Atmospheric and Oceanic Optics

, Volume 23, Issue 6, pp 508–522 | Cite as

Physics of formation and analytical description of glory properties

  • N. P. Romanov
  • S. O. Dubnichenko
Optics of Clusters, Aerosols, and Hydrosoles


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 0.9x to 0.95x. 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 δx, 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 δx = 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.


Phase Function Oceanic Optic Refraction Index Geometric Optic Light Ring 
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  1. 1.
    H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957; Inostr. Liter., 1961).Google Scholar
  2. 2.
    V. Khare and H. M. Nussenzveig, “Theory of Glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).CrossRefADSGoogle Scholar
  3. 3.
    H. M. Nussenzveig, “Complex Angular Momentum Theory of the Rainbows and the Glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    W. J. Wiscombe, “Improved Mie Scattering Algorithms,” Appl. Opt. 19, 1505–1509 (1980).CrossRefADSGoogle Scholar
  5. 5.
    B. Mayer, M. Schroder, R. Preusker, and L. Schuller, “Remote Sensing of Water Cloud Droplet Size Distributions Using the Backscatter Glory: A Case Study,” Atmos. Chem. Phys. Discuss. 4, 1255–1263 (2004).ADSGoogle Scholar
  6. 6.
    P. Laven, “Simulation of Rainbows, Coronas and Glories by Use of Theory Mie,” Appl. Opt. 42, 436–444 (2003).CrossRefADSGoogle Scholar
  7. 7.
    P. Laven, “Atmospheric Glories: Simulations and Observations,” Appl. Opt. 44, 5667–5675 (2005).CrossRefADSGoogle Scholar
  8. 8.
    P. Laven, “Noncircular Glories and Their Relationship to Cloud Droplet Size,” Appl. Opt. 47, H25–H30 (2008).CrossRefADSGoogle Scholar
  9. 9.
    P. Laven, “Effects of Refractive Index on Glories,” Appl. Opt. 47, H133–H142 (2008).CrossRefADSGoogle Scholar
  10. 10.
    H. M. Nussenzveig, “Does the Glory Have a Simple Explanation?” Opt. Lett. 27, 1379–1381 (2002).CrossRefADSGoogle Scholar
  11. 11.
    P. Laven, “How Are Glories Formed?” Appl. Opt. 44, 5675–5683 (2005).CrossRefADSGoogle Scholar
  12. 12.
    A. N. Nevzorov, “Glory Phenomenon and a Nature of Liquid-Drop Fraction in Cold Clouds,” Opt. Atmosf. Okeana 20(8), 674–681 (2007).Google Scholar
  13. 13.
    V. P. Pinchuk and N. P. Romanov, “Resonant Structure of Cross Sections of Absorption, Full and Inverse Scattering of Spherical Particles with Moderate Absorption,” in Proc. of the 4th All-Union Symp. on Laser Probing of the Atmosphere (Tomsk, 1976), pp. 110–113.Google Scholar
  14. 14.
    V. A. Korshunov, N. P. Romanov, and A. V. Sharadin, “Large-Scale Feattures of Inverse Scattering Cross-Section of Aqueous Spheres,” in Proc. of the All-Union Symp. on Propagation of Optical Emission in Dispersed Medium (Gidrometeoizdat, Moscow, 1978), pp. 27–31.Google Scholar
  15. 15.
    S. T. Shipley and J. A. Weinman, “A Numerical Study of Scattering by Large Dielectric Spheres,” J. Opt. Soc. Am. 68, 130–134 (1978).CrossRefADSGoogle Scholar
  16. 16.
    N. P. Romanov, “Classification and Properties of Own Frequencies of Electromagnetic Oscillations of Sphere,” Tr. IEM No. 45 (135) (Gidrometeoizdat, Moscow, 1988), pp. 3–73.Google Scholar
  17. 17.
    N. P. Romanov, “Study of Methods and Errors in Riccatti-Bessel Functions Computations,” Opt. Atmosf. Okeana 20, 701–709 (2007).Google Scholar
  18. 18.
    N. P. Romanov, “A Computational Method and Properties of Phase Scattering Functions of Transparent Balls in the Geometric Optics Approximation,” Opt. Atmosf. Okeana 22, 435–444 (2009).CrossRefGoogle Scholar
  19. 19.
    G. S. Landsberg, Optics (Fizmatgiz, Moscow, 1976) [in Russian].Google Scholar
  20. 20.
    D. Deirmendjan, Electromagnetic Scattering on Spherical Polydispersion (Elsevier, New York, 1962; Mir, Moscow, 1971).Google Scholar
  21. 21.
    C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).Google Scholar
  22. 22.
    P. Debye, “Der Lichtdruck Auf Kugeln Von Beliebigem Material,” Ann. Phys. IV Folge, 30, 57–136 (1909).CrossRefADSGoogle Scholar
  23. 23.
    Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (Dover, New York, 1965; Nauka, Moscow, 1979).Google Scholar
  24. 24.
    Tables of Bessel Functions Zeros (VTs AN SSSR, Moscow, 1967) [in Russian].Google Scholar
  25. 25.
    M. Vollmer, “Effects of Absorbing Particles on Coronas and Glories,” Appl. Opt. 44, 5658–5666 (2005).CrossRefADSGoogle Scholar
  26. 26.
    P. L. Israelevich, J. H. Joseph, Z. Levin, and Y. Yair, “First Observation of Glory from Space,” Bull. Am. Meteorol. Soc. 90, 1772–1774 (2009).CrossRefGoogle Scholar
  27. 27.
    A. Nevzorov, “Glory on Clouds: What Hides Behind It,” Nauka Zhizn’, No. 1, 58–61 (2010).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • N. P. Romanov
    • 1
  • S. O. Dubnichenko
    • 1
  1. 1.Scientific and Industrial Association TaifunKaluzhskaya oblast, ObninskRussia

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