Abstract

In an interferometer, the interference fringe signal is typically linearly detected and modulated to a specific frequency region. A nonlinear detector yields the interference fringes of the fundamental and high-harmonic waves in different frequency regions. We analyze the formation of nonlinearly detected interference fringes. We demonstrate, for the first time, that the interference fringes of high-harmonic waves can also be used to determine the position of zero optical path length difference between reference and object mirrors. This noise-adaptive selectability of the interference fringe signal is guaranteed by the fact that the positions of the peak envelopes of the interference fringes for the fundamental and high-harmonic waves are matched at zero optical path length. The proposed method is verified using experimental data. This technique can be applied not only to surface profiling but also to length measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  2. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
    [Crossref]
  3. 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]
  4. Y. L. Chen, Y. Shimizu, J. Tamada, Y. Kudo, S. Madokoro, K. Nakamura, and W. Gao, “Optical frequency domain angle measurement in a femtosecond laser autocollimator,” Opt. Express 25(14), 16725–16738 (2017).
    [Crossref] [PubMed]
  5. 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(1), 1894 (2013).
    [Crossref] [PubMed]
  6. T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer,” Precis. Eng. 37(3), 694–698 (2013).
    [Crossref]
  9. Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct Measurement of the Group Refractive Index of Air with Interferometry between Adjacent Femtosecond Pulses,” Appl. Opt. 41(21), 4318–4324 (2002).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  13. C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
    [Crossref]
  14. X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
    [Crossref] [PubMed]
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    [Crossref]
  16. W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
    [Crossref]
  17. W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
    [Crossref]
  18. B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
    [Crossref]
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    [Crossref] [PubMed]
  21. 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]
  22. D. Wei and M. Aketagawa, “Analysis of the second harmonic generation of a femtosecond optical frequency comb,” Opt. Eng. 53(12), 122604 (2014).
    [Crossref]

2018 (1)

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

2017 (2)

Y. L. Chen, Y. Shimizu, J. Tamada, Y. Kudo, S. Madokoro, K. Nakamura, and W. Gao, “Optical frequency domain angle measurement in a femtosecond laser autocollimator,” Opt. Express 25(14), 16725–16738 (2017).
[Crossref] [PubMed]

T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
[Crossref] [PubMed]

2015 (3)

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]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

2014 (2)

D. Wei and M. Aketagawa, “Comparison of length measurements provided by a femtosecond optical frequency comb,” Opt. Express 22(6), 7040–7045 (2014).
[Crossref] [PubMed]

D. Wei and M. Aketagawa, “Analysis of the second harmonic generation of a femtosecond optical frequency comb,” Opt. Eng. 53(12), 122604 (2014).
[Crossref]

2013 (3)

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer,” Precis. Eng. 37(3), 694–698 (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(1), 1894 (2013).
[Crossref] [PubMed]

2012 (3)

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[Crossref]

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[Crossref] [PubMed]

2011 (1)

2009 (2)

D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009).
[Crossref] [PubMed]

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

2008 (1)

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[Crossref]

2004 (1)

2002 (1)

Aketagawa, M.

D. Wei and M. Aketagawa, “Analysis of the second harmonic generation of a femtosecond optical frequency comb,” Opt. Eng. 53(12), 122604 (2014).
[Crossref]

D. Wei and M. Aketagawa, “Comparison of length measurements provided by a femtosecond optical frequency comb,” Opt. Express 22(6), 7040–7045 (2014).
[Crossref] [PubMed]

Aoto, T.

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[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(1), 1894 (2013).
[Crossref] [PubMed]

Berg, S. A.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[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, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[Crossref]

Chen, Y. L.

Coddington, I.

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

Cui, M.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[Crossref]

Gao, W.

Hirokazu, M.

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

Inaba, H.

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(1), 1894 (2013).
[Crossref] [PubMed]

Kato, T.

T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
[Crossref] [PubMed]

Kiyoshi, T.

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

Kudo, Y.

Li, J.

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Madokoro, S.

Matsumoto, H.

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer,” Precis. Eng. 37(3), 694–698 (2013).
[Crossref]

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[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]

D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009).
[Crossref] [PubMed]

Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct Measurement of the Group Refractive Index of Air with Interferometry between Adjacent Femtosecond Pulses,” Appl. Opt. 41(21), 4318–4324 (2002).
[Crossref] [PubMed]

Minoshima, K.

T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
[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(1), 1894 (2013).
[Crossref] [PubMed]

Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct Measurement of the Group Refractive Index of Air with Interferometry between Adjacent Femtosecond Pulses,” Appl. Opt. 41(21), 4318–4324 (2002).
[Crossref] [PubMed]

Nakamura, K.

Narin, C.

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

Nenadovic, L.

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

Newbury, N. R.

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

Satoru, T.

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

Schouten, R. N.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[Crossref]

Shimizu, Y.

Sudatham, W.

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

Swann, W. C.

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

Takahashi, M.

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(1), 1894 (2013).
[Crossref] [PubMed]

Takahashi, S.

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[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]

D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009).
[Crossref] [PubMed]

Takamasu, K.

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer,” Precis. Eng. 37(3), 694–698 (2013).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[Crossref] [PubMed]

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[Crossref]

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]

D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express 17(9), 7011–7018 (2009).
[Crossref] [PubMed]

Tamada, J.

