Abstract

A two-color scheme of heterodyne laser interferometer is devised for distance measurements with the capability of real-time compensation of the refractive index of the ambient air. A fundamental wavelength of 1555 nm and its second harmonic wavelength of 777.5 nm are generated, with stabilization to the frequency comb of a femtosecond laser, to provide fractional stability of the order of 3.0 × 10−12 at 1 s averaging. Achieved uncertainty is of the order of 10−8 in measuring distances of 2.5 m without sensing the refractive index of air in adverse environmental conditions.

© 2015 Optical Society of America

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  1. A. J. Fleming, “A review of nanometer resolution position sensors: operation and performance,” Sens. Actuators A Phys. 190, 106–126 (2013).
    [Crossref]
  2. E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
    [Crossref]
  3. H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
    [Crossref]
  4. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [Crossref]
  5. G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
  8. 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]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  16. A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced errors,” Jpn. J. Appl. Phys. 28(Part 2), L473–L475 (1989).
    [Crossref]
  17. L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
    [Crossref]
  18. H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
    [Crossref]
  19. 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]
  20. S.-W. Kim, “Metrology: combs rule,” Nat. Photonics 3(6), 313–314 (2009).
    [Crossref]
  21. N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
    [Crossref]
  22. 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]
  23. 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]
  24. 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]
  25. S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
    [Crossref]
  26. G. Wang, Y. S. Jang, S. Hyun, B. J. Chun, H. J. Kang, S. Yan, S.-W. Kim, and Y.-J. Kim, “Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser,” Opt. Express 23(7), 9121–9129 (2015).
    [Crossref] [PubMed]

2015 (1)

2013 (3)

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]

A. J. Fleming, “A review of nanometer resolution position sensors: operation and performance,” Sens. Actuators A Phys. 190, 106–126 (2013).
[Crossref]

2012 (2)

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

2011 (3)

2009 (2)

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

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

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]

1999 (1)

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

1998 (2)

N. Khélifa, H. Fang, J. Xu, P. Juncar, and M. Himbert, “Refractometer for tracking changes in the refractive index of air near 780 nm,” Appl. Opt. 37(1), 156–161 (1998).
[Crossref] [PubMed]

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)

1993 (2)

H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
[Crossref]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

1992 (1)

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

1989 (1)

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced errors,” Jpn. J. Appl. Phys. 28(Part 2), L473–L475 (1989).
[Crossref]

1986 (1)

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

1980 (1)

1972 (1)

1968 (1)

J. C. Owens, “The use of atmospheric dispersion in optical distance measurement,” Bull. Geod. 89(1), 277–291 (1968).
[Crossref]

1967 (1)

K. B. Earnshaw and J. C. Owens, “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]

Abshire, J. B.

Arai, K.

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]

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]

Berkovic, G.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Birch, K. P.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (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]

Chun, B. J.

Ciddor, P. E.

Downs, M. J.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[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, “Dual wavelength optical distance measuring instrument, which corrects for air density,” IEEE J. Quantum Electron. 3(11), 544–550 (1967).
[Crossref]

Egan, P.

Fang, H.

Fleming, A. J.

A. J. Fleming, “A review of nanometer resolution position sensors: operation and performance,” Sens. Actuators A Phys. 190, 106–126 (2013).
[Crossref]

Flugge, J.

H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
[Crossref]

Füßl, R.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Hausotte, T.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Hernandez, E. N.

Himbert, M.

Honda, T.

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

Hyun, S.

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, 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]

Ishida, A.

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced errors,” Jpn. J. Appl. Phys. 28(Part 2), L473–L475 (1989).
[Crossref]

Iwashaki, S.

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

Jäger, G.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Jang, Y. S.

Jin, J.

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

Juncar, P.

Kang, H. J.

Khélifa, N.

Kim, S.-W.

G. Wang, Y. S. Jang, S. Hyun, B. J. Chun, H. J. Kang, S. Yan, S.-W. Kim, and Y.-J. Kim, “Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser,” Opt. Express 23(7), 9121–9129 (2015).
[Crossref] [PubMed]

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

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

Kim, Y.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and 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.

Kunzmann, H.

H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
[Crossref]

Manske, E.

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[Crossref]

Matsumoto, H.

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[Crossref]

Meiners-Hagen, K.

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]

Minoshima, K.

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]

Newbury, N. R.

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

Owens, J. C.

J. C. Owens, “The use of atmospheric dispersion in optical distance measurement,” Bull. Geod. 89(1), 277–291 (1968).
[Crossref]

K. B. Earnshaw and J. C. Owens, “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]

Pfeifer, T.

H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
[Crossref]

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]

Reinboth, F.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

Schellekens, P.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

Seta, K.

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

Shafir, E.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Spronck, J.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

Stone, J. A.

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]

Wang, G.

Wilkening, G.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

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, 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]

Xu, J.

Yan, S.

Zeng, L.

