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In this paper, the Fabry-Perot etalon is used to multiply the repetition rate of the fiber optical frequency comb. The repetition rate is amplified from 250 MHz to 10 GHz, and the corresponding pulse interval is reduced from 1200 mm to 30 mm. For the pulse cross correlation ranging method, the repetition rate multiplication can greatly reduce the length requirement of the scanning reference arm. We analyze in detail the principle of cross correlation interferometry based on repetition rate multiplication frequency comb. A numerical mode of the function is comprehensively established. The basic parameters of optical source and Fabry-Perot cavity for the influence of filtered optical spectrum and cross correlation fringe are analyzed through the numerical simulation. The multiplied frequency comb is utilized for absolute ranging with the help of a pulse cross correlation method. By comparison, our result differs from the result obtained by a conventional counting interferometer only by 4 μm for distances up to 210 mm.
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Keywords:
- optical frequency comb /
- repetition rate multiplication /
- absolute distance measurement /
- cross correlation interferometry
[1] Gao W, Kim S W, Bosse H, Haitjema H, Chen Y L, Lu X D, Knapp W, Weckenmann, Estler W T, Kunzmann H A 2015 CIRP Annals – Manuf. Techn. 64 773
Google Scholar
[2] Schmitt R H, Peterek M, Morse E, Knapp W, Galetto M, Härtig F, Goch G, Ben H, Forbes A 2016 CIRP Annals-Manuf. Techn. 65 643
Google Scholar
[3] Abbott B P, Abbott R, Abbott T D, Zweizig J 2016 Phys. Rev. Lett. 116 061102
Google Scholar
[4] Pellegrini S, Buller G S, Smith J M, Wallace A M, Cova S 2000 Meas. Sci. Technol. 11 712
Google Scholar
[5] Bobroff N 1993 Meas. Sci. Technol. 4 907
Google Scholar
[6] Falaggis K, Towers D P, Towers C E 2009 Opt. Lett. 34 950
Google Scholar
[7] Lu S, Lee C 2002 Meas. Sci. Technol. 13 1382
Google Scholar
[8] John D, Ben H, Andrew J L, Andrew J L, Armin J H R, Matthew S W 2014 Opt. Express 22 24869
Google Scholar
[9] Kim S W 2009 Nat. Photonics 3 313
Google Scholar
[10] Diddams S A, Vahala K, Udem T 2020 Science 369 267
Google Scholar
[11] Baumann E, Giorgetta F R, Coddington I, Sinclair L C, Knabe K, Swann W C, Newbury N R 2013 Opt. Lett. 38 2026
Google Scholar
[12] 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
[13] Minoshima K, Matsumoto H 2000 Appl. Opt. 39 5512
Google Scholar
[14] 张晓声, 易旺民, 胡明皓, 杨再华, 吴冠豪 2016 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
[15] Joo K N, Kim S W 2006 Opt. Express 14 5954
Google Scholar
[16] Lesundak A, Voigt D, Cip O, Van den Berg S A 2017 Opt. Express 25 32570
Google Scholar
[17] Ye J 2004 Opt. Lett. 29 1153
Google Scholar
[18] Nakajima Y, Minoshima K 2015 Opt. Express 23 25979
Google Scholar
[19] Wu G H, Zhang F M, Liu T L, Balling P, Li J S, Qu X H 2016 Opt. Lett. 41 2366
Google Scholar
[20] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photonics 3 351
Google Scholar
[21] 夏文泽, 刘洋, 赫明钊, 曹士英, 杨伟雷, 张福民, 缪东晶, 李建双 2021 70 180601
Google Scholar
Xia W Z, Liu Y, He M Z, Cao S Y, Yang W L, Zhang F M, Miao D J, Li J S 2021 Acta Phys. Sin. 70 180601
Google Scholar
[22] 赵显宇, 曲兴华, 陈嘉伟, 郑继辉, 王金栋, 张福民 2020 69 090601
Google Scholar
Zhao X Y, Qu X H, Chen J W, Zheng J H, Wang J D, Zhang F M 2020 Acta Phys. Sin. 69 090601
Google Scholar
[23] Suh M G, Vahala K J 2018 Science 359 6378
Google Scholar
[24] Chen J, Sickler J W, Fendel P, Ippen E P, Kärtner F X, Wilken T, Holzwarth R, Hänsch T W 2008 Opt. Lett. 33 959
Google Scholar
[25] Haboucha A, Zhang W, Li T, Lours M, Luiten A N, Coq Y L, Santarelli G 2011 Opt. Lett. 36 3654
Google Scholar
[26] Lee J, Kim S W, Kim Y J 2015 Opt. Express 23 10117
Google Scholar
[27] Zeitouny M, Cui M, Bhattacharya N 2010 Phys. Rev. A 82 23808
Google Scholar
[28] Bonsch G, Potulski E 1998 Metrologia 35 133
Google Scholar
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图 1 脉冲互相关测距原理示意图(OFC, 光频梳; BS, 分束镜; Mr, 参考镜; Mt, 目标镜; M0, 零点参考镜; PD, 光电探测器; Scope, 示波器)
Figure 1. Schematic of the pulse cross-correlation ranging principle. OFC, optical frequency comb; BS, beam splitter; Mr, reference mirror; M0, zero position mirror; Mt, target mirror; PD, photodetector; Scope, oscilloscope.
