Abstract

In the known three-wavelength distance-measuring systems two optical wavelengths are used and a microwave is added for air-humidity influence consideration. In our research, which proceeds from results obtained at the National Research Laboratory of Metrology (Japan), the possibility of constructing a three-optical-wavelength ranging system is discussed. We investigate different versions by using a CO2 laser as the source of the third wavelength. Analysis shows that the three-wavelength system with two lasers (YAG:Nd 3+ laser, which yields first- and second-harmonic radiation, and a CO2 laser) seems to be optimum. A possible schematic structure of the three-wavelength YAG–CO2 laser system is given.

© 1994 Optical Society of America

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References

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  1. M. T. Prilepin, A. N. Golubev, “Instrumental methods of geodetic refractometry,” in Achievements of Science and Engineering, Vol. 15 of the Geodesy and Aerial Surveying series (VINITI, Moscow, 1979), p. 91.
  2. J. C. Owens, “Lasers in metrology and geodesy,” in Laser Applications (Academic, New York, 1971), Vol. 1, Chap. 2.
  3. K. B. Earnshaw, E. N. Hernandez, “Two-laser optical distance-measuring instrument that corrects for the atmospheric index of refraction,” Appl. Opt. 11, 749–754 (1972).
    [CrossRef] [PubMed]
  4. R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).
  5. G. Shipley, R. H. Bradsell, “Georan I, a compact two-colour EDM instrument,” Surv. Rev. XXIII(179), 210–233 (1976).
    [CrossRef]
  6. N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.
  7. G. D. Thayer, “Atmospheric effects on multiple-frequency range measurements,” ESSA Tech. Rep. IER 56-ITSA 53 (U.S. GPO, Washington, D.C., 1967).
  8. M. C. Thompson, “Space averages of air and water vapor densities by dispersion for refractive correction of electromagnetic range measurements,” J. Geophys. Res. 73, 3097–3102 (1968).
    [CrossRef]
  9. V. N. Bondarenko, “On determining a refractive index of air by dispersion method with using radio waves,” Geod. Cartogr. 5, 52–59 (1972).
  10. G. R. Huggett, L. E. Slater, “Precision electromagnetic distance-measuring instrument for determining secular strain and fault movement,” Tectonophysics 29, 1–4 (1975).
    [CrossRef]
  11. L. E. Slater, G. R. Huggett, “A multiwavelength distance-measuring instrument for geophysical experiments,” J. Geophys. Res. 81, 6299–6306 (1976).
    [CrossRef]
  12. A. N. Golubev, “On the theory of determining refractive index of air by dispersion method,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 6, 25–31 (1969).
  13. H. Matsumoto, “The refractivities of water vapor for CO2 laser lines,” Opt. Commun. 50, 356–358 (1984).
    [CrossRef]
  14. H. Matsumoto, “The refractive index of moist air in the 3-pLm region,” Metrologia 18, 49–52 (1982).
    [CrossRef]
  15. R. Turner, E. K. Pfitzer, “Practical application of the CO2 laser to long distance measurement by interferometry,” Metrologia 6, 94–97 (1970).
    [CrossRef]
  16. B. Edlen, “The refractive index of air,” Metrologia 2, 71–80 (1966).
    [CrossRef]
  17. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).
    [CrossRef] [PubMed]
  18. A. N. Golubev, “The optical range-measuring system with a correction for the refractive index of air,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 5, 129–132 (1972).

1984 (1)

H. Matsumoto, “The refractivities of water vapor for CO2 laser lines,” Opt. Commun. 50, 356–358 (1984).
[CrossRef]

1982 (1)

H. Matsumoto, “The refractive index of moist air in the 3-pLm region,” Metrologia 18, 49–52 (1982).
[CrossRef]

1976 (2)

G. Shipley, R. H. Bradsell, “Georan I, a compact two-colour EDM instrument,” Surv. Rev. XXIII(179), 210–233 (1976).
[CrossRef]

L. E. Slater, G. R. Huggett, “A multiwavelength distance-measuring instrument for geophysical experiments,” J. Geophys. Res. 81, 6299–6306 (1976).
[CrossRef]

1975 (1)

G. R. Huggett, L. E. Slater, “Precision electromagnetic distance-measuring instrument for determining secular strain and fault movement,” Tectonophysics 29, 1–4 (1975).
[CrossRef]

1972 (3)

V. N. Bondarenko, “On determining a refractive index of air by dispersion method with using radio waves,” Geod. Cartogr. 5, 52–59 (1972).

