Abstract

Equations for Rayleigh scattering in a mixture of gases are derived and compared to frequent approxi mations in the literature. The traditional Rayleigh scattering equation as modified by King for scatter from a pure gas is correct, whereas another version sometimes appearing in modern literature is erroneous. Use of a mixture’s refractive index, which is equivalent to assuming the isotropic molecular polarizabilities of the component gases are identical, is an approximation. Another common approximation is using only number-density weighting of the King factors. Approximation errors can be large when the major components of a mixture have disparate optical properties. Fortunately, the errors for Earth’s air are much smaller and comparable to errors from other sources.

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  1. V. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  2. K. N. Liou, An Introduction to Atmospheric Radiation, Second Edition (Academic, 2002).
  3. B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
    [CrossRef]
  4. C. Tomasi, V. Vitale, B. Petkov, A. Lupi, and A. Cacciari, “Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres,” Appl. Opt. 44, 3320-3341(2005).
    [CrossRef] [PubMed]
  5. B. W. Forgan, “General method for calibrating sun photometers,” Appl. Opt. 33, 4841-4850 (1994).
    [CrossRef] [PubMed]
  6. V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
    [CrossRef]
  7. F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
    [CrossRef]
  8. J. Biele, G. Beyerle, and G. Baumgarten, “Polarization lidar: corrections of instrumental effects,” Opt. Express 7, 427-434(2000).
    [CrossRef] [PubMed]
  9. E. J. McCartney, Optics of the Atmosphere (Wiley, 1976).
  10. J. A. Sutton and J. F. Driscoll, “Rayleigh scattering cross sections of combustion species at 266, 355, and 532 nm for thermometry applications,” Opt. Lett. 29, 2620-2622 (2004).
    [CrossRef] [PubMed]
  11. S. Kampmann, A. Leipertz, K. Döbbeling, J. Haumann, and T. Sattelmayer, “Two-dimensional temperature measurements in a technical combustor with laser Rayleigh scattering,” Appl. Opt. 32, 6167-6172 (1993).
    [CrossRef] [PubMed]
  12. Lord Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107-120, 274-279 (1871).
  13. Lord Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375-384(1899).
  14. R. M. Measures, Laser Remote Sensing (Krieger, 1992).
  15. R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
    [CrossRef]
  16. D. A. Long, Raman Spectroscopy (McGraw-Hill, 1977).
  17. L. V. King, “On the complex anisotropic molecule in relation to the dispersion and scattering of light,” Proc. R. Soc. London Ser. A 104, 333-357 (1923).
    [CrossRef]
  18. Lord Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373-381 (1918).
  19. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  20. A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533-535 (1981).
    [CrossRef] [PubMed]
  21. A. T. Young, “ On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328-330 (1981).
    [CrossRef]
  22. A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427-3428 (1980).
    [CrossRef] [PubMed]
  23. A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
    [CrossRef]
  24. D. R. Bates, “Rayleigh scattering by air,” Planet. Space Sci. 32, 785-790 (1984).
    [CrossRef]
  25. A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765-2773 (1995).
    [CrossRef] [PubMed]
  26. T. J. Greytak and G. B. Benedek, “Spectrum of light scattered from thermal fluctuations in gases,” Phys. Rev. Lett. 17, 179-182 (1966).
    [CrossRef]
  27. C. F. Bohren and E. E. Clothiaux, Fundamentals of Atmospheric Radiation (Wiley-VCH, 2006).
    [CrossRef]
  28. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  29. Lord Rayleigh, “On the resultant of a large number of vibrations of the same pitch and of arbitrary phase,” Philos. Mag. 10, 73-78 (1880).
  30. J. S. Marshall and W. Hitschfeld, “Interpretation of the fluctuating echo from randomly distributed scatterers: Part I,” Can. J. Phys. 31, 194 (1953).
    [CrossRef]
  31. A. E. Siegmann, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350-1356 (1966).
    [CrossRef]
  32. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).
  33. H. Naus and W. Ubachs, “Experimental verification of Rayleigh scattering cross sections,” Opt. Lett. 25, 347-349(2000).
    [CrossRef]
