Abstract

Interferometric measurement of distance using a femtosecond frequency comb is demonstrated and compared with a counting interferometer displacement measurement. A numerical model of pulse propagation in air is developed and the results are compared with experimental data for short distances. The relative agreement for distance measurement in known laboratory conditions is better than 10-7. According to the model, similar precision seems feasible even for long-distance measurement in air if conditions are sufficiently known. It is demonstrated that the relative width of the interferogram envelope even decreases with the measured length, and a fringe contrast higher than 90% could be obtained for kilometer distances in air, if optimal spectral width for that length and wavelength is used. The possibility of comb radiation delivery to the interferometer by an optical fiber is shown by model and experiment, which is important from a practical point of view.

© 2009 Optical Society of America

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References

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  1. For a general review see, e.g., S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
    [CrossRef]
  2. P. Gill, "Optical frequency standards," Metrologia 42, S125-S137 (2005).
    [CrossRef]
  3. L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
    [CrossRef]
  4. E. V. Baklanov and A. K. Dmitriev, "Absolute length measurements with a femtosecond laser," Quantum Electron. 32, 925-928 (2002).
    [CrossRef]
  5. J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Opt. Lett. 29, 1153-1155 (2004), opticsinfobase.org/abstract.cfm?URI=ol-29-10-1153">http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-10-1153.
    [CrossRef] [PubMed]
  6. K.-N. Joo, Y. Kim, and S.-W. Kim, "Distance measurements by combined method based on a femtosecond pulse laser," Opt. Express 16, 19799-19806 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-19799.
    [CrossRef] [PubMed]
  7. Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, "High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source," Appl. Opt. 47, 2715-2720 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-14-2715.
    [CrossRef] [PubMed]
  8. M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
    [CrossRef]
  9. K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, "Ultrahigh dynamic-range length metrology using optical frequency combs," NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf.
  10. J. Zhang, Z. H. Lu, and L. J. Wang, "Precision measurement of the refractive index of carbon dioxide with a frequency comb," Opt. Lett. 32, 3212-3214 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-21-3212
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  11. Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp.
  12. J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
    [CrossRef]
  13. Y. Yamaoka, L. Zeng, K. Minoshima, and H. Matsumoto, "Measurements and numerical analysis for femtosecond pulse deformations after propagation of hundreds of meters in air with water-vapor absorption lines," Appl. Opt. 43, 5523-5530 (2004).
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  14. P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008).
    [CrossRef]
  15. 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, 4318-4324 (2002).
    [CrossRef] [PubMed]
  16. J.-P. Wallerand, A. Abou-Zeid, T. Badr, P. Balling, J. Jokela, R. Kugler, M. Matus, M. Merimaa, M. Poutanen, E. Prieto, S. van den Berg, and M. Zucco, "Towards new absolute long-distance measurement in air," 2008 NCSL International Workshop and Symposium, Orlando (USA), http://www.longdistanceproject.eu/files/towards_new_absolute.pdf.

2008

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008).
[CrossRef]

Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, "High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source," Appl. Opt. 47, 2715-2720 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-14-2715.
[CrossRef] [PubMed]

K.-N. Joo, Y. Kim, and S.-W. Kim, "Distance measurements by combined method based on a femtosecond pulse laser," Opt. Express 16, 19799-19806 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-19799.
[CrossRef] [PubMed]

2007

2005

P. Gill, "Optical frequency standards," Metrologia 42, S125-S137 (2005).
[CrossRef]

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

2004

2003

For a general review see, e.g., S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

2002

1997

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

Baklanov, E. V.

E. V. Baklanov and A. K. Dmitriev, "Absolute length measurements with a femtosecond laser," Quantum Electron. 32, 925-928 (2002).
[CrossRef]

Balling, P.

P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008).
[CrossRef]

Bartels, A.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

Bhattacharya, N.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

Cui, M.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

Decker, J. E.

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

Diddams, S.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

Dmitriev, A. K.

E. V. Baklanov and A. K. Dmitriev, "Absolute length measurements with a femtosecond laser," Quantum Electron. 32, 925-928 (2002).
[CrossRef]

Fortier, T.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

Gill, P.

P. Gill, "Optical frequency standards," Metrologia 42, S125-S137 (2005).
[CrossRef]

Hollberg, L.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

Joo, K.-N.

Kim, K.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

Kim, S.-W.

Kim, Y.

Kren, P.

P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008).
[CrossRef]

Le Floch, S.

Lévêque, S.

Lu, Z. H.

Matsumoto, H.

Minoshima, K.

Pekelsky, J. R.

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

Salvadé, Y.

Schouten, R. N.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

Schuhler, N.

van den Berg, S. A.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

Wang, L. J.

Yamaoka, Y.

Ye, J.

