Abstract

Two-color interferometry is powerful for the correction of the air refractive index especially in the turbulent air over long distance, since the empirical equations could introduce considerable measurement uncertainty if the environmental parameters cannot be measured with sufficient precision. In this paper, we demonstrate a method for absolute distance measurement with high-accuracy correction of air refractive index using two-color dispersive interferometry. The distances corresponding to the two wavelengths can be measured via the spectrograms captured by a CCD camera pair in real time. In the long-term experiment of the correction of air refractive index, the experimental results show a standard deviation of 3.3 × 10−8 for 12-h continuous measurement without the precise knowledge of the environmental conditions, while the variation of the air refractive index is about 2 × 10−6. In the case of absolute distance measurement, the comparison with the fringe counting interferometer shows an agreement within 2.5 μm in 12 m range.

© 2016 Optical Society of America

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2016 (2)

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

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[Crossref] [PubMed]

2015 (12)

T. Yasui, K. Hayashi, R. Ichikawa, H. Cahyadi, Y. D. Hsieh, Y. Mizutani, H. Yamamoto, T. Iwata, H. Inaba, and K. Minoshima, “Real-time absolute frequency measurement of continuous-wave terahertz radiation based on dual terahertz combs of photocarriers with different frequency spacings,” Opt. Express 23(9), 11367–11377 (2015).
[Crossref] [PubMed]

J. Zhu, P. Cui, Y. Guo, L. Yang, and J. Lin, “Pulse-to-pulse alignment based on interference fringes and the second-order temporal coherence function of optical frequency combs for distance measurement,” Opt. Express 23(10), 13069–13081 (2015).
[Crossref] [PubMed]

T. Pikálek and Z. Buchta, “Air refractive index measurement using low-coherence interferometry,” Appl. Opt. 54(16), 5024–5030 (2015).
[Crossref] [PubMed]

Y. Nakajima and K. Minoshima, “Highly stabilized optical frequency comb interferometer with a long fiber-based reference path towards arbitrary distance measurement,” Opt. Express 23(20), 25979–25987 (2015).
[Crossref] [PubMed]

H. J. Kang, B. J. Chun, Y. S. Jang, Y. J. Kim, and S. W. Kim, “Real-time compensation of the refractive index of air in distance measurement,” Opt. Express 23(20), 26377–26385 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

G. Wu, S. Xiong, K. Ni, Z. Zhu, and Q. Zhou, “Parameter optimization of a dual-comb ranging system by using a numerical simulation method,” Opt. Express 23(25), 32044–32053 (2015).
[Crossref] [PubMed]

L. J. Yang, H. Y. Zhang, Y. Li, and H. Y. Wei, “Absolute group refractive index measurement of air by dispersive interferometry using frequency comb,” Opt. Express 23(26), 33597–33607 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

G. Prellinger, K. Meiners-Hagen, and F. Pollinger, “Spectroscopically in situ traceable heterodyne frequency-scanning interferometry for distances up to 50 m,” Meas. Sci. Technol. 26(8), 084003 (2015).
[Crossref]

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (3)

G. Wu, M. Takahashi, H. Inaba, and K. Minoshima, “Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement,” Opt. Lett. 38(12), 2140–2143 (2013).
[Crossref] [PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

2011 (5)

2010 (1)

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

2009 (3)

S. W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[Crossref] [PubMed]

2008 (1)

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

2007 (1)

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2003 (1)

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

2000 (1)

1998 (1)

G. Boensch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

1996 (1)

1994 (2)

A. N. Golubev and A. M. Chekhovsky, “Three-color optical range finding,” Appl. Opt. 33(31), 7511–7517 (1994).
[Crossref] [PubMed]

K. Minoshima, H. Matsumoto, Z. Zhang, and T. Yagi, “Simultaneous 3-D imaging using chirped ultrashort optical pulses,” Jpn. J. Appl. Phys. 33(Part 2, No. 9B), L1348–L1351 (1994).
[Crossref]

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

1981 (1)

G. R. Huggett, “Two-color terrameter,” Tectonophysics 71(1-4), 29–39 (1981).
[Crossref]

1972 (1)

1967 (1)

K. B. Earnshaw and J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. 3(11), 544–550 (1967).
[Crossref]

1965 (1)

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Abou-Zeid, A.

