Abstract

On the basis of analyzing sinusoidal phase-modulating Fabry–Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry–Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal.

© 2001 Optical Society of America

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  1. T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
    [Crossref]
  2. T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).
  3. A. Araya, S. Telada, K. Tochikubo, S. Taniguchi, R. Takahashi, K. Kawabe, D. Tatsumi, T. Yamazaki, S. Kawamura, S. Miyoki, S. Moriwaki, M. Musha, S. Nagano, M. Fujimoto, K. Horikoshi, N. Mio, Y. Naito, A. Takamori, K. Yamamoto, “Absolute-length determination of a long-baseline Fabry–Perot cavity by means of resonating modulation sidebands,” Appl. Opt. 38, 2848–2856 (1999).
    [Crossref]
  4. P. T. Woods, K. C. Shotton, W. R. C. Rowley, “Frequency determination of visible laser light by interferometric comparison with upconverted CO2 laser radiation,” Appl. Opt. 17, 1048–1053 (1978).
    [Crossref] [PubMed]
  5. K. S. Repasky, J. L. Carlsten, “Simple method for measuring frequency chirps with a Fabry–Perot interferometer,” Appl. Opt. 39, 5500–5504 (2000).
    [Crossref]
  6. S. Sato, M. Ohashi, M. Fujimoto, M. Fukushima, K. Waseda, S. Miyoki, N. Mavalvala, H. Yamamoto, “High-gain power recycling of a Fabry–Perot Michelson interferometer for a gravitational-wave antenna,” Appl. Opt. 39, 4616–4620 (2000).
    [Crossref]
  7. T. T. Lyons, M. W. Regehr, F. J. Raab, “Shot noise in gravitational-wave detectors with Fabry–Perot arms,” Appl. Opt. 39, 6761–6770 (2000).
    [Crossref]
  8. S. J. Bentley, R. W. Boyd, W. E. Butler, A. C. Melissinos, “Measurement of the thermal contribution to the nonlinear refractive index of air at 1064 nm,” Opt. Lett. 25, 1192–1194 (2000).
    [Crossref]
  9. T. Liu, G. F. Fernando, “A frequency division multiplexed low-finesse fiber optic Fabry–Perot sensor system for strain and displacement measurements,” Rev. Sci. Instrum. 71, 1275–1278 (2000).
    [Crossref]
  10. M. Schmidt, N. Furstenau, “Fiber-optic extrinsic Fabry–Perot interferometer sensors with three-wavelength digital phase demodulation,” Opt. Lett. 24, 599–601 (1999).
    [Crossref]
  11. S. C. Kaddu, S. F. Collins, D. J. Booth, “Multiplexed intrinsic optical fibre Fabry–Perot temperature and strain sensors addressed using white-light interferometry,” Meas. Sci. Technol. 10, 416–420 (1999).
    [Crossref]
  12. A. Courteville, Y. Salvade, R. Dandliker, “High-precision velocimetry: optimization of a Fabry–Perot interferometer,” Appl. Opt. 39, 1521–1526 (2000).
    [Crossref]
  13. T. K. Gangopadhyay, P. J. Henderson, “Vibration: history and measurement with an extrinsic Fabry–Perot sensor with solid-state laser interferometry,” Appl. Opt. 38, 2471–2477 (1999).
    [Crossref]
  14. R. A. Atkins, J. H. Gardner, W. N. Gibler, C. E. Lee, M. D. Oakland, M. O. Spears, V. P. Swenson, H. F. Taylor, J. J. McCoy, G. Beshouri, “Fiber-optic pressure sensors for internal combustion engines,” Appl. Opt. 33, 1315–1320 (1994).
    [Crossref] [PubMed]
  15. N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
    [Crossref]
  16. G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
    [Crossref]
  17. O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [Crossref] [PubMed]
  18. O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometry using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
    [Crossref] [PubMed]
  19. B. Chen, “Research on the technique of nano-measurement based on a laser dual Fabry–Perot interferometer,” Ph.D. dissertation (Zhejiang University, Hangzhou, China, 2000).

2000 (6)

1999 (4)

1998 (2)

T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
[Crossref]

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

1997 (1)

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

1994 (1)

1992 (1)

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

1987 (1)

1986 (1)

1978 (1)

Araya, A.

Atkins, R. A.

Basile, G.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

Bentley, S. J.

Bergamin, A.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

Beshouri, G.

Booth, D. J.

S. C. Kaddu, S. F. Collins, D. J. Booth, “Multiplexed intrinsic optical fibre Fabry–Perot temperature and strain sensors addressed using white-light interferometry,” Meas. Sci. Technol. 10, 416–420 (1999).
[Crossref]

Boyd, R. W.