K. B. Earnshaw, E. N. Hernandez, “Two-laser optical distance-measuring instrument that corrects for the atmospheric index of refraction,” Appl. Opt. 11, 749–754 (1972).
[CrossRef] [PubMed]

A. N. Golubev, “The optical range-measuring system with a correction for the refractive index of air,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 5, 129–132 (1972).

1970 (1)

R. Turner, E. K. Pfitzer, “Practical application of the CO2 laser to long distance measurement by interferometry,” Metrologia 6, 94–97 (1970).
[CrossRef]

1969 (1)

A. N. Golubev, “On the theory of determining refractive index of air by dispersion method,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 6, 25–31 (1969).

1968 (1)

M. C. Thompson, “Space averages of air and water vapor densities by dispersion for refractive correction of electromagnetic range measurements,” J. Geophys. Res. 73, 3097–3102 (1968).
[CrossRef]

1967 (2)

R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).

J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).
[CrossRef] [PubMed]

1966 (1)

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

Armand, N. A.

N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.

Bondarenko, V. N.

V. N. Bondarenko, “On determining a refractive index of air by dispersion method with using radio waves,” Geod. Cartogr. 5, 52–59 (1972).

Bradsell, R. H.

G. Shipley, R. H. Bradsell, “Georan I, a compact two-colour EDM instrument,” Surv. Rev. XXIII(179), 210–233 (1976).
[CrossRef]

Castellano, V.

R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).

Cohn, E. L.

R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).

Earnshaw, K. B.

Edlen, B.

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

Fowler, R. A.

R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).

Golubev, A. N.

A. N. Golubev, “The optical range-measuring system with a correction for the refractive index of air,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 5, 129–132 (1972).

A. N. Golubev, “On the theory of determining refractive index of air by dispersion method,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 6, 25–31 (1969).

M. T. Prilepin, A. N. Golubev, “Instrumental methods of geodetic refractometry,” in Achievements of Science and Engineering, Vol. 15 of the Geodesy and Aerial Surveying series (VINITI, Moscow, 1979), p. 91.

Hernandez, E. N.

Huggett, G. R.

L. E. Slater, G. R. Huggett, “A multiwavelength distance-measuring instrument for geophysical experiments,” J. Geophys. Res. 81, 6299–6306 (1976).
[CrossRef]

G. R. Huggett, L. E. Slater, “Precision electromagnetic distance-measuring instrument for determining secular strain and fault movement,” Tectonophysics 29, 1–4 (1975).
[CrossRef]

Lomakin, A. N.

N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.

Matsumoto, H.

H. Matsumoto, “The refractivities of water vapor for CO2 laser lines,” Opt. Commun. 50, 356–358 (1984).
[CrossRef]

H. Matsumoto, “The refractive index of moist air in the 3-pLm region,” Metrologia 18, 49–52 (1982).
[CrossRef]

Owens, J. C.

J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).
[CrossRef] [PubMed]

J. C. Owens, “Lasers in metrology and geodesy,” in Laser Applications (Academic, New York, 1971), Vol. 1, Chap. 2.

Pfitzer, E. K.

R. Turner, E. K. Pfitzer, “Practical application of the CO2 laser to long distance measurement by interferometry,” Metrologia 6, 94–97 (1970).
[CrossRef]

Prilepin, M. T.

M. T. Prilepin, A. N. Golubev, “Instrumental methods of geodetic refractometry,” in Achievements of Science and Engineering, Vol. 15 of the Geodesy and Aerial Surveying series (VINITI, Moscow, 1979), p. 91.

N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.

Shipley, G.

G. Shipley, R. H. Bradsell, “Georan I, a compact two-colour EDM instrument,” Surv. Rev. XXIII(179), 210–233 (1976).
[CrossRef]

Slater, L. E.

L. E. Slater, G. R. Huggett, “A multiwavelength distance-measuring instrument for geophysical experiments,” J. Geophys. Res. 81, 6299–6306 (1976).
[CrossRef]

G. R. Huggett, L. E. Slater, “Precision electromagnetic distance-measuring instrument for determining secular strain and fault movement,” Tectonophysics 29, 1–4 (1975).
[CrossRef]

Tarakanov, S. V.

