Abstract

It is well known that scattering lidars, i.e., Mie, aerosol-wind, Rayleigh, high-spectral-resolution, molecular-wind, rotational Raman, and vibrational Raman lidars, are workhorses for probing atmospheric properties, including the backscatter ratio, aerosol extinction coefficient, temperature, pressure, density, and winds. The spectral structure of molecular scattering (strength and bandwidth) and its constituent spectra associated with Rayleigh and vibrational Raman scattering are reviewed. Revisiting the correct name by distinguishing Cabannes scattering from Rayleigh scattering, and sharpening the definition of each scattering component in the Rayleigh scattering spectrum, the review allows a systematic, logical, and useful comparison in strength and bandwidth between each scattering component and in receiver bandwidths (for both nighttime and daytime operation) between the various scattering lidars for atmospheric sensing.

© 2001 Optical Society of America

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References

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  1. J. Cabannes, “Un nouveau ph’enom’ene d’optique: le battements qui se produisent lorsque des mol’ecules anisotropes en rotation et vibration diffusent de la lumi’ere visible ou ultraviolette,” C. R. Acad. Sci. 186, 1201–1202 (1928).
  2. J. Cabannes, Y. Rocard, “La Th’eorie ’electromagn’etique de Maxell-Lorentz et la diffusion mol’eculaire de la lumi’ere,” J. Phys. Rad. 10, (6) 52–71 (1929).
    [CrossRef]
  3. A. Hauchecorne, M.-L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 78, 565–568 (1980).
    [CrossRef]
  4. A. T. Young, “Rayleigh scattering,” Phys. Today42–48 (January1982).
  5. I. L. Feblinskii, Molecular Scattering of Light (Plenum, New York, 1968).
    [CrossRef]
  6. H. Rosen, P. Robrish, O. Chamberlain, “Remote detection of pollutants using resonance Raman scattering,” Appl. Opt. 14, 2703–2706 (1975).
    [CrossRef] [PubMed]
  7. H. Inaba, “Detection of atoms and molecules by Raman scattering and resonance fluorescence,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 153–236.
    [CrossRef]
  8. R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
    [CrossRef]
  9. C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
    [CrossRef]
  10. H. Edner, J. Johansson, S. Svanberg, E. Wallinder, “Fluorescence lidar multicolor imaging of vegetation,” Appl. Opt. 33, 2471–2479 (1994).
    [CrossRef] [PubMed]
  11. R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), Chap. 8.
  12. G. Placzek, Handbuch der Radiologie, Vol. 6, Part 2, E. Marx, ed. (Akadecmischer Verlag, Leipzig, 1934).
  13. R. Gaufres, S. Sportouch, “The Placzek–Teller coefficients bJ′,KJ,K for negative ΔJ,” J. Mol. Spectrosc. 39, 527–530 (1971).
    [CrossRef]
  14. G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).
  15. L. V. King, “On the complex anisotropic molecule in relation to the dispersion and scattering of light,” Proc. R. Soc. London A 104, 333–357 (1923).
    [CrossRef]
  16. N. J. Bridge, A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Sect. A 295, 334–349 (1966).
    [CrossRef]
  17. Shardanand, A. D. Prasad Rao, “Absolute Rayleigh–scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA TN D-8442 (March1977).
  18. R. B. Miles, D. M. Nosenchuck, “Three-dimensional quantitative flow diagnostics,” in Lecture Notes in Engineering: Advances in Fluid Dynamics Measurement, (Springer-Verlag, Berlin, 1989), pp. 33–107.
    [CrossRef]
  19. D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
    [CrossRef]
  20. H. W. Schrötter, H. W. Köckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, Topics in Current Applied Physics, A. Weber, ed. (Springer-Verlag, Berlin, 1979), p. 123.
  21. J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).
  22. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8.
  23. U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).
  24. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 369.

2000 (1)

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

1994 (1)

1990 (1)

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

1984 (1)

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

1982 (1)

A. T. Young, “Rayleigh scattering,” Phys. Today42–48 (January1982).

1980 (1)

A. Hauchecorne, M.-L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 78, 565–568 (1980).
[CrossRef]

1975 (1)

1974 (2)

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

1971 (1)

R. Gaufres, S. Sportouch, “The Placzek–Teller coefficients bJ′,KJ,K for negative ΔJ,” J. Mol. Spectrosc. 39, 527–530 (1971).
[CrossRef]

1966 (1)

N. J. Bridge, A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Sect. A 295, 334–349 (1966).
[CrossRef]

1929 (1)

J. Cabannes, Y. Rocard, “La Th’eorie ’electromagn’etique de Maxell-Lorentz et la diffusion mol’eculaire de la lumi’ere,” J. Phys. Rad. 10, (6) 52–71 (1929).
[CrossRef]

1928 (1)

J. Cabannes, “Un nouveau ph’enom’ene d’optique: le battements qui se produisent lorsque des mol’ecules anisotropes en rotation et vibration diffusent de la lumi’ere visible ou ultraviolette,” C. R. Acad. Sci. 186, 1201–1202 (1928).

