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Sheared beam imaging (SBI) is considered a computational imaging technique that transmits three sheared coherent laser beamlets for illumination, and a sensor array to receive the intensity of the speckle pattern reflected from the target. The SBI can be used to image remote objects through a turbulent medium with no need of any adaptive optics. However, while imaging low-orbit moving targets, the number of detectors of sensor array required by the receiving system of SBI is very large, and the development of sensor array is difficult and costly. In this work, a spatial domain sparse sampling technique is proposed for the SBI system through transmitting five laser beamlets to illuminate the target carrying more of its spectral information, which can reduce the number of detectors of the sensor array. Firstly, the principle of the sparse imaging technique is deduced. Then, a sparse reconstruction algorithm is studied. The phase difference and amplitude information of the target in the echo signal after sparse sampling can be extracted accurately by searching for the accurate positions of the beat frequency components. The wavefront phases can be demodulated by the least-squares method, and wavefront amplitude can be obtained by the algebraic operation of speckle amplitude. The reconstructed wavefront is used to formulate the two-dimension image of the target. Theoretically, without affecting the resolution, the number of detectors of the sensor array can be reduced to half of the traditional three-beam method, which breaks through the limitation that the detector spacing of sensor array is equal to the shear length of beamlet. From the simulation results, when the number of detectors of the sensor array is reduced by 50%, the proposed sparse reconstruction algorithm has almost the same quality as the reconstructed image with the traditional three-beam method.
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Keywords:
- sheared beam imaging /
- spatial domain sparse sampling /
- sparse reconstruction algorithm /
- sensor array
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图 1 SBI技术稀疏采样原理示意图
Figure 1. Schematic diagram of sparse sampling principle of SBI technique.
图 2 四光束成像系统的激光发射排布方式
Figure 2. Laser emission arrangement of four-beam imaging system.
图 3 四光束成像相位复原算法示意图
Figure 3. Schematic diagram of phase retrieval algorithm for four-beam imaging method.
图 4 五光束稀疏采样成像相位复原算法示意图
Figure 4. Schematic diagram of phase retrieval algorithm for five-beam sparse sampling imaging method.
图 5 重构图像及其Strehl比(SNR: 10 dB) (a), (d), (g) 原始图像, SR = 1; (b) 传统三光束算法, SR = 0.8033; (e) 传统三光束算法, SR = 0.8444; (h) 传统三光束算法, SR = 0.8314; (c) 稀疏重构算法, SR = 0.7935; (f) 稀疏重构算法, SR = 0.8482; (i) 稀疏重构算法, SR = 0.8367
Figure 5. The reconstructed image and Strehl ratios (SNR: 10 dB): (a), (d), (g) Origin target image, SR = 1; (b) traditional method, SR = 0.8033; (e) traditional method, SR = 0.8444; (h) traditional method, SR = 0.8314; (c) sparse reconstruction method, SR = 0.7935; (f) sparse reconstruction method, SR = 0.8482; (i) sparse reconstruction method, SR = 0.8367.
图 6 回波信号振幅频谱(SNR: 10 dB) (a) 传统三光束方法; (b) 稀疏采样方法
Figure 6. Amplitude spectrum of echo signals (SNR: 10 dB): (a) Traditional method; (b) sparse sampling method.
图 7 重构图像及其Strehl比(SNR: 1 dB) (a), (d), (g) 原始图像, SR = 1; (b) 传统三光束算法, SR = 0.7554; (e) 传统三光束算法, SR = 0.8309; (h) 传统三光束算法, SR = 0.7954; (c) 稀疏重构算法, SR = 0.7589; (f) 稀疏重构算法, SR = 0.8250; (i) 稀疏重构算法, SR = 0.8092
Figure 7. The reconstructed image and Strehl ratios (SNR: 1 dB): (a), (d), (g) Origin target image, SR = 1; (b) traditional method, SR = 0.7935; (e) traditional method, SR = 0.8309; (h) traditional method, SR = 0.7954; (c) sparse reconstruction method, SR = 0.7589; (f) sparse reconstruction method, SR = 0.8250; (i) sparse reconstruction method, SR = 0.8092.
图 8 回波信号振幅频谱(SNR: 1 dB) (a) 传统三光束方法; (b) 稀疏采样方法
Figure 8. Amplitude spectrum of echo signals (SNR: 1 dB): (a) Traditional method; (b) sparse sampling method.