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

Arai, K.

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

Balling, P.

Bender, P. L.

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Bhattacharya, N.

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, and H. P. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011).
[Crossref] [PubMed]

Birch, K. P.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Boensch, G.

G. Boensch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

Bosse, H.

Buchta, Z.

Cahyadi, H.

Cao, S.

Chekhovsky, A. M.

Chun, B. J.

Ciddor, P. E.

Coddington, I.

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Cui, M.

Cui, P.

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Downs, M. J.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Earnshaw, K. B.

K. B. Earnshaw and E. N. Hernandez, “Two-laser optical distance-measuring instrument that corrects for the atmospheric index of refraction,” Appl. Opt. 11(4), 749–754 (1972).
[Crossref] [PubMed]

K. B. Earnshaw and J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. 3(11), 544–550 (1967).
[Crossref]

Gohle, C.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Golubev, A. N.

Guo, Y.

Han, S.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

Hänsch, T. W.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Hayashi, K.

Hernandez, E. N.

Hieta, T.

Hsieh, Y. D.

Huggett, G. R.

G. R. Huggett, “Two-color terrameter,” Tectonophysics 71(1-4), 29–39 (1981).
[Crossref]

Ichikawa, R.

Inaba, H.

Iwata, T.

Jang, H.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

Jang, Y. S.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

H. J. Kang, B. J. Chun, Y. S. Jang, Y. J. Kim, and S. W. Kim, “Real-time compensation of the refractive index of air in distance measurement,” Opt. Express 23(20), 26377–26385 (2015).
[Crossref] [PubMed]

Joo, K. N.

Kang, H. J.

Kim, S. W.

H. J. Kang, B. J. Chun, Y. S. Jang, Y. J. Kim, and S. W. Kim, “Real-time compensation of the refractive index of air in distance measurement,” Opt. Express 23(20), 26377–26385 (2015).
[Crossref] [PubMed]

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

S. W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

K. N. Joo and S. W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006).
[Crossref] [PubMed]

Kim, S.-W.

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kim, Y.

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kim, Y. J.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

H. J. Kang, B. J. Chun, Y. S. Jang, Y. J. Kim, and S. W. Kim, “Real-time compensation of the refractive index of air in distance measurement,” Opt. Express 23(20), 26377–26385 (2015).
[Crossref] [PubMed]

Kren, P.

Lassila, A.

Lee, J.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, K.

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, S.

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Li, J.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett. 41(10), 2366–2369 (2016).
[Crossref] [PubMed]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

Li, Y.

Lin, J.

Liu, T.

Mašika, P.

Matsumoto, H.

Meiners-Hagen, K.

G. Prellinger, K. Meiners-Hagen, and F. Pollinger, “Spectroscopically in situ traceable heterodyne frequency-scanning interferometry for distances up to 50 m,” Meas. Sci. Technol. 26(8), 084003 (2015).
[Crossref]

R. Yang, F. Pollinger, K. Meiners-Hagen, J. Tan, and H. Bosse, “Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair,” Opt. Lett. 39(20), 5834–5837 (2014).
[Crossref] [PubMed]

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

Meng, F.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

Merimaa, M.

Minoshima, K.

Y. Nakajima and K. Minoshima, “Highly stabilized optical frequency comb interferometer with a long fiber-based reference path towards arbitrary distance measurement,” Opt. Express 23(20), 25979–25987 (2015).
[Crossref] [PubMed]

T. Yasui, K. Hayashi, R. Ichikawa, H. Cahyadi, Y. D. Hsieh, Y. Mizutani, H. Yamamoto, T. Iwata, H. Inaba, and K. Minoshima, “Real-time absolute frequency measurement of continuous-wave terahertz radiation based on dual terahertz combs of photocarriers with different frequency spacings,” Opt. Express 23(9), 11367–11377 (2015).
[Crossref] [PubMed]

G. Wu, M. Takahashi, H. Inaba, and K. Minoshima, “Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement,” Opt. Lett. 38(12), 2140–2143 (2013).
[Crossref] [PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000).
[Crossref] [PubMed]

K. Minoshima, H. Matsumoto, Z. Zhang, and T. Yagi, “Simultaneous 3-D imaging using chirped ultrashort optical pulses,” Jpn. J. Appl. Phys. 33(Part 2, No. 9B), L1348–L1351 (1994).
[Crossref]

Mizutani, Y.

