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Atmospheric and Oceanic Optics

, Volume 27, Issue 1, pp 33–47 | Cite as

Large-scale structure and asymptotic regularities of scattering phase function for water drops in the visible spectrum range

  • N. P. Romanov
  • S. A. Borodin
  • S. O. Dubnichenko
  • L. D. Novikova
Optics of Clusters, Aerosols, and Hydrosoles
  • 33 Downloads

Abstract

The mechanisms of radiation scattering by a sphere in the range of angles θ of 0–180° is analyzed by comparing the exact scattering phase functions calculated with the Mie theory and the interference phase functions with the use of diffraction and partial rays of geometric optics (GO). It is found that the large-scale oscillation regularities of the exact scattering phase function at the high Mie parameters x correspond to an interference pattern of two or three rays with corrected amplitude of the diffraction ray and phase shifts of GO rays. For integral characteristics, the error of computation using the interference formulae in the range of angles θ = 0–10° does not exceed units of percent for x > 10 and tends to zero as x increases. For other ranges, depending on the combination of parity of the integer parts in the π intervals of the total scattering angle, the tendency of oscillation periods over θ toward zero is seen according to the x −1, x −2/3 (rainbow), and x −1/2 laws, while the Mie parameter increases, and the oscillation period over x begins to depend only on θ. The results of the calculations of the exact scattering phase functions averaged over the intervals Δθ = 10–15° for the refraction index m = 4/3 are presented in the form of approximate relations with the asymptotic tendency to the GO scattering phase function.

Keywords

Phase Function Oceanic Optic Geometric Optic Oscillation Structure Scatter Phase Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H.C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, New York, 1957).Google Scholar
  2. 2.
    C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).Google Scholar
  3. 3.
    W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19(9), 1505–1509 (1980).ADSCrossRefGoogle Scholar
  4. 4.
    N. P. Romanov, “Study of methods and errors in computation of Ricattyi-Bessel functions,” Atmos. Ocean. Opt. 20(8), 638–646 (2007).Google Scholar
  5. 5.
    W. J. Glantschning and S.-H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20(14), 2499–2509 (1981).ADSCrossRefGoogle Scholar
  6. 6.
    A. Ungut, G. Grehan, and G. Gouesbet, “Comparisons between geometrical optics and Lorenz-Mie theory,” Appl. Opt. 20(17), 2911–2918 (1981).ADSCrossRefGoogle Scholar
  7. 7.
    H. F. M. Bosch, K. J. Ptasinski, and P. J. A. M. Kerkhof, “Edge contribution to forward scattering by spheres,” Appl. Opt. 35(13), 2285–2291 (1996).ADSCrossRefGoogle Scholar
  8. 8.
    X. Zhou, S. Li, and K. Stamnes, “Geometrical-optical code for computing the optical properties of large dielectric spheres,” Appl. Opt. 42(21), 4295–4306 (2003).ADSCrossRefGoogle Scholar
  9. 9.
    N. P. Romanov, “A computational method and properties of phase scattering functions of transparent balls under the geometric optics approximation,” Atmos. Ocean. Opt. 22(3), 273–283 (2009).CrossRefGoogle Scholar
  10. 10.
    N. P. Romanov and S. O. Dubnichenko, “Physics of formation and analytical description of glory properties,” Atmos. Ocean. Opt. 23(6), 508–522 (2010).CrossRefGoogle Scholar
  11. 11.
    G. Korn and T. Korn, Reference Book on Mathematics (Fizmatlit, Moscow, 1978) [in Russian].Google Scholar
  12. 12.
    J. A. Adam, “Geometric optics and rainbows: generalization of a result by Huygens,” Appl. Opt. 47(34), H11–H13 (2008).ADSCrossRefGoogle Scholar
  13. 13.
    G. S. Gorelik, Oscillations and Waves (Fizmatlit, Moscow, 2007), 3rd ed. [in Russian].Google Scholar
  14. 14.
    T. Wang Ru and H. C. van De Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30(1), 106–117 (1991).ADSCrossRefGoogle Scholar
  15. 15.
    M. Grossman, E. Schmidt, and A. Haussmann, “Photographic evidence for third-order rainbow,” Appl. Opt. 50(28), 134–141 (2011).CrossRefGoogle Scholar
  16. 16.
    A. N. Nevzorov, “On the theory and physics of glory formation,” Opt. Atmosf. Okeana 24(4), 344–348 (2011).Google Scholar
  17. 17.
    M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon, Oxford, 1964).Google Scholar
  18. 18.
    I. Sagedhi, A. Munoz, P. Laven, W. Jarosz, F. Seron, D. Gutierrez, and H. W. Jensen, “Physically-based simulation of rainbows,” ACM Transactions on Graphics 31(1), 1–12 (2011).Google Scholar
  19. 19.
    P. Laven, “Simulation of rainbows, coronas and glories by use of Mie theory,” Appl. Opt. 42(3), 436–444 (2003).ADSCrossRefGoogle Scholar
  20. 20.
    S. O. Dubnichenko and N. P. Romanov, “Interference structure and asymptotic regularities of light scattering by water droplets,” in Proc. of the XVIII Intern. Symp. “Atmospheric and Oceanic Optics. Atmospheric Physics”, Irkutsk, July 2012 (Publishing House of IAO SB RAS, Tomsk, 2012), p. 27 [in Russian].Google Scholar
  21. 21.
    S. A. Borodin and N. P. Romanov, “Interference structure of light scattering by weakly absorbing balls in the region of diffraction maximum,” in Proc. of the XVIII Intern. Symp. “Atmospheric and Oceanic Optics. Atmospheric Physics”, Irkutsk, July 2012 (Publishing House of IAO SB RAS, Tomsk, 2012), pp. 20–21 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • N. P. Romanov
    • 1
  • S. A. Borodin
    • 1
  • S. O. Dubnichenko
    • 1
  • L. D. Novikova
    • 1
  1. 1.Typhoon Research and Production AssociationKaluzhskaya oblast, ObninskRussia

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