N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.

Thayer, G. D.

G. D. Thayer, “Atmospheric effects on multiple-frequency range measurements,” ESSA Tech. Rep. IER 56-ITSA 53 (U.S. GPO, Washington, D.C., 1967).

Thompson, M. C.

M. C. Thompson, “Space averages of air and water vapor densities by dispersion for refractive correction of electromagnetic range measurements,” J. Geophys. Res. 73, 3097–3102 (1968).
[CrossRef]

Turner, R.

R. Turner, E. K. Pfitzer, “Practical application of the CO2 laser to long distance measurement by interferometry,” Metrologia 6, 94–97 (1970).
[CrossRef]

Appl. Opt. (2)

Geod. Cartogr. (1)

V. N. Bondarenko, “On determining a refractive index of air by dispersion method with using radio waves,” Geod. Cartogr. 5, 52–59 (1972).

Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka (2)

A. N. Golubev, “The optical range-measuring system with a correction for the refractive index of air,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 5, 129–132 (1972).

A. N. Golubev, “On the theory of determining refractive index of air by dispersion method,” Izv. Vyssh. Uchebn. Zaved. Geod. Aerofotos’emka 6, 25–31 (1969).

J. Astronaut. Sci. (1)

R. A. Fowler, V. Castellano, E. L. Cohn, “A planetary geodetic laser survey system,” J. Astronaut. Sci. 14(5), 225–229 (1967).

J. Geophys. Res. (2)

M. C. Thompson, “Space averages of air and water vapor densities by dispersion for refractive correction of electromagnetic range measurements,” J. Geophys. Res. 73, 3097–3102 (1968).
[CrossRef]

L. E. Slater, G. R. Huggett, “A multiwavelength distance-measuring instrument for geophysical experiments,” J. Geophys. Res. 81, 6299–6306 (1976).
[CrossRef]

Metrologia (3)

H. Matsumoto, “The refractive index of moist air in the 3-pLm region,” Metrologia 18, 49–52 (1982).
[CrossRef]

R. Turner, E. K. Pfitzer, “Practical application of the CO2 laser to long distance measurement by interferometry,” Metrologia 6, 94–97 (1970).
[CrossRef]

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

Opt. Commun. (1)

H. Matsumoto, “The refractivities of water vapor for CO2 laser lines,” Opt. Commun. 50, 356–358 (1984).
[CrossRef]

Surv. Rev. (1)

G. Shipley, R. H. Bradsell, “Georan I, a compact two-colour EDM instrument,” Surv. Rev. XXIII(179), 210–233 (1976).
[CrossRef]

Tectonophysics (1)

G. R. Huggett, L. E. Slater, “Precision electromagnetic distance-measuring instrument for determining secular strain and fault movement,” Tectonophysics 29, 1–4 (1975).
[CrossRef]

Other (4)

M. T. Prilepin, A. N. Golubev, “Instrumental methods of geodetic refractometry,” in Achievements of Science and Engineering, Vol. 15 of the Geodesy and Aerial Surveying series (VINITI, Moscow, 1979), p. 91.

J. C. Owens, “Lasers in metrology and geodesy,” in Laser Applications (Academic, New York, 1971), Vol. 1, Chap. 2.

N. A. Armand, A. N. Lomakin, M. T. Prilepin, S. V. Tarakanov, “Two-wavelength laser rangefinder for high-accuracy measurements,” presented at the Seventh International Symposium on Recent Crustal Movements, Tallinn, Estonia, 1986.

G. D. Thayer, “Atmospheric effects on multiple-frequency range measurements,” ESSA Tech. Rep. IER 56-ITSA 53 (U.S. GPO, Washington, D.C., 1967).

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Figures (1)

Fig. 1
Fig. 1

Block diagram of the three-color YAG–CO2 laser instrument: SHG, second-harmonic generator; PBS’s, polarizing beam splitters; EOM’s, electro-optical modulators; AFC’s, automatic frequency controls; SW, switch; VCO’s, voltage-controlled oscillators; RO, reference oscillator; FC’s, frequency counters; LPF’s, low-pass filters; Div, frequency divider.