Nakajima, Y.

Nenadovic, L.

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Newbury, N.

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Newbury, N. R.

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

Ni, K.

Owens, J. C.

K. B. Earnshaw and J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. 3(11), 544–550 (1967).
[Crossref]

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Pan, L.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

Pikálek, T.

Pollinger, F.

G. Prellinger, K. Meiners-Hagen, and F. Pollinger, “Spectroscopically in situ traceable heterodyne frequency-scanning interferometry for distances up to 50 m,” Meas. Sci. Technol. 26(8), 084003 (2015).
[Crossref]

R. Yang, F. Pollinger, K. Meiners-Hagen, J. Tan, and H. Bosse, “Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair,” Opt. Lett. 39(20), 5834–5837 (2014).
[Crossref] [PubMed]

Potulski, E.

G. Boensch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

Prellinger, G.

G. Prellinger, K. Meiners-Hagen, and F. Pollinger, “Spectroscopically in situ traceable heterodyne frequency-scanning interferometry for distances up to 50 m,” Meas. Sci. Technol. 26(8), 084003 (2015).
[Crossref]

Qu, X.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett. 41(10), 2366–2369 (2016).
[Crossref] [PubMed]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, S. Cao, S. Xing, and X. Qu, “Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser,” Opt. Express 22(9), 10380–10397 (2014).
[Crossref] [PubMed]

Schliesser, A.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Seppä, J.

Stein, B.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Swann, C.

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Takahashi, M.

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

G. Wu, M. Takahashi, H. Inaba, and K. Minoshima, “Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement,” Opt. Lett. 38(12), 2140–2143 (2013).
[Crossref] [PubMed]

Takahashi, S.

Takamasu, K.

Tan, J.

Udem, T.

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Urbach, H. P.

Vainio, M.

van den Berg, S. A.

van Eldik, S.

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

Wei, D.

Wei, H. Y.

Wu, G.

G. Wu, S. Xiong, K. Ni, Z. Zhu, and Q. Zhou, “Parameter optimization of a dual-comb ranging system by using a numerical simulation method,” Opt. Express 23(25), 32044–32053 (2015).
[Crossref] [PubMed]

G. Wu, M. Takahashi, H. Inaba, and K. Minoshima, “Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement,” Opt. Lett. 38(12), 2140–2143 (2013).
[Crossref] [PubMed]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

Wu, H.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett. 41(10), 2366–2369 (2016).
[Crossref] [PubMed]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, S. Cao, S. Xing, and X. Qu, “Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser,” Opt. Express 22(9), 10380–10397 (2014).
[Crossref] [PubMed]

Xing, S.

Xiong, S.

Yagi, T.

K. Minoshima, H. Matsumoto, Z. Zhang, and T. Yagi, “Simultaneous 3-D imaging using chirped ultrashort optical pulses,” Jpn. J. Appl. Phys. 33(Part 2, No. 9B), L1348–L1351 (1994).
[Crossref]

Yamamoto, H.

Yang, L.

Yang, L. J.

Yang, R.

Yasui, T.

Ye, J.

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004).
[Crossref] [PubMed]

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Zeitouny, M. G.

Zhang, F.

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett. 41(10), 2366–2369 (2016).
[Crossref] [PubMed]

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, S. Cao, S. Xing, and X. Qu, “Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser,” Opt. Express 22(9), 10380–10397 (2014).
[Crossref] [PubMed]

Zhang, H. Y.

Zhang, Z.

K. Minoshima, H. Matsumoto, Z. Zhang, and T. Yagi, “Simultaneous 3-D imaging using chirped ultrashort optical pulses,” Jpn. J. Appl. Phys. 33(Part 2, No. 9B), L1348–L1351 (1994).
[Crossref]

Zhou, Q.

Zhu, J.

Zhu, Z.

