Abstract

A lidar with high spectral resolution can be used to measure atmospheric temperature profiles according to conservative performance calculations. The technique analyzed relies on determining the temperature-dependent Rayleigh-scattering linewidth with two stabilized Michelson interferometers in parallel. From ratios of four integrated flux values from two photomultipliers, one can determine temperature profiles within a 1 K standard deviation to 5 km with 50-m height resolution in 1¼ min using a laser of 1-W average power and a telescope of 30-cm diam.

© 1981 Optical Society of America

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References

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  1. G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).
  2. G. Benedetti-Michelangeli, G. Fiocco, in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed. (Elsevier, Amsterdam, 1974), pp. 211–219.
  3. L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.
  4. L. A. Johnson, “Coherent Lidar as a Tool for Remote Temperature Sensing in the Troposphere,” NOAA Tech. Memo. ERL-WPL-41 (1979).
  5. I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 81–100.
    [Crossref]
  6. R. D. Mountain, Rev. Mod. Phys. 38, 205 (1966).
    [Crossref]
  7. A. Sugawara, S. Yip, Phys. Fluids 10, 1911 (1967).
    [Crossref]
  8. G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).
  9. C. M. Hammond, T. A. Wiggins, J. Chem. Phys. 65, 2788 (1976).
    [Crossref]
  10. S. Yip, M. Nelkin, Phys. Rev. 135, A1241 (1964).
    [Crossref]
  11. S. Yip, J. Acoust. Soc. Am. 49, 941 (1971).
    [Crossref]
  12. T. J. Greytak, G. B. Benedek, Phys. Rev. Lett. 17, 179 (1966).
    [Crossref]
  13. R. P. Sandoval, R. L. Armstrong, Phys. Rev. A. 13, 752 (1976).
    [Crossref]
  14. See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.
  15. S. Chapman, T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge U.P., London, 1970), pp. 45, 82.
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), pp. 300–323.
  17. A. Skov Jensen, Optimum Strategies of Parameter Estimation for a Poisson-Distributed Signal, Risϕ-M-1959 (Risϕ National Laboratory, DK-4000 Roskilde, Denmark, 1977), pp. 7–8.
  18. R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957).
    [Crossref]
  19. R. R. Rudder, D. R. Bach, J. Opt. Soc. Am. 58, 1260 (1968).
    [Crossref]
  20. Committee on Extension to the Standard Atmosphere, U.S. Standard Atmosphere, 1962 (Supt. Documents, U.S. GPO, Washington, D.C., 1962), p. 67.
  21. J. V. Hughes, Appl. Opt. 3, 1135 (1964).
    [Crossref]
  22. K. Ya Kondratev, Ed., Radiation Characteristics of the Atmosphere and the Earth's Surface, NASA TT 71-58003 (U.S. GPO, Washington, D.C., 1973), pp. 334–335.
  23. W. L. Wolfe, G. J. Zissis, Eds., Infrared Handbook (Office of Naval Research, Washington, D.C.,1978), pp. 4-30–4-36.
  24. R. L. Schwiesow, R. F. Calfee, Appl. Opt. 18, 3911 (1979).
    [Crossref] [PubMed]
  25. L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66-828 (1966).
  26. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).
  27. C. M. Penney, R. L. St Peters, M. Lapp, J. Opt. Soc. Am. 64, 712 (1974).
    [Crossref]
  28. A. Cohen, J. A. Cooney, K. N. Geller, Appl. Opt. 15, 2896 (1976).
    [Crossref] [PubMed]
  29. See, for example, I. S. Sokolnikoff, R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1966), pp. 652–660.
  30. L. Lading, A. Skov Jensen, Appl. Opt. 19, 2750 (1980).
    [Crossref] [PubMed]
  31. J. Cooney, J. Appl. Meteorol. 11, 108 (1972).
    [Crossref]
  32. J. A. Cooney, M. Pina, Appl. Opt. 15, 602 (1976).
    [Crossref] [PubMed]
  33. R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
    [Crossref]
  34. J. B. Mason, Appl. Opt. 14, 76 (1975).
    [PubMed]

1980 (1)

1979 (2)

R. L. Schwiesow, R. F. Calfee, Appl. Opt. 18, 3911 (1979).
[Crossref] [PubMed]

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

1976 (4)

A. Cohen, J. A. Cooney, K. N. Geller, Appl. Opt. 15, 2896 (1976).
[Crossref] [PubMed]

J. A. Cooney, M. Pina, Appl. Opt. 15, 602 (1976).
[Crossref] [PubMed]

R. P. Sandoval, R. L. Armstrong, Phys. Rev. A. 13, 752 (1976).
[Crossref]

C. M. Hammond, T. A. Wiggins, J. Chem. Phys. 65, 2788 (1976).
[Crossref]

1975 (1)

1974 (2)

G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).

