Abstract

Interferometry associated with an external cavity laser of long coherence length and broad wavelength tuning range shows promising features for use in measurements of absolute distance. As far as we know, the processing of the interferometric signals has until now been performed by Fourier analysis or fringe counting. Here we report on the use of an autoregressive model to determine fringe pattern frequencies. This concept was applied to an interferometric device fed by a continuously tunable external-cavity laser diode operating at a central wavelength near 1.5 μm. A standard uncertainty of 4 × 10-5 without averaging at a distance of 4.7 m was obtained.

© 2003 Optical Society of America

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References

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  1. M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
    [CrossRef]
  2. K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
    [CrossRef]
  3. G. Beheim, K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21, 93–94 (1985).
    [CrossRef]
  4. G. Beheim, K. Fritsch, “Range finding using frequency-modulated laser diode,” Appl. Opt. 25, 1439–4142 (1986).
    [CrossRef] [PubMed]
  5. J. A. Stone, A. Stejskal, L. Howard, “Absolute interferometry with a 670-nm external cavity diode laser,” Appl. Opt. 38, 5981–5994 (1999).
    [CrossRef]
  6. J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
    [CrossRef]
  7. T.-H. Li, “A fast algorithm for efficient estimation of frequencies,” in Signal Processing IX, Theories and Applications: Proceedings of the Ninth European Signal Processing Conference, S. Theodoridis, I. Pitas, A. Soutairis, N. Kalouptsidis, eds. (Typorama, Patra, Greece, 1998), Vol. 1, p. 65–68.
  8. J. J. Talamonti, R. B. Kay, D. J. Krebs, “Numerical model estimating the capabilities and limitations of the fast Fourier transform technique in absolute interferometry,” Appl. Opt. 35, 2182–2191 (1996).
    [CrossRef] [PubMed]
  9. L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 105.
  10. S. M. Kay, Modern Spectral Estimation, Theory and Application (Prentice-Hall, Englewood Cliffs, N.J., 1988), Chap. 13.
  11. A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).
  12. R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. W. Wyant, ed., Proc. SPIE429, 43–54 (1983).
  13. G. E. P. Box, G. M. Jenkins, Times Series Analysis: Forecasting and Control (Holden-Day, San Francisco, Calif., 1976).
  14. Ref. 10, pp. 228–231.
  15. H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. AC-19, 716–723 (1974).
    [CrossRef]
  16. W. Y. Chen, G. R. Stegen, “Experiments with maximum entropy power spectra of sinusoids,” J. Geophys. Res. 79, 3019–3022 (1974).
    [CrossRef]

2001 (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

2000 (1)

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

1999 (1)

1998 (1)

A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).

1996 (1)

1995 (1)

J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

1986 (1)

1985 (1)

G. Beheim, K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21, 93–94 (1985).
[CrossRef]

1974 (2)

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. AC-19, 716–723 (1974).
[CrossRef]

W. Y. Chen, G. R. Stegen, “Experiments with maximum entropy power spectra of sinusoids,” J. Geophys. Res. 79, 3019–3022 (1974).
[CrossRef]

Akaike, H.

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. AC-19, 716–723 (1974).
[CrossRef]

Amann, M. C.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Beheim, G.

G. Beheim, K. Fritsch, “Range finding using frequency-modulated laser diode,” Appl. Opt. 25, 1439–4142 (1986).
[CrossRef] [PubMed]

G. Beheim, K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21, 93–94 (1985).
[CrossRef]

Bosch, T.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Box, G. E. P.

G. E. P. Box, G. M. Jenkins, Times Series Analysis: Forecasting and Control (Holden-Day, San Francisco, Calif., 1976).

Castanié, F.

A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).

Chen, W. Y.

W. Y. Chen, G. R. Stegen, “Experiments with maximum entropy power spectra of sinusoids,” J. Geophys. Res. 79, 3019–3022 (1974).
[CrossRef]

Ducasse, A.

A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).

Fritsch, K.

G. Beheim, K. Fritsch, “Range finding using frequency-modulated laser diode,” Appl. Opt. 25, 1439–4142 (1986).
[CrossRef] [PubMed]

G. Beheim, K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21, 93–94 (1985).
[CrossRef]

Gold, B.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 105.

Hara, T.

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

Hartmann, M.

J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Howard, L.

Ito, H.

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

Jenkins, G. M.

G. E. P. Box, G. M. Jenkins, Times Series Analysis: Forecasting and Control (Holden-Day, San Francisco, Calif., 1976).

Kay, R. B.

Kay, S. M.

