google Scholar
Shao X P, Su Y, Liu J P, Liu F, Li W, Xi T L 2021 Acta Photon. Sin. 50 931
Google Scholar
[6] 赵明, 王希明, 张晓慧, 张望 2019 激光与光电子学进展 56 121
Google Scholar
Zhao M, Wang X M, Zhang X H, Zhang W 2019 Laser & Optoelectronics Progress 56 121
Google Scholar
[7] Xiang M, Pan A, Zhao Y, Fan X, Yao B 2021 Opt. Lett. 46 29
Google Scholar
[8] 李道京, 朱宇, 胡烜, 于海锋, 周凯, 张润宁, 刘磊 2020 雷达学报 9 195
Google Scholar
Li D J, Zhu Y, Hu X, Yu H F, Zhou K, Zhang R N, Liu L 2020 J. Radars 9 195
Google Scholar
[9] Rogers C, Piggott A Y, Thomson D J, Wiser R F, Nicolaescu R 2021 Nature 590 256
Google Scholar
[10] 李道京, 周凯, 崔岸婧, 乔明, 吴淑梅, 王烨菲, 姚园, 吴疆, 高敬涵 2021 激光与光电子学进展 58 342
Google Scholar
Li D J, Zhou K, Cui A J, Qiao M, Wu S M, Wang Y F, Yao Y, Wu J, Gao J H 2021 Laser & Optoelectronics Progress 58 342
Google Scholar
[11] 李琦, 丁胜晖, 李运达, 薛凯, 王骐 2012 激光与光电子学进展 49 46
Google Scholar
Li Q, Ding S H, Li Y D, Xue K, Wang Q 2012 Laser & Optoelectronics Progress 49 46
Google Scholar
[12] 马利红, 王辉, 金洪震, 李勇 2012 中国激光 39 215
Google Scholar
Ma L H, Wang H, Jin H Z, Li Y 2012 Chinese J of Lasers 39 215
Google Scholar
[13] 保铮, 邢孟道, 王彤 2005 雷达成像技术 (北京: 电子工业出版社)pp30—44
Bao Z, Xing M D, Wang T 2005 Radar Imaging Technology (Beijing: Publishing House of Electronics Industry) pp30–44 (in Chinese)
[14] 戴永江 2002 激光雷达原理 (北京: 国防工业出版社) pp256–260
Dai Y J 2002 Principle of Lidar (Beijing: National Defense Industry Press) pp256—260 (in Chinese)
[15] 谢宗良, 马浩统, 任戈, 亓波, 丁科 2015 光学学报 35 102
Google Scholar
Xie Z L, Ma H T, Ren G, Qi B, Ding K 2015 Acta Opt. Sin. 35 102
Google Scholar
[16] Tang W, Guo Y, Yi W, Yang J, Zhu J, Wang W, Li X 2019 Opt. Commun. 443 144
Google Scholar
[17] 李烈辰 2015 博士学位论文 (北京: 中国科学院大学)
Li L C 2015 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinses)
[18] Rousseau D, Delahaies A, Chapeau-Blondeau F 2009 IEEE Signal Processing Letters 17 36
Google Scholar
[19] Tian H, Li D J 2017 IET Radar, Sonar & Navigation 11 1886
Google Scholar
[20] 张文辉, 曹良才, 金国藩 2019 红外与激光工程 48 104
Google Scholar
Zhang W H, Cao L C, Jin G F 2019 Infrared and Laser Engineering 48 104
Google Scholar
[21] 张美玲, 郜鹏, 温凯, 卓可群, 王阳, 刘立新, 闵俊伟, 姚保利 2021 光子学报 50 9
Google Scholar
Zhang M L, Gao P, Wen K, Zhuo K Q, Wang Y, Liu L X, Min J W, Yao B L 2021 Acta Photonica Sinica 50 9
Google Scholar
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