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[1] Hutchin R A 1993 Proc. SPIE 2029 161
Google Scholar
[2] Voelz D G, Gonglewski J D, Idell P S 1993 Proc. SPIE 2029 169
Google Scholar
[3] Hutchin R A 2012 US Patent 20120162631 [2012-6-28]
[4] Hutchin R A 2012 US Patent 20120292481 [2012-11-22]
[5] Voelz D G 1995 Proc. SPIE 2566 74
Google Scholar
[6] Voelz D G, Belsher J F, Ulibarri A L, Gamiz V 2002 Proc. SPIE 4489 35
Google Scholar
[7] 兰富洋, 罗秀娟, 陈明徕, 张羽, 刘辉 2017 物理学报 66 204202
Google Scholar
Lan F Y, Luo X J, Chen M L, Zhang Y, Liu H 2017 Acta Phys. Sin. 66 204202
Google Scholar
[8] 罗秀娟, 刘辉, 张羽, 陈明徕, 兰富洋 2019 中国光学 12 753
Luo X J, Liu H, Zhang Y, Chen M L, Lan F Y 2019 Chin. Opt. 12 753 (in Chinese)
[9] 兰富洋 2019 博士学位论文 (北京: 中国科学院大学)
Lan F Y 2019 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[10] 陈明徕, 罗秀娟, 张羽, 兰富洋, 刘辉, 曹蓓, 夏爱利 2017 物理学报 66 024203
Google Scholar
Chen M L, Luo X J, Zhang Y, Lan F Y, Liu H, Cao B, Xia A L 2017 Acta Phys. Sin. 66 024203
Google Scholar
[11] Fairchild P, Payne I 2013 IEEE Aerospace Conference Big Sky Montana, USA, March 2–9, 2013 p1
[12] Rider D B, Voelz D G, Bush K A, Magee E 1993 Proc. SPIE 2029 150
Google Scholar
[13] Bush K A, Barnard C C, Voelz D G 1996 Proc. SPIE 2828 362
Google Scholar
[14] Sica L 1996 Appl. Opt. 35 264
Google Scholar
[15] Landesman B T, Olson D F 1994 Proc. SPIE 2302 14
Google Scholar
[16] 兰富洋, 罗秀娟, 樊学武, 张羽, 陈明徕, 刘辉, 贾辉 2018 物理学报 67 204201
Google Scholar
Lan F Y, Luo X J, Fan X W, Zhang Y, Chen M L, Liu H, Jia H 2018 Acta Phys. Sin. 67 204201
Google Scholar
[17] Gamiz V L 1994 Proc. SPIE 2302 2
Google Scholar
[18] Stahl S M, Kremer R, Fairchild P, Hughes K, Spivey B 1996 Proc. SPIE 2847 150
Google Scholar
[19] Olson D F, Long S M, Ulibarri L J 2000 Proc. SPIE 4091 323
Google Scholar
[20] 陆长明, 陈明徕, 罗秀娟, 张羽, 刘辉, 兰富洋, 曹蓓 2017 物理学报 66 114201
Google Scholar
Lu C M, Chen M L, Luo X J, Zhang Y, Liu L, Lan F Y, Cao B 2017 Acta Phys. Sin. 66 114201
Google Scholar
[21] Fienup J R US Patent 006597304 B2 [2003-7-22]
[22] Speckle-Based Imaging, Optical Physics Companyhttp://www.opci.com/technologies/ speckle-based-imaging [2017-1-9]
[23] 董磊, 卢振武, 刘欣悦 2019 中国光学 12 138
Google Scholar
Dong L, Lu Z W, Liu X Y 2019 Chin. Opt. 12 138
Google Scholar
[24] Takajo H, Takahashi T 1988 J. Opt. Soc. Am. A 5 416
Google Scholar
[25] Idell P S, Gonglewski J D 1990 Opt. Lett. 15 1309
Google Scholar
[26] 张羽, 李治国, 刘辉, 陈明徕, 罗秀娟, 马彩文, 张怀利 2021 光子学报 50 1201004
Google Scholar
Zhang Y, Li Z G, Liu H, Chen M L, Luo X J, Ma C W, Zhang H L 2021 Acta Photonica Sin. 50 1201004
Google Scholar
[27] Xiang M, Pan A, Zhao Y Y, Fan X W, Zhao H, Li C, Yao B L 2021 Opt. Lett. 46 29
Google Scholar
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