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

K. B. Earnshaw and J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. 3(11), 544–550 (1967).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Wu, F. Zhang, F. Meng, P. Balling, J. Li, L. Pan, and X. Qu, “Absolute distance measurement using frequency comb and a single-frequency laser,” IEEE Photonics Technol. Lett. 27(24), 2587–2590 (2015).
[Crossref]

J. Geophys. Res. (1)

P. L. Bender and J. C. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70(10), 2461–2462 (1965).
[Crossref]

Jpn. J. Appl. Phys. (1)

K. Minoshima, H. Matsumoto, Z. Zhang, and T. Yagi, “Simultaneous 3-D imaging using chirped ultrashort optical pulses,” Jpn. J. Appl. Phys. 33(Part 2, No. 9B), L1348–L1351 (1994).
[Crossref]

Meas. Sci. Technol. (4)

H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016).
[Crossref]

K. Meiners-Hagen and A. Abou-Zeid, “Refractive index determination in length measurement by two-colour interferometry,” Meas. Sci. Technol. 19(8), 084004 (2008).
[Crossref]

G. Wu, K. Arai, M. Takahashi, H. Inaba, and K. Minoshima, “High-accuracy correction of air refractive index by using two-color heterodyne interferometry of optical frequency combs,” Meas. Sci. Technol. 24(1), 015203 (2013).
[Crossref]

G. Prellinger, K. Meiners-Hagen, and F. Pollinger, “Spectroscopically in situ traceable heterodyne frequency-scanning interferometry for distances up to 50 m,” Meas. Sci. Technol. 26(8), 084003 (2015).
[Crossref]

Metrologia (2)

G. Boensch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen’s formulae,” Metrologia 35(2), 133–139 (1998).
[Crossref]

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Nat. Photonics (4)

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

I. Coddington, C. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurement at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

S. W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

J. Lee, Y. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Opt. Express (13)

K. Minoshima, K. Arai, and H. Inaba, “High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs,” Opt. Express 19(27), 26095–26105 (2011).
[Crossref] [PubMed]

H. Wu, F. Zhang, S. Cao, S. Xing, and X. Qu, “Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser,” Opt. Express 22(9), 10380–10397 (2014).
[Crossref] [PubMed]

T. Yasui, K. Hayashi, R. Ichikawa, H. Cahyadi, Y. D. Hsieh, Y. Mizutani, H. Yamamoto, T. Iwata, H. Inaba, and K. Minoshima, “Real-time absolute frequency measurement of continuous-wave terahertz radiation based on dual terahertz combs of photocarriers with different frequency spacings,” Opt. Express 23(9), 11367–11377 (2015).
[Crossref] [PubMed]

J. Zhu, P. Cui, Y. Guo, L. Yang, and J. Lin, “Pulse-to-pulse alignment based on interference fringes and the second-order temporal coherence function of optical frequency combs for distance measurement,” Opt. Express 23(10), 13069–13081 (2015).
[Crossref] [PubMed]

K. N. Joo and S. W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006).
[Crossref] [PubMed]

P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[Crossref] [PubMed]

D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express 19(6), 4881–4889 (2011).
[Crossref] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, and H. P. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011).
[Crossref] [PubMed]

Y. Nakajima and K. Minoshima, “Highly stabilized optical frequency comb interferometer with a long fiber-based reference path towards arbitrary distance measurement,” Opt. Express 23(20), 25979–25987 (2015).
[Crossref] [PubMed]

H. J. Kang, B. J. Chun, Y. S. Jang, Y. J. Kim, and S. W. Kim, “Real-time compensation of the refractive index of air in distance measurement,” Opt. Express 23(20), 26377–26385 (2015).
[Crossref] [PubMed]

H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015).
[Crossref] [PubMed]

G. Wu, S. Xiong, K. Ni, Z. Zhu, and Q. Zhou, “Parameter optimization of a dual-comb ranging system by using a numerical simulation method,” Opt. Express 23(25), 32044–32053 (2015).
[Crossref] [PubMed]

L. J. Yang, H. Y. Zhang, Y. Li, and H. Y. Wei, “Absolute group refractive index measurement of air by dispersive interferometry using frequency comb,” Opt. Express 23(26), 33597–33607 (2015).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99(26), 263902 (2007).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Sci. Rep. (3)

