Abstract

Laser-frequency-based displacement metrology and a control system directly traceable to a time standard are developed. The setup is based on a Fabry–Perot (FP) cavity. Two resonant frequencies of the FP cavity are probed for displacement measurement. An optical-frequency-comb generator is utilized to improve the measurement resolution. A displacement resolution of approximately 1.3nm was achieved, and displacement control using a phase-locked loop was demonstrated.

© 2009 Optical Society of America

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References

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  1. H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
    [CrossRef]
  2. U. Brand and K. Herrmann, Meas. Sci. Technol. 7, 911 (1996).
    [CrossRef]
  3. L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
    [CrossRef]
  4. T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
    [CrossRef]
  5. J. R. Lawall, J. Opt. Soc. Am. A 22, 2786 (2005).
    [CrossRef]
  6. Y. Bitou, T. R. Schibli, and K. Minoshima, Opt. Express 14, 644 (2006).
    [CrossRef] [PubMed]
  7. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  8. P. E. Ciddor, Appl. Opt. 35, 1566 (1996).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2001 (1)

L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
[CrossRef]

2000 (1)

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
[CrossRef]

1996 (3)

U. Brand and K. Herrmann, Meas. Sci. Technol. 7, 911 (1996).
[CrossRef]

T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
[CrossRef]

P. E. Ciddor, Appl. Opt. 35, 1566 (1996).
[CrossRef] [PubMed]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Bitou, Y.

Brand, U.

U. Brand and K. Herrmann, Meas. Sci. Technol. 7, 911 (1996).
[CrossRef]

Ciddor, P. E.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Dunn, T. J.

T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Fu, J.

L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
[CrossRef]

Haitjema, H.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Herrmann, K.

U. Brand and K. Herrmann, Meas. Sci. Technol. 7, 911 (1996).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Howard, L.

L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
[CrossRef]

Jain, K.

T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Lawall, J. R.

Lee, T.-M.

T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
[CrossRef]

Minoshima, K.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Schellekens, P. H. J.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
[CrossRef]

Schibli, T. R.

Stone, J.

L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Wetzels, S. F. C. L.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

T. J. Dunn, T.-M. Lee, and K. Jain, J. Vac. Sci. Technol. B 14, 3960 (1996).
[CrossRef]

Meas. Sci. Technol. (1)

U. Brand and K. Herrmann, Meas. Sci. Technol. 7, 911 (1996).
[CrossRef]

Metrologia (1)

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, Metrologia 37, 25 (2000).
[CrossRef]

Opt. Express (1)

Precis. Eng. (1)

L. Howard, J. Stone, and J. Fu, Precis. Eng. 25, 321 (2001).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for the laser-frequency-based displacement measurement system utilizing two modes of the FP cavity. PBS, polarizing beam splitter; ML, mode-matching lens.

Fig. 2
Fig. 2

Experimental setup for the optical-frequency difference measurement system using an optical-frequency-comb generator.

Fig. 3
Fig. 3

Example of a measured beat frequency.

Fig. 4
Fig. 4

Allan standard deviation of the measured beat frequency.

Fig. 5
Fig. 5

Time variation of the measured beat frequency when a displacement control signal with a triangular wave having an amplitude of 70 kHz was applied through the PLL.

Equations (2)

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F = f 1 f 2 = N comb f EO ± f beat ,
Δ L = c N c Δ F 2 n F ( F + Δ F ) c Δ f beat 2 n N c FSR 2 ,

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