Abstract

A new method has been demonstrated for absolute-length measurements of a long-baseline Fabry–Perot cavity by use of phase-modulated light. This method is based on determination of a free spectral range (FSR) of the cavity from the frequency difference between a carrier and phase-modulation sidebands, both of which resonate in the cavity. Sensitive response of the Fabry–Perot cavity near resonant frequencies ensures accurate determination of the FSR and thus of the absolute length of the cavity. This method was applied to a 300-m Fabry–Perot cavity of the TAMA gravitational wave detector that is being developed at the National Astronomical Observatory, Tokyo. With a modulation frequency of ∼12 MHz, we successfully determined the absolute cavity length with resolution of 1 µm (3 × 10-9 in strain) and observed local ground strain variations of 6 × 10-8.

© 1999 Optical Society of America

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References

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  1. T. J. Quinn, “Mise en pratique of the definition of the metre (1992),” Metrologia 30, 523–541 (1994).
    [CrossRef]
  2. A. N. Golubev, “Absolute laser interferometric distance measurement,” Survey Rev. 32, 109–117 (1993).
  3. E. Bergstrand, “Distance measuring by means of modulated light,” Bull. Geod. 24, 243–249 (1952).
    [CrossRef]
  4. In this paper we assume that the whole optical path is in vacuum to realize the most accurate measurement without correcting for the effects of the refractive index of the ambient air.
  5. K. M. Baird, “The role of interferometry in long distance measurement,” Metrologia 4, 135–144 (1968).
    [CrossRef]
  6. I. Fujima, S. Iwasaki, K. Seta, “High-resolution distance meter using optical intensity modulation at 28 GHz,” Meas. Sci. Tech. 9, 1049–1052 (1998).
    [CrossRef]
  7. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  8. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  9. S. Telada, “Development of a mode cleaner for a laser interferometer gravitational wave detector,” Ph.D. dissertation (Graduate University for Advanced Studies, Tokyo, 1997), pp. 32–38.
  10. K. Tsubonothe TAMA collaboration, “TAMA project,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 183–191.
  11. The name of the project is derived from the region where the detector is located.
  12. The mirrors are 100 mm in diameter and 60 mm long. The input mirror is flat, and the end mirror is concave with a radius of curvature of 450 m.
  13. R. Takahashi, F. Kuwahara, K. Kuroda, “Vibration isolation stack for TAMA300,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 95–102.
  14. E. Morrison, B. J. Meers, D. I. Robertson, H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
    [CrossRef] [PubMed]
  15. K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.
  16. Groundwater is utilized by a hospital located in the vicinity of the National Astronomical Observatory, Tokyo. The groundwater pump is activated automatically when the water reservoir becomes near empty, typically 11 to 14 times in the daytime. The depth of the well is ∼90 m, and about 15 m3 of water is pumped up from a 60-m depth for every pumping cycle.
  17. S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).
  18. G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
    [CrossRef]
  19. S. Sato, S. Miyoki, M. Ohashi, M.-K. Fujimoto, T. Yamazaki, M. Fukushima, A. Ueda, K. Ueda, K. Watanabe, K. Nakamura, K. Etoh, N. Kitajima, K. Ito, I. Kataoka, “Loss factors of mirrors for a gravitational wave antenna,” Appl. Opt. 38, 2880–2885 (1999).
    [CrossRef]
  20. H. Benioff, “A linear strain seismograph,” Bull. Seismol. Soc. Am. 25, 283–309 (1935).
  21. V. Vali, R. C. Bostrom, “One thousand meter laser interferometer,” Rev. Sci. Instrum. 39, 1304–1306 (1968).
    [CrossRef]

1999

1998

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

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

1994

1993

A. N. Golubev, “Absolute laser interferometric distance measurement,” Survey Rev. 32, 109–117 (1993).

1985

S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1968

K. M. Baird, “The role of interferometry in long distance measurement,” Metrologia 4, 135–144 (1968).
[CrossRef]

V. Vali, R. C. Bostrom, “One thousand meter laser interferometer,” Rev. Sci. Instrum. 39, 1304–1306 (1968).
[CrossRef]

1966

1952

E. Bergstrand, “Distance measuring by means of modulated light,” Bull. Geod. 24, 243–249 (1952).
[CrossRef]

1935

H. Benioff, “A linear strain seismograph,” Bull. Seismol. Soc. Am. 25, 283–309 (1935).

Baird, K. M.

K. M. Baird, “The role of interferometry in long distance measurement,” Metrologia 4, 135–144 (1968).
[CrossRef]

Barwood, G. P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Benioff, H.