  34. D. A. Whiteman, “Examination of the traditional Raman lidar technique. I. Evaluating the temperature-dependent lidar equations,” Appl. Opt. 42, 2571-2592 (2003).
    [CrossRef] [PubMed]
  35. M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293-310 (2005).
    [CrossRef]
  36. D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
    [CrossRef]
  37. S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
    [CrossRef]
  38. R. Penndorf, “Tables of the refractive index for standard air and the Rayleigh scattering coefficient for the spectral region between 0.2 and 20.0 μ and their application to atmospheric optics,” J. Opt. Soc. Am. 47, 176-182(1957).
    [CrossRef]
  39. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
    [CrossRef]
  40. R. R. Rudder and D. R. Bach, “Rayleigh scattering of ruby-laser light by neutral gases,” J. Opt. Soc. Am. 58, 1260-1266(1968).
    [CrossRef]
  41. F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
    [CrossRef]
  42. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  43. H. R. Gordon, J. W. Brown, and R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862-871 (1988).
    [CrossRef] [PubMed]
  44. P. M. Teillet, “Rayleigh optical depth comparisons from various sources,” Appl. Opt. 29, 1897-1900 (1990).
    [CrossRef] [PubMed]
  45. K. V. Chance and R. J. D. Spurr, “Ring effect studies: Rayleigh scattering, including molecular parameters for rotational Raman scattering, and the Fraunhofer spectrum,” Appl. Opt. 36, 5224-5230 (1997).
    [CrossRef] [PubMed]
  46. D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432-436 (1977).
    [CrossRef]
  47. Shardanand and A. D. Prasad-Rao, “Absolute Rayleigh scattering cross section of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA Tech. Note TN D-8442 (1977).
  48. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  49. W. F. Murphy, “The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule,” J. Chem. Phys. 67, 5877-5882 (1977).
    [CrossRef]
  50. G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
    [CrossRef]
  51. N. J. Bridge and A. D. Buckingham, “The polarization of laser light scattered by gases,” Proc. R. Soc. London Ser. A 295, 334-349 (1966).
    [CrossRef]
  52. R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
    [CrossRef]
  53. J. Oddershede and E. N. Svendsen, “Dynamic polarizabilities and Raman intensities of CO, N2, HCl and Cl2,” Chem. Phys. 64, 359-369 (1982).
    [CrossRef]
  54. W. L. Eberhard, “Comment: On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. (to be published).
  55. R. D. Sharma, “Contribution of the polarizability anisotropy to Rayleigh scattering,” J. Geophys. Res. 112, A05306 (2007).
    [CrossRef]
  56. J. Joiner, P. K. Bhartia, R. P. Cebula, E. Hilsenrath, R. D. McPeters, and H. Park, “Rotational Raman scattering (Ring effect) in satellite backscatter ultraviolet measurements,” Appl. Opt. 34, 4513-4525 (1995).
    [CrossRef] [PubMed]
  57. C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
    [CrossRef]
  58. C. J. F. Böttcher, Theory of Electric Polarization (Elsevier, 1952).
  59. C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.
  60. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  61. H. A. Lorentz, “Ueber die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte,” Ann. Phys. 245, 641-664 (1880).
    [CrossRef]
  62. L. V. Lorenz, “Ueber die Refractionsconstante,” Ann. Phys. 247, 70-103 (1880).
    [CrossRef]
  63. D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704-709 (1982).
    [CrossRef]
  64. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51-59(1967).
    [CrossRef] [PubMed]
  65. E. R. Peck and B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059-1063 (1966).
    [CrossRef]
  66. C. R. Mansfield and E. R. Peck, “Dispersion of helium,” J. Opt. Soc. Am. 59, 199-204 (1969).
    [CrossRef]
  67. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
    [CrossRef]
  68. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566-1573 (1996).
    [CrossRef] [PubMed]
  69. K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
    [CrossRef]
  70. E. R. Peck and B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059-1063 (1966).
    [CrossRef]
  71. P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
    [CrossRef]
  72. G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edléns formulae,” Metrologia 35, 133-139 (1998).
    [CrossRef]

