双合成波长数字全息低噪声分级解包裹方法

刘磊; 徐志博; 钱文硕; 李文杰; 谢芳; 钟志; 单明广

doi:10.7498/aps.70.20210669

摘要

双波长数字全息中差分合成波长可拓展无相位包裹测量纵深范围, 但显著放大相位噪声; 加性合成波长可抑制相位噪声, 但大幅缩小无相位包裹测量范围. 因此, 本文利用差分合成波长无包裹测量范围大与加性合成波长噪声低的特性, 提出一种双合成波长数字全息低噪声分级解包裹方法. 该方法利用由差分合成波长获得的“相位差”引导单波长包裹相位进行解包裹, 然后再利用单波长的解包裹后的光程差引导加性合成波长获得的包裹“相位和”进行解包裹, 通过分级实现双波长低噪声解包裹. 实验结果表明, 该方法可以简单、快速地实现双波长数字全息低噪声解包裹.

关键词:

Abstract

Dual-wavelength digital holography can expand the unambiguous measurement depth in phase unwrapping by using a differential synthetic wavelength which is longer than the single illumination wavelength. However, the phase noise is significantly amplified due to the magnification of the differential synthetic wavelength, resulting in a lower measurement accuracy. On the other hand, a lower noise level can be achieved by using additive synthetic-wavelength which is shorter than the single illumination wavelength. However, the corresponding unambiguous measurement depth is greatly reduced due to the phase ambiguity. In this case, combining the merits of the differential synthetic-wavelength and the additive synthetic-wavelength, different low noise phase unwrapping algorithms have been developed in recent years. However, these algorithms are complex and time consuming because they need to calculate multiple intermediate variables or search for the constrained boundary conditions in two-dimensional space. Therefore, in this paper, we develop a hierarchical phase unwrapping algorithm by using the two synthetic wavelengths for dual-wavelength digital holography to realize low noise and fast unambiguous measurement with large depth. In this algorithm, the unwrapped phase difference obtained by the differential synthetic wavelength is used to guide the wrapped phase of one single wavelength to realize phase unwrapping, and then the optical path difference obtained by the single-wavelength unwrapped phase is employed to guide the wrapped phase sum, and thus realizing phase unwrapping. As a result, the phase noise is attenuated and the depth sensitivity is preserved for dual-wavelength phase unwrapping. After theoretical analysis, a series of simulation experiments is carried out on the reconstructed quality, anti-noise characteristics and speed through comparing with state-of-the-art dual-wavelength phase unwrapping algorithms, including the conventional algorithm, the linear programming algorithm and the direct linear programming algorithm. In this case, a flipping dual-wavelength common-path digital holography with orthogonal carrier is built to acquire multiplexed off-axis hologram in one shot and illustrate the operation of the algorithm with circular step target, and stability test of the setup. Both the simulation and experimental results show that the proposed method can be simplified and deterministic, resulting in a lower noise phase unwrapping in a time of 20.5 ms for a phase map of one megapixel. We expect that the proposed method can have practical applications in measurement that requires high accuracy, fast speed, and large depth.

Keywords:

作者及机构信息

1.
哈尔滨工程大学，信息与通信工程学院，哈尔滨　150001

2.
哈尔滨工程大学，先进船舶通信与信息技术工信部重点实验室，哈尔滨　150001

通信作者: 单明广, smgsir@gmail.com

基金项目: 国家自然科学基金(批准号: 61775046)、黑龙江省自然科学基金(批准号:LC2018027)和中央高校基本科研业务费资助的课题

Authors and contacts

1.
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

2.
Key Laboratory of Advanced Marine Communication and Information Technology, Ministry of Industry and Information Technology, Harbin Engineering University, Harbin 150001, China

Corresponding author: Shan Ming-Guang, smgsir@gmail.com

Funds: Project supported by National Natural Science Foundation of China (Grant No. 61775046), Natural Science Foundation of Heilongjiang Province, China (Grant No. LC2018027), and Fundamental Research Funds for the Central Universities

