Abstract

A laser-frequency-based displacement measurement system with sub-nanometer uncertainty using an optical frequency comb generator is developed. In this method, the optical frequency of a tunable laser is locked to the resonance of a Fabry-Perot cavity. One of the two mirrors of this Fabry-Perot cavity is connected to the element whose displacement is to be measured. Wide range optical frequency and displacement measurements were realized by using an optical frequency comb generator, which consists of an electro-optic modulator placed inside of an optical resonator. We demonstrate a displacement measurement of up to 10 μm with 220 pm uncertainty under the stable condition.

© 2006 Optical Society of America

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References

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  1. C.-M. Wu and C.-S. Su, "Nonlinearity in measurements of length by optical interferometry," Meas. Sci. Technol. 7, 62-68 (1996)
    [CrossRef]
  2. C.-M. Wu and R. D. Deslattes, "Analytical modeling of the periodic nonlinearity in heterodyne interferometry," Appl. Opt. 37, 6696-6700 (1998).
    [CrossRef]
  3. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, "Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems," Appl. Opt. 43, 2443-2448 (2004).
    [CrossRef] [PubMed]
  4. S. Gonda, T. Doi, T. Kurosawa, T. Tanimura, H. Hisata, T. Yamagishi, H. Fujimoto, and H. Yukawa, "Real-time, interferometrically measuring atomic force microscope for direct calibration of standards," Rev. Sci. Instrum. 70, 3362-3368 (1999).
    [CrossRef]
  5. T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, "A simple method for the compensation of the nonlinearity in the heterodyne interferometer," Meas. Sci. Technol. 13, 222-225 (2002).
    [CrossRef]
  6. M. Sawabe, F. Maeda. Y. Yamaryo, T. Simomura, Y. Saruki, T. Kubo, H. Sakai, and S. Aoyagi, "A new vacuum intrerferometric comparator for calibrating the fine linear encoders and scales," Precision Eng. 28, 320-328 (2004).
    [CrossRef]
  7. J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Rev. Sci. Instrum. 71, 2669-2676 (2000).
    [CrossRef]
  8. E. Riis, H. Simonsen, T. Worm, U. Nielsen, and F. Besenbacher, "Calibration of the electrical response of piezoelectric elements at low voltage using laser interferometry," Appl. Phys. Lett. 54, 2530-28531 (1989).
    [CrossRef]
  9. H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia 37, 25-33 (2000).
    [CrossRef]
  10. U. Brand and K. Herrmann, "A laser measurement system for the high-precision calibration of displacement transducers," Meas. Sci. Technol. 7, 911-917 (1996).
    [CrossRef]
  11. L. Howard, J. Stone, and J. Fu, "Real-time displacement measurements with a Fabry-Perot cavity and a diode laser," Precision Eng. 25, 321-335 (2001).
    [CrossRef]
  12. R. M. Silver, H. Zou, S. Gonda, B. Damazo, J. Jun, C. Jensen, and L. Howard, "Atomic-resolution measurements with a new tunable diode laser-based interferometer," Opt. Eng. 43, 79-76 (2004).
    [CrossRef]
  13. M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron 29, 2693-2701 (1993).
    [CrossRef]
  14. Y. Zhang, J. Ishikawa, and F.-L. Hong, "Accurate frequency atlas of molecular iodine near 532 nm measured by an optical frequency comb generator," Opt. Commum. 200, 209-215 (2001).
    [CrossRef]
  15. P. E. Ciddor, "Refractive index of the air: new equationa for the visible and near infrared," Appl. Opt. 35, 1566-1573 (1996).
    [CrossRef] [PubMed]
  16. J. Ye, S. Swartz, P. Jungner, and J. L. Hall, "Hyperfine structure and absolute frequency of the 87Rb5P3/2 state," Opt. Lett. 21, 1280-1282 (1996).
    [CrossRef] [PubMed]
  17. Y. Bitou, K. Sasaki, H. Inaba, F.-L. Hong, and A. Onae, "Rubidium-stabilized diode laser for highprecision interferometer," Opt. Eng. 43, 900-903 (2004).
    [CrossRef]
  18. T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, "Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb," Opt. Lett. 30, 2323-2325 (2005).
    [CrossRef] [PubMed]
  19. B. Chen, R. Zhu, Z. Wu, D. Li, and S. Guo, "Nanometer measurement with a dual Fabry-Perot interferometer," Appl. Opt. 40, 5632-5637 (2001).
    [CrossRef]

Appl. Opt.

C.-M. Wu and R. D. Deslattes, "Analytical modeling of the periodic nonlinearity in heterodyne interferometry," Appl. Opt. 37, 6696-6700 (1998).
[CrossRef]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, "Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems," Appl. Opt. 43, 2443-2448 (2004).
[CrossRef] [PubMed]

P. E. Ciddor, "Refractive index of the air: new equationa for the visible and near infrared," Appl. Opt. 35, 1566-1573 (1996).
[CrossRef] [PubMed]

B. Chen, R. Zhu, Z. Wu, D. Li, and S. Guo, "Nanometer measurement with a dual Fabry-Perot interferometer," Appl. Opt. 40, 5632-5637 (2001).
[CrossRef]

Appl. Phys. Lett.

E. Riis, H. Simonsen, T. Worm, U. Nielsen, and F. Besenbacher, "Calibration of the electrical response of piezoelectric elements at low voltage using laser interferometry," Appl. Phys. Lett. 54, 2530-28531 (1989).
[CrossRef]

IEEE J. Quantum Electron

M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron 29, 2693-2701 (1993).
[CrossRef]

Meas. Sci. Technol.

