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现存的同-离轴混合数字全息技术可同时解决同轴全息共轭像消除困难和离轴全息分辨率受限的问题, 但需预测衍射距离, 不仅复杂耗时, 且精度有限; 而远心成像技术可获得非衍射图像, 无需预测衍射距离, 并具有可消除球面像差和散焦像差等特性. 因此, 本文将远心成像技术引入同-离轴混合数字全息技术中, 提出一种远心同-离轴混合数字全息高分辨率重建方法. 该方法利用远心同-离轴混合数字全息系统, 分别采集聚焦的离轴全息图和同轴全息图; 进而将离轴全息图获得的低分辨率相位信息与同轴全息图获得的振幅信息相复合, 作为迭代恢复过程的物光复振幅初始值, 并分别在空域和频域进行约束迭代, 实现高分辨率重建. 实验结果表明, 该方法无需衍射距离等先验信息, 便可很好地消除共轭像和系统畸变的干扰, 并可充分利用图像传感器的空间带宽积, 实现物体的高分辨率重建.In-line digital holography usually employs a phase retrieval algorithm to decouple the phase information but fails to eliminate the unwanted DC and twin image terms when the measured sample does not agree with the sparsity. While the off-axis digital holography can efficiently remove the unwanted image terms but can not reserve the high frequencies of the sample to realize high resolution. The in-line-and-off-axis hybrid digital holography was then developed to provide a relatively high resolution digital holographic imaging without considering the effect of the unwanted terms. In other words, the in-line-and-off-axis hybrid digital holography merges all of the best virtues of the mentioned-above methods in an efficient and elegant way. However, this state-of-the-art method requires prior knowledge about the diffraction distance, which results in time-consuming and low accuracy. In other sense, telecentric technology can realize non-diffractive imaging without the knowledge about the diffraction distance or spherical aberration or defocusing aberration. Therefore, in this paper, a novel in-line-and-off-axis hybrid digital holography is proposed by introducing telecentric imaging architecture, and the corresponding reconstruction method is further proposed by utilizing constrained iterative approach. In this method, telecentric in-line-and-off-axis hybrid digital holography is first used to acquire focused off-axis and in-line holograms, respectively. The low resolution phase information is reconstructed from the off-axis hologram by using Fourier transform method with the help of the sample-free off-axis hologram, and then multiplexed with the amplitude information obtained from the in-line hologram to act as the initial complex amplitude in the iterative recovery process. As a result, constrained iterations are carried out in the spatial domain and frequency domain to realize high resolution and high speed reconstruction. After simulations, we build an experimental setup and demonstrate the operation of the method with USAF resolution target, onion cells and bee wings. Both the simulation and experimental results show that the proposed method can require no prior knowledge to suppress the phase disturbance caused by the unwanted image terms and optical aberrations, resulting in high speed and full utilization of spatial bandwidth product of the digital camera to yield high resolution reconstruction. We hope that the proposed method will have most practical applications in the case where large resolution, high speed and good quality are needed.
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Keywords:
- digital holography /
- telecentric imaging /
- iterative recovery /
- high resolution
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图 1 远心同-离轴混合数字全息成像系统示意图
Fig. 1. Schematic of the telecentric in-line-and-off-axis hybrid digital holography system.
图 2 远心同-离轴混合数字全息重建算法框图
Fig. 2. Schematic of telecentric in-line-and-off-axis hybrid digital holographic reconstruction algorithm.
图 4 同轴全息图再现结果 (a)振幅像; (b)相位像
Fig. 4. Reconstructed results of in-line hologram: (a) Amplitude image; (b) phase image.
图 5 离轴全息图再现结果 (a)振幅像; (b)相位像
Fig. 5. Reconstructed results of off-axis hologram: (a) Amplitude image; (b) phase image.
图 6 再现像误差随迭代次数变化 (a)振幅均方误差收敛曲线; (b)相位均方误差收敛曲线
Fig. 6. Mean squared errors at each iteration: (a) Amplitude mean square error convergence curve; (b) phase mean square error convergence curve.