2009

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

2008

D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
[CrossRef]

2007

R. D. Sharma, “Contribution of the polarizability anisotropy to Rayleigh scattering,” J. Geophys. Res. 112, A05306 (2007).
[CrossRef]

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

2005

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293-310 (2005).
[CrossRef]

C. Tomasi, V. Vitale, B. Petkov, A. Lupi, and A. Cacciari, “Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres,” Appl. Opt. 44, 3320-3341(2005).
[CrossRef] [PubMed]

2004

2003

2002

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

2001

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
[CrossRef]

2000

1999

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

1998

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edléns formulae,” Metrologia 35, 133-139 (1998).
[CrossRef]

1997

1996

1995

1994

1993

1990

1988

1984

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

1982

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704-709 (1982).
[CrossRef]

J. Oddershede and E. N. Svendsen, “Dynamic polarizabilities and Raman intensities of CO, N2, HCl and Cl2,” Chem. Phys. 64, 359-369 (1982).
[CrossRef]

1981

A. T. Young, “ On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328-330 (1981).
[CrossRef]

A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533-535 (1981).
[CrossRef] [PubMed]

1980

1977

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432-436 (1977).
[CrossRef]

W. F. Murphy, “The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule,” J. Chem. Phys. 67, 5877-5882 (1977).
[CrossRef]

1976

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
[CrossRef]

1975

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
[CrossRef]

1974

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

1973

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

1972

F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
[CrossRef]

1971

R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
[CrossRef]

1969

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

C. R. Mansfield and E. R. Peck, “Dispersion of helium,” J. Opt. Soc. Am. 59, 199-204 (1969).
[CrossRef]

1968

1967

1966

A. E. Siegmann, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350-1356 (1966).
[CrossRef]

T. J. Greytak and G. B. Benedek, “Spectrum of light scattered from thermal fluctuations in gases,” Phys. Rev. Lett. 17, 179-182 (1966).
[CrossRef]

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

E. R. Peck and B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059-1063 (1966).
[CrossRef]

E. R. Peck and B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059-1063 (1966).
[CrossRef]

1957

1953

J. S. Marshall and W. Hitschfeld, “Interpretation of the fluctuating echo from randomly distributed scatterers: Part I,” Can. J. Phys. 31, 194 (1953).
[CrossRef]

1923

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

1918

Lord Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373-381 (1918).

1899

Lord Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375-384(1899).

1880

Lord Rayleigh, “On the resultant of a large number of vibrations of the same pitch and of arbitrary phase,” Philos. Mag. 10, 73-78 (1880).

H. A. Lorentz, “Ueber die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte,” Ann. Phys. 245, 641-664 (1880).
[CrossRef]

L. V. Lorenz, “Ueber die Refractionsconstante,” Ann. Phys. 247, 70-103 (1880).
[CrossRef]

1871

Lord Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107-120, 274-279 (1871).

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Alms, G. R.

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704-709 (1982).
[CrossRef]

Aval, G. M.

R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
[CrossRef]

Bach, D. R.

Barrett, J. J.

R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
[CrossRef]

Basu, S.

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

Bates, D. R.

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

Baumgarten, G.

Benedek, G. B.

T. J. Greytak and G. B. Benedek, “Spectrum of light scattered from thermal fluctuations in gases,” Phys. Rev. Lett. 17, 179-182 (1966).
[CrossRef]

Beyerle, G.

Bhartia, P. K.

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Biele, J.

Birch, K. P.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

Bodhaine, B. A.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Bohren, C. F.

C. F. Bohren and E. E. Clothiaux, Fundamentals of Atmospheric Radiation (Wiley-VCH, 2006).
[CrossRef]

Bönsch, G.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edléns formulae,” Metrologia 35, 133-139 (1998).
[CrossRef]

Bordewijk, P.

C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Böttcher, C. J. F.

C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.

C. J. F. Böttcher, Theory of Electric Polarization (Elsevier, 1952).

Bridge, N. J.

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

Brown, J. W.

Bucholtz, A.

Buckingham, A. D.

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

Burnham, A. K.

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
[CrossRef]

Cacciari, A.

Cebula, R. P.

Chance, K. V.

Chandrasekhar, V. S.

V. S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chiu, G.

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

Ciddor, P. E.

Clothiaux, E. E.

C. F. Bohren and E. E. Clothiaux, Fundamentals of Atmospheric Radiation (Wiley-VCH, 2006).
[CrossRef]

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).

Daniel, J. S.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Degenstein, D. A.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Döbbeling, K.

Downs, M. J.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

Driscoll, J. F.

Dutton, E. G.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Eberhard, W. L.

W. L. Eberhard, “Comment: On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. (to be published).

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

Evans, R. H.

Evans, W. F. J.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Fernald, F. G.

F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
[CrossRef]

Flygare, W. H.

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
[CrossRef]

Forgan, B. W.

Forkey, J. N.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
[CrossRef]

Gattinger, R. L.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Gordon, H. R.

Greytak, T. J.

T. J. Greytak and G. B. Benedek, “Spectrum of light scattered from thermal fluctuations in gases,” Phys. Rev. Lett. 17, 179-182 (1966).
[CrossRef]

Gucker, F. T.

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Haumann, J.

Herman, B. M.

F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
[CrossRef]

Hilsenrath, E.

Hitschfeld, W.

J. S. Marshall and W. Hitschfeld, “Interpretation of the fluctuating echo from randomly distributed scatterers: Part I,” Can. J. Phys. 31, 194 (1953).
[CrossRef]

Hoyt, D. V.