1923 (1)

L. V. King, “On the complex anisotropic molecule in relation to the dispersion and scattering of light,” Proc. R. Soc. London A 104, 333–357 (1923).
[CrossRef]

Adolfsen, K.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Alvarez, R. J.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

Bates, D. R.

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

Baumgarten, G.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Bills, R. E.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

Boley, C. D.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8.

Bridge, N. J.

N. J. Bridge, A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Sect. A 295, 334–349 (1966).
[CrossRef]

Buckingham, A. D.

N. J. Bridge, A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Sect. A 295, 334–349 (1966).
[CrossRef]

Cabannes, J.

J. Cabannes, Y. Rocard, “La Th’eorie ’electromagn’etique de Maxell-Lorentz et la diffusion mol’eculaire de la lumi’ere,” J. Phys. Rad. 10, (6) 52–71 (1929).
[CrossRef]

J. Cabannes, “Un nouveau ph’enom’ene d’optique: le battements qui se produisent lorsque des mol’ecules anisotropes en rotation et vibration diffusent de la lumi’ere visible ou ultraviolette,” C. R. Acad. Sci. 186, 1201–1202 (1928).

Caldwell, L. M.

J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).

Chamberlain, O.

Chanin, M.-L.

A. Hauchecorne, M.-L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 78, 565–568 (1980).
[CrossRef]

Desai, R. C.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Edner, H.

Feblinskii, I. L.

I. L. Feblinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[CrossRef]

Fiedler, J.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Fricke, K. H.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Gardner, C. S.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

Gaufres, R.

R. Gaufres, S. Sportouch, “The Placzek–Teller coefficients bJ′,KJ,K for negative ΔJ,” J. Mol. Spectrosc. 39, 527–530 (1971).
[CrossRef]

Hair, J. W.

J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).

Hauchecorne, A.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

A. Hauchecorne, M.-L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 78, 565–568 (1980).
[CrossRef]

Inaba, H.

H. Inaba, “Detection of atoms and molecules by Raman scattering and resonance fluorescence,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 153–236.
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 369.

Johansson, J.

King, L. V.

L. V. King, “On the complex anisotropic molecule in relation to the dispersion and scattering of light,” Proc. R. Soc. London A 104, 333–357 (1923).
[CrossRef]

Köckner, H. W.

H. W. Schrötter, H. W. Köckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, Topics in Current Applied Physics, A. Weber, ed. (Springer-Verlag, Berlin, 1979), p. 123.

Krueger, D. A.

J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).

Latifi, H.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), Chap. 8.

Miles, R. B.

R. B. Miles, D. M. Nosenchuck, “Three-dimensional quantitative flow diagnostics,” in Lecture Notes in Engineering: Advances in Fluid Dynamics Measurement, (Springer-Verlag, Berlin, 1989), pp. 33–107.
[CrossRef]

Nelke, G.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Nosenchuck, D. M.

R. B. Miles, D. M. Nosenchuck, “Three-dimensional quantitative flow diagnostics,” in Lecture Notes in Engineering: Advances in Fluid Dynamics Measurement, (Springer-Verlag, Berlin, 1989), pp. 33–107.
[CrossRef]

Placzek, G.

G. Placzek, Handbuch der Radiologie, Vol. 6, Part 2, E. Marx, ed. (Akadecmischer Verlag, Leipzig, 1934).

Prasad Rao, A. D.

Shardanand, A. D. Prasad Rao, “Absolute Rayleigh–scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA TN D-8442 (March1977).

Rees, D.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Robrish, P.

Rocard, Y.

J. Cabannes, Y. Rocard, “La Th’eorie ’electromagn’etique de Maxell-Lorentz et la diffusion mol’eculaire de la lumi’ere,” J. Phys. Rad. 10, (6) 52–71 (1929).
[CrossRef]

Rosen, H.

Schotland, R. M.

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

Schrötter, H. W.

H. W. Schrötter, H. W. Köckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, Topics in Current Applied Physics, A. Weber, ed. (Springer-Verlag, Berlin, 1979), p. 123.

Shardanand,

Shardanand, A. D. Prasad Rao, “Absolute Rayleigh–scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA TN D-8442 (March1977).

She, C. Y.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

She, C.-Y.

J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).

Sportouch, S.