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

Adv. Opt. Photonics (1)

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Ann. CIRP (1)

H. Kunzmann, T. Pfeifer, and J. Flugge, “Scales vs laser interferometers, performance and comparison of two measuring systems,” Ann. CIRP 42(2), 753–767 (1993).
[Crossref]

Appl. Opt. (5)

Bull. Geod. (1)

J. C. Owens, “The use of atmospheric dispersion in optical distance measurement,” Bull. Geod. 89(1), 277–291 (1968).
[Crossref]

IEEE J. Quantum Electron. (1)

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

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced errors,” Jpn. J. Appl. Phys. 28(Part 2), L473–L475 (1989).
[Crossref]

Meas. Sci. Technol. (7)

L. Zeng, K. Seta, H. Matsumoto, and S. Iwashaki, “Length measurement by a two-colour interferometer using two close wavelengths to reduce errors caused by air turbulence,” Meas. Sci. Technol. 10(7), 587–591 (1999).
[Crossref]

H. Matsumoto and T. Honda, “High-accuracy length-measuring interferometer using the two-colour method of compensating for the refractive index of air,” Meas. Sci. Technol. 3(11), 1084–1086 (1992).
[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]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

E. Manske, G. Jäger, T. Hausotte, and R. Füßl, “Recent developments and challenges of nanopositioning and nanomeasuring technology,” Meas. Sci. Technol. 23(7), 074001 (2012).
[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]

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

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, and J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22(4), 279–287 (1986).
[Crossref]

Nat. Photonics (2)

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

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

Opt. Express (2)

Sci. Rep. (1)

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]

Sens. Actuators A Phys. (1)

A. J. Fleming, “A review of nanometer resolution position sensors: operation and performance,” Sens. Actuators A Phys. 190, 106–126 (2013).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Distance measurement uncertainty of laser interferometry dominated by three limiting factors; phase measurement error (Δe⋅λ), air refractive index (n) and source frequency (f).

Fig. 2
Fig. 2

Two-color heterodyne interferometer configured for real-time compensation of the refractive index of air. OC: optical coupler, PLL: phase locked loop, C: collimator, DFB: distributed feedback, FL: focusing lens, PPLN: periodically poled LiNbO3LiNbO3, SOA: semiconductor optical amplifier, DM: dichroic mirror, BS: beam splitter, AOM: acousto-optic modulator, M: mirror, PD: photodetector, CC: corner-cube, LPF: low pass filter, T: temperature, P: pressure, H: humidity, CO2: carbon dioxide concentration, PD: photo-detector, Meas.: measurement, Ref.: reference, and Rb: rubidium.

Fig. 3
Fig. 3

Stabilization of two wavelengths λ1 and λ2 for two-color interferometry. (a) Fractional stability in terms of the Allan deviation of the optical comb used for stabilization of the fundamental wavelength λ1. The beat frequency of λ1 with the optical comb is shown to indicate the stability of λ1 is comparable to that of the optical comb. (b) Optical spectra and signal-to-noise ratios of λ1 (1555 nm) and its second harmonic wavelength λ2 (777.5 nm).

Fig. 4
Fig. 4

Two-color measurement result for a given distance L of 2.5 m in well-controlled environment. (a) Optical path length (OPL) variation during 250 s for ΔD1 for the fundamental wavelength λ1 and ΔD2 for the second harmonic wavelength λ2. The difference ΔD2 - ΔD1 shows a standard deviation of σ = 5.33 × 10−10 m. The vertical plot of ΔD1 is upshifted by 5 nm to avoid overlap. (b) Calculation of one-color OPL ΔD1/L and two-color correction term AΔ(D2-D1)/L. (c) Compensated distance by two-color method shows a relative stability of 7.03 × 10−9 in standard deviation at an updated rate of 40 kHz. 100-point averaging by reducing the updated rate to 1 Hz enhances the standard deviation to σ = 3.15 × 10−9. Also shown is the base temperature measured using a thermometer. (d) Variation of the refractive index of air calculated by two-color measurement. For comparison, the refractive index of air estimated by substituting measured environmental parameters to the Ciddor’s equation is shown. The residual between the two-color method and the Ciddor’s equation is σ = 2.77 × 10−9. The residual value is downshifted by 3.0 × 10−9 to avoid overlap.

Fig. 5
Fig. 5

Two-color measurement in dynamic environment. (a) Air flow induced for experiment. (b) Measured temporal fluctuation of ΔD1 and ΔD2. The difference ΔD2 − ΔD1 shows a standard deviation of σ = 2.68 × 10−9 m. ΔD2 is downshifted by 0.2 μm. (c) Geometrical distance calculated by two-color interferometer shows a temporal variation of σ = 4.53 × 10−8 during air injection of 60 s. (d) Air refractive index variation and its residual. The standard deviation of the residual corresponds to 8.15 × 10−9 when the environment was stable at 0<t<135 and 275<t<325. The residual is downshifted by 1.0 × 10−7 to avoid overlap.

Equations (3)

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ΔL=(Δm+Δe)λ+(m+e)ΔλΔeλ+(Δλ/λ)L
| u(L) | 2 = | ΔL | 2 = | Δeλ | 2 + | ( Δn n )L | 2 + | ( Δf f )L | 2
L= D 1 A( D 2 D 1 ) where A=( n 1 1)/( n 2 n 1 )

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