图 7 同-离轴混合数字全息再现结果 (a)振幅像; (b)相位像
Fig. 7. Reconstructed results obtained by the in-line-and-off-axis hybrid digital holography: (a) Amplitude image; (b) phase image.
图 8 USAF分辨率板实验结果 (a)同轴全息图; (b)离轴全息图; (c) 同轴数字全息再现像; (d)离轴数字全息再现像; (e)同-离轴混合数字全息再现像
Fig. 8. Experimental results of USAF resolution target: (a) In-line hologram; (b) off-axis hologram; (c) amplitude reconstructed image of the in-line hologram; (d) amplitude reconstructed image of the off-axis hologram; (e) amplitude reconstructed image of the in-line-and-off-axis hybrid digital holography.
图 9 洋葱表皮细胞实验结果 (a)同轴全息图; (b)离轴全息图; (c)同轴数字全息再现强度像; (d)同轴数字全息再现相位像; (e) 离轴数字全息再现强度像; (f) 离轴数字全息再现相位像; (g) 混合数字全息再现强度像; (h) 混合数字全息再现相位像; (i)相位剖面曲线
Fig. 9. Experimental results of onion epidermal cell: (a) In-line hologram; (b) off-axis hologram; (c) amplitude reconstructed image of the in-line hologram; (d) phase reconstructed image of the in-line hologram; (e) amplitude reconstructed image of the off-axis hologram; (f) phase reconstructed image of the off-axis hologram; (g) amplitude reconstructed image of the in-line-and-off-axis hybrid digital holography; (h) phase reconstructed image of the in-line-and-off-axis hybrid digital holography; (i) phase profile curves.
图 10 蜜蜂翅膀实验结果 (a)同轴全息图; (b)离轴全息图; (c)同轴数字全息再现强度像; (d)同轴数字全息再现相位像; (e) 离轴数字全息再现强度像; (f) 离轴数字全息再现相位像; (g) 混合数字全息再现强度像; (h) 混合数字全息再现相位像; (i)相位剖面曲线
Fig. 10. Experimental results of bee wings: (a) In-line hologram; (b) off-axis hologram; (c) amplitude reconstructed image of the in-line hologram; (d) phase reconstructed image of the in-line hologram; (e) amplitude reconstructed image of the off-axis hologram; (f) phase reconstructed image of the off-axis hologram; (g) amplitude reconstructed image of the in-line-and-off-axis hybrid digital holography; (h) phase reconstructed image of the in-line-and-off-axis hybrid digital holography; (i) phase profile curves
表 1 不同算法重建振幅和相位的峰值信噪比
Table 1. Peak signal-to-noise ratio (PSNR) of amplitudes and phases reconstructed by different algorithms.
同轴算法 离轴算法 混合算法 振幅PSNR/dB 71.55 66.54 82.37 相位PSNR/dB 43.69 55.29 57.70 
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[1] Schnars U, Juptner W 1994 Appl. Opt. 33 179
Google Scholar
[2] Wang Z, Millet L J, Gillette M U, Popescu G 2008 Opt. Lett. 33 1270
Google Scholar
[3] Aguilar J C, Raul Berriel-Valdos L, Felix Aguilar J 2013 Opt. Eng. 52 104103
Google Scholar
[4] Kemper B, Vollmer A, Rommel C E, Schnekenburger J, Von B G, Biomed J 2011 J. Biomed. Opt. 16 026014
Google Scholar
[5] Zhao W Q, Qiu L R, Xiao Y, Yang J M 2016 Opt. Express 24 22813
Google Scholar
[6] Donnarumma D, Brodoline A, Alexandre D 2016 Opt. Express 24 26887
Google Scholar
