Abstract

A high-accuracy optical distance meter with a mode-locked femtosecond laser is proposed for distance measurements in a 310-m-long optical tunnel. We measured the phase shift of the optical beat component between longitudinal modes of a mode-locked laser. A high resolution of 50 µm at 240-m distance was obtained without cyclic error correction. The group refractive index of air is automatically extracted to an accuracy of 6 parts per million (ppm) by two-color measurement with the pulses of fundamental and second-harmonic wavelengths. Finally, an absolute mechanical distance of 240 m was obtained to within 8-ppm accuracy by use of a series of beat frequencies with the advantage of a wide range of intermode frequency, together with the results of the two-color measurement.

© 2000 Optical Society of America

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References

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  1. M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
    [CrossRef]
  2. J. Rueger, Electronic Distance Measurement (Springer-Verlag, New York, 1990).
    [CrossRef]
  3. P. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
    [CrossRef]
  4. I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
    [CrossRef]
  5. K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
    [CrossRef]
  6. R. Balhorn, F. Lebovsky, D. Ullrich, “Untersuchungen zur Entfermungsmessung mit Stabilisierten Zweifrequenzlasern,” Technical Report (Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschweig, Germany, 1974), pp. 151–153.
  7. D. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
    [CrossRef]
  8. K. E. Im, C. S. Gardner, J. B. Abshire, J. F. McGarry, “Experimental evaluation of the performance of pulsed two-color laser-ranging systems,” J. Opt. Soc. Am. A 4, 820–833 (1987).
    [CrossRef]
  9. R. Muijlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189–189 (1988).
    [CrossRef]
  10. P. Bender, J. Owens, “Correction of optical distance measurements for the fluctuating atmospheric index of refraction,” J. Geophys. Res. 70, 2461–2462 (1965).
    [CrossRef]

1998 (1)

I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

1997 (1)

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

1988 (1)

R. Muijlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189–189 (1988).
[CrossRef]

1987 (1)

1985 (1)

K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

1967 (1)

P. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[CrossRef]

1966 (1)

D. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
[CrossRef]

1965 (1)

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

Abshire, J. B.

Allan, D.

D. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
[CrossRef]

Balhorn, R.

R. Balhorn, F. Lebovsky, D. Ullrich, “Untersuchungen zur Entfermungsmessung mit Stabilisierten Zweifrequenzlasern,” Technical Report (Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschweig, Germany, 1974), pp. 151–153.

Bender, P.

P. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[CrossRef]

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

Fermann, M. E.

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

Fujima, I.

I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Galvanauskas, A.

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

Gardner, C. S.

Harter, D.

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

Im, K. E.

Iwasaki, S.

I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Lebovsky, F.

R. Balhorn, F. Lebovsky, D. Ullrich, “Untersuchungen zur Entfermungsmessung mit Stabilisierten Zweifrequenzlasern,” Technical Report (Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschweig, Germany, 1974), pp. 151–153.

McGarry, J. F.

Muijlwijk, R.

R. Muijlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189–189 (1988).
[CrossRef]

Oh’ishi, T.

K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Owens, J.

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

Rueger, J.

J. Rueger, Electronic Distance Measurement (Springer-Verlag, New York, 1990).
[CrossRef]

Seino, S.

K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Seta, K.

I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Sucha, G.

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

Ullrich, D.

R. Balhorn, F. Lebovsky, D. Ullrich, “Untersuchungen zur Entfermungsmessung mit Stabilisierten Zweifrequenzlasern,” Technical Report (Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschweig, Germany, 1974), pp. 151–153.

J. Appl. Phys. B (1)

M. E. Fermann, A. Galvanauskas, G. Sucha, D. Harter, “Fiber lasers for ultrafast optics,” J. Appl. Phys. B 65, 259–275 (1997).
[CrossRef]

J. Geophys. Res. (1)

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

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

K. Seta, T. Oh’ishi, S. Seino, “Optical distance measurement using inter-mode beat of laser,” Jpn. J. Appl. Phys. 24, 1374–1375 (1985).
[CrossRef]

Meas. Sci. Technol. (1)

I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Technol. 9, 1049–1052 (1998).
[CrossRef]

Metrologia (1)

R. Muijlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189–189 (1988).
[CrossRef]

Proc. IEEE (2)

P. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[CrossRef]

D. Allan, “Statistics of atomic frequency standards,” Proc. IEEE 54, 221–230 (1966).
[CrossRef]

Other (2)

J. Rueger, Electronic Distance Measurement (Springer-Verlag, New York, 1990).
[CrossRef]

R. Balhorn, F. Lebovsky, D. Ullrich, “Untersuchungen zur Entfermungsmessung mit Stabilisierten Zweifrequenzlasern,” Technical Report (Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschweig, Germany, 1974), pp. 151–153.

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Figures (4)

Fig. 1
Fig. 1

Stability of the repetition rate of the mode-locked fiber laser that we used for this study (second-harmonic wavelength), which was evaluated by the square root of Allan variance.

Fig. 2
Fig. 2

Experimental setup for the high-accuracy distance meter with the intermode beats of a femtosecond mode-locked laser. The laser source generates both fundamental (ω) and second-harmonic (2ω) beams. Here only 2ω is used. PD, photodetector; L, lens; M, reflecting mirror; CR, corner reflector; BS, beam splitter; DM, dichroic mirror; CM, curved mirror; S, beam stopper; ϕ, phase difference between probe and reference.

Fig. 3
Fig. 3

Experimental setup for two-color measurement for self-correction of the group refractive index of air in the distance meter by use of the intermode beats of a femtosecond mode-locked laser. We used the pulses of two wavelengths. The abbreviations mean the same as in Fig. 2. Mirror M2 spatially reflects a portion of the beams. When the measurement is taken for 0-m propagation, the long traveling beams are blocked by S2. In contrast, for 240-m propagation, the beam that is partially reflected by M2 is blocked by S1.

Fig. 4
Fig. 4

Results of the phase measurement (crosses) when the delay line was scanned. The displacement represents a change from the 240-m distance. The residual nonlinearity after linear fitting is also shown (solid curve). Standard deviation of the nonlinearity is 50 µm without cyclic error.

Tables (1)

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Table 1 Linear Fitting Results of the Phases by Two-Color Measurements

Equations (7)

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N+ϕ/2π=2f ng Dc.
ng=np-λ npλ,
Δϕ2ω-ω240-0=ϕ2ω240-ϕ2ω0-ϕω240-ϕω0.
Δϕ2ω-ω240-0=2π×Δn2ω-ωg D f/c.
A=n2ωg-1Δn2ω-ωg.
n2ωg-1experiment=287±10×10-6,
n2ωg-1Edle´n=277±6×10-6

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