S. M. Kay, Modern Spectral Estimation, Theory and Application (Prentice-Hall, Englewood Cliffs, N.J., 1988), Chap. 13.

Krebs, D. J.

Lescure, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Li, T.-H.

T.-H. Li, “A fast algorithm for efficient estimation of frequencies,” in Signal Processing IX, Theories and Applications: Proceedings of the Ninth European Signal Processing Conference, S. Theodoridis, I. Pitas, A. Soutairis, N. Kalouptsidis, eds. (Typorama, Patra, Greece, 1998), Vol. 1, p. 65–68.

Mailhes, C.

A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).

Miyahara, T.

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

Myllyla, R.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Nakamura, K.

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

Pfeifer, T.

J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Rabiner, L. R.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 105.

Rioux, M.

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Stegen, G. R.

W. Y. Chen, G. R. Stegen, “Experiments with maximum entropy power spectra of sinusoids,” J. Geophys. Res. 79, 3019–3022 (1974).
[CrossRef]

Stejskal, A.

Stone, J. A.

Talamonti, J. J.

Tansey, R. J.

R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. W. Wyant, ed., Proc. SPIE429, 43–54 (1983).

Thiel, J.

J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Yoshida, M.

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (1)

G. Beheim, K. Fritsch, “Remote displacement measurements using a laser diode,” Electron. Lett. 21, 93–94 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Nakamura, T. Hara, M. Yoshida, T. Miyahara, H. Ito, “Optical frequency domain ranging by a frequency shifted feedback laser,” IEEE J. Quantum Electron. 36, 305–316 (2000).
[CrossRef]

IEEE Trans. Autom. Control. (1)

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. AC-19, 716–723 (1974).
[CrossRef]

J. Geophys. Res. (1)

W. Y. Chen, G. R. Stegen, “Experiments with maximum entropy power spectra of sinusoids,” J. Geophys. Res. 79, 3019–3022 (1974).
[CrossRef]

Measurement (1)

J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Opt. Eng. (1)

M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40, 10–19 (2001).
[CrossRef]

Traitement du Signal (1)

A. Ducasse, C. Mailhes, F. Castanié, “Panorama des méthodes paramétriques,” Traitement du Signal 15, 149–162 (1998).

Other (6)

R. J. Tansey, “An absolute distance interferometer using a dye laser heterodyne interferometer and spatial separation of beams,” in Precision Surface Metrology, J. W. Wyant, ed., Proc. SPIE429, 43–54 (1983).

G. E. P. Box, G. M. Jenkins, Times Series Analysis: Forecasting and Control (Holden-Day, San Francisco, Calif., 1976).

Ref. 10, pp. 228–231.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 105.

S. M. Kay, Modern Spectral Estimation, Theory and Application (Prentice-Hall, Englewood Cliffs, N.J., 1988), Chap. 13.

T.-H. Li, “A fast algorithm for efficient estimation of frequencies,” in Signal Processing IX, Theories and Applications: Proceedings of the Ninth European Signal Processing Conference, S. Theodoridis, I. Pitas, A. Soutairis, N. Kalouptsidis, eds. (Typorama, Patra, Greece, 1998), Vol. 1, p. 65–68.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: L, lens; RR, retroreflectors; OF, optical fibers; BSC, beam splitter cube; PD, photodiodes; D obj, optical path difference.

Fig. 2
Fig. 2

Squares, deviations of the measurements from the mean value for the sixth point presented in Fig. 3.

Fig. 3
Fig. 3

⊕, experimental data. Error bars, standard deviation. The 0-mm reference corresponds to the initial distance of the mechanical translator.

Fig. 4
Fig. 4

Linearity error. Each filled square represents the mean value of 20 acquisitions.

Equations (18)

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

νt=ν0+βt,
It=Bt+Atcos2πfobjt+φ0,
fobj=β 2Dobjc,
fref=β Drefc.
Dobj=12fobjfref Dref.
un=-k=1p akun-k+wn,
In=-k=1p akIn-k.
Hz=11+k=1p akz-k.
In=k=1K Ak cos2πfkn+ϕk=-k=12K akIn-k.
1+k=12K akz-k=k=1K1-Zkz-11-Zk*z-1.
AICK=N lnγˆ2K+2K,
In=a1In-1+a2In-2.
a1=-rII1rII0, a2=-rII2+a1rII1ρ1,
ρ1=1-|a1|2rII0.
1-a1z-1-a2z-2=1-Z1z-11-Z1*z-1=0.
Z1=expj2πfˆ1, Z1*=exp-j2πfˆ1,
fˆ1=Imln Z12π.
varfˆ16σw2A12NN2-12π2,

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