[7] Zhang J W, Dai S Q, Ma C J, Di J L, Zhao J L 2017 Opt. Lett. 42 3462
Google Scholar
[8] Yang W J, Liu X J, Lu W L, Guo X T, Popescu G 2018 Precis. Eng. 51 348
Google Scholar
[9] Qiu L R, Wang Y, Wu H X, Sun Y B, Cui H, Zhao W Q, Yuan L, Zhan C L 2018 Opt. Express 26 2314
Google Scholar
[10] Hu C F, Zhu S S, Gao L 2018 Opt. Lett. 43 3373
Google Scholar
[11] 周宏强, 万玉红, 满天龙 2018 物理学报 67 044202
Google Scholar
Zhou H Q, Wan Y H, Man T L 2018 Acta Phys. Sin. 67 044202
Google Scholar
[12] 张益溢, 吴佳琛, 郝然, 金尚忠, 曹良才 2020 物理学报 69 164201
Google Scholar
Zhang Y Y, Wu J C, Hao R, Jin S Z, Cao L C 2020 Acta Phys. Sin. 69 164201
Google Scholar
[13] Liu J Q, Zhu L Q, Zhang F, Dong M L, Qu X H 2019 Appl. Opt. 58 4042
Google Scholar
[14] 王华英, 刘飞飞, 宋修法, 廖微, 赵宝群, 于梦杰, 刘佐强 2013 物理学报 62 024207
Google Scholar
Wang H Y, Liu F F, Liao W, Song X F, Yu M J, Liu Z Q 2013 Acta Phys. Sin. 62 024207
Google Scholar
[15] Cuche E, Marquet P, Depeursinge C 1999 Appl. Opt. 38 6994
Google Scholar
[16] Pham H V, Edwards C, Lynford L G, Popescu G 2013 Appl. Opt. 52 A97
Google Scholar
[17] Gao P, Harder I, Nercissian V, Mantel K, Yao B 2010 Opt. Lett. 35 712
Google Scholar
[18] Bai H Y, Shan M G, Zhong Z, Guo L L, Zhang Y B 2015 Appl. Opt. 54 9513
Google Scholar
[19] Yamaguchi I, Zhang T 1997 Opt. Lett. 22 1268
Google Scholar
[20] Oshima T, Matsudo Y, Kakue T, Arai D, Shimobaba T, Ito T 2015 Opt. Commun. 350 270
Google Scholar
[21] Gerchberg R W, Saxton W O 1972 Optik 35 237
[22] Fienup J 1982 Appl. Opt. 21 2758
Google Scholar
[23] Latychevskaia T, Fink H W 2007 Phy. Rev. Lett. 98 233901
Google Scholar
[24] Rong L, Li Y, Liu S, Xiao W, Pan F, Wang D Y 2013 Opt. Laser Eng. 51 553
Google Scholar
[25] Yang G Z, Dong B Z, Gu B Y, Zhuang J Y, Ersoy O K 1994 Appl. Opt. 33 209
Google Scholar
[26] Zhang W H, Cao L C, David J B, Zhang H, Cang J, Jin G F 2018 Phy. Rev. Lett. 121 093902
Google Scholar
[27] Orzó L 2015 Opt. Express 23 16638
Google Scholar
[28] 王凤鹏, 王大勇, 王云新, 戎路, 赵洁 2018 中国激光 45 0609001
Google Scholar
Wang F P, Wang D Y, Wang Y X, Rong L, Zhao J 2018 Chinese Journal of Lasers 45 0609001
Google Scholar
[29] Khare K, Ali P T S, Joseph J 2013 Opt. Express 21 5634
Google Scholar
[30] Wu X Y, Yu Y J, Zhou W J 2014 Opt. Express 22 19860
Google Scholar
[31] Zhong M, Cui J, Hyun J S, Pan L, Duan P, Zhang S 2020 Meas. Sci. Technol. 31 085003
Google Scholar
[32] Sanchez-Ortiga E, Ferraro P, Martinez-Corral M 2011 Opt. Soc. Am. A 28 1410
Google Scholar
[33] Zhong Z, Bai H Y, Shan M G, Zhang Y B, Guo L L 2017 Opt. Laser Eng. 97 9
Google Scholar
[34] Hao B G, Shan M G, Zhong Z, Diao M, Wang Y, Zhang Y B 2015 J. Opt. 17 035602
Google Scholar
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