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针对连续太赫兹波叠层成像重建算法收敛较为迟滞的问题, 提出一种连续太赫兹波双物距叠层成像方法及相关重建算法, 使用不同记录距离形成的差异化衍射图幅值作为重建算法记录平面的约束条件, 增加了记录平面数据多样性和衍射信息冗余度. 仿真结果表明, 本方法可以加快算法收敛速率, 有效减少迭代次数, 提高连续太赫兹波定量相衬成像计算效率. 随后构建了基于2.52 THz光泵连续太赫兹激光器的双物距叠层成像实验装置, 应用双物距记录方法及改进算法重建获得了聚丙烯基字母图案样品的幅值和相位分布, 结果表明改进方法可以减少算法迭代次数, 提升计算效率, 同时改善相位像重建结果保真度.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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[4] Yakovlev E V, Zaytsev K I, Dolganova I N, Yurchenko S O 2015 IEEE Trans Terahertz. Sci. Technol. 5 810Google Scholar
[5] Kowalski M, Kastek M, Walczakowski M, Palka N, Szustakowski M 2015 Appl. Opt. 54 3826Google Scholar
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[8] Yousefi B, Sfarra S, Castanedo C I, Maldague X P V 2017 Infrared Phys. Techn. 85 163Google Scholar
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[15] Rong L, Tang C, Wang D, Li B, Tan F, Wang Y, Shi X 2019 Opt. Express 27 938Google Scholar
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[17] Thibault P, Dierolf M, Bunk O, Menzel A, Pfeiffer F, 2009 Ultramicroscopy 109 338Google Scholar
[18] Maiden A, Johnson D, Li P 2017 Optica 4 736Google Scholar
[19] Pfeiffer F 2018 Nat. Photonics 12 9Google Scholar
[20] 肖俊, 李登宇, 王雅丽, 史祎诗 2016 物理学报 65 154203Google Scholar
Xiao J, Li D Y, Wang Y L, Shi Y S 2016 Acta Phys. Sin. 65 154203Google Scholar
[21] Fienup J R 1978 Opt. Lett. 3 27Google Scholar
[22] Fienup J R 1982 Appl. Opt. 21 2758Google Scholar
[23] Sanz M, Picazo-Bueno J A, García J, Micó V 2015 Opt. Express 23 21352Google Scholar
[24] Zhang H, Bian Z, Jiang S, Liu J, Song P, Zheng G 2019 Opt. Lett. 44 1976Google Scholar
[25] Li Y, Xiao W, Pan F, Rong L 2014 Chin. Opt. Lett. 12 020901Google Scholar
[26] Pedrini G, Osten W, Zhang Y 2005 Opt. Lett. 30 833Google 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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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
Fig. 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
Fig. 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 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
Fig. 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 053702Google Scholar
[2] Ahi K 2019 Measurement 138 614Google Scholar
[3] Kowalski M, Kastek M 2016 IEEE Trans. Inf. Forensics Secur. 11 2028Google Scholar
[4] Yakovlev E V, Zaytsev K I, Dolganova I N, Yurchenko S O 2015 IEEE Trans Terahertz. Sci. Technol. 5 810Google Scholar
[5] Kowalski M, Kastek M, Walczakowski M, Palka N, Szustakowski M 2015 Appl. Opt. 54 3826Google Scholar
[6] Angrisani L, Bonavolontà F, Cavallo G, Liccardo A, Schiano L M R 2018 Measurement 116 83Google Scholar
[7] Zaytsev K I, Karasik V E, Fokina I N, Alekhnovich V I 2013 Opt. Eng. 52 68203Google Scholar
[8] Yousefi B, Sfarra S, Castanedo C I, Maldague X P V 2017 Infrared Phys. Techn. 85 163Google 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 282Google Scholar
[10] Löffler T, May T, Am Weg C, Alcin A, Hils Bernd, Roskos H 2007 Appl. Phys. Lett. 90 91111Google Scholar
[11] Ding S H, Li Q, Li Y D, Wang Q 2011 Opt. Lett. 36 1993Google 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 8445Google Scholar
[13] Hou L, Han X W, Yang L, Shi W 2017 Chin. Phys. Lett. 34 054207Google Scholar
[14] Valzania L, Feurer T, Zolliker P, Hack E 2018 Opt. Lett. 43 543Google Scholar
[15] Rong L, Tang C, Wang D, Li B, Tan F, Wang Y, Shi X 2019 Opt. Express 27 938Google Scholar
[16] Maiden A M, Rodenburg J M, 2009 Ultramicroscopy 109 1256Google Scholar
[17] Thibault P, Dierolf M, Bunk O, Menzel A, Pfeiffer F, 2009 Ultramicroscopy 109 338Google Scholar
[18] Maiden A, Johnson D, Li P 2017 Optica 4 736Google Scholar
[19] Pfeiffer F 2018 Nat. Photonics 12 9Google Scholar
[20] 肖俊, 李登宇, 王雅丽, 史祎诗 2016 物理学报 65 154203Google Scholar
Xiao J, Li D Y, Wang Y L, Shi Y S 2016 Acta Phys. Sin. 65 154203Google Scholar
[21] Fienup J R 1978 Opt. Lett. 3 27Google Scholar
[22] Fienup J R 1982 Appl. Opt. 21 2758Google Scholar
[23] Sanz M, Picazo-Bueno J A, García J, Micó V 2015 Opt. Express 23 21352Google Scholar
[24] Zhang H, Bian Z, Jiang S, Liu J, Song P, Zheng G 2019 Opt. Lett. 44 1976Google Scholar
[25] Li Y, Xiao W, Pan F, Rong L 2014 Chin. Opt. Lett. 12 020901Google Scholar
[26] Pedrini G, Osten W, Zhang Y 2005 Opt. Lett. 30 833Google 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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