C. M. Penney, R. L. St Peters, M. Lapp, J. Opt. Soc. Am. 64, 712 (1974).
[Crossref]

1972 (1)

J. Cooney, J. Appl. Meteorol. 11, 108 (1972).
[Crossref]

1971 (2)

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

S. Yip, J. Acoust. Soc. Am. 49, 941 (1971).
[Crossref]

1968 (1)

1967 (1)

A. Sugawara, S. Yip, Phys. Fluids 10, 1911 (1967).
[Crossref]

1966 (2)

R. D. Mountain, Rev. Mod. Phys. 38, 205 (1966).
[Crossref]

T. J. Greytak, G. B. Benedek, Phys. Rev. Lett. 17, 179 (1966).
[Crossref]

1964 (2)

S. Yip, M. Nelkin, Phys. Rev. 135, A1241 (1964).
[Crossref]

J. V. Hughes, Appl. Opt. 3, 1135 (1964).
[Crossref]

1957 (1)

Armstrong, R. L.

R. P. Sandoval, R. L. Armstrong, Phys. Rev. A. 13, 752 (1976).
[Crossref]

Bach, D. R.

Benedek, G. B.

T. J. Greytak, G. B. Benedek, Phys. Rev. Lett. 17, 179 (1966).
[Crossref]

Benedetti-Michelangeli, G.

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

G. Benedetti-Michelangeli, G. Fiocco, in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed. (Elsevier, Amsterdam, 1974), pp. 211–219.

Boley, C. D.

G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), pp. 300–323.

Calfee, R. F.

Chapman, S.

S. Chapman, T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge U.P., London, 1970), pp. 45, 82.

Cohen, A.

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

A. Cohen, J. A. Cooney, K. N. Geller, Appl. Opt. 15, 2896 (1976).
[Crossref] [PubMed]

Cooney, J.

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

J. Cooney, J. Appl. Meteorol. 11, 108 (1972).
[Crossref]

Cooney, J. A.

Cowling, T. G.

S. Chapman, T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge U.P., London, 1970), pp. 45, 82.

Desai, R. C.

G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).

Eggers, D. F.

See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.

Elterman, L.

L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66-828 (1966).

Fabelinskii, I. L.

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 81–100.
[Crossref]

Farina, J.

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

Fiocco, G.

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

G. Benedetti-Michelangeli, G. Fiocco, in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed. (Elsevier, Amsterdam, 1974), pp. 211–219.

Fog, C.

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

Geller, K.

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

Geller, K. N.

Gill, R.

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

Gregory, N. W.

See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.

Greytak, T. J.

T. J. Greytak, G. B. Benedek, Phys. Rev. Lett. 17, 179 (1966).
[Crossref]

Halsey, G. D.

See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.

Hammond, C. M.

C. M. Hammond, T. A. Wiggins, J. Chem. Phys. 65, 2788 (1976).
[Crossref]

Hughes, J. V.

Johnson, L. A.

L. A. Johnson, “Coherent Lidar as a Tool for Remote Temperature Sensing in the Troposphere,” NOAA Tech. Memo. ERL-WPL-41 (1979).

Lading, L.

L. Lading, A. Skov Jensen, Appl. Opt. 19, 2750 (1980).
[Crossref] [PubMed]

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

Lapp, M.

Madonna, E.

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

Maischberger, K.

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

Mason, J. B.

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

Mountain, R. D.

R. D. Mountain, Rev. Mod. Phys. 38, 205 (1966).
[Crossref]

Nelkin, M.

S. Yip, M. Nelkin, Phys. Rev. 135, A1241 (1964).
[Crossref]

Penndorf, R.

Penney, C. M.

Peters, R. L. St

Pina, M.

Rabinovitch, B. S.

See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.

Rasmussen, E.

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

Redheffer, R. M.

See, for example, I. S. Sokolnikoff, R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1966), pp. 652–660.

Rudder, R. R.

Sandoval, R. P.