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432-436 (1977).
[CrossRef]

Huber, M. C. E.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
[CrossRef]

Ityaksov, D.

D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Joiner, J.

Kampmann, S.

Karikeyan, B.

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

Khanna, B. N.

King, L. V.

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

Kovalev, V. A.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

Langford, A. O.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Leipertz, A.

Lempert, W. R.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
[CrossRef]

Linnartz, H.

D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
[CrossRef]

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation, Second Edition (Academic, 2002).

Llewellyn, E. J.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Long, D. A.

D. A. Long, Raman Spectroscopy (McGraw-Hill, 1977).

Lorentz, H. A.

H. A. Lorentz, “Ueber die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte,” Ann. Phys. 245, 641-664 (1880).
[CrossRef]

Lorenz, L. V.

L. V. Lorenz, “Ueber die Refractionsconstante,” Ann. Phys. 247, 70-103 (1880).
[CrossRef]

Lupi, A.

Mansfield, C. R.

Marshall, J. S.

J. S. Marshall and W. Hitschfeld, “Interpretation of the fluctuating echo from randomly distributed scatterers: Part I,” Can. J. Phys. 31, 194 (1953).
[CrossRef]

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, 1976).

McDade, I. C.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

McPeters, R. D.

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Krieger, 1992).

Melamed, M. L.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Miles, R. B.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
[CrossRef]

Miller, H. L.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Murphy, W. F.

W. F. Murphy, “The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule,” J. Chem. Phys. 67, 5877-5882 (1977).
[CrossRef]

Naus, H.

Oddershede, J.

J. Oddershede and E. N. Svendsen, “Dynamic polarizabilities and Raman intensities of CO, N2, HCl and Cl2,” Chem. Phys. 64, 359-369 (1982).
[CrossRef]

Owens, J. C.

Park, H.

Parkinson, W. H.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
[CrossRef]

Peck, E. R.

Penndorf, R.

Petkov, B.

Portmann, R. W.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Potulski, E.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edléns formulae,” Metrologia 35, 133-139 (1998).
[CrossRef]

Prasad-Rao, A. D.

Shardanand and A. D. Prasad-Rao, “Absolute Rayleigh scattering cross section of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA Tech. Note TN D-8442 (1977).

Pulido, A. A.

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

Rai, J.

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373-381 (1918).

Lord Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375-384(1899).

Lord Rayleigh, “On the resultant of a large number of vibrations of the same pitch and of arbitrary phase,” Philos. Mag. 10, 73-78 (1880).

Lord Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107-120, 274-279 (1871).

Reagan, J. A.

F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
[CrossRef]

Rip, A.

C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.

Rowell, R. L.

R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
[CrossRef]

Rudder, R. R.

Sattelmayer, T.

Schofield, R.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Shardanand,

Shardanand and A. D. Prasad-Rao, “Absolute Rayleigh scattering cross section of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA Tech. Note TN D-8442 (1977).

Sharma, R. D.

R. D. Sharma, “Contribution of the polarizability anisotropy to Rayleigh scattering,” J. Geophys. Res. 112, A05306 (2007).
[CrossRef]

Siegmann, A. E.

A. E. Siegmann, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350-1356 (1966).
[CrossRef]

Sioris, C. E.

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Slusser, J. R.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Smith, P. L.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
[CrossRef]

Sneep, M.

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293-310 (2005).
[CrossRef]

Solomon, S.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Spurr, R. J. D.

Srivastava, S. S.

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Sutton, J. A.

Svendsen, E. N.

J. Oddershede and E. N. Svendsen, “Dynamic polarizabilities and Raman intensities of CO, N2, HCl and Cl2,” Chem. Phys. 64, 359-369 (1982).
[CrossRef]

Teillet, P. M.

Tomasi, C.

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Ubachs, W.

D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
[CrossRef]

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293-310 (2005).
[CrossRef]

H. Naus and W. Ubachs, “Experimental verification of Rayleigh scattering cross sections,” Opt. Lett. 25, 347-349(2000).
[CrossRef]

van Belle, O. C.

C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Vitale, V.

Vyas, N. K.

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

Whiteman, D. A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Wood, N. B.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Young, A. T.

Adv. Space Res.

S. S. Srivastava, N. K. Vyas, J. Rai, and B. Karikeyan, “On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. 44, 1058-1066 (2009).
[CrossRef]

Am. J. Phys.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704-709 (1982).
[CrossRef]

Ann. Phys.