Zeng, L.

Zhang, J.

Appl. Opt.

Eur. Phys. J. D

P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ.

M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246.
[CrossRef]

Metrologia

P. Gill, "Optical frequency standards," Metrologia 42, S125-S137 (2005).
[CrossRef]

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005).
[CrossRef]

J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Quantum Electron.

E. V. Baklanov and A. K. Dmitriev, "Absolute length measurements with a femtosecond laser," Quantum Electron. 32, 925-928 (2002).
[CrossRef]

Rev. Mod. Phys.

For a general review see, e.g., S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Other

J.-P. Wallerand, A. Abou-Zeid, T. Badr, P. Balling, J. Jokela, R. Kugler, M. Matus, M. Merimaa, M. Poutanen, E. Prieto, S. van den Berg, and M. Zucco, "Towards new absolute long-distance measurement in air," 2008 NCSL International Workshop and Symposium, Orlando (USA), http://www.longdistanceproject.eu/files/towards_new_absolute.pdf.

K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, "Ultrahigh dynamic-range length metrology using optical frequency combs," NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf.

Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp.

Supplementary Material (1)

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Figures (11)

Fig. 1.
Fig. 1.

Schematic representation of the setup for interferometric distance measurement with a frequency comb.

Fig. 2.
Fig. 2.

Typical model results. Left chart, relative spectra (red, light intensity; green, electric field intensity) and dispersion (black, right axis). Middle chart, electric fields of reference and measuring pulses. Right chart, linear (black) and second-order (blue) interferogram in percents relative to intensity of interferogram of the reference pulse with itself.

Fig. 3.
Fig. 3.

Modeled E fields (left) and interferograms (right) for the same condition as in Fig. 2 but with linear chirp -10 μm/160 THz. The horizontal scale range is doubled compared to Fig. 2. The centers of envelopes of each pulse of the train are shifted by -23 μm due to this chirp. The black curve (first-order interferogram) is exactly the same as in Fig. 2.

Fig. 4.
Fig. 4.

Spectral modulation of ~800 nm radiation due to interference after the measuring pulse has passed different path lengths in air. All plots are for fringes in the very center of the interferogram. Red original (input) spectra, blue modulated spectra, horizontal scale wavelength in nanometers. Top, 1.5 m distance; bottom, 50 m distance; left, light fringe; right, dark fringe.

Fig. 5.
Fig. 5.

Modeled interferograms for the same condition as in Fig. 2 and path length difference 100 m (distance 50 m). Left, full spectra; right, after “optimal” rectangular filter ±13.0 nm.

Fig. 6.
Fig. 6.

Setup used for comparison of comb interferometer (CI) and counting laser interferometer (LI).

Fig. 7.
Fig. 7.

Comparison of the spectra detected by a spectrometer (solid curve) and calculated by Fourier analysis of an interferogram (dots). The difference between spectra leads to a relative deviation of mean group refractive indices of 1.01×10-7.

Fig. 8.
Fig. 8.

Result of comparison of comb interferometer and classical counting interferometer for 1.5 m distance/displacement measurement.

Fig. 9.
Fig. 9.

Illustration of good agreement between detected interferogram and modeled shapes and of envelope development with increasing distance traveled in air. Top, spectra calculated from top left interferogram and used for modeling. Experimental profiles are left and modeled right. Top pair of profiles for zero arm difference, bottom pair for 1.5 m distance (2*lpp ).

Fig. 10.
Fig. 10.

Separation of NIR and blue (SHG fro NIR) parts of originally overlapping pulses by different group velocities for 3 m path in air (1.5 m distance). Spectra and fringe resolved pictures of measured and modeled interferograms are shown in (Media 1).

Fig. 11.
Fig. 11.

Results of CI-LI comparison for evaluating stationary phase points for three different wavelengths. Effectively it means the direct measurement of group refractive indices at these wavelengths by laser interferometer LI. The deviation of experimentally measured group refractive index (or of lpp(λ)) from the calculated by Ciddor formula is shown. The systematic deviation of results 1–11 was caused by wrong comb beam collimation.

Tables (2)

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Table 1. Optimal Filter Widths for Different Central Wavelengths and Distances

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Table 2. Sensitivity Coefficients of Mean Group Refractive Index on Central Wavelength and on Environment Parametersa

Equations (7)

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

vg=ωk,
ng=cvgn+fnf=nλcnλn+fcn(fc+fr)n(fcfr)2fr,
E(xn)=iEicoskixn.
Id=n=N/2N/2(Er(xn)+Em(xn+d))2
Id2=n=N/2N/2(Er(xn)+Em(xn+d))4 .
I(λi,L)=2Ei2 (1+coskiL) .
Δx(λ)=φ(λ,x0)λ·λ22π.

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