Large-Scale Structure and Asymptotic Regularities of Scattering Phase Function for Water Drops in the Visible Spectrum Range

摘要

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.