H. A. Lorentz, “Ueber die Beziehung zwischen der Fortpflanzungsgeschwindigkeit des Lichtes und der Körperdichte,” Ann. Phys. 245, 641-664 (1880).
[CrossRef]

L. V. Lorenz, “Ueber die Refractionsconstante,” Ann. Phys. 247, 70-103 (1880).
[CrossRef]

Appl. Opt.

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

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566-1573 (1996).
[CrossRef] [PubMed]

H. R. Gordon, J. W. Brown, and R. H. Evans, “Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner,” Appl. Opt. 27, 862-871 (1988).
[CrossRef] [PubMed]

P. M. Teillet, “Rayleigh optical depth comparisons from various sources,” Appl. Opt. 29, 1897-1900 (1990).
[CrossRef] [PubMed]

K. V. Chance and R. J. D. Spurr, “Ring effect studies: Rayleigh scattering, including molecular parameters for rotational Raman scattering, and the Fraunhofer spectrum,” Appl. Opt. 36, 5224-5230 (1997).
[CrossRef] [PubMed]

J. Joiner, P. K. Bhartia, R. P. Cebula, E. Hilsenrath, R. D. McPeters, and H. Park, “Rotational Raman scattering (Ring effect) in satellite backscatter ultraviolet measurements,” Appl. Opt. 34, 4513-4525 (1995).
[CrossRef] [PubMed]

D. A. Whiteman, “Examination of the traditional Raman lidar technique. I. Evaluating the temperature-dependent lidar equations,” Appl. Opt. 42, 2571-2592 (2003).
[CrossRef] [PubMed]

A. T. Young, “Rayleigh scattering,” Appl. Opt. 20, 533-535 (1981).
[CrossRef] [PubMed]

A. T. Young, “Revised depolarization corrections for atmospheric extinction,” Appl. Opt. 19, 3427-3428 (1980).
[CrossRef] [PubMed]

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765-2773 (1995).
[CrossRef] [PubMed]

C. Tomasi, V. Vitale, B. Petkov, A. Lupi, and A. Cacciari, “Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres,” Appl. Opt. 44, 3320-3341(2005).
[CrossRef] [PubMed]

B. W. Forgan, “General method for calibrating sun photometers,” Appl. Opt. 33, 4841-4850 (1994).
[CrossRef] [PubMed]

S. Kampmann, A. Leipertz, K. Döbbeling, J. Haumann, and T. Sattelmayer, “Two-dimensional temperature measurements in a technical combustor with laser Rayleigh scattering,” Appl. Opt. 32, 6167-6172 (1993).
[CrossRef] [PubMed]

Atmos. Chem. Phys.

A. O. Langford, R. Schofield, J. S. Daniel, R. W. Portmann, M. L. Melamed, H. L. Miller, E. G. Dutton, and S. Solomon, “On the variability of the Ring effect in the near ultraviolet: understanding the role of aerosols and multiple scattering,” Atmos. Chem. Phys. 7, 575-586 (2007).
[CrossRef]

Can. J. Phys.

J. S. Marshall and W. Hitschfeld, “Interpretation of the fluctuating echo from randomly distributed scatterers: Part I,” Can. J. Phys. 31, 194 (1953).
[CrossRef]

C. E. Sioris, W. F. J. Evans, R. L. Gattinger, I. C. McDade, D. A. Degenstein, and E. J. Llewellyn, “Ground-based Ring-effect measurements with the OSIRIS development model,” Can. J. Phys. 80, 483-491 (2002).
[CrossRef]

Chem. Phys.

J. Oddershede and E. N. Svendsen, “Dynamic polarizabilities and Raman intensities of CO, N2, HCl and Cl2,” Chem. Phys. 64, 359-369 (1982).
[CrossRef]

J. Appl. Meteorol.

D. V. Hoyt, “A redetermination of the Rayleigh optical depth and its application to selected solar radiation problems,” J. Appl. Meteorol. 16, 432-436 (1977).
[CrossRef]

A. T. Young, “ On the Rayleigh-scattering optical depth of the atmosphere,” J. Appl. Meteorol. 20, 328-330 (1981).
[CrossRef]

F. G. Fernald, B. M. Herman, and J. A. Reagan, “Determination of aerosol height distributions by lidar,” J. Appl. Meteorol. 11, 482-489 (1972).
[CrossRef]

J. Atmos. Ocean. Technol.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, and J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

J. Chem. Phys.

F. T. Gucker, S. Basu, A. A. Pulido, and G. Chiu, “Intensity and polarization of light scattered by some permanent gases and vapors,” J. Chem. Phys. 50, 2526-2535 (1969).
[CrossRef]

W. F. Murphy, “The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule,” J. Chem. Phys. 67, 5877-5882 (1977).
[CrossRef]

