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## Spectral interferometry based absolute distance measurement using frequency comb

Wu Han-Zhong, Cao Shi-Ying, Zhang Fu-Min, Qu Xing-Hua
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• #### 摘要

详细分析了光学频率梳光谱干涉的原理, 建立了较全面的光谱干涉的数学模型, 为实现绝对距离测量提供理论分析基础. 基于光谱干涉, 指出通过光谱干涉条纹的振荡频率, 即一次傅里叶变换, 可以实现绝对距离测量, 数值模拟结果表明, 最大测量误差为1.5 nm; 提出了一种等效的多波长并行零差干涉的方法, 分析了多波长并行零差干涉法的测距原理. 数值模拟结果表明, 多波长并行零差干涉法的最大误差为8.7 nm; 通过脉冲啁啾实现绝对测距, 分析了基于脉冲啁啾实现绝对测距的原理, 数值模拟结果表明, 最大测距误差为5.3 nm.

#### Abstract

Spectral interferometry using frequency comb has become a powerful approach to absolute distance measurement. In this paper, we analyze the principle of spectral interferometry in detail. With the consideration of dispersion, pulse chirp and the power ratio of the reference pulse and the measurement pulse, we develop a Gaussian model, which can be used to determine distances. The frequency of the spectral interference fringe is of key importance. The distances can be directly determined by the frequency of the spectral interference fringe through one-step fast Fourier transform with no filters during the data processing. The simulation results show that the maximum deviation is 1.5 nm when the distance is 1.5 mm theoretically. The comb consists of hundreds of thousands of teeth in the spectral domain, and each tooth can be regarded as a cw laser. We propose a method based on the phases of two close modes. The principle is introduced, and the maximum deviation is 8.7 nm with a distance of 1.5 mm while the minimum deviation is 0.3 nm corresponding to distance of 0.5 mm. We theoretically show that the linear pulse chirp can be used for distance measurement. The measurement principle is analyzed, and the simulation shows that the maximum deviation is 5.3 nm when the distance is 1.2 mm.

#### 作者及机构信息

###### 1. 天津大学精密测试技术及仪器国家重点实验室, 天津 300072; 2. 中国计量科学研究院时间频率计量研究所, 北京 100013
• 基金项目: 国家自然科学基金(批准号: 51327006, 51105274)和高等学校博士学科点专项科研基金(批准号: 20120032130002)资助的课题.

#### Authors and contacts

###### 1. State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China; 2. Division of Time and Frequency Metrology, National Institute of Metrology, Beijing 100013, China
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51327006, 51105274), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032130002).

#### 参考文献

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#### 施引文献

•  [1] Liao S S, Yang T, Dong J J 2014 Chin. Phys. B 23 073201 [2] Zhu M H, Wu X J, Wei H Y, Zhang L Q, Zhang J T, Li Y 2013 Acta Phys. Sin. 62 070702 (in Chinese) [朱敏昊, 吴学健, 尉昊赟, 张丽琼, 张继涛, 李岩 2013 物理学报 62 070702] [3] Xing S J, Zhang F M, Cao S Y, Wang G W, Qu X H 2013 Acta Phys. Sin. 62 170603 (in Chinese) [邢书剑, 张福民, 曹士英, 王高文, 曲兴华 2013 物理学报 62 170603] [4] Zhang Y C, Wu J Z, Li Y Q, Jin L, Ma J, Wang L R, Zhao Y T, Xiao L T, Jia S T 2012 Chin. Phys. B 21 113701 [5] Wu H Z, Cao S Y, Zhang F M, Xing S J, Qu X H 2014 Acta Phys. Sin. 63 100601 (in Chinese) [吴翰钟, 曹士英, 张福民, 邢书剑, 曲兴华 2014 物理学报 63 100601] [6] Minoshima K, Matsumoto H 2000 Appl. Opt. 39 5512 [7] Baumann E, Giorgetta F R, Coddington I, Sinclair L C, Knabe K, Swann W C, Newbury N R 2013 Opt. Lett. 38 2026 [8] Hyun S, Kim Y J, Kim Y, Kim S W 2010 CIRP Annals: Manufacturing Technology 59 555 [9] Schuhler N, Salvadé Y, Lévêque S, Dändliker R, Holzwarth R 2006 Opt. Lett. 31 3101 [10] Salvadé Y, Schuhler N, Lévêque S, Floch S L 2008 Appl. Opt. 47 2715 [11] Ye J 2004 Opt. Lett. 29 1153 [12] Wang X N, Takahashi S, Takamasu K, Matsumoto H 2012 Opt. Express 20 2725 [13] Balling P, Křen P, Mašika P, van den Berg S A 2009 Opt. Express 17 9300 [14] Wu H, Zhang F, Cao S, Xing S, Qu X 2014 Opt. Express 22 10380 [15] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photon. 3 351 [16] Zhang H, Wei H, Wu X, Yang H, Li Y 2014 Opt. Express 22 6597 [17] Lee J, Han S, Lee K, Bae E, Kim S, Lee S, Kim S W, Kim Y J 2013 Meas. Sci. Technol. 24 045201 [18] Joo K, Kim S 2006 Opt. Express 14 5954 [19] Cui M, Zeitouny M G, Bhattacharya N, van den Berg S A, Urbach H P 2011 Opt. Express 19 6549 [20] Berg van den S A, Persijn S T, Kok G J P 2012 Phys. Rev. Lett. 108 183901 [21] Li Y, Hu K, Ji R, Liu D, Zhou W 2014 Opt. Eng. 53 122409
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##### 出版历程
• 收稿日期:  2014-08-15
• 修回日期:  2014-09-05
• 刊出日期:  2015-01-05

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