Skip to main content

A computational method and properties of phase scattering functions of transparent balls under the geometric optics approximation

Abstract

This paper gives a systematic description of the basic laws of scattering within the framework of geometric optics, along with a graphical representation for the refractive index m = 4/3 of partial phase scattering functions representing beams after p transitions inside a ball. Then, it studies a computational procedure for partial phase scattering functions depending on the scattering angle. This is an iterative procedure employing an expansion of the inverse dependence of the incidence angle on the scattering angle. For a series of m values from 1.1 to 1.8, the paper presents the graphs of aggregate phase scattering functions obtained with this procedure. It follows from the analysis of the graphs that with the increase of the refractive index from 1.1 to 1.5, the angle (in which 90% of scattered energy is concentrated) is observed to grow from ∼ 20° to 90°. At growing values of m > √2, a sharp increase of backward scattering is observed. It is caused by shifting of the partial beam with p = 2 into this region. In a wide range of scattering angles in the frontal semisphere and in individual subranges in the back semisphere, the value of the aggregate phase scattering function is determined by the sum of the partial phase scattering functions with p = 0 and 1, for which there are analytical expressions.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    K. S. Shifrin, Light Scattering by Turbid Medium (Leningrad, Moscow, 1951) [in Russian].

    Google Scholar 

  2. 2.

    H. Ch. Hulst van de, Light Scattering by Small Particles (Inostrannaya Literatura, Moscow, 1961) [in Russian].

    Google Scholar 

  3. 3.

    C. F. Boren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1983).

    Google Scholar 

  4. 4.

    K. S. Shifrin, Introduction to Ocean Optics (Gidrometeoizdat, Leningrad, 1983) [in Russian].

    Google Scholar 

  5. 5.

    V. Nevzorov, “The Glory Phenomenon and Nature of the Liquid Drop Fraction in Atmospheric Clouds,” Optika Atmosfery i Okeana 20(8), 674 (2007).

    Google Scholar 

  6. 6.

    V. V. Sterlyadkin, “Light Scattering by Rain Drops,” Optika Atmosfery i Okeana 13(5), 534 (2000).

    Google Scholar 

  7. 7.

    A. S. Glushchenko and V. V. Sterlyadkin, “Optical Properties of Rain Drops. Scattering to the Frontal Observation Semisphere under Horizontal Illumination,” Optika Atmosfery i Okeana 18(3), 207 (2005).

    Google Scholar 

  8. 8.

    G. S. Landsberg, Optics (Fizmatgiz, Moscow, 1976) 926 [in Russian].

    Google Scholar 

  9. 9.

    G. M. Fikhtengol’ts, A Course of Differential and Integral Computations (Fizmatgiz, Moscow, 1969), Vol. 1 [in Russian].

    Google Scholar 

  10. 10.

    P. Laven, “How Are Glories Formed,” Appl. Opt. 44(27), 5675 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to N. P. Romanov.

Additional information

Original Russian Text © N.P. Romanov, 2009, published in Optika Atmosfery i Okeana.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Romanov, N.P. A computational method and properties of phase scattering functions of transparent balls under the geometric optics approximation. Atmos Ocean Opt 22, 273–283 (2009). https://doi.org/10.1134/S1024856009030038

Download citation

Key words

  • phase scattering function
  • refractive index
  • angular dependence
  • geometric optics