Abstract

We discuss the measurements of the changes in air refractive indices and geometrical distances by means of a two-color phase-modulated fringe-counting interferometer. We analytically classified the optical path lengths for IR and visible light into the changes in the air refractive index and the distance by using a dispersion formula for air. The interferometer was tested over a 235-m path in the testing tunnel of the National Research Laboratory of Metrology, which has a sensor system for measuring air conditions.

The refractive-index change by the two-color interferometer agreed with the value calculated by the air conditions within an accuracy of 0.15 ppm.

© 1992 Optical Society of America

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References

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  1. K. M. Baird, “The role of interferometry in long distance measurement,” Metrologia 4, 135–144 (1968).
    [Crossref]
  2. D. C. Angnew, “Strainmeters and tiltmeters,” Rev. Geophys. 24, 579–624 (1986).
    [Crossref]
  3. P. L. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
    [Crossref]
  4. A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced error,” Jpn. J. Appl. Phys. 28, L473–L475 (1989).
    [Crossref]
  5. Y. Zhu, H. Matsumoto, T. O’ishi, “Long-arm two-color interferometer for measuring the change of air refractive index,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 538–539 (1990).
  6. B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
    [Crossref]
  7. C. B. Hogge, R. R. Butts, “Effects of using different wavelengths in wavefront sensing and correction,” J. Opt. Soc. Am. 72, 606–609 (1982).
    [Crossref]
  8. R. Mujilwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
    [Crossref]
  9. Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).
  10. Y. Zhu, H. Matsumoto, T. O’ishi, “Arm-length measurement of an interferometer using the optical-frequency-scanning technique,” Appl. Opt. 30, 3561–3562 (1991).
    [Crossref] [PubMed]

1991 (1)

1990 (1)

Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).

1989 (1)

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced error,” Jpn. J. Appl. Phys. 28, L473–L475 (1989).
[Crossref]

1988 (1)

R. Mujilwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[Crossref]

1986 (1)

D. C. Angnew, “Strainmeters and tiltmeters,” Rev. Geophys. 24, 579–624 (1986).
[Crossref]

1982 (1)

1968 (1)

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

1967 (1)

P. L. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[Crossref]

1966 (1)

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[Crossref]

Angnew, D. C.

D. C. Angnew, “Strainmeters and tiltmeters,” Rev. Geophys. 24, 579–624 (1986).
[Crossref]

Baird, K. M.

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

Bender, P. L.

P. L. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[Crossref]

Butts, R. R.

Dake, Y.

Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[Crossref]

Hogge, C. B.

Ishida, A.

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced error,” Jpn. J. Appl. Phys. 28, L473–L475 (1989).
[Crossref]

Matsumoto, H.

Y. Zhu, H. Matsumoto, T. O’ishi, “Arm-length measurement of an interferometer using the optical-frequency-scanning technique,” Appl. Opt. 30, 3561–3562 (1991).
[Crossref] [PubMed]

Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).

Y. Zhu, H. Matsumoto, T. O’ishi, “Long-arm two-color interferometer for measuring the change of air refractive index,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 538–539 (1990).

Mujilwijk, R.

R. Mujilwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[Crossref]

O’ishi, T.

Y. Zhu, H. Matsumoto, T. O’ishi, “Arm-length measurement of an interferometer using the optical-frequency-scanning technique,” Appl. Opt. 30, 3561–3562 (1991).
[Crossref] [PubMed]

Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).

Y. Zhu, H. Matsumoto, T. O’ishi, “Long-arm two-color interferometer for measuring the change of air refractive index,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 538–539 (1990).

Zhu, Y.

Y. Zhu, H. Matsumoto, T. O’ishi, “Arm-length measurement of an interferometer using the optical-frequency-scanning technique,” Appl. Opt. 30, 3561–3562 (1991).
[Crossref] [PubMed]

Y. Zhu, H. Matsumoto, T. O’ishi, “Long-arm two-color interferometer for measuring the change of air refractive index,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 538–539 (1990).

Appl. Opt. (1)

Bull. Natl. Res. Lab. Metrol. Tokyo (1)

Y. Dake, H. Matsumoto, T. O’ishi, “Measurement of phase and intensity fluctuations of a laser beam in turbulence for long-path interferometer,” Bull. Natl. Res. Lab. Metrol. Tokyo 39, 436–442 (1990).

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

A. Ishida, “Two-wavelength displacement-measuring interferometer using second-harmonic light to eliminate air-turbulence-induced error,” Jpn. J. Appl. Phys. 28, L473–L475 (1989).
[Crossref]

Metrologia (3)

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

R. Mujilwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[Crossref]

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
[Crossref]

Proc. IEEE (1)

P. L. Bender, “Laser measurements of long distances,” Proc. IEEE 55, 1039–1045 (1967).
[Crossref]

Rev. Geophys. (1)

D. C. Angnew, “Strainmeters and tiltmeters,” Rev. Geophys. 24, 579–624 (1986).
[Crossref]

Other (1)

Y. Zhu, H. Matsumoto, T. O’ishi, “Long-arm two-color interferometer for measuring the change of air refractive index,” in Optics in Complex Systems, F. Lanz, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 538–539 (1990).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of a laser stabilization system for the wavelength ratio of the He–Ne/YAG lasers.

Fig. 2
Fig. 2

Schematic diagram of a two-color long-arm interferometer by using two interference-fringe signals in phase quadrature.

Fig. 3
Fig. 3

Intensity fluctuation of a He–Ne laser beam in the tunnel by using a plane mirror and a corner cube as a reflector.

Fig. 4
Fig. 4

Block diagram showing the processing of the interference-fringe signals.

Fig. 5
Fig. 5

Experimental results at a distance of several meters: (a) for the He–Ne laser, (b) for the YAG laser, and (c) for 17 times the difference between the results in (a) and (b).

Fig. 6
Fig. 6

Experimental results at a distance of 235 m: (a) for the He–Ne laser, (b) for the YAG laser, and (c) for the A value multiplication of the difference between the results in (a) and (b).

Fig. 7
Fig. 7

Comparison of the air refractive indices obtained by (a) the two-color interferometric method and (b) the Edlén formula method.

Equations (8)

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D i = Δ n i L + Δ L             ( i = 1 or 2 ) ,
Δ L = D 1 - A ( D 1 - D 2 ) , A ( n 1 - 1 ) / ( n 1 - n 2 ) ( n 10 - 1 ) / ( n 10 - n 20 ) .
Δ n 1 = A ( D 1 - D 2 ) / L .
δ θ 2 ( σ 1 2 - σ 2 2 ) ,
( n 1 - 1 ) α + β σ 1 2 ,
A = ( α + β σ 1 2 ) / β ( σ 1 2 - σ 2 2 ) .
δ D = A δ θ α + β σ 1 2 β ( σ 1 2 - σ 2 2 ) 1 / 2 α β λ 1 .
δ ( Δ n 1 ) = A ( δ D 1 - δ D 2 ) / L = A ( δ λ 1 / λ 1 - δ λ 2 / λ 2 ) .

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