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In industrial sites and outdoor long-distance measurements, the difficulty in accurately measuring and correcting the refractive index of air is a critical factor affecting precise distance measurement. In order to develop a simple, long-range, and high-precision absolute distance measurement technique, in this work an absolute distance measurement method is presented based on multi-pulse spectral interferometry by using an optical frequency comb. This method can dynamically correct the measurement errors introduced by group refractive index fluctuations. Firstly, a mathematical model for multi-pulse spectral interferometry is established. By performing a single Fourier transform on the multi-pulse spectral interference signal, the time delay measured in the pseudo-time domain can be used to simultaneously determine the group refractive index of the measurement path and the measured distance. Secondly, by fine-tuning the repetition frequency and using difference computation, the measurement range can be extended from the non-ambiguity range of traditional spectral interferometry to arbitrary lengths. Finally, extensive numerical simulations and analyses are conducted to validate the performance of the proposed method. The simulation results demonstrate that with a reference distance of 0.1 m, the maximum absolute error in group refractive index measurement is 0.12×10–6, and the maximum distance measurement error is 33 nm in a range of 0—200 m. In order to measure the group refractive index in real time under changing atmospheric conditions and compensate for ranging errors caused by changes in air refractive index, even under changing atmospheric conditions, the maximum distance measurement error is 38 nm, ensuring sub-micron-level measurement accuracy over long distances. The research results indicate that this method can be applied to large-scale and high-precision absolute distance measurement.
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Keywords:
- optical frequency comb /
- multi-pulse spectral interferometry /
- absolute distance measurement /
- air refractive index
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图 1 测距系统原理图
Figure 1. Principle of distance measurement system.
图 2 多脉冲光谱干涉条纹和时间延迟 (a)频域; (b)伪时域
Figure 2. Multi-pulse spectral interferometry and time delay: (a) Frequency domain; (b) pseudo-time domain.
图 3 被测距离与非模糊范围的关系
Figure 3. Target distance and non-ambiguous range.
图 4 参考距离d与群折射率$ {n_{\text{g}}} $之间的关系
Figure 4. Measurement errors of $ {n_{\text{g}}} $ by different d.
图 5 不同被测距离的测距误差
Figure 5. Range errors by different target distances.
图 6 测距分辨力实验结果
Figure 6. Experimental results of ranging resolution.
图 7 大气环境条件改变时的测距误差 (a)温度升高1 ℃; (b)湿度增大15%; (c)气压提高100 Pa; (d) CO2的体积分数增大10–4
Figure 7. Range errors by different atmosphere conditions: (a) Temperature increase by 1 ℃; (b) humidity increase by 15%; (c) air pressure increase by 100 Pa; (d) CO2 content increase by 10–4.
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[1] 贾琳华, 郑继辉, 张福民, 曲兴华 2023 机械工程学报 59 244
Google Scholar
Jia L H, Zheng J H, Zhang F M, Qu X H 2023 J. Mech. Eng. 59 244
Google Scholar
[2] Ahn C M, Na Y J, Kim J 2023 Opt. Laser Eng. 162 107414
Google Scholar
[3] Yu D R, Chen Z Y, Yang X, Xu Y L, Jin Z Y, Ma P X, Zhang Y F, Yu S, Lo B, Guo H 2023 Photon. Res. 11 2222
Google Scholar
[4] Ray P, Salido-Monzu D, Presl R, Butt J, Wieser A 2024 Opt. Express 32 12667
Google Scholar
[5] Liang X, Wu T F, Lin J R, Yang L H, Zhu J G 2023 Nanomanuf. Metrol. 6 6
Google Scholar
[6] Cui M, Zeitouny M G, Bhattacharya N, Van Den Berg S A, Urbach H P, Braat J J M 2009 Opt. Lett. 34 1982
Google Scholar
[7] Wei D, Takahashi S, Uehara K, Minoshima K, Hong F L, Nakajima M, Nakamura K 2011 Opt. Express 19 4881
Google Scholar
[8] Zheng J, Wang Y, Wang X, Zhang F, Zhang W 2021 Appl. Phys. Lett. 118 261106
Google Scholar
[9] 梁旭, 林嘉睿, 吴腾飞, 赵晖, 邾继贵 2022 71 090602
Google Scholar
Liang X, Lin J R, Wu T F, Zhao H, Zhu J G 2022 Acta Phys. Sin. 71 090602
Google Scholar
[10] Zhou S Y, Xiong S L, Zhu Z B, Wu G H 2019 Opt. Express 27 22868
Google Scholar
[11] Wright H, Sun J H, McKendrick D, Weston N, Reid D T 2021 Opt. Express 29 37037
Google Scholar
[12] Zhou S Y, Jiang R L, Zhang R X, Shi L H, Zhang D, Wu G H 2023 Opt. Lett. 48 1104
Google Scholar
[13] Han S M, Yang L H, Song Y J, Niu Q, Shi Y Q, Yu H Y, Hu X Y, Zhu J G 2024 Rev. Sci. Instrum. 95 043703
Google Scholar
[14] Doloca N R, Meiners-Hagen K, Wedde M, Pollinger F, Abou-Zeid A 2010 Meas. Sci. Technol. 21 115302
Google Scholar
[15] Zhao X Y, Qu X H, Zhang F M, Zhao Y H, Tang G Q 2018 Opt. Lett. 43 807
Google Scholar
[16] 王国超, 李星辉, 颜树华, 谭立龙, 管文良 2021 70 040601
Google Scholar
Wang G C, Li X H, Yan S H, Tan L L, Guan W L 2021 Acta Phys. Sin. 70 040601
Google Scholar
[17] Wu H Z, Zhang F M, Meng F, Liu T Y, Li J S, Pan L, Qu X H 2016 Meas. Sci. Technol. 27 015202
Google Scholar
[18] Gao H R, Huang L, Xu X, Wang D G, Ge P X, Zhao H N 2024 Meas. Sci. Technol. 35 105009
Google Scholar
[19] Wang J D, Huang J S, Liu Q H, Du W, Zhang F M, Zhu T 2024 Photon. Res. 12 313
Google Scholar
[20] Niu Q, Zheng J H, Cheng X R, Liu J C, Jia L H, Ni L M, Nian J, Zhang F M, Qu X H 2022 Opt. Express 30 35029
Google Scholar
[21] Xia H Y, Zhang C X 2010 Opt. Express 18 4118
Google Scholar
[22] Wang J D, Lu Z Z, Wang W Q, Zhang F M, Chen J W, Wang Y, Zheng J H, Chu S T, Zhao W, Brent E, Qu X H, Zhang W F 2020 Photon. Res. 8 1964
Google Scholar
[23] Jang Y S, Liu H, Yang J H, Yu M B, Kwong D L, Wong C W 2021 Phys. Rev. Lett. 126 023903
Google Scholar
[24] 徐昕阳, 赵海涵, 钱治文, 刘超, 翟京生, 吴翰钟 2021 70 220601
Google Scholar
Xu X Y, Zhao H H, Qian Z W, Liu C, Zhai J S, Wu H Z 2021 Acta Phys. Sin. 70 220601
Google Scholar
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