R. P. Sandoval, R. L. Armstrong, Phys. Rev. A. 13, 752 (1976).
[Crossref]

Schwiesow, R.

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

Schwiesow, R. L.

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

Skov Jensen, A.

L. Lading, A. Skov Jensen, Appl. Opt. 19, 2750 (1980).
[Crossref] [PubMed]

A. Skov Jensen, Optimum Strategies of Parameter Estimation for a Poisson-Distributed Signal, Risϕ-M-1959 (Risϕ National Laboratory, DK-4000 Roskilde, Denmark, 1977), pp. 7–8.

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

Sokolnikoff, I. S.

See, for example, I. S. Sokolnikoff, R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1966), pp. 652–660.

Sugawara, A.

A. Sugawara, S. Yip, Phys. Fluids 10, 1911 (1967).
[Crossref]

Tenti, G.

G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

Wiggins, T. A.

C. M. Hammond, T. A. Wiggins, J. Chem. Phys. 65, 2788 (1976).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), pp. 300–323.

Yip, S.

S. Yip, J. Acoust. Soc. Am. 49, 941 (1971).
[Crossref]

A. Sugawara, S. Yip, Phys. Fluids 10, 1911 (1967).
[Crossref]

S. Yip, M. Nelkin, Phys. Rev. 135, A1241 (1964).
[Crossref]

Appl. Opt. (6)

Can. J. Phys. (1)

G. Tenti, C. D. Boley, R. C. Desai, Can. J. Phys. 52, 285 (1974).

J. Acoust. Soc. Am. (1)

S. Yip, J. Acoust. Soc. Am. 49, 941 (1971).
[Crossref]

J. Appl. Meteorol. (2)

R. Gill, K. Geller, J. Farina, J. Cooney, A. Cohen, J. Appl. Meteorol. 18, 225 (1979).
[Crossref]

J. Cooney, J. Appl. Meteorol. 11, 108 (1972).
[Crossref]

J. Chem. Phys. (1)

C. M. Hammond, T. A. Wiggins, J. Chem. Phys. 65, 2788 (1976).
[Crossref]

J. Opt. Soc. Am. (3)

Nature London Phys. Sci. (1)

G. Fiocco, G. Benedetti-Michelangeli, K. Maischberger, E. Madonna, Nature London Phys. Sci. 229, 78 (1971).

Phys. Fluids (1)

A. Sugawara, S. Yip, Phys. Fluids 10, 1911 (1967).
[Crossref]

Phys. Rev. (1)

S. Yip, M. Nelkin, Phys. Rev. 135, A1241 (1964).
[Crossref]

Phys. Rev. A. (1)

R. P. Sandoval, R. L. Armstrong, Phys. Rev. A. 13, 752 (1976).
[Crossref]

Phys. Rev. Lett. (1)

T. J. Greytak, G. B. Benedek, Phys. Rev. Lett. 17, 179 (1966).
[Crossref]

Rev. Mod. Phys. (1)

R. D. Mountain, Rev. Mod. Phys. 38, 205 (1966).
[Crossref]

Other (14)

G. Benedetti-Michelangeli, G. Fiocco, in Structure and Dynamics of the Upper Atmosphere, F. Verniani, Ed. (Elsevier, Amsterdam, 1974), pp. 211–219.

L. Lading, A. Skov Jensen, R. Schwiesow, C. Fog, E. Rasmussen, in Abstracts Ninth International Laser Radar Conference (AMS, Boston, 1979), p. 244.

L. A. Johnson, “Coherent Lidar as a Tool for Remote Temperature Sensing in the Troposphere,” NOAA Tech. Memo. ERL-WPL-41 (1979).

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968), pp. 81–100.
[Crossref]

Committee on Extension to the Standard Atmosphere, U.S. Standard Atmosphere, 1962 (Supt. Documents, U.S. GPO, Washington, D.C., 1962), p. 67.

See, for example, D. F. Eggers, N. W. Gregory, G. D. Halsey, B. S. Rabinovitch, Physical Chemistry (Wiley, New York, 1964), pp. 138–155.

S. Chapman, T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge U.P., London, 1970), pp. 45, 82.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), pp. 300–323.

A. Skov Jensen, Optimum Strategies of Parameter Estimation for a Poisson-Distributed Signal, Risϕ-M-1959 (Risϕ National Laboratory, DK-4000 Roskilde, Denmark, 1977), pp. 7–8.

