Physics of formation and analytical description of glory properties

Based on an analysis of the contribution of Mie series terms with the parameter x , equal to the ratio of a sphere circumference length to light wavelength, it is shown that the central bright spot of the glory is determined by light scattering at sphere resonance frequencies with harmonic numbers l res exceeding x , while light rings are formed by a group of harmonics with l from 0.9 x to 0.95 x . The formation of internal surface waves generated due to the interaction of rays tunneling through the sphere with the sphere surface is substantiated as the mechanism of formation of bright rings of the glory. To describe the phase function near the backscattering direction averaged over the basic period of resonant oscillation δ x , an approximation formula is proposed in the form of Bessel function squares of zero and second order, as well as the geometric optics (GO) phase function. The coefficients of this formula are given for a refraction index m = 4/3, for which δ x = 0.82. It was found for a range of m from 1.33 to 1.34 that the product of the sum (〈 x 〉 + 2) and the angular dimensions of the first light ring, the second dark one, and subsequent alternating rings do not depend on m and are 3.16, 5.13, 6.65, 8.31, and 9.86, respectively. These values are close to the alternating zeros of the first derivative and the second-order Bessel function.