Abstract

This paper presents a comparison of length measurements between the wavelength and the adjacent pulse repetition interval length (APRIL) provided by a femtosecond optical frequency comb. A theoretical estimation of the frequency stability for stabilizing the wavelength and APRIL, the frequency parameters that affect the stability of the APRIL in air, and the ambiguity in the length measurement by the APRIL are investigated. We find that the APRIL can be used as a low-cost measurement for the absolute length over a range of hundreds of meters in laboratory conditions.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. X. Wang, S. Takahashi, K. Takamasu, 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]
  13. D. Wei, K. Takamasu, 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]
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    [CrossRef]
  15. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer, 2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. E. Bengt, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
    [CrossRef]
  19. J. A. Stone and J. H. Zimmerman, “Index of refraction of air,” Available in: http://emtoolbox.nist.gov/Wavelength/Edlen.asp .
  20. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

2014

D. Wei, M. Aketagawa, “Characteristics of an adjacent pulse repetition interval length as a scale for length,” Opt. Eng. 53(5), 051502 (2014).
[CrossRef]

2013

X. Wang, S. Takahashi, K. Takamasu, 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, 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]

2012

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

2010

2009

2008

M. Cui, R. N. Schouten, N. Bhattacharya, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

2006

2004

2002

1996

1993

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

1966

E. Bengt, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Aketagawa, M.

D. Wei, M. Aketagawa, “Characteristics of an adjacent pulse repetition interval length as a scale for length,” Opt. Eng. 53(5), 051502 (2014).
[CrossRef]

Aoto, T.

H. Matsumoto, X. Wang, K. Takamasu, 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]

Araki, T.

Bengt, E.

E. Bengt, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Berg, S. A.

M. Cui, R. N. Schouten, N. Bhattacharya, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

Bhattacharya, N.

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, J. J. M. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[CrossRef] [PubMed]

M. Cui, R. N. Schouten, N. Bhattacharya, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

Birch, K. P.

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

Braat, J. J. M.

Ciddor, P. E.

Cui, M.

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, J. J. M. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[CrossRef] [PubMed]

M. Cui, R. N. Schouten, N. Bhattacharya, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

Dändliker, R.

Downs, M. J.

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

Hagihara, Y.

Hirokazu, M.

C. Narin, T. Satoru, T. Kiyoshi, 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]

Holzwarth, R.

Hyun, S.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Jin, J.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Kabetani, Y.

Kim, S.-W.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Kim, Y.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Kim, Y.-J.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

Kiyoshi, T.

C. Narin, T. Satoru, T. Kiyoshi, 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]

Lévêque, S.

Matsumoto, H.

D. Wei, K. Takamasu, 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, 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, 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, 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]

Y. Yamaoka, K. Minoshima, 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.

Narin, C.

C. Narin, T. Satoru, T. Kiyoshi, 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]

Ohgi, Y.

Salvadé, Y.

Satoru, T.

C. Narin, T. Satoru, T. Kiyoshi, 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, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

Schuhler, N.

Takahashi, S.

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

Takamasu, K.

X. Wang, S. Takahashi, K. Takamasu, 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, 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, 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, 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]

Urbach, H. P.

van den Berg, S. A.

Wang, X.

X. Wang, S. Takahashi, K. Takamasu, 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, 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, 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]

Wei, D.

D. Wei, M. Aketagawa, “Characteristics of an adjacent pulse repetition interval length as a scale for length,” Opt. Eng. 53(5), 051502 (2014).
[CrossRef]

D. Wei, K. Takamasu, 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]

Yamaoka, Y.

Yasui, T.

Ye, J.

Yokoyama, S.

Yokoyama, T.

Zeitouny, M. G.

Appl. Opt.

Appl. Phys. Express

H. Matsumoto, X. Wang, K. Takamasu, 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. Europ. Opt. Soc. Rap. Public.

M. Cui, R. N. Schouten, N. Bhattacharya, S. A. Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Europ. Opt. Soc. Rap. Public. 3, 08003 (2008).

Meas. Sci. Technol.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[CrossRef]

C. Narin, T. Satoru, T. Kiyoshi, 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]

Metrologia

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

E. Bengt, “The Refractive Index of Air,” Metrologia 2(2), 71–80 (1966).
[CrossRef]

Opt. Eng.

D. Wei, M. Aketagawa, “Characteristics of an adjacent pulse repetition interval length as a scale for length,” Opt. Eng. 53(5), 051502 (2014).
[CrossRef]

Opt. Express

Opt. Lett.

Precis. Eng.

X. Wang, S. Takahashi, K. Takamasu, 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, 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]

Other

J. A. Stone and J. H. Zimmerman, “Index of refraction of air,” Available in: http://emtoolbox.nist.gov/Wavelength/Edlen.asp .

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer, 2005).

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Figures (1)

Fig. 1
Fig. 1

Change in the group refractive index according to the shift in the offset frequency.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

f P =(Q+P)× f rep = f CEO +P× f rep ,
u( f rep )/ f rep =u( f P )/ f P .
u( f P )/ f P =[ u( f CEO )+P×u( f rep ) ]/( f CEO +P× f rep ).
u( f P )/ f P [ u( f CEO )/ f CEO +P×u( f rep )/ f CEO ]/(P× f rep / f CEO ).
u( f CEO )/ f CEO +P×u( f rep )/ f CEO 2×u( f CEO )/ f CEO .
u( f CEO )/ f CEO 1 2 (u( f P )/ f P )×(P× f rep / f CEO ).
δ vac = c vac /f rep .
u( δ vac ) / δ vac = u( f rep ) / f rep .
δ air = δ vac / n g ( λ cen_vac ),
n g ( λ cen_vac )= n p ( λ cen_vac ) λ cen_vac × (d n p ( λ vac )/d λ vac ) λ cen_vac ,
δ air (t)= δ vac (t)/ n g ( λ cen_vac (t),T(t),P(t),H(t)).
L air (t)=(M+N)× δ air (t),
Δ L air ( t 1 , t 2 )=(M+N)× c vac × [ 1/ [ f rep ( t 2 )× n g ( λ cen_vac ( t 2 ),T( t 2 ),P( t 2 ),H( t 2 )) ] 1/ [ f rep ( t 1 )× n g ( λ cen_vac ( t 1 ),T( t 1 ),P( t 1 ),H( t 1 )) ] ].
Δ L air ( t 1 , t 2 ) / [ c vac / f rep ( t 1 ) ] =(M+N)×[ Δ n g 1 ( t 1 , t 2 ) ],
Δ L air ( t 1 , t 2 ) / [ c vac / f rep ( t 1 ) ] <1
(M+N)×Δ n g 1 ( t 1 , t 2 )<1.

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