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321-3326 (1975).
[CrossRef]

R. L. Rowell, G. M. Aval, and J. J. Barrett, “Rayleigh-Raman depolarization of laser light scattered by gases,” J. Chem. Phys. 54, 1960-1964 (1971).
[CrossRef]

J. Geophys. Res.

R. D. Sharma, “Contribution of the polarizability anisotropy to Rayleigh scattering,” J. Geophys. Res. 112, A05306 (2007).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293-310 (2005).
[CrossRef]

Meas. Sci. Technol.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12, R33-R51 (2001).
[CrossRef]

Metrologia

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edléns formulae,” Metrologia 35, 133-139 (1998).
[CrossRef]

Mol. Phys.

D. Ityaksov, H. Linnartz, and W. Ubachs, “Deep-UV Rayleigh scattering of N2, CH4 and SF6,” Mol. Phys. 106, 2471-2479(2008).
[CrossRef]

Opt. Commun.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Mag.

Lord Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373-381 (1918).

Lord Rayleigh, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107-120, 274-279 (1871).

Lord Rayleigh, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375-384(1899).

Lord Rayleigh, “On the resultant of a large number of vibrations of the same pitch and of arbitrary phase,” Philos. Mag. 10, 73-78 (1880).

Phys. Rev. A

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422-1434 (1976).
[CrossRef]

Phys. Rev. Lett.

T. J. Greytak and G. B. Benedek, “Spectrum of light scattered from thermal fluctuations in gases,” Phys. Rev. Lett. 17, 179-182 (1966).
[CrossRef]

Planet. Space Sci.

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

Proc. IEEE

A. E. Siegmann, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350-1356 (1966).
[CrossRef]

Proc. R. Soc. London Ser. A

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

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

Space Sci. Rev.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Other

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).

C. F. Bohren and E. E. Clothiaux, Fundamentals of Atmospheric Radiation (Wiley-VCH, 2006).
[CrossRef]

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

R. M. Measures, Laser Remote Sensing (Krieger, 1992).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

D. A. Long, Raman Spectroscopy (McGraw-Hill, 1977).

E. J. McCartney, Optics of the Atmosphere (Wiley, 1976).

V. A. Kovalev and W. E. Eichinger, Elastic Lidar (Wiley, 2004).
[CrossRef]

V. S. Chandrasekhar, Radiative Transfer (Dover, 1960).

K. N. Liou, An Introduction to Atmospheric Radiation, Second Edition (Academic, 2002).

W. L. Eberhard, “Comment: On the different approaches of Rayleigh optical depth determination,” Adv. Space Res. (to be published).

C. J. F. Böttcher, Theory of Electric Polarization (Elsevier, 1952).

C. J. F. Böttcher, O. C. van Belle, P. Bordewijk, and A. Rip, Theory of Electric Polarization (Elsevier, 1973), Vol. I.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Shardanand and A. D. Prasad-Rao, “Absolute Rayleigh scattering cross section of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA Tech. Note TN D-8442 (1977).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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Figures (7)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Errors from using approximate equations for total Rayleigh scatter β at a 0.5 μm wavelength versus mixture ratio of He and CO 2 : ε L for L 2 = 1 at STP, ε a for a ¯ 2 instead of a 2 ¯ , ε F for F N ¯ instead of F ¯ , ε B T for all three of these approximations, as in [3, 4], and ε L ( STP × 40 ) for 40 times more density than STP.

Fig. 3
Fig. 3

Average polarizabilities for the constituents in the four-component dry air and five-component moist air, and the square root of a 2 ¯ for dry air defined in Eq. (54) and used in the correct Rayleigh-scatter equation (53).

Fig. 4
Fig. 4

F i used for the four-component dry air (Ar is 1.0000) and F ¯ according to Eq. (55).

Fig. 5
Fig. 5

Errors from using approximations for the four-component dry air versus wavelength: ε L at STP, ε a , ε F , and ε B T as in Fig. 2; ε B T ( 90 ° ) for side scatter and ε B T ( 180 ° ) for backscatter using all three approximations; and ε B T ( STP × 0.5 ) at density half that at STP.

Fig. 6
Fig. 6

Errors from using approximations for the five-component moist air example versus wavelength for 101325 Pa pressure, 35.0 ° C temperature, and 89.6% relative humidity, giving N w = 0.05 N ε x as in Fig. 5 (note shift in vertical scale).

Fig. 7
Fig. 7

Polarization ratio for the four-component dry air at side scatter δ for natural (unpolarized) incident light and for lidar backscatter δ lidar for linearly polarized incident light, each based on both the correctly-weighted F ¯ from Eq. (55) and the number- density-weighted approximation F N ¯ from Eq. (68).