Butler, W. E.

Carlsten, J. L.

Cavagnero, G.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

Chen, B.

B. Chen, “Research on the technique of nano-measurement based on a laser dual Fabry–Perot interferometer,” Ph.D. dissertation (Zhejiang University, Hangzhou, China, 2000).

Claus, R. O.

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

Collins, S. F.

S. C. Kaddu, S. F. Collins, D. J. Booth, “Multiplexed intrinsic optical fibre Fabry–Perot temperature and strain sensors addressed using white-light interferometry,” Meas. Sci. Technol. 10, 416–420 (1999).
[Crossref]

Courteville, A.

Dandliker, R.

Fernando, G. F.

T. Liu, G. F. Fernando, “A frequency division multiplexed low-finesse fiber optic Fabry–Perot sensor system for strain and displacement measurements,” Rev. Sci. Instrum. 71, 1275–1278 (2000).
[Crossref]

Fujimoto, M.

Fukushima, M.

Furstenau, N.

M. Schmidt, N. Furstenau, “Fiber-optic extrinsic Fabry–Perot interferometer sensors with three-wavelength digital phase demodulation,” Opt. Lett. 24, 599–601 (1999).
[Crossref]

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Gangopadhyay, T. K.

Gardner, J. H.

Gibler, W. N.

Goetze, W.

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Henderson, P. J.

Horack, H.

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Horikoshi, K.

Kaddu, S. C.

S. C. Kaddu, S. F. Collins, D. J. Booth, “Multiplexed intrinsic optical fibre Fabry–Perot temperature and strain sensors addressed using white-light interferometry,” Meas. Sci. Technol. 10, 416–420 (1999).
[Crossref]

Kawabe, K.

Kawamura, S.

Lee, C. E.

Li, T.

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

Liu, T.

T. Liu, G. F. Fernando, “A frequency division multiplexed low-finesse fiber optic Fabry–Perot sensor system for strain and displacement measurements,” Rev. Sci. Instrum. 71, 1275–1278 (2000).
[Crossref]

Lyons, T. T.

Mana, G.

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

Mavalvala, N.

May, R. G.

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

McCoy, J. J.

Melissinos, A. C.

Mio, N.

Miyoki, S.

Moriwaki, S.

Musha, M.

Nagano, S.

Naito, Y.

Oakland, M. D.

Ohashi, M.

Okazaki, H.

Raab, F. J.

Regehr, M. W.

Repasky, K. S.

Rowley, W. R. C.

Sakai, M.

Salvade, Y.

Sasaki, O.

Sato, S.

Schmidt, M.

M. Schmidt, N. Furstenau, “Fiber-optic extrinsic Fabry–Perot interferometer sensors with three-wavelength digital phase demodulation,” Opt. Lett. 24, 599–601 (1999).
[Crossref]

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Schmidt, W.

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Shotton, K. C.

Spears, M. O.

Swenson, V. P.

Takahashi, R.

Takamori, A.

Taniguchi, S.

Tatsumi, D.

Taylor, H. F.

Telada, S.

Tochikubo, K.

Wang, A.

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

Wang, T.

T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
[Crossref]

Waseda, K.

Woods, P. T.

Yamamoto, H.

Yamamoto, K.

Yamazaki, T.

Yang, Z.

T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
[Crossref]

Zhang, S.

T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
[Crossref]

Acta Metrolog. Sin. (1)

T. Li, R. G. May, A. Wang, R. O. Claus, “An optical scanning fiber dual-interferometer system for measuring small distance,” Acta Metrolog. Sin. 19, 9–14 (1998).

Appl. Opt. (10)

P. T. Woods, K. C. Shotton, W. R. C. Rowley, “Frequency determination of visible laser light by interferometric comparison with upconverted CO2 laser radiation,” Appl. Opt. 17, 1048–1053 (1978).
[Crossref] [PubMed]

O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[Crossref] [PubMed]

O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometry using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
[Crossref] [PubMed]

R. A. Atkins, J. H. Gardner, W. N. Gibler, C. E. Lee, M. D. Oakland, M. O. Spears, V. P. Swenson, H. F. Taylor, J. J. McCoy, G. Beshouri, “Fiber-optic pressure sensors for internal combustion engines,” Appl. Opt. 33, 1315–1320 (1994).
[Crossref] [PubMed]

T. K. Gangopadhyay, P. J. Henderson, “Vibration: history and measurement with an extrinsic Fabry–Perot sensor with solid-state laser interferometry,” Appl. Opt. 38, 2471–2477 (1999).
[Crossref]