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参考文献

[1]	Gabor D 1948 Nature 161 777 Google Scholar
[2]	Lu X X, Chen J P, Liu S D, Ma Z J, Zhang Z, Zhong L Y 2012 Opt. Las. Eng. 50 1431 Google Scholar
[3]	Popescu P, Ikeda T, Dasari R R, Feld M S 2006 Opt. lett. 31 775 Google Scholar
[4]	Girshovitz P Shaked N T 2013 Opt. Express 21 5701 Google Scholar
[5]	Guo R L, Yao B L, Gao P, Min J W, Han J, Yu X, Lei M, Yan S H, Yang Y L, Dan D, Ye T 2013 Appl. Opt. 52 3484 Google Scholar
[6]	Hao B G, Diao M, Shan M G, Zhang Y B, Zhong Z 2013 Opt. Express 21 2126 Google Scholar
[7]	Frenklach I, Girshovitz P, Shaked N T 2014 Opt. Lett. 39 1525 Google Scholar
[8]	Rawat S, Komatsu S, Markman A, Anand A, Javidi B 2017 Appl. Opt. 56 D127 Google Scholar
[9]	Hu C F, Zhu S S, Gao L, Popescu G 2018 Opt. Lett. 43 3373 Google Scholar
[10]	Picazo-Bueno J A, Trusiak M, MicóV 2019 Opt. Express 27 5655 Google Scholar
[11]	Shaked N T, Micó V, Trusiak M, Kuś A, Mirsky S K 2020 Adv. Opt. Photon. 12 556 Google Scholar
[12]	Polhemus C 1973 Appl. Opt. 12 2071 Google Scholar
[13]	Gass J, Dakoff A, Kim M K 2003 Opt. Lett. 28 1141 Google Scholar
[14]	Kühn J, Colomb T, Montfort F, Charrière F, Emery Y, Cuche E, Marquet P, Depeursinge C 2007 Opt. Express 15 7231 Google Scholar
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[18]	Wang Z M, Jiao J N, Qu W J, Yang F, Li H R, Tian A L, Asundi A 2017 Appl. Opt. 56 424 Google Scholar
[19]	Di J L, Zhang J W, Xi T L, Ma C J, Zhao J L 2015 J. Micro/Nanolithography, MEMS, and MOEMS 14 041313 Google Scholar
[20]	Xiong J X, Zhong L Y, Liu S D, Qiu X, Zhou Y F, Tian J D, Lu X X 2017 Opt. Express 25 7181 Google Scholar
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施引文献

图 1 分级解包裹流程图

Fig. 1. Flowchart of Hierarchical phase unwrapping.

下载: 全尺寸图片幻灯片

图 2 (a)待测物体高度图; (b)离轴全息图; (c) λ₁和(d) λ₂对应的包裹相位

Fig. 2. (a) Original height map of the simulated sample; (b) simulated multiplexed off-axis hologram; and corresponding wrapped phase maps at (c) λ₁ and (d) λ₂.

下载: 全尺寸图片幻灯片

图 3 (a)算法I, (b)算法Ⅱ, (c)算法Ⅲ和(d)算法Ⅳ的恢复结果; (e)算法I, (f)算法Ⅱ, (g)算法Ⅲ和(h)算法Ⅳ恢复结果的残差图

Fig. 3. Reconstructed results by (a) Algorithm I, (b) Algorithm Ⅱ, (c) Algorithm Ⅲ, and (d) Algorithm Ⅳ; and the corresponding residue maps obtained by (e) Algorithm I, (f) Algorithm Ⅱ, (g) Algorithm Ⅲ, (h) Algorithm Ⅳ.

下载: 全尺寸图片幻灯片

图 4 残差图(图3(e)—3(h))中黑色虚线标注数据

Fig. 4. Data marked with the black dashed lines in residue maps shown in Fig.3(e)-3(h).

下载: 全尺寸图片幻灯片

图 5 残差图(图3(e)—3(h))中(a)标准差和(b)峰谷值

Fig. 5. Standard deviation and peak-valley value of residue maps shown in Fig.3(e)-3(h).

下载: 全尺寸图片幻灯片

图 6 视场翻转双波长载波正交数字全息原理图

Fig. 6. Flipping dual-wavelength common-path digital holography with orthogonal carrier.

下载: 全尺寸图片幻灯片

图 7 (a)复合全息图; (b)频谱图; (c) λ₁和(d) λ₂对应的包裹相位

Fig. 7. (a) Multiplexed hologram and its (b) power spectrum; and corresponding wrapped phase maps at (c) λ₁ and (d) λ₂.

下载: 全尺寸图片幻灯片

图 8 圆柱恢复结果　(a)算法I; (b)算法Ⅱ; (c)算法Ⅲ; (d)算法Ⅳ

Fig. 8. Reconstructed results of the step target by (a) Algorithm I; (b) Algorithm Ⅱ; (c) Algorithm Ⅲ; (d) Algorithm Ⅳ.

下载: 全尺寸图片幻灯片

图 9 恢复结果的一维剖面图(图8中白色虚线)

Fig. 9. Reconstructed result of 1 D height profiles(along the white dashed lines in Fig.8).