Equations (81)

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σ = 8 π 3 3 λ 4 N 2 ( n 2 1 ) 2 ( 3 n 2 + 2 ) 2 F ,
β = N σ
= 8 π 3 3 λ 4 N ( n 2 1 ) 2 ( 3 n 2 + 2 ) 2 F .
F = 6 + 3 δ 6 7 δ ,
δ = 6 γ 2 45 a 2 + 7 γ 2 ,
ν i = N i / N ,
E I ( t ) = E I y cos ( ω t ξ 0 k x ) y ^ + E I z cos ( ω t ξ 0 k x ) z ^ ,
k = ω n / c = 2 π n / λ ,
E I z = E I cos ψ , E I y = E I sin ψ ,
S I = E I × H I = I I x ^ ,
I I = 1 2 ε μ E I 2 = 1 2 ε μ ( E I y 2 + E I z 2 ) ,
E L = L E I ,
L = n 2 + 2 3
a i = 3 ε 0 N i n i 2 1 n i 2 + 2 ,
a = 3 ε 0 N ε i / ε 0 1 ε i / ε 0 + 2 ,
i N i a i = 3 ε 0 n 2 1 n 2 + 2 = 3 ε 0 i N i 1 N i s n i s 2 1 n i s 2 + 2 ,
p i j = α i j E L .
α i j = [ α x y i j α x z i j α y y i j α y z i j α z y i j α z z i j ] .
E i j ( R , t ) = ω 2 4 π R i j ε 0 c 2 s ^ i j × ( p i j × s ^ i j ) cos [ ω t ξ 0 k ( x i j + R i j ) ] ,
E i j = ω 2 4 π R i j ε 0 c 2 p i j sin φ i j .
E ( R , t ) = ω 2 4 π ε 0 c 2 i j 1 R i j s ^ i j × ( p i j × s ^ i j ) cos [ ω t ξ 0 k ( x i j + R i j ) ] .
E ( R , t ) = ω 2 4 π ε 0 c 2 1 R i j s ^ × ( p i j × s ^ ) cos [ ω t ξ 0 k ( x i j + R i j ) ] .
I = 1 2 ε μ i j | E i j | 2 ,
E i j = ω 2 4 π ε 0 c 2 1 R | s ^ × ( p i j × s ^ ) | .
β ( s ^ ) Ω = R 2 I ( N , s ^ ) I I = ω 4 16 π 2 ε 0 2 c 4 1 | E I | 2 i = 1 N g j = 1 N i | s ^ × ( p i j × s ^ ) | 2 .
β ( s ^ ) Ω = i = 1 N g β i ( s ^ ) Ω ,
β i ( s ^ ) Ω = π 2 ε 0 2 λ 4 1 | E I | 2 j = 1 N i | s ^ × ( p i j × s ^ ) | 2
s ^ = cos θ x x ^ + cos θ y y ^ + cos θ z z ^ ,
h ^ = cos θ y x ^ cos θ x y ^ ( cos 2 θ x + cos 2 θ y ) 1 / 2 ,
v ^ = cos θ x cos θ z x ^ + cos θ y cos θ z y ^ ( cos 2 θ x + cos 2 θ y ) 1 / 2 ( cos 2 θ x + cos 2 θ y ) 1 / 2 z ^ .
E i j ( R , t ) = E i j h ( R , t ) + E i j v ( R , t ) ,
E i j h ( R ) = ω 2 4 π ε 0 c 2 1 R s ^ × ( p i j × s ^ ) · h ^ , E i j v ( R ) = ω 2 4 π ε 0 c 2 1 R s ^ × ( p i j × s ^ ) · v ^ .
I = 1 2 ε μ ( i = 1 N g j = 1 N i E i j h 2 + i = 1 N g j = 1 N i E i j v 2 ) ,
β i ( s ^ ) Ω = β i h ( s ^ ) Ω + β i v ( s ^ ) Ω ,
β i h ( s ^ ) Ω = π 2 ε 0 2 λ 4 1 | E I | 2 j = 1 N i ( s ^ × ( p i j × s ^ ) · h ^ ) 2 ,
β i v ( s ^ ) Ω = π 2 ε 0 2 λ 4 1 | E I | 2 j = 1 N i ( s ^ × ( p i j × s ^ ) · v ^ ) 2 .
