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Terahertz (THz) radiation lies between the millimeter and infrared region of the electromagnetic spectrum, which is typically defined as the frequency range of 0.1–10 THz and the corresponding wavelength ranges from 30 μm to 3 mm. Terahertz radiation due to wide spectrum, high penetration, low energy, and other important features, has been a valuable tool for imaging and non-destructive testing on a submillimeter scale. Continuous-wave (CW) terahertz ptychography is a type of phase-contrast technique with advantages of simple set-up and large field-of-view. It retrieves the complex-valued transmission function of the specimen and the probe function at the same time. The extended ptychographic iterative engine (ePIE) algorithm is used as the reconstruction algorithm in the field of ptychography, because it is relatively simple, and can use computer memory efficiently. However, the problem of algorithm convergence delay makes us unable to acquire the reconstruction result very quickly. Since the ptychography is a problem of retrieving phase information, physical constraints affect the convergence speed of the algorithm strongly. In this paper, we propose a dual-plane ePIE (dp-ePIE) algorithm for CW THz ptychography. By moving detector along the axis and capturing diffraction patterns of one zone of an object at two recording planes, then, two sets of patterns used as the constraints simultaneously can increase the diversity of experimental parameter. Hence, the convergence rate can be improved. The simulation results suggest better reconstruction fidelity with a faster convergence rate by the dp-ePIE algorithm. The dual-plane terahertz ptychography experimental setup is built based on 2.52 THz optically pumped laser and Pyrocam-III pyroelectric array detector. Compared with other methods to increase the diversity of measurement, the setup of dual-plane ptychography can be compact and simple, thus reducing the terahertz wave transmission loss. A polypropylene sample is adopted and it is approximated as a pure phase object. No-reference structural sharpness (NRSS) is utilized as a quantitative evaluation index. It takes 45.086 s to achieve NRSS value of 0.9831 by using the dp-ePIE algorithm in 10 iterations, while the NRSS value and calculation time for e-PIE algorithm are 0.9531 and 57.117 s (20 loops), respectively. The experimental results show that the dp-ePIE algorithm can obtain high-quality amplitude and phase distribution with less iterations than the traditional ePIE algorithm.
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Keywords:
- terahertz imaging /
- ptychography /
- phase retrieval /
- dual-plane
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Google Scholar
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Google Scholar
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图 1 双物距叠层成像的原理图
Figure 1. Schematic diagram of dual plane ptychographic imaging.
图 2 仿真实验原理图
Figure 2. Schematic diagram of the terahertz dual-plane ptychographic simulation.
图 3 仿真实验中的样品 (a) 振幅分布, (b) 相位分布
Figure 3. Sample for ptychographic simulation: (a) Input amplitude distribution; (b) input phase distribution.
图 4 收敛度评价曲线
Figure 4. Convergence of the ePIE and dp-ePIE algorithms.
图 5 叠层仿真重建结果 (a1)、(b1), (c1)、(d1)和(e1)、(f1)分别表示ePIE算法迭代4次、20次及50次迭代重建振幅分布与相位分布; (a2)、(b2), (c2)、(d2)和(e2)、(f2)分别表示dp-ePIE算法迭代4次、20次及50次迭代重建振幅分布与相位分布
Figure 5. Comparison of simulation results with ePIE and dp-ePIE: (a1) and (b1), (c1) and (d1), (e1) and (f1) are the amplitude and phase reconstruction with ePIE algorithm; (a2) and (b2), (c2) and (d2), (e2) and (f2) are the amplitude and phase reconstruction with dp-ePIE algorithm.
图 6 重建结果的相关系数比较 (a) dp-ePIE与ePIE算法幅值重建结果与迭代次数关系; (b) dp-ePIE与ePIE算法相位重建结果与迭代次数关系
Figure 6. Comparison of correlation coefficients of reconstruction results: (a) Comparison of correlation coefficients of amplitude reconstruction results with dp-ePIE and ePIE; (b) comparison of correlation coefficients of phase reconstruction results with dp-ePIE and ePIE.
图 7 重建像相关系数与探测器采集位置间隔距离关系曲线
Figure 7. Relation between correlation coefficients of reconstruction image and different recording intervals.
图 8 连续太赫兹波叠层成像实验装置示意图
Figure 8. Setup of continuous-wave terahertz dual-plane ptychography.
图 9 聚丙烯可回收三角标志图案样品 (a)三角标志模型; (b)样品实物图
Figure 9. Sample of recyclable polypropylene triangle pattern: (a) Model of the sample; (b) picture of the sample.