K. Lee, J. Lee, Y. S. Jang, S. Han, H. Jang, Y. J. Kim, and S. W. Kim, “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep. 5, 15726 (2015).
[Crossref] [PubMed]

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

G. Wu, M. Takahashi, K. Arai, H. Inaba, and K. Minoshima, “Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs,” Sci. Rep. 3, 1894 (2013).
[PubMed]

Tectonophysics (1)

G. R. Huggett, “Two-color terrameter,” Tectonophysics 71(1-4), 29–39 (1981).
[Crossref]

Other (2)

K. Miyano, G. Wu, T. Makino, and K. Minoshima, “Air refractive index self-correction exceeding empirical equation accuracy using two-color interferometry with optical frequency comb,” in Proceedings of CLEO:2016, STh4H.4 (2016).

Evaluation of measurement data – Guide to the expression of uncertainty in measurement. (2008) http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315ehtml/C045315e.html?csnumberCsnumber=50461 .

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Figures (12)

Fig. 1
Fig. 1

Experimental setup using two-color dispersive interferometry. HWP: half wave plate; PPLN: periodically poled LiNbO3; SHG: second harmonic generation; BS: beam splitter; DM: dichroic mirror.

Fig. 2
Fig. 2

(a): Spectrum of the fundamental harmonic; (b): spectrum of the second harmonic.

Fig. 3
Fig. 3

The scheme of the CCD calibration by using a spectrometer. (a): the spectrogram of the fundamental harmonic captured by the CCD camera; (b): the spectrogram measured by the spectrometer.

Fig. 4
Fig. 4

Procedure of the CCD calibration. (a): one selected line (209 pixel in the vertical direction) as the sample spectrogram; (b): the unwrapped phase versus the CCD pixel number. The black line is the measured data, and the red line is the fitting curve; (c): the unwrapped phase corresponding to the spectrogram shown in Fig. 3(b).

Fig. 5
Fig. 5

Calibration of the CCD camera for the fundamental signal.

Fig. 6
Fig. 6

(a): Spectrogram captured by CCD camera for the second harmonic; (b): calibration of the CCD camera for the second harmonic.

Fig. 7
Fig. 7

Long-term variation in the difference between the two-color air refractive indices (n2-n1). (a): the curve of ∆(n2-n1) obtained by the two-color method of dispersive interferometry; (b): the curve of ∆(n2-n1) obtained by Ciddor formula based on the well-measured environmental conditions. (c): difference between the measured curve and the calculated curve.

Fig. 8
Fig. 8

Long-term measurement of the air refractive index variation corresponding to the fundamental harmonic. (a): the curve obtained by the method of dispersive interferometry; (b): the curve obtained by Ciddor formula; (c): difference between (a) and (b).

Fig. 9
Fig. 9

Self-correction of air refractive index by using two-color method of dispersive interferometry. (a): the curve of one-color measurement, ∆D1/D; (b): the curve of two-color measurement, A·∆(D2-D1)/D; (c): difference between (a) and (b).

Fig. 10
Fig. 10

The spectrograms captured by the CCD cameras of the fundamental and second harmonic at different distances.

Fig. 11
Fig. 11

(a): Experimental results of the fundamental harmonic; (b): experimental results of the second harmonic.

Fig. 12
Fig. 12

Experimental results with correction of air refractive index using two-color method.

Equations (9)

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D= D 1 A( D 2 D 1 ) with A= ( n 1 1 ) / ( n 2 n 1 )
ΔD D = Δ D 1 AΔ( D 2 D 1 )ΔA( D 2 D 1 )ΔAΔ( D 2 D 1 ) D
Δ( n 2 n 1 )= Δ( D 2 D 1 ) /D ( D 2 D 1 ) / D 2 ΔD
Δ n 1 = Δ D 1 /D D 1 / D 2 ΔD
ΔD D = Δ D 1 AΔ( D 2 D 1 ) D
D 1 = Nc f rep + k f k fc
D 2 = Nc f rep + k s k sc
u D 2 = u D 1 2 + ( A u D 2 D 1 ) 2 + [ ( D 2 D 1 ) u A ] 2
u D 1 2 = ( Nc f rep 2 u f rep ) 2 + ( k f u k fc ) 2 + ( k fc u k f ) 2

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