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Optical frequency combs of the femtosecond laser have been widely used in time-frequency technology and precision spectrum measurement. The absolute ranging technology derived from time-frequency characteristics of the optical frequency comb is expected to become the incomparable means of length metrology and distance measurement in the future due to its traceability to time-frequency standard and capability of large scale and high precision. This paper proposes a real-time absolute ranging method with multi-wavelength interferometry referenced to optical frequency comb, which enables multiple continuous-wave lasers to be synchronously calibrated to selected modes of the frequency comb by means of optical phase-locked loop. With synchronous phase measurement and calculation with excess fraction algorithm, absolute distance measurement by multi-wavelength interferometry is ultimately fulfilled. The proposed measurement method can not only retain high resolution and high accuracy of traditional laser interferometry, but also can be traced to a time-frequency reference, which is of metrological significance to high-precision length and distance measurement, especially to the definition of “meter” for physical reproduction. Measured results for ranging experiments have proved that the non-ambiguity range of the four-wavelength interferometer reaches 44.6 mm, and fluctuations of air refractive index cause the non-ambiguity range change with the order of nanometers. Through theoretical analysis, it is pointed out that the non-ambiguity range of the multi-wavelength interferometer in the actual measurement environment is restricted by the calculated error of air refractive index, especially the estimation accuracy and fluctuation degree of the refractive index relationship between wavelengths. And in a good laboratory conditions, the non-ambiguity range of real-time absolute ranging by frequency-comb-calibrated multi-wavelength interferometry can reach several meters or even tens of meters. At the same time, a 2-meter linear displacement comparison has been carried out, the P.V. value of the residual errors for linear fitting is 36.1 nm, and such residual errors match the magnitude of uncertainty of air refractive index calculated by empirical formula, which prove that the multi-wavelength interferometry can perform meter-level absolute ranging. The proposed research can be directly applied to precision manufacturing of large-scale semiconductors up to several meters, and is beneficial to promoting the accuracy of laser ranging for space mission.
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Keywords:
- absolute distance measurement /
- optical frequency comb of the femtosecond laser /
- multi-wavelength interferometry /
- non-ambiguous range
[1] Berkovic G, Shafir E 2012 Adv. Opt. Photon. 4 441
Google Scholar
[2] Estler W T, Edmundson K L, Peggs G N, Parker D H 2002 CIRP Ann. Manuf. Technol. 51 587
Google Scholar
[3] Manske E, Jager G, Hausotte T, Fub R 2012 Meas. Sci. Technol. 23 074001
Google Scholar
[4] Bobroff N 1993 Meas. Sci. Technol. 4 907
Google Scholar
[5] Lay O P, Dubovitsky S, Peters R D, Burger J P, Steier W H 2003 Opt. Lett. 28 890
Google Scholar
[6] Bourdet G L, Orszag A G 1979 Appl. Opt. 18 225
Google Scholar
[7] Zimmermann E, Salvadé Y, Dändliker R 1996 Opt. Lett. 21 531
Google Scholar
[8] Meiners-Hagen K, Schoedel R, Pollinger F, Abou-Zeid A 2009 Meas. Sci. Rev. 9 16
Google Scholar
[9] Dändliker R, Thalmann R, Prongue D 1988 Opt. Lett. 13 339
Google Scholar
[10] Groot P 2001 Opt. Eng. 40 28