图 2 FP标准具滤梳齿示意图
Figure 2. Schematic of filtered frequency comb using a FP etalon.
图 3 光频梳重频对透射光谱的影响 (a) 理想透射谱; (c) fr = 250.001 MHz时的透射谱; (e) fr = 250.1 MHz时的透射谱; (b), (d), (f) 分别为 (a), (c), (e)的局部放大图
Figure 3. Influence of frequency comb repetition rate on transmission spectrum: (a) Ideal transmission spectrum; (c) the transmission spectrum at fr = 250.001 MHz; (e) the transmission spectrum at fr = 250.1 MHz; (b), (d), (f) partial enlarged views of (a), (c), (e).
图 4 光频梳偏频对透射光谱的影响, 其中(b)为(a)的局部放大图
Figure 4. Influence of frequency comb offset frequency on transmission spectrum. (b) is partial enlarged view of (a).
图 5 FP标准具参数对透射光谱的影响 (a) 不同腔长偏差; (c) 不同群延迟色散, (e) 不同中心波长; (b), (d), (f) 分别为(a), (c), (e)的局部放大图
Figure 5. Influence of FP etalon parameter on the transmission spectrum: (a) Different cavity length deviations; (c) different group delay dispersions; (e) different center wavelengths; (b), (d), (f) partial enlarged views of (a), (c), (e).
图 6 光源参数对透射光谱强度的影响 (a) 重频; (b) 偏频; (c) 腔长; (d) 群延迟色散
Figure 6. Influence of light source parameter on the transmission intensity: (a) Repetition rate; (b) offset frequency; (c) cavity length; (d) group delay dispersion.
图 7 光源参数对互相关信号的影响 (a) 不同重频偏差下的干涉条纹; (c) 不同偏频偏差下的干涉条纹; (b), (d) 分别为(a), (c)的局部放大图
Figure 7. Influence of light source parameter on cross-correlation signal: (a) Interference fringe under different repetition rate; (c) interference fringe under different offset frequency; (b), (d) partial enlarged views of (a), (c).
图 8 FP标准具参数对互相关信号的影响 (a) 不同群延迟色散下的干涉条纹; (c) 不同精细度下的干涉条纹; (b), (d) 分别为(a), (c)的局部放大图
Figure 8. Influence of FP etalon parameter on cross-correlation signal: (a) Interference fringe under different group delay dispersion; (c) interference fringe under different finesse; (b), (d) partial enlarged views of (a), (c).
图 9 重频倍增光频梳时域互相关绝对测距原理示意图(Frequency comb, 光频梳; CL1—3, 准直器; Lens1和Lens2, 模式匹配透镜; Cavity mirror, FP标准具的腔镜; EYDFA, 铒镱共掺光纤放大器; M1, 平面反射镜; BS1—3, 光学分束器; CR1—6, 角锥棱镜; PD1和PD2, 光电探测器; SRM, 半反半透薄膜; RIO, 单频激光器; XL-80, 雷尼绍干涉仪; Scope, 示波器; 黄色线, 单模光纤; 深蓝色线, 电学线缆; 红色线, 光频梳出射的激光光束; 浅蓝色线, RIO单频激光器出射的激光光束; 绿色线, 雷尼绍干涉仪出射的激光光束)
Figure 9. Schematic of cross-correlation ranging based on repetition rate multiplying optical frequency comb. OFC, optical frequency comb; CL1—3, collimator; Lens1 and Lens2, mode matching lens; EYDFA, erbium ytterbium doped fiber amplifier; M1, plane mirror; BS1—3, beam splitter; CR1—6, retroreflector; PD1 and PD2, photodetector; SRM, semi-reflective film; RIO, RIO single wavelength laser; XL-80, Renishaw commercial interferometer; Scope, oscilloscope; yellow line, single-mode fiber; dark bule line, the electrical cable; red line, the laser beam emitted by the optical frequency comb; light blue line, the laser beam emitted by the RIO single wavelength laser; green line, the laser beam emitted by the Renishaw interferometer.
图 10 光频梳经过FP标准具前后的光谱和射频谱 (a) 未经FP标准具的光谱; (b) 经过FP标准具后的光谱; (c) 未经FP标准具的射频谱; (d) 经过FP标准具后的射频谱.
Figure 10. Optical spectrum and the radio frequency spectrum of the optical frequency comb before and after passing through the FP cavity: (a) Optical spectrum before FP cavity; (b) optical spectrum after FP cavity; (c) radio frequency spectrum before FP cavity; (d) radio frequency spectrum after FP cavity.