p i j = p i j x x ^ + p i j y y ^ + p i j z z ^ .
p i x 2 ¯ = E L 2 3 γ i 2 45 ,
p i y 2 ¯ = E L 2 [ 3 γ i 2 45 + sin 2 ψ ( 45 a i 2 + γ i 2 45 ) ] ,
p i z 2 ¯ = E L 2 [ 3 γ i 2 45 + cos 2 ψ ( 45 a i 2 + γ i 2 45 ) ] ,
p i y p i z ¯ = E L 2 sin ψ cos ψ ( 45 a i 2 + γ i 2 45 ) ,
β i h ( s ^ ) Ω = π 2 N i ε 0 2 λ 4 | E L | 2 | E I | 2 [ ( 3 γ i 2 45 ) + ( 45 a i 2 + γ i 2 45 ) sin 2 ψ ( sin 2 θ z cos 2 θ y sin 2 θ z ) ] ,
β i v ( s ^ ) Ω = π 2 N i ε 0 2 λ 4 | E L | 2 | E I | 2 [ ( 3 γ i 2 45 ) + ( 45 a i 2 + γ i 2 45 ) ( sin ψ cos θ y cos θ z sin θ z cos ψ sin θ z ) 2 ] ,
β Ω = π 2 ε 0 2 λ 4 N L 2 i = 1 N g υ i a i 2 [ ( 1 + 7 γ i 2 45 a i 2 ) ( 1 + γ i 2 45 a i 2 ) ( sin ψ cos θ y + cos ψ cos θ z ) 2 ] .
β = 8 π 3 N 3 ε 0 2 λ 4 L 2 i = 1 N g υ i a i 2 ( 1 + 2 γ i 2 9 a i 2 ) .
F i = ( 1 + 2 γ i 2 9 a i 2 ) = ( 6 + 3 δ i 6 7 δ i ) ,
δ i = 6 γ i 2 45 a i 2 + 7 γ i 2 .
β = 8 π 3 3 ε 0 2 λ 4 L 2 N i = 1 N g υ i a i 2 F i .
σ 1 i = 8 π 3 3 ε 0 2 λ 4 a i 2 F i ,
β = L 2 N i = 1 N g υ i σ 1 i .
σ 1 i = 24 π 3 λ 4 1 N i s 2 ( n i s 2 1 n i s 2 + 2 ) 2 F i ,
β = 24 π 3 λ 4 ( n 2 + 2 3 ) 2 i = 1 N g N i N i s 2 ( n i s 2 1 n i s 2 + 2 ) 2 F i .
β = 8 π 3 3 ε 0 2 λ 4 L 2 N a 2 ¯ F ¯ ,
a 2 ¯ = i N g υ i a i 2 ,
F ¯ = ( a 2 ¯ ) 1 i = 1 N g υ i a i 2 F i .
σ ¯ = β / N = L 2 i = 1 N g υ i σ 1 i .
β = L 2 N σ 1
= 8 π 3 3 ε 0 2 λ 4 L 2 N a 2 F
= 24 π 3 λ 4 ( n 2 + 2 3 ) 2 N N s 2 ( n s 2 1 n s 2 + 2 ) 2 F .
β = 8 π 3 3 λ 4 1 N ( n 2 1 ) 2 F ,
σ p = 128 π 5 r 6 3 λ 4 ( n p 2 1 n p 2 + 2 ) 2 ,
β L = 8 π 3 3 ε 0 2 λ 4 N a 2 ¯ F ¯ .
β L / β = L 2 .
β a = 24 π 3 λ 4 N L 2 ( n 2 1 n 2 + 2 ) 2 F .
a ¯ = i υ i a i ,
β a = 8 π 3 3 ε 0 2 λ 4 L 2 N a ¯ 2 F ¯ ,
β a / β = a ¯ 2 / a 2 ¯ .
F N ¯ = i υ i F i ,
β F = 8 π 3 3 ε 0 2 λ 4 L 2 N a 2 ¯ F N ¯ ,
β F / β = F N ¯ / F ¯ .
Δ ( a i 2 ) = a i 2 a 2 ¯ ,
Δ F i = F i F N ¯ ,
F N ¯ / F ¯ = [ 1 + i υ i Δ ( a i 2 ) a 2 ¯ Δ F i F N ¯ ] 1 .
β B T / β = a ¯ 2 F N ¯ / L 2 a 2 ¯ F ¯ .
ε x = β x β 1 ,
r = n 1 ,
Δ β β = 2 Δ r ,
δ = 6 i υ i γ i 2 45 i υ i a i 2 + 7 i υ i γ i 2 .
γ i 2 = 45 a i 2 δ i 6 7 δ i ,
δ = 6 ( F ¯ 1 ) 7 F ¯ + 3 .
δ lidar = δ 2 δ .

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