Large-scale structure and asymptotic regularities of phase scattering function for water in the visible spectrum range
N.P. Romanov, S.A. Borodin, S.O. Dubnichenko, L.D. Novikova
Russian Federal Service on Hydrometeorology and Environmental Monitoring Research and Production Association “Typhoon”, 4, Pobeda str., Obninsk, Kaluga Region, 249038 Russia
Keywords: phase scattering function, interference, diffraction, geometrical optics, Mie theory
Abstract
The analysis of mechanisms of radiation scattered in the range of angles θ from 0 to 180° is made for a sphere by comparing the exact phase scattering functions calculated with the Mie theory and interference phase scattering functions with the use of diffraction and partial rays of geometric optics (GO). In view of refinements of relative phase shifts of all rays and the amplitude of the diffraction ray, it appeared that large-scale oscillation regularities of the exact phase scattering function at high Mie parameters x corresponded to the interference pattern of two or three rays mentioned above. For integral characteristics a computation error with the interference formulae in the range of angles θ = 0 ÷ 10° does not exceed units of percent for х > 10 and within the large x values it tends to zero. For other ranges, depending on the difference in the combination of the integer parts parity in the p intervals of the total scattering angle tendency of oscillation periods over the angle to zero is seen according to the laws of х–1, х–2/3 (rainbows) and х–1/2. The oscillation period over x begins to depend only on θ. The results of the calculations of exact phase scattering functions average over the intervals Δθ = 10 ÷ 15° for the refraction index m = 4/3 are presented in the form of approximation relationships with the asymptotic tendency to the GO phase scattering function.
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