C.-M. Wu and C.-S. Su, "Nonlinearity in measurements of length by optical interferometry," Meas. Sci. Technol. 7, 62-68 (1996)
[CrossRef]

U. Brand and K. Herrmann, "A laser measurement system for the high-precision calibration of displacement transducers," Meas. Sci. Technol. 7, 911-917 (1996).
[CrossRef]

T. Eom, T. Choi, K. Lee, H. Choi, and S. Lee, "A simple method for the compensation of the nonlinearity in the heterodyne interferometer," Meas. Sci. Technol. 13, 222-225 (2002).
[CrossRef]

Metrologia

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia 37, 25-33 (2000).
[CrossRef]

Opt. Commum.

Y. Zhang, J. Ishikawa, and F.-L. Hong, "Accurate frequency atlas of molecular iodine near 532 nm measured by an optical frequency comb generator," Opt. Commum. 200, 209-215 (2001).
[CrossRef]

Opt. Eng.

R. M. Silver, H. Zou, S. Gonda, B. Damazo, J. Jun, C. Jensen, and L. Howard, "Atomic-resolution measurements with a new tunable diode laser-based interferometer," Opt. Eng. 43, 79-76 (2004).
[CrossRef]

Y. Bitou, K. Sasaki, H. Inaba, F.-L. Hong, and A. Onae, "Rubidium-stabilized diode laser for highprecision interferometer," Opt. Eng. 43, 900-903 (2004).
[CrossRef]

Opt. Lett.

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, "Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb," Opt. Lett. 30, 2323-2325 (2005).
[CrossRef] [PubMed]

J. Ye, S. Swartz, P. Jungner, and J. L. Hall, "Hyperfine structure and absolute frequency of the 87Rb5P3/2 state," Opt. Lett. 21, 1280-1282 (1996).
[CrossRef] [PubMed]

Precision Eng.

L. Howard, J. Stone, and J. Fu, "Real-time displacement measurements with a Fabry-Perot cavity and a diode laser," Precision Eng. 25, 321-335 (2001).
[CrossRef]

M. Sawabe, F. Maeda. Y. Yamaryo, T. Simomura, Y. Saruki, T. Kubo, H. Sakai, and S. Aoyagi, "A new vacuum intrerferometric comparator for calibrating the fine linear encoders and scales," Precision Eng. 28, 320-328 (2004).
[CrossRef]

Rev. Sci. Instrum.

J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Rev. Sci. Instrum. 71, 2669-2676 (2000).
[CrossRef]

S. Gonda, T. Doi, T. Kurosawa, T. Tanimura, H. Hisata, T. Yamagishi, H. Fujimoto, and H. Yukawa, "Real-time, interferometrically measuring atomic force microscope for direct calibration of standards," Rev. Sci. Instrum. 70, 3362-3368 (1999).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic layout of the laser-frequency-based displacement measurement system. ECLD, external cavity laser diode; PBS, polarizing beam splitter; BE, beam expander.

Fig. 2
Fig. 2

Error signal E(f) used for locking optical frequency of ECLD to FP cavity.

Fig. 3
Fig. 3

Experimental setup for the optical frequency measurement using an optical frequency comb generator. AOM, acousto-optic modulator; BS, beam splitter; APD, avalanche photodiode; PZT, piezoelectric transducer.

Fig. 4
Fig. 4

Spectrum of comb envelope observed by an optical spectrum analyzer.

Fig. 5
Fig. 5

Schematic explanation of the relative positions of the optical frequency comb lines and the optical frequency locked to the FP cavity.

Fig. 6
Fig. 6

Example of measured beat signal f beat after filtering and amplification. The resolution bandwidth was 300 kHz.

Fig. 7
Fig. 7

Variation of the RF power transmitted through the bandpass filter during the tuning of f FP caused by length changes of the FP cavity.

Fig. 8
Fig. 8

Temporal variation of the measured beat-note signal f beat under stable environmental condition (temperature and air pressure).

Fig. 9
Fig. 9

Beat frequency change Δf when displacements ΔL of around 1, 5, and 10 μm were sequentially applied to the FP cavity. The mode number changes Δk of comb-lines were 3, 16, and 32 when ΔL = 1, 5, and 10 μm, respectively.

Equations (12)

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

Δ L = Δ f nf L ,
2 n 0 L 0 + λ 0 ϕ 0 2 π = m 0 C f 0 ,
2 n M L 0 + λ M ϕ M 2 π = ( m 0 + Δm ) C f M ,
2 n d ( L 0 + Δ L ) + λ d ϕ d 2 π = m 0 C f d ,
Δ L = C Δ f Δm 2 n d f d Δ F + 1 2 n d ( f M Δ f f d Δ f Δ L M Δ L d ) .
Δ L M = 2 Δ n M L 0 + λ M ϕ M 2 π λ 0 ϕ 0 2 π ,
Δ L d = 2 Δ n d L 0 + λ d ϕ d 2 π λ 0 ϕ 0 2 π ,
Δ L = C Δ f Δm 2 n d f d Δ F .
Δ C Δ f Δm 2 n d f d Δ F + Δ F 8 n d f d Δ L M
C Δ f Δm 2 n d f d Δ F + Δ F 8 n d f d ( 2 Δ n M L 0 + λ 0 Δ ϕ M 2 π ) ,
f FP = f Rb ± k f EO ± f beat ,
[ u ( Δ L ) Δ L ] 2 = [ u ( Δ f ) Δ f ] 2 + [ u ( Δ F ) Δ F ] 2 + [ u ( Δ f d ) Δ f d ] 2 + [ u ( Δ n d ) Δ n d ] 2 .

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