See, for example, I. S. Sokolnikoff, R. M. Redheffer, Mathematics of Physics and Modern Engineering (McGraw-Hill, New York, 1966), pp. 652–660.

L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66-828 (1966).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical Properties of the Atmosphere (Revised),” AFCRL-71-0279 (1971).

K. Ya Kondratev, Ed., Radiation Characteristics of the Atmosphere and the Earth's Surface, NASA TT 71-58003 (U.S. GPO, Washington, D.C., 1973), pp. 334–335.

W. L. Wolfe, G. J. Zissis, Eds., Infrared Handbook (Office of Naval Research, Washington, D.C.,1978), pp. 4-30–4-36.

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Figures (2)

Fig. 1
Fig. 1

Envelope of the interferogram for a Gaussian Rayleigh scattering line when an ideal Michelson interferometer is used. Output of the interferometer as a function of optical delay varies between the two limiting lines plotted. Delay is given in terms of the dimensionless variable dM1/2, where d is an optical path difference and M is proportional to temperature. For a fixed delay, an increase in temperature increases the minimum signal or decreases the maximum; i.e., an increase in temperature increases the decay of the interferogram contrast as the delay increases (narrows the interferogram) because the Rayleigh spectrum becomes wider. Incident signal at the input is 2L. Light not transmitted is reflected from an ideal interferometer.

Fig. 2
Fig. 2

Envelope of a composite interferogram for a signal consisting of a, comparatively broadband sky background of intensity 2Z and spectral bandwidth constant Y ≳ 16M, Rayleigh scattering of intensity 2L, and bandwidth constant M (proportional to temperature), and narrowband aerosol scattering of intensity 2B ≃ 2L and bandwidth constant C ≲ 10−4 M. Contribution of the background to interference minima is appproximately the constant value Z for all delays of >0.2, and the contribution of the aerosol signal to the minima is ∼0 for delays of <3. The study evaluates a linewidth measurement technique measuring interferometer output at minima near a delay of dM1/2 ≃ 1 and dM1/2 ≃ 3, first in the absence of Rayleigh and aerosol scattering to determine Z and relative channel sensitivity and second with Rayleigh and aerosol backscatter to determine M (and thereby temperature) with more precision than a ±20 K initial guess.

Tables (2)

Tables Icon

Table I Assumed Lidar System Parameters

Tables Icon

Table II Assumed Atmospheric Parameters

Equations (16)

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

I ( ω ) = N | A | 2 ( c 2 / 4 π ω 0 2 bT ) 1 / 2 exp [ ( ω 0 ω ) 2 c 2 / 4 ω 0 2 bT ] .
I ( d ) = ( ¼ ) N | A | 2 { 2 + exp ( 4 d 2 ω 0 2 b T / c 4 ) × [ exp ( + i 2 d ω 0 / c ) + exp ( i 2 d ω 0 / c ) ] } .
S r ( d , M ) = L [ 1 + ( 1 ) m exp ( d 2 M ) ] .
M = ( 4 ω 0 2 b / c 4 ) T .
S b ( d , Y ) = Z [ 1 + ( 1 ) m exp ( d 2 Y ) ] ,
S a ( d , C ) = B [ 1 + ( 1 ) m exp ( d 2 C ) ] .
S ( d ) = S r + S b + S a .
S 1 = L [ 1 exp ( d 1 2 M ) ] + Z + cor 1 , gS 2 = L [ 1 exp ( d 2 2 M ) ] + Z + cor 2 .
S / M = Ld 2 exp ( d 2 M ) ,
dM 1 / 2 = 1 .
d 1 = 1 / M 1 / 2 , d 2 = 3 / M 1 / 2 .
R = ( S 1 Z ) / ( gS 2 Z ) = [ 1 exp ( d 1 2 M ) ] / [ 1 exp ( d 2 2 M ) ] ,
Δ R 1.02 L 1 / 2 .
Δ R / R = { [ Δ ( S 1 Z ) / ( S 1 Z ) ] 2 + [ Δ ( gS 2 Z ) / ( gS 2 Z ) ] 2 } 1 / 2 [ ( Δ S 1 / S 1 ) 2 + ( Δ S 2 / S 2 ) 2 ] 1 / 2 ( 1 / S 1 + 1 / S 2 ) 1 / 2
Δ T / T = Δ M / M 2.77 L 1 / 2 .
N s = E t σ nlat η exp ( 2 α Z ) / ( h ν H 2 )

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