R. Gaufres, S. Sportouch, “The Placzek–Teller coefficients bJ′,KJ,K for negative ΔJ,” J. Mol. Spectrosc. 39, 527–530 (1971).
[CrossRef]

Svanberg, S.

Tenti, G.

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

von Cossart, G.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

von Zahn, U.

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Wallinder, E.

Young, A. T.

A. T. Young, “Rayleigh scattering,” Phys. Today42–48 (January1982).

Yu, J. R.

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

Ann. Geophys. (1)

U. von Zahn, G. von Cossart, J. Fiedler, K. H. Fricke, G. Nelke, G. Baumgarten, D. Rees, A. Hauchecorne, K. Adolfsen, “The ALOMAR Rayleigh/Mie/Raman lidar: objectives, configuration, and performance,” Ann. Geophys. 18, 815–833 (2000).

Appl. Opt. (2)

C. R. Acad. Sci. (1)

J. Cabannes, “Un nouveau ph’enom’ene d’optique: le battements qui se produisent lorsque des mol’ecules anisotropes en rotation et vibration diffusent de la lumi’ere visible ou ultraviolette,” C. R. Acad. Sci. 186, 1201–1202 (1928).

Can. J. Phys. (1)

G. Tenti, C. D. Boley, R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

Geophys. Res. Lett. (2)

A. Hauchecorne, M.-L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 78, 565–568 (1980).
[CrossRef]

C. Y. She, H. Latifi, J. R. Yu, R. J. Alvarez, R. E. Bills, C. S. Gardner, “Two-frequency lidar technique for mesospheric Na temperature measurements,” Geophys. Res. Lett. 17, 929–932 (1990).
[CrossRef]

J. Appl. Meteorol. (1)

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

J. Mol. Spectrosc. (1)

R. Gaufres, S. Sportouch, “The Placzek–Teller coefficients bJ′,KJ,K for negative ΔJ,” J. Mol. Spectrosc. 39, 527–530 (1971).
[CrossRef]

J. Phys. Rad. (1)

J. Cabannes, Y. Rocard, “La Th’eorie ’electromagn’etique de Maxell-Lorentz et la diffusion mol’eculaire de la lumi’ere,” J. Phys. Rad. 10, (6) 52–71 (1929).
[CrossRef]

Phys. Today (1)

A. T. Young, “Rayleigh scattering,” Phys. Today42–48 (January1982).

Planet. Space Sci. (1)

D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785–790 (1984).
[CrossRef]

Proc. R. Soc. London A (1)

L. V. King, “On the complex anisotropic molecule in relation to the dispersion and scattering of light,” Proc. R. Soc. London A 104, 333–357 (1923).
[CrossRef]

Proc. R. Soc. London Sect. A (1)

N. J. Bridge, A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Sect. A 295, 334–349 (1966).
[CrossRef]

Other (10)

Shardanand, A. D. Prasad Rao, “Absolute Rayleigh–scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA TN D-8442 (March1977).

R. B. Miles, D. M. Nosenchuck, “Three-dimensional quantitative flow diagnostics,” in Lecture Notes in Engineering: Advances in Fluid Dynamics Measurement, (Springer-Verlag, Berlin, 1989), pp. 33–107.
[CrossRef]

H. W. Schrötter, H. W. Köckner, “Raman scattering cross sections in gases and liquids,” in Raman Spectroscopy of Gases and Liquids, Topics in Current Applied Physics, A. Weber, ed. (Springer-Verlag, Berlin, 1979), p. 123.

J. W. Hair, L. M. Caldwell, D. A. Krueger, C.-Y. She, “High spectral resolution lidar with iodine vapor filters: measurement of atmospheric state and aerosol profiles,” Appl. Opt. (to be published).

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 8.

I. L. Feblinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[CrossRef]

H. Inaba, “Detection of atoms and molecules by Raman scattering and resonance fluorescence,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, Berlin, 1976), pp. 153–236.
[CrossRef]

R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon, Oxford, 1983), Chap. 8.

G. Placzek, Handbuch der Radiologie, Vol. 6, Part 2, E. Marx, ed. (Akadecmischer Verlag, Leipzig, 1934).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 369.

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Figures (6)

Fig. 1
Fig. 1

Rayleigh and Raman spectra of N2 at 275 K. At this temperature the vibrational anti-Stokes intensity is negligible.

Fig. 2
Fig. 2

Placzek and Teller factors, showing the probability of O-, Q-, and S-branch transitions of rotational Raman scattering as a function of the rotational quantum number J.

Fig. 3
Fig. 3

Pure rotational Raman-scattering spectrum of air including the unshifted component. Note that, owing to the Pauli exclusion principle, the intensity for even J values is a factor of 2 higher than that for odd J values in N2 and only odd J values are allowed for O2. See text for explanation.