图 10 两种叠层重建算法分别迭代10次后可回收标志的重建结果 (a1), (b1)分别表示ePIE算法重建振幅分布及相位分布; (a2), (b2)表示dp-ePIE算法重建振幅分布及相位分布
Figure 10. The reconstructed results after 10 iterations by two different reconstruction algorithms: (a1), (b1) Represent the amplitude and phase reconstructed based on ePIE algorithm: (a2), (b2) represent the amplitude and phase reconstructed based dp-ePIE algorithm.
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[1] Zaytsev K I, Kudrin K G, Karasik V E, Reshetov I V, Yurchenko, S O 2015 Appl. Phys. Lett. 106 053702
Google Scholar
[2] Ahi K 2019 Measurement 138 614
Google Scholar
[3] Kowalski M, Kastek M 2016 IEEE Trans. Inf. Forensics Secur. 11 2028
Google Scholar
[4] Yakovlev E V, Zaytsev K I, Dolganova I N, Yurchenko S O 2015 IEEE Trans Terahertz. Sci. Technol. 5 810
Google Scholar
[5] Kowalski M, Kastek M, Walczakowski M, Palka N, Szustakowski M 2015 Appl. Opt. 54 3826
Google Scholar
[6] Angrisani L, Bonavolontà F, Cavallo G, Liccardo A, Schiano L M R 2018 Measurement 116 83
Google Scholar
[7] Zaytsev K I, Karasik V E, Fokina I N, Alekhnovich V I 2013 Opt. Eng. 52 68203
Google Scholar
[8] Yousefi B, Sfarra S, Castanedo C I, Maldague X P V 2017 Infrared Phys. Techn. 85 163
Google Scholar
[9] Zhang H, Robitaille F, Grosse C U, Clemente I, Martins J O, Sfarra S, Maldague X P V 2018 Composites Part A 107 282
Google Scholar
[10] Löffler T, May T, Am Weg C, Alcin A, Hils Bernd, Roskos H 2007 Appl. Phys. Lett. 90 91111
Google Scholar
[11] Ding S H, Li Q, Li Y D, Wang Q 2011 Opt. Lett. 36 1993
Google Scholar
[12] Rong L, Latychevskaia T, Chen C H, Wang D Y, Yu Z P, Zhou X, Li Z Y, Huang H C, Wang Y X, Zhou Z 2015 Sci. Rep. 5 8445
Google Scholar
[13] Hou L, Han X W, Yang L, Shi W 2017 Chin. Phys. Lett. 34 054207
Google Scholar
[14] Valzania L, Feurer T, Zolliker P, Hack E 2018 Opt. Lett. 43 543
Google Scholar
[15] Rong L, Tang C, Wang D, Li B, Tan F, Wang Y, Shi X 2019 Opt. Express 27 938
Google Scholar
[16] Maiden A M, Rodenburg J M, 2009 Ultramicroscopy 109 1256
Google Scholar
[17] Thibault P, Dierolf M, Bunk O, Menzel A, Pfeiffer F, 2009 Ultramicroscopy 109 338
Google Scholar
[18] Maiden A, Johnson D, Li P 2017 Optica 4 736
Google Scholar
[19] Pfeiffer F 2018 Nat. Photonics 12 9
Google Scholar
[20] 肖俊, 李登宇, 王雅丽, 史祎诗 2016 物理学报 65 154203
Google Scholar
Xiao J, Li D Y, Wang Y L, Shi Y S 2016 Acta Phys. Sin. 65 154203
Google Scholar
[21] Fienup J R 1978 Opt. Lett. 3 27
Google Scholar
[22] Fienup J R 1982 Appl. Opt. 21 2758
Google Scholar
[23] Sanz M, Picazo-Bueno J A, García J, Micó V 2015 Opt. Express 23 21352
Google Scholar
[24] Zhang H, Bian Z, Jiang S, Liu J, Song P, Zheng G 2019 Opt. Lett. 44 1976
Google Scholar
[25] Li Y, Xiao W, Pan F, Rong L 2014 Chin. Opt. Lett. 12 020901
Google Scholar
[26] Pedrini G, Osten W, Zhang Y 2005 Opt. Lett. 30 833
Google Scholar
[27] 谢小甫, 周进, 吴钦章 2010 计算机应用 30 921
Xie X F, Zhou J, Wu Q Z 2010 Journal of Computer Application 30 921
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