下载: 全尺寸图片幻灯片

图 10 液滴酒精恢复结果　(a)算法I; (b)算法Ⅱ; (c)算法Ⅲ; (d)算法Ⅳ;

Fig. 10. Reconstructed result of a drop of alcohol: (a) Algorithm I; (b) Algorithm Ⅱ; (c) Algorithm Ⅲ, ; (d) Algorithm Ⅳ..

下载: 全尺寸图片幻灯片

图 11 恢复结果的一维剖面图(图10中白色虚线)

Fig. 11. Reconstructed result of 1 D height profiles (along the white dashed lines in Fig.10).

下载: 全尺寸图片幻灯片

图 12 稳定性实验

Fig. 12. Stability test for the proposed method.

下载: 全尺寸图片幻灯片

[1]	Gabor D 1948 Nature 161 777 Google Scholar
[2]	Lu X X, Chen J P, Liu S D, Ma Z J, Zhang Z, Zhong L Y 2012 Opt. Las. Eng. 50 1431 Google Scholar
[3]	Popescu P, Ikeda T, Dasari R R, Feld M S 2006 Opt. lett. 31 775 Google Scholar
[4]	Girshovitz P Shaked N T 2013 Opt. Express 21 5701 Google Scholar
[5]	Guo R L, Yao B L, Gao P, Min J W, Han J, Yu X, Lei M, Yan S H, Yang Y L, Dan D, Ye T 2013 Appl. Opt. 52 3484 Google Scholar
[6]	Hao B G, Diao M, Shan M G, Zhang Y B, Zhong Z 2013 Opt. Express 21 2126 Google Scholar
[7]	Frenklach I, Girshovitz P, Shaked N T 2014 Opt. Lett. 39 1525 Google Scholar
[8]	Rawat S, Komatsu S, Markman A, Anand A, Javidi B 2017 Appl. Opt. 56 D127 Google Scholar
[9]	Hu C F, Zhu S S, Gao L, Popescu G 2018 Opt. Lett. 43 3373 Google Scholar
[10]	Picazo-Bueno J A, Trusiak M, MicóV 2019 Opt. Express 27 5655 Google Scholar
[11]	Shaked N T, Micó V, Trusiak M, Kuś A, Mirsky S K 2020 Adv. Opt. Photon. 12 556 Google Scholar
[12]	Polhemus C 1973 Appl. Opt. 12 2071 Google Scholar
[13]	Gass J, Dakoff A, Kim M K 2003 Opt. Lett. 28 1141 Google Scholar
[14]	Kühn J, Colomb T, Montfort F, Charrière F, Emery Y, Cuche E, Marquet P, Depeursinge C 2007 Opt. Express 15 7231 Google Scholar
[15]	Min J W, Yao B L, Zhou M L, Guo R L, Lei M, Yang Y L, Dan D, Yan S H, Peng T 2014 J. Opt. 16 125409 Google Scholar
[16]	袁飞, 袁操今, 聂守平, 朱竹青, 马青玉, 李莹, 朱文艳, 冯少彤 2014 物理学报 63 166 Google Scholar Yuan F, Yuan C J, Nie S P, Zhu Z Q, Ma Q Y, Li Y, Zhu W Y, Feng S T 2014 Acta Phys. Sin. 63 166 Google Scholar
[17]	Khmaladze A, Matz R L, Zhang C, Wang T, Banaszak Holl M M, Chen Z 2011 Opt. Lett. 36 912 Google Scholar
[18]	Wang Z M, Jiao J N, Qu W J, Yang F, Li H R, Tian A L, Asundi A 2017 Appl. Opt. 56 424 Google Scholar
[19]	Di J L, Zhang J W, Xi T L, Ma C J, Zhao J L 2015 J. Micro/Nanolithography, MEMS, and MOEMS 14 041313 Google Scholar
[20]	Xiong J X, Zhong L Y, Liu S D, Qiu X, Zhou Y F, Tian J D, Lu X X 2017 Opt. Express 25 7181 Google Scholar
[21]	Shan M G, Liu L, Zhong Z, Liu B, Zhang Y B 2019 Opt. Las. Eng. 117 1 Google Scholar
[22]	Liu Q, Li L L, Huang X J, Zhang H, Yue X B 2020 J. Opt. 22 045701 Google Scholar
[23]	Shan M G, Liu L, Zhong Z, Liu B, Luan G Y, Zhang Y B 2017 Opt. Express 25 26253 Google Scholar
[24]	Liu L, Shan M G, Zhong Z, Liu B, Luan G Y, Diao M, Zhang Y B 2017 Opt. Lett. 42 4331 Google Scholar

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双合成波长数字全息低噪声分级解包裹方法