Tables (1)

Tables Icon

Table 1 Correction Coefficients for a Three-Color System with a CO2 Laser (Magnitudes)

Equations (28)

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D = R 1 - A d ( R 1 - R 2 ) + δ ,
n i - 1 = ( T 0 / P 0 ) ( n 0 i - 1 ) ( P d / T ) + ( T 0 / e 0 ) × ( μ 0 i - 1 ) ( e / T ) ,
n 1 - 1 = ( T 0 / P 0 ) ( n 01 - 1 ) P d / T + ( T 0 / e 0 ) ( μ 01 - 1 ) e / T , n 2 - 1 = ( T / P 0 ) ( n 02 - 1 ) P d / T + ( T / e 0 ) ( μ 02 - 1 ) e / T , n 3 - 1 = ( T 0 / P 0 ) ( n 03 - 1 ) P d / T + ( T 0 / e 0 ) ( μ 03 - 1 ) e / T ,
n 1 - 1 = A Δ R 12 + B Δ R 1 D ,
D = R 1 - A ( R 1 - R 2 ) - B ( R 1 - R 3 ) ,
A = ( n 01 - 1 ) Δ μ 0 ( 13 ) - ( μ 01 - 1 ) Δ n 0 ( 13 ) Δ n 0 ( 12 ) Δ μ 0 ( 13 ) - Δ n 0 ( 13 ) Δ μ 0 ( 12 ) ,
B = ( μ 01 - 1 ) Δ n 0 ( 12 ) - ( n 01 - 1 ) Δ μ 0 ( 12 ) Δ n 0 ( 12 ) Δ μ 0 ( 13 ) - Δ n 0 ( 13 ) Δ μ 0 ( 12 )
n i - 1 = α i ρ d + β i ρ w             ( i = 1 , 2 , 3 ) ,
D = R 1 - A ( R 1 - R 2 ) - B ( R 1 - R 3 ) ,
A = α 1 β 3 - α 3 β 1 ( α 2 - α 1 ) ( β 3 - β 1 ) - ( α 3 - α 1 ) ( β 2 - β 1 ) ,
B = α 2 β 1 - α 1 β 2 ( α 2 - α 1 ) ( β 3 - β 1 ) - ( α 3 - α 1 ) ( β 2 - β 1 ) .
D = R 1 - A ( R 1 - R 2 ) + B ( R 1 - R 3 ) .
( n 0 - 1 ) 10 6 = 267.963 + 3 × 1.5033 / λ 2 + 5 × 0.01344 / λ 4 .
( μ 0 - 1 ) 10 6 = 2.95235 + 3 × 0.026422 / λ 2 + 5 × 0.0003238 / λ 4 + 7 × 0.00004028 / λ 6 .
R i = D n i = c N / 2 ( f 0 + δ f i ) ,
D = c N 2 ( A f 0 + δ f 2 - A f 0 + δ f 1 - B f 0 + δ f 3 ) ,
D = c N / 2 f corr ,
f corr = ( A f 0 + δ f 2 - A f 0 + δ f 1 - B f 0 + δ f 3 ) - 1
D max = c / 4 f 0 Δ n max ,
R 1 = c N 1 / 2 ( f 0 + δ f 1 ) , R 2 = c ( N 1 + a ) / 2 ( f 0 + δ f 2 ) , R 3 = c ( N 1 - b ) / 2 ( f 0 + δ f 3 ) ,
D = c 2 ( N 1 f corr + a A f 0 + δ f 2 + b B f 0 + δ f 3 ) .
R 3 = c N k / 2 ( f 0 / k + δ f k ) = c k N k / 2 ( f 0 + k δ f k ) ,
D = c 2 N 1 ( A f 0 + δ f 2 - A f 0 + δ f 1 ) + a A f 0 + δ f 2 - k N k B f 0 + k δ f k .
D = c 2 N 1 ( A f 0 + δ f 2 - A f 0 + δ f 1 ) + a A f 0 + δ f 2 - ( N 1 - b ) B f 0 + δ f 3 .
k N k f 0 + k δ f k = N 1 - b f 0 + δ f 3 ,
N 1 = N k k n 1 n 3 f 0 + δ f 1 f 0 + k δ f k .
m D = c m δ f 2 f 2 N 1 ( 2 A 2 + A 2 ) 1 / 2
m δ f = m D D f A [ ( A / A ) 2 + 2 ] - 1 / 2 .

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