H. Benioff, “A linear strain seismograph,” Bull. Seismol. Soc. Am. 25, 283–309 (1935).

Bergstrand, E.

E. Bergstrand, “Distance measuring by means of modulated light,” Bull. Geod. 24, 243–249 (1952).
[CrossRef]

Bostrom, R. C.

V. Vali, R. C. Bostrom, “One thousand meter laser interferometer,” Rev. Sci. Instrum. 39, 1304–1306 (1968).
[CrossRef]

Doi, H.

S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Etoh, K.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Fujima, I.

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

Fujimoto, M.-K.

Fukushima, M.

Gill, P.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Golubev, A. N.

A. N. Golubev, “Absolute laser interferometric distance measurement,” Survey Rev. 32, 109–117 (1993).

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hirahara, K.

S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ito, K.

Iwasaki, S.

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

Kataoka, I.

Kawabe, K.

K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.

Kitajima, N.

Kogelnik, H.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kuroda, K.

R. Takahashi, F. Kuwahara, K. Kuroda, “Vibration isolation stack for TAMA300,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 95–102.

Kuwahara, F.

R. Takahashi, F. Kuwahara, K. Kuroda, “Vibration isolation stack for TAMA300,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 95–102.

Li, T.

Meers, B. J.

Miyoki, S.

Morrison, E.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Nakamura, K.

Ohashi, M.

Quinn, T. J.

T. J. Quinn, “Mise en pratique of the definition of the metre (1992),” Metrologia 30, 523–541 (1994).
[CrossRef]

Robertson, D. I.

Rowley, W. R. C.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Sasaki, A.

K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.

Sato, S.

Seta, K.

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

Takahashi, R.

R. Takahashi, F. Kuwahara, K. Kuroda, “Vibration isolation stack for TAMA300,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 95–102.

Takemoto, S.

S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).

Telada, S.

S. Telada, “Development of a mode cleaner for a laser interferometer gravitational wave detector,” Ph.D. dissertation (Graduate University for Advanced Studies, Tokyo, 1997), pp. 32–38.

Tochikubo, K.

K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.

Tsubono, K.

K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.

K. Tsubonothe TAMA collaboration, “TAMA project,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 183–191.

Ueda, A.

Ueda, K.

Vali, V.

V. Vali, R. C. Bostrom, “One thousand meter laser interferometer,” Rev. Sci. Instrum. 39, 1304–1306 (1968).
[CrossRef]

Ward, H.

E. Morrison, B. J. Meers, D. I. Robertson, H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Watanabe, K.

Yamazaki, T.

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Bull. Geod.

E. Bergstrand, “Distance measuring by means of modulated light,” Bull. Geod. 24, 243–249 (1952).
[CrossRef]

Bull. Seismol. Soc. Am.

H. Benioff, “A linear strain seismograph,” Bull. Seismol. Soc. Am. 25, 283–309 (1935).

J. Geod. Soc. Jpn.

S. Takemoto, H. Doi, K. Hirahara, “Observation of ground-strains using a laser extensometer system installed in shallow trenches,” J. Geod. Soc. Jpn. 31, 295–304 (1985).

Meas. Sci. Tech.

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

Meas. Sci. Technol.

G. P. Barwood, P. Gill, W. R. C. Rowley, “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes,” Meas. Sci. Technol. 9, 1036–1041 (1998).
[CrossRef]

Metrologia

K. M. Baird, “The role of interferometry in long distance measurement,” Metrologia 4, 135–144 (1968).
[CrossRef]

T. J. Quinn, “Mise en pratique of the definition of the metre (1992),” Metrologia 30, 523–541 (1994).
[CrossRef]

Rev. Sci. Instrum.

V. Vali, R. C. Bostrom, “One thousand meter laser interferometer,” Rev. Sci. Instrum. 39, 1304–1306 (1968).
[CrossRef]

Survey Rev.

A. N. Golubev, “Absolute laser interferometric distance measurement,” Survey Rev. 32, 109–117 (1993).

Other

In this paper we assume that the whole optical path is in vacuum to realize the most accurate measurement without correcting for the effects of the refractive index of the ambient air.

S. Telada, “Development of a mode cleaner for a laser interferometer gravitational wave detector,” Ph.D. dissertation (Graduate University for Advanced Studies, Tokyo, 1997), pp. 32–38.

K. Tsubonothe TAMA collaboration, “TAMA project,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 183–191.

The name of the project is derived from the region where the detector is located.

The mirrors are 100 mm in diameter and 60 mm long. The input mirror is flat, and the end mirror is concave with a radius of curvature of 450 m.