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[14] Diddams S A, Jones D J, Ye J, Cundiff S T, Hall J L, Ranka J K, Windeler R S, Holzwarth R, Udem T, Hansch T W 2000 Phys. Rev. Lett. 84 5102
Google Scholar
[15] Udem T, Holzwarth R, Hansch T W 2002 Nature 416 233
Google Scholar
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Google Scholar
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Google Scholar
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Wang G C, Yan S H, Yang J, Lin C B, Yang D X, Zou P F 2013 Acta Phys. Sin. 62 070601
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Zhang X S, Yi W M, Hu M H, Yang Z H, Wu G H 2016 Acta Phys. Sin. 65 080602
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Google Scholar
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Google Scholar
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[31] 孟祥松, 张福民, 曲兴华 2015 物理学报 23 230601
Google Scholar
Meng X S, Zhang F M, Qu X H 2015 Acta Phys. Sin. 23 230601
Google Scholar
[32] Kim S W 2009 Nat. Photonics 3 313
Google Scholar
[33] 姜海峰 2018 物理学报 67 160602
Google Scholar
Jiang H F 2018 Acta Phys. Sin. 67 160602
Google Scholar
[34] Chun B J, Hyun S, Kim S, Kim S W, Kim Y J 2013 Opt. Express 21 29179
Google Scholar
[35] Felder R 2003 Metrologia 42 323
Google Scholar
[36] Wei D, Takamasu K, Matsumoto H 2013 Precis. Eng. 37 694
Google Scholar
[37] Tilford C R 1977 Appl. Opt. 16 1857
Google Scholar
[38] 王国超, 魏春华, 颜树华 2014 光学学报 34 111
Google Scholar
Wang G C, Wei C H, Yan S H 2014 Acta Optic. Sin. 34 111
Google Scholar
[39] Falaggis K, Towers D P, Towers C E 2013 Appl. Opt. 52 5758
Google Scholar
[40] Towers C E, Towers D P, Julian D C 2004 Opt. Express 12 1136
Google Scholar
[41] Ma L, Zucco M, Picard S 2003 IEEE J. Sel. Top. Quantum Electron. 9 1066
Google Scholar
[42] 王国超, 谭立龙, 颜树华, 魏春华 2017 光学学报 37 160
Google Scholar
Wang G C, Wei C H, Yan S H 2017 Acta Optic. Sin. 37 160
Google Scholar
[43] Hyun S, Kim Y J, Kim Y, Kim S W 2010 CIRP Ann.-Manuf. Techn. 59 555
Google Scholar
[44] 王国超 2015 博士学位论文 (长沙: 国防科技大学)
Wang G C 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[45] Ciddor P E 1996 Appl. Opt. 35 1566
Google Scholar
[46] Birch K P, Downs M J 1993 Metrologia 30 155
Google Scholar
[47] Wu G H, Takahashi M, Arai K, Inaba H, Minoshima K 2013 Sci. Rep. 3 1894
Google Scholar
[48] Minoshima K, Arai K, Inaba H 2011 Opt. Express 19 26095
Google Scholar
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图 1 基于飞秒光梳多路同步锁相的多波长干涉测距原理及非模糊度量程示意图
Figure 1. Schematic diagram of the synthetic wavelengths and measuring NAR of Frequency-Comb-Referenced Multi-Wavelength Interferometry.
图 2 多波长干涉实时绝对测距系统. FBGA, 光纤光栅滤波阵列; OPLL, 光学锁相环; OS, 光开关; WM, 波长计; FC, 光纤耦合器; AOM, 声光调制器; C, 准直器; M, 反射镜; BS, 分光棱镜; DM, 双色镜; RR, 角锥反射镜; PDA, 光电探测器阵列
Figure 2. Schematic configuration diagram of real-time absolute distance measurement by Frequency-Comb-Referenced Multi-Wavelength Interferometry.
图 3 多波长光源和相位测量结果 (a) 多波长发生器光谱测量结果; (b) 锁频激光的频率稳定度分析结果; (c) 多路同步相位解调实时测量结果
Figure 3. Test results for preparation of real-time and meter-scale absolute distance measurement: (a) Parallel generated four wavelengths for MWI; (b) frequency stability evaluation; (c) simultaneously detected phases for MWI in real time.
图 4 验证NAR的线性位移对比实验
Figure 4. Linear comparison between ADM by MWI and displacement by HPI for NAR demonstration.
图 5 空气折射率变化对NAR的影响 (a) 空气折射率的波动情况; (b) 理论NAR受空气折射率影响的计算结果
Figure 5. Influence of air refractive index on NAR: (a) Fluctuation of air refractive index for observation of 272 s;. (b) calculated result of theoretical NAR under the fluctuation of air refractive index.