Uchida, M.

T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
[Crossref] [PubMed]

van den Berg, S. A.

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]

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]

Wang, X.

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express 20(3), 2725–2732 (2012).
[Crossref] [PubMed]

Wang, Z.

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Wei, D.

Wu, G.

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(1), 1894 (2013).
[Crossref] [PubMed]

Wu, H.

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Xue, B.

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Yamaoka, Y.

Ye, J.

Zhang, K.

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (1)

H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto, “Absolute Measurement of Baselines up to 403 m Using Heterodyne Temporal Coherence Interferometer with Optical Frequency Comb,” Appl. Phys. Express 5(4), 046601 (2012).
[Crossref]

J. Eur. Opt. Soc. Rapid. Publ. (1)

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid. Publ. 3, 08003 (2008).
[Crossref]

Meas. Sci. Technol. (1)

C. Narin, T. Satoru, T. Kiyoshi, and M. Hirokazu, “A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser,” Meas. Sci. Technol. 23(5), 054003 (2012).
[Crossref]

Measurement (1)

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Non-contact measurement technique for dimensional metrology using optical comb,” Measurement 78, 381–387 (2015).
[Crossref]

Nat. Photonics (1)

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

Opt. Eng. (1)

D. Wei and M. Aketagawa, “Analysis of the second harmonic generation of a femtosecond optical frequency comb,” Opt. Eng. 53(12), 122604 (2014).
[Crossref]

Opt. Express (5)

Opt. Lasers Eng. (1)

B. Xue, Z. Wang, K. Zhang, J. Li, and H. Wu, “Absolute distance measurement using optical sampling by sweeping the repetition frequency,” Opt. Lasers Eng. 109, 1–6 (2018).
[Crossref]

Opt. Lett. (1)

Precis. Eng. (3)

D. Wei, K. Takamasu, and H. Matsumoto, “A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer,” Precis. Eng. 37(3), 694–698 (2013).
[Crossref]

X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto, “Spatial positioning measurements up to 150m using temporal coherence of optical frequency comb,” Precis. Eng. 37(3), 635–639 (2013).
[Crossref]

W. Sudatham, H. Matsumoto, S. Takahashi, and K. Takamasu, “Verification of the positioning accuracy of industrial coordinate measuring machine using optical-comb pulsed interferometer with a rough metal ball target,” Precis. Eng. 41, 63–67 (2015).
[Crossref]

Sci. Rep. (3)

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(1), 1894 (2013).
[Crossref] [PubMed]

T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 3670 (2017).
[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]

Other (2)

F. Träger, Springer handbook of lasers and optics (Springer, 2007).

J. Ye and S. T. Cundiff, Femtosecond optical frequency comb: principle, operation, and applications (Springer, 2005).

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of a Michelson-type pulse-train interferometer with a nonlinear detector.
Fig. 2
Fig. 2 Calculated interference fringes.
Fig. 3
Fig. 3 Calculated spectrum of Fourier-transformed fringe pattern, with a magnified portion of the nonzero spectrum (inset).
Fig. 4
Fig. 4 Reconstructed envelopes of the fringe pattern of (a) the fundamental wave and (b) the second harmonic wave, and (c) the difference of the two normalized envelopes.
Fig. 5
Fig. 5 Optical scheme of proof-of-principle experiment.
Fig. 6
Fig. 6 Reconstructed interference signal (dotted line) and envelope (solid line) of the (a) fundamental and (b) second harmonic waves.
Fig. 7
Fig. 7 Variations in difference between two envelope peak points.

Equations (13)

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I(τ)= { | E train_o (t)+ E train_r (t+τ) | 2 } 2 ,
I(τ)= [ I ref + I obj +2Re E train_o (t) E train_r * (t+τ) ] 2 .
I(τ)= [ I ref + I obj +2 I ref I obj | C t (τ) |cos(2π ν 0 τ) ] 2 .
S(ν)= 2 ln( 2 π ) Δν exp{ 4(ln2) ( ν ν 0 Δν ) 2 }× comb ν rep (ν).
I(τ)= [ I ref + I obj + 2 I ref I obj ν rep exp[ ( πΔντ 2 ln2 ) 2 ] comb 1 ν rep (τ)cos(2π ν 0 τ) ] 2 .
I(Z)= [ I bg +γLexp[ ( Z 2 l c ) 2 ] comb L (Z)×cos( 2π λ 0 Z) ] 2 .
I(h)= [ I bg +γLexp[ ( h l c ) 2 ] comb L (2h)×cos( 4π λ 0 h) ] 2 .
I(h)= I f0 (h)+ I f1 (h)+ I f2 (h).
I f0 (h)= I bg 2 + 1 2 γ 2 L 2 exp[ 2 ( h l c ) 2 ] comb L (2h),
I f1 (h)=2 I bg ×γLexp[ ( h l c ) 2 ] comb L (2h)×cos( 4π λ 0 h),
I f2 (h)= 1 2 γ 2 L 2 exp[ 2 ( h l c ) 2 ] comb L (2h)×cos( 8π λ 0 h).
I f1 (0)=2 I bg ×γL
I f2 (0)= 1 2 γ 2 L 2 .

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