Fig. 4
Fig. 4

Doppler-broadened spectrum of the Cabannes line.

Fig. 5
Fig. 5

Total Rayleigh-scattering cross section (in 10-29 m2, solid curve) and the associated King correction factor (dotted curve) as a function of wavelength. They are from Bates19 and plotted here. The wavelengths of particular interest to lidar operation are marked.

Fig. 6
Fig. 6

Scattering geometry. The incident beam is polarized in the x direction and propagates along the z axis. The scattered light propagates along with two perpendicular polarizations along ∊̂1 and ∊̂2.

Tables (3)

Tables Icon

Table 1 Rayleigh Cross Sections and Derived Anisotropy and Depolarization Ratios at 532 nm

Tables Icon

Table 2 Differential Raman Backscatteringa Cross Sectionsb for N 2 , O 2 , and Air

Tables Icon

Table 3 Relative Signal Strength and Bandwidth Comparison between Different Scattering Lidar for Atmospheric Parameter Measurements

Equations (23)

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

POJJ-2=3JJ-1/22J-12J+13/8  for the O branch, PQJJ=JJ+1/2J-12J+31/4  for the Q branch, PSJJ+2=3J+1J+2/22J+12J+33/8  for the S branch.
PJ, v=2I+12J+1×expBeJJ+1/0.6952T/ZT,
ZT=I,J2I+12J+1×exp-BeJJ+1/0.6952T
σπR=dσ1Rπ, π/2/dΩ+dσ2Rπ, π/2/dΩ=νπ2/νsλs4α2+7γ2/45=σπP+σπDP,
σπC=σπP+0.25 σπDP=νπ2/νsλs4α2+7γ2/180=σπP1+7RA/180, σπRR=0.75 σπDP=νπ2/νsλs421γ2/180=σπP21RA/180,
σπR=σπC+σπRR=σπP+σπDP=σπP1+7RA/45, σTR=νπ2/νsλs42/3α2+10γ2/45=2/3σπP1+10RA/45.
σR=4πσTR=νπ2/νsλs48π/3α2FK=8π/3σπPFK; FK=1+2/9RA,
σcsR=νπ2/νsλs48π/3α2=32π3n-12/3N2λ4,
RA=4.5FK-1,  δ=3RA/45+4RA.
R=βaz+βmz/βmz=1+βaz/βmz,
dP/dΩ=cks4/32π2o|nˆ×p×nˆ|2=π2c/2oλs4|nˆ×p×nˆ|2,
dσRθ, ϕ/dΩ=νπ2/νsλs4γ2/15y2+z2+α2+4γ2/45x2,
dσ1Rθ, ϕ/dΩ=νπ2/νsλs4γ2/15cos2ϕ+α2+4γ2/45sin2 ϕ, dσ2Rθ, ϕ/dΩ=νπ2/νsλs4×γ2/15cos2 θ sin2 ϕ +sin2 θ+α2+4γ2/45cos2 θ cos2 ϕ.
dσ1Rπ/2, π/2/dΩ=νπ2/νsλs4α2+4γ2/45
dσ2Rπ/2, π/2/dΩ=νπ2/νsλs4γ2/15
σ1,πR=dσ1Rπ, π/2/dΩ=νπ2/νsλs4α2+4γ2/45, σ2,πR=dσ2Rπ, π/2/dΩ=νπ2/νsλs4γ2/15,
σπR=dσ1Rπ, π/2/dΩ+dσ2Rπ, π/2/dΩ=νπ2/νsλs4α2+7γ2/45=νπ2/νsλs4α2+0.257γ2/45+0.757γ2/45=σπC+σπRR,
σπPdσPπ, π/2/dΩ=νπ2/νsλs4α2, σπDPdσDPπ, π/2/dΩ=νπ2/νsλs47γ2/45,
cos2 ϕ=1/4π cos2 ϕdΩ=sin2 ϕ=0.5,cos2 θ=1/3, sin2 θ=2/3,cos2 θ sin2 ϕ=cos2 θ cos2 ϕ=1/6,
σTR=1/4π dσ1Rθ, ϕ/dΩ+dσ2Rθ, ϕ/dΩdΩ=νπ2/νsλs42/3α2+10γ2/45.
σR=4πσTR=νπ2/νsλs48π/3α21+10RA/45=νπ2/νsλs48π/3α2FK,
q1Rπσ1,πR/σTR=1.5α2+4γ2/45/α2+10γ2/45, q2Rπσ2,πR/σTR=1.5γ2/15/α2+10γ2/45, qRπq1Rπ+q2Rπ=1.51-γ2/15/α2+10γ2/45,
δσ2,πR/σ1,πR=γ2/15/α2+4γ2/45=3RA/45+4RA.

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