图 6
$\alpha = {\beta _i} \cdot \left( {{n_1} - {n_i}} \right)$ 随参数变化的波动大小 (a)$ {\beta _i} \cdot \left( {{n_1} - {n_i}} \right) $ 随波长间距变化的波动仿真结果; (b)${\beta _i} \cdot \left( {{n_1} - {n_i}} \right)$ 随温度变化时的波动仿真结果, 波长间隔为25 nm, 波长选定为1555 nmFigure 6. Influences of the parameter variations on the value of
${\beta _i} \cdot \left( {{n_1} - {n_i}} \right)$ : (a) Fluctuation of${\beta _i} \cdot \left( {{n_1} - {n_i}} \right)$ as variations of wavelength gap; (b) fluctuation of${\beta _i} \cdot \left( {{n_1} - {n_i}} \right)$ as variations of ambient temperature.
图 7 MWI与商用激光干涉仪的2 m线性位移对比实验结果
Figure 7. Linear comparison between MWI and the commercial laser interferometer over a 2.0-meter displacement.
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[1] Berkovic G, Shafir E 2012 Adv. Opt. Photon. 4 441
Google Scholar
[2] Estler W T, Edmundson K L, Peggs G N, Parker D H 2002 CIRP Ann. Manuf. Technol. 51 587
Google Scholar
[3] Manske E, Jager G, Hausotte T, Fub R 2012 Meas. Sci. Technol. 23 074001
Google Scholar
[4] Bobroff N 1993 Meas. Sci. Technol. 4 907
Google Scholar
[5] Lay O P, Dubovitsky S, Peters R D, Burger J P, Steier W H 2003 Opt. Lett. 28 890
Google Scholar
[6] Bourdet G L, Orszag A G 1979 Appl. Opt. 18 225
Google Scholar
[7] Zimmermann E, Salvadé Y, Dändliker R 1996 Opt. Lett. 21 531
Google Scholar
[8] Meiners-Hagen K, Schoedel R, Pollinger F, Abou-Zeid A 2009 Meas. Sci. Rev. 9 16
Google Scholar
[9] Dändliker R, Thalmann R, Prongue D 1988 Opt. Lett. 13 339
Google Scholar
[10] Groot P 2001 Opt. Eng. 40 28
Google Scholar
[11] 时光, 张福民, 曲兴华, 孟祥松 2014 物理学报 63 184209
Google Scholar
Shi G, Zhang F M, Qu X H, Meng X S 2014 Acta Phys. Sin. 63 184209
Google Scholar
[12] Coe P A, Howell D F, Nickerson R B 2004 Meas. Sci. Technol. 15 2175
Google Scholar
[13] Williams C C, Wickramasinghe H K 1989 Opt. Lett. 145 42
Google Scholar
[14] Diddams S A, Jones D J, Ye J, Cundiff S T, Hall J L, Ranka J K, Windeler R S, Holzwarth R, Udem T, Hansch T W 2000 Phys. Rev. Lett. 84 5102
Google Scholar
[15] Udem T, Holzwarth R, Hansch T W 2002 Nature 416 233
Google Scholar
[16] Jones D J, Diddams S A, Ranka J K, Stentz A, Windeler R W, Hall J L, Cundiff S T 2000 Science 288 635
Google Scholar
[17] Minoshima K, Matsumoto H 2000 Appl. Opt. 39 5512
Google Scholar
[18] 王国超, 颜树华, 杨俊, 林存宝, 杨东兴, 邹鹏飞 2013 物理学报 62 070601
Google Scholar
Wang G C, Yan S H, Yang J, Lin C B, Yang D X, Zou P F 2013 Acta Phys. Sin. 62 070601
Google Scholar
[19] 张晓声, 易旺民, 胡明皓, 杨再华, 吴冠豪 2016 物理学报 65 080602
Google Scholar
Zhang X S, Yi W M, Hu M H, Yang Z H, Wu G H 2016 Acta Phys. Sin. 65 080602
Google Scholar
[20] Lee J, Kim Y J, Lee K, Lee S, Kim S W 2010 Nat. Photonics 4 716