R. Takahashi, F. Kuwahara, K. Kuroda, “Vibration isolation stack for TAMA300,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 95–102.

K. Tochikubo, A. Sasaki, K. Kawabe, K. Tsubono, “Automatic alignment control for the TAMA interferometer,” in Gravitational Wave Detection: Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1997), pp. 365–367.

Groundwater is utilized by a hospital located in the vicinity of the National Astronomical Observatory, Tokyo. The groundwater pump is activated automatically when the water reservoir becomes near empty, typically 11 to 14 times in the daytime. The depth of the well is ∼90 m, and about 15 m3 of water is pumped up from a 60-m depth for every pumping cycle.

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Figures (5)

Fig. 1
Fig. 1

Calculated sideband-locking signal as a function of modulation frequencies near a resonance. Typical parameters for a 300-m Fabry–Perot cavity are assumed: r 1 2 = r 2 2 = 0.9937 (resulting in a finesse ℱ = 5.0 × 102 and a FWHM of resonance of 1.0 kHz) and Δν n = 10 Hz. The demodulation signal in quadrature phase, which is antisymmetric about Δν m , is plotted.

Fig. 2
Fig. 2

Experimental setup for absolute-length measurements. The output of the laser is introduced into the 300-m cavity through electro-optic modulators (EOM’s). Phase modulation at 15.25 MHz (ν c ) is used for carrier locking of the laser frequency and alignment control of the cavity. Phase modulation at ∼12 MHz (ν m ) together with frequency modulation at 350 Hz (ν n ) is used for sideband locking by a VCXO. The oscillation frequency of the VCXO (=ν m ) is monitored by a frequency counter, which is synchronized with a global-positioning-system– (GPS–) locked time base to facilitate accurate observation of the FSR.

Fig. 3
Fig. 3

Data observed in the period from 22:00 h (JST) on 18 March to 12:00 h on 23 March 1998. (a) Modulation frequency of the sideband (left axis) and corresponding absolute length of the cavity (right axis). (b) Feedback signal to the laser frequency (left axis) and corresponding cavity length change (right axis); the data can be affected both by changes in cavity length and by drift of laser frequency. (c) Temperatures on an optical table near the laser and of the input chamber and the end chamber. Apparently the laser frequency is affected by ambient temperature.

Fig. 4
Fig. 4

(a) Magnified view of spiky changes in Fig. 3(a). (b) Synchronous observation of absolute length (length) and pumping status (pump). The rise of a spiky change (i.e., shrinkage in the cavity length) exactly agrees with the pumping of groundwater.

Fig. 5
Fig. 5

Locations of the 300-m Fabry–Perot cavity and the pumping well. The distance from the center of the cavity to the well is ∼200 m.

Tables (3)

Tables Icon

Table 1 Summary of Modulations Used in the System

Tables Icon

Table 2 Parameters of the 300-m Fabry–Perot Cavity

Tables Icon

Table 3 Accuracy Estimation for Long-Baseline Absolute-Length Measurementsa

Equations (27)

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

L=c2νmϕ2π+N,
δL=c2νmδϕ2π=λm2 α,
νn=c2Ln+1πcos-11-L/R11-L/R21/2
νFSR=νn+1-νn=c/2L,
=πr1r21-r1r2,
Ar=r1-t12r2 exp-2iωL/c1-r1r2 exp-2iωL/c A0 expiωtΦFPA0 expiωt,
ΦFPr21-r121-r1r222Lc2πδν,
δνm/νm=δL/L.
δL1-r1r22r21-r12c2νmδϕ2π,
r21-r121-r1r22π  =1-r121-r1r2.
A0 expiωt+Δϕ sin ωmt=A0k=- JkΔϕexpiω+kωmtA0(J0Δϕexpiωt+J1Δϕexpiω+ωmt-expiω-ωmt),
16A02J0ΔϕJ1Δϕ×r1r2t121-r22r12+t121-r1r24Lc2ΔωΔωm8A02Δϕ t12t221-r1r22 2ΔνΔνmνFSR2.
Δν=Δνn sin ωnt  Δνn  νFSR/.
L=24c/2νm.
δν/ν=δL/L,
δLλm2π α,
L=c/2νm1-νm2,
N=νm1/νm1-νm2.
δνfreqβνm1;
δνlockc2Lπ α.
Nνm1νm1-νm2±νm1νm1-νm22maxδνfreq, δνlock.
νm1minγβ, γπαc2L
δLc2νm1π α.
νm1γπαc2L.
δLπ222α2γ L.
νm1γβc2L.
δLβL.

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