A. Courteville, Y. Salvade, R. Dandliker, “High-precision velocimetry: optimization of a Fabry–Perot interferometer,” Appl. Opt. 39, 1521–1526 (2000).
[Crossref]

A. Araya, S. Telada, K. Tochikubo, S. Taniguchi, R. Takahashi, K. Kawabe, D. Tatsumi, T. Yamazaki, S. Kawamura, S. Miyoki, S. Moriwaki, M. Musha, S. Nagano, M. Fujimoto, K. Horikoshi, N. Mio, Y. Naito, A. Takamori, K. Yamamoto, “Absolute-length determination of a long-baseline Fabry–Perot cavity by means of resonating modulation sidebands,” Appl. Opt. 38, 2848–2856 (1999).
[Crossref]

K. S. Repasky, J. L. Carlsten, “Simple method for measuring frequency chirps with a Fabry–Perot interferometer,” Appl. Opt. 39, 5500–5504 (2000).
[Crossref]

S. Sato, M. Ohashi, M. Fujimoto, M. Fukushima, K. Waseda, S. Miyoki, N. Mavalvala, H. Yamamoto, “High-gain power recycling of a Fabry–Perot Michelson interferometer for a gravitational-wave antenna,” Appl. Opt. 39, 4616–4620 (2000).
[Crossref]

T. T. Lyons, M. W. Regehr, F. J. Raab, “Shot noise in gravitational-wave detectors with Fabry–Perot arms,” Appl. Opt. 39, 6761–6770 (2000).
[Crossref]

IEE Proc. Optoelectron. (1)

N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry–Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
[Crossref]

Meas. Sci. Technol. (1)

S. C. Kaddu, S. F. Collins, D. J. Booth, “Multiplexed intrinsic optical fibre Fabry–Perot temperature and strain sensors addressed using white-light interferometry,” Meas. Sci. Technol. 10, 416–420 (1999).
[Crossref]

Metrologia (1)

G. Basile, A. Bergamin, G. Cavagnero, G. Mana, “Phase modulation in high-resolution optical interferometry,” Metrologia 28, 455–461 (1992).
[Crossref]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

T. Liu, G. F. Fernando, “A frequency division multiplexed low-finesse fiber optic Fabry–Perot sensor system for strain and displacement measurements,” Rev. Sci. Instrum. 71, 1275–1278 (2000).
[Crossref]

Sens. Actuators A (1)

T. Wang, S. Zhang, Z. Yang, “A high precision displacement sensor using a low-finesse fiber-optic Fabry–Perot interferometer,” Sens. Actuators A 69, 134–138 (1998).
[Crossref]

Other (1)

B. Chen, “Research on the technique of nano-measurement based on a laser dual Fabry–Perot interferometer,” Ph.D. dissertation (Zhejiang University, Hangzhou, China, 2000).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the nanometer measurement system using a dual Fabry–Perot interferometer. BPFs, bandpass filters; other abbreviations defined in text.

Fig. 2
Fig. 2

Schematic of phase modulation near the maximum point of the transmitted intensity.

Fig. 3
Fig. 3

Schematic of the time interval Δt to be detected.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup.

Fig. 5
Fig. 5

The two elementary frequency signals of the transmitted intensities of a dual Fabry–Perot interferometer.

Fig. 6
Fig. 6

Result of fitting the data (V′, d′) of Table 1.

Fig. 7
Fig. 7

Result of fitting the data (V′, d′) of Table 2.

Tables (3)

Tables Icon

Table 1 Result 1 of Our Experimenta

Tables Icon

Table 2 Result 2 of Our Experimenta

Tables Icon

Table 3 SEM of Time Interval Δt

Equations (17)

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

IT=I01+F sin2 φ/2,
ITI01-F sin2φ/2.
IT=I01-F2+F2cos Δφ.
IT=I01-F2+F2cos4πnλ Δd.
ΔdPZT=KcV=KcV0 sinωmt+ϕm,
IT=I01-F2+F2cos×4πnλ KcV0 sinωmt+ϕm+ϑ.
I1S=I0FJ1xsinωmt+ϕmsin ϑ,
I1C=I0/2FJ0xcosωmt+ϕmcos ϑ,
ωmt1+ϕm-ϑ1=ωmt2+ϕm-ϑ2
Δϑ=ωmt2-t1.
Δd=KTΔt,
d=-0.31+2.02V.
σ=1N-1i=1Ndi--0.31+2.02Vi21/20.18 nm.
d=-0.20+2.33V.
σ=1N-1i=1Ndi--0.20+2.33Vi21/20.20 nm.
KVFP=KV1+KV2/2=2.02+2.33/22.18 nm/V.
ε=2.32-2.182.32×100%6.03%,

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