图 11 重频倍增光频梳互相关干涉信号 (a) 仿真结果; (b) 实验结果; (c)多脉冲序列干涉图样
Figure 11. Cross-correlation interference signal with a repetition rate multiplication frequency comb: (a) Simulation result; (b) experimental result; (c) multi-pulse train interference pattern.
图 12 重频倍增光频梳脉冲互相关测距图样 (a)互相关干涉信号; (b) 互相关干涉信号峰值附近位置放大图样; (c) 包络峰值信号提取
Figure 12. Cross correlation pattern based on repetition rate multiplying frequency comb: (a) Cross correlation signal; (b) magnified view of the horizontal axis near the envelope peak for (a); (c) extracted envelope and the Gaussian fitting results.
图 13 长度比对实验结果(红色圆圈表示五次测量结果的平均值; 误差棒表示测量结果的标准差)
Figure 13. Length comparison experiment result. The red circle represents the average result of five repeated measurements. Error bar indicates the standard deviation of the measurement result.
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[1] Gao W, Kim S W, Bosse H, Haitjema H, Chen Y L, Lu X D, Knapp W, Weckenmann, Estler W T, Kunzmann H A 2015 CIRP Annals – Manuf. Techn. 64 773
Google Scholar
[2] Schmitt R H, Peterek M, Morse E, Knapp W, Galetto M, Härtig F, Goch G, Ben H, Forbes A 2016 CIRP Annals-Manuf. Techn. 65 643
Google Scholar
[3] Abbott B P, Abbott R, Abbott T D, Zweizig J 2016 Phys. Rev. Lett. 116 061102
Google Scholar
[4] Pellegrini S, Buller G S, Smith J M, Wallace A M, Cova S 2000 Meas. Sci. Technol. 11 712
Google Scholar
[5] Bobroff N 1993 Meas. Sci. Technol. 4 907
Google Scholar
[6] Falaggis K, Towers D P, Towers C E 2009 Opt. Lett. 34 950
Google Scholar
[7] Lu S, Lee C 2002 Meas. Sci. Technol. 13 1382
Google Scholar
[8] John D, Ben H, Andrew J L, Andrew J L, Armin J H R, Matthew S W 2014 Opt. Express 22 24869
Google Scholar
[9] Kim S W 2009 Nat. Photonics 3 313
Google Scholar
[10] Diddams S A, Vahala K, Udem T 2020 Science 369 267
Google Scholar
[11] Baumann E, Giorgetta F R, Coddington I, Sinclair L C, Knabe K, Swann W C, Newbury N R 2013 Opt. Lett. 38 2026
Google Scholar
[12] 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
[13] Minoshima K, Matsumoto H 2000 Appl. Opt. 39 5512
Google Scholar
[14] 张晓声, 易旺民, 胡明皓, 杨再华, 吴冠豪 2016 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
[15] Joo K N, Kim S W 2006 Opt. Express 14 5954
Google Scholar
[16] Lesundak A, Voigt D, Cip O, Van den Berg S A 2017 Opt. Express 25 32570
Google Scholar
[17] Ye J 2004 Opt. Lett. 29 1153
Google Scholar
[18] Nakajima Y, Minoshima K 2015 Opt. Express 23 25979
Google Scholar
[19] Wu G H, Zhang F M, Liu T L, Balling P, Li J S, Qu X H 2016 Opt. Lett. 41 2366
Google Scholar
[20] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photonics 3 351
Google Scholar
[21] 夏文泽, 刘洋, 赫明钊, 曹士英, 杨伟雷, 张福民, 缪东晶, 李建双 2021 70 180601
Google Scholar
Xia W Z, Liu Y, He M Z, Cao S Y, Yang W L, Zhang F M, Miao D J, Li J S 2021 Acta Phys. Sin. 70 180601
Google Scholar
[22] 赵显宇, 曲兴华, 陈嘉伟, 郑继辉, 王金栋, 张福民 2020 69 090601
Google Scholar
Zhao X Y, Qu X H, Chen J W, Zheng J H, Wang J D, Zhang F M 2020 Acta Phys. Sin. 69 090601
Google Scholar
[23] Suh M G, Vahala K J 2018 Science 359 6378
Google Scholar
[24] Chen J, Sickler J W, Fendel P, Ippen E P, Kärtner F X, Wilken T, Holzwarth R, Hänsch T W 2008 Opt. Lett. 33 959
Google Scholar
[25] Haboucha A, Zhang W, Li T, Lours M, Luiten A N, Coq Y L, Santarelli G 2011 Opt. Lett. 36 3654
Google Scholar
[26] Lee J, Kim S W, Kim Y J 2015 Opt. Express 23 10117
Google Scholar
[27] Zeitouny M, Cui M, Bhattacharya N 2010 Phys. Rev. A 82 23808
Google Scholar
[28] Bonsch G, Potulski E 1998 Metrologia 35 133
Google Scholar
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