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


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.

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Correspondence to N. P. Romanov.

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

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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).

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Key words

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