Google Scholar
[21] 秦鹏, 陈伟, 宋有建, 胡明列, 柴路, 王清月 2012 物理学报 61 240601
Google Scholar
Qin P, Chen W, Song Y J, Hu M L, Chai L, Wang C Y 2012 Acta Phys. Sin. 61 240601
Google Scholar
[22] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photonics 3 351
Google Scholar
[23] Lee J, Han S, Lee K, Bae E, Kim S, Lee S, Kim S W, Kim Y J 2013 Meas. Sci. Technol. 24 045201
Google Scholar
[24] Joo K N, Kim S W 2006 Opt. Express 14 5954
Google Scholar
[25] Van den Berg S A, Persijn S T, Kok G, Zeitouny M G, Bhattacharya N 2012 Phys. Rev. Lett. 108 183901
Google Scholar
[26] Wang G C, Jang Y S, Hyun S, Chun B J, Kang H J, Yan S H, Kim S W, Kim Y J 2015 Opt. Express 23 9121
Google Scholar
[27] Hyun S, Kim Y J, Kim Y, Jin J, Kim S W 2009 Meas. Sci. Technol. 20 095302
Google Scholar
[28] Jang Y S, Wang G C, Hyun S, Kang H J, Chun B J, Kim Y J, Kim S W 2016 Sci. Rep. 6 31770
Google Scholar
[29] Ye J 2004 Opt. Lett. 29 1153
Google Scholar
[30] Wei D, Takahashi S, Takamasu K, Matsumoto H 2009 Opt. Lett. 34 2775
Google Scholar
[31] 孟祥松, 张福民, 曲兴华 2015 物理学报 23 230601
Google Scholar
Meng X S, Zhang F M, Qu X H 2015 Acta Phys. Sin. 23 230601
Google Scholar
[32] Kim S W 2009 Nat. Photonics 3 313
Google Scholar
[33] 姜海峰 2018 物理学报 67 160602
Google Scholar
Jiang H F 2018 Acta Phys. Sin. 67 160602
Google Scholar
[34] Chun B J, Hyun S, Kim S, Kim S W, Kim Y J 2013 Opt. Express 21 29179
Google Scholar
[35] Felder R 2003 Metrologia 42 323
Google Scholar
[36] Wei D, Takamasu K, Matsumoto H 2013 Precis. Eng. 37 694
Google Scholar
[37] Tilford C R 1977 Appl. Opt. 16 1857
Google Scholar
[38] 王国超, 魏春华, 颜树华 2014 光学学报 34 111
Google Scholar
Wang G C, Wei C H, Yan S H 2014 Acta Optic. Sin. 34 111
Google Scholar
[39] Falaggis K, Towers D P, Towers C E 2013 Appl. Opt. 52 5758
Google Scholar
[40] Towers C E, Towers D P, Julian D C 2004 Opt. Express 12 1136
Google Scholar
[41] Ma L, Zucco M, Picard S 2003 IEEE J. Sel. Top. Quantum Electron. 9 1066
Google Scholar
[42] 王国超, 谭立龙, 颜树华, 魏春华 2017 光学学报 37 160
Google Scholar
Wang G C, Wei C H, Yan S H 2017 Acta Optic. Sin. 37 160
Google Scholar
[43] Hyun S, Kim Y J, Kim Y, Kim S W 2010 CIRP Ann.-Manuf. Techn. 59 555
Google Scholar
[44] 王国超 2015 博士学位论文 (长沙: 国防科技大学)
Wang G C 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[45] Ciddor P E 1996 Appl. Opt. 35 1566
Google Scholar
[46] Birch K P, Downs M J 1993 Metrologia 30 155
Google Scholar
[47] Wu G H, Takahashi M, Arai K, Inaba H, Minoshima K 2013 Sci. Rep. 3 1894
Google Scholar
[48] Minoshima K, Arai K, Inaba H 2011 Opt. Express 19 26095
Google Scholar
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