Skip to main content

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 0.9x 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.

This is a preview of subscription content, access via your institution.


  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957; Inostr. Liter., 1961).

    Google Scholar 

  2. V. Khare and H. M. Nussenzveig, “Theory of Glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).

    Article  ADS  Google Scholar 

  3. H. M. Nussenzveig, “Complex Angular Momentum Theory of the Rainbows and the Glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  4. W. J. Wiscombe, “Improved Mie Scattering Algorithms,” Appl. Opt. 19, 1505–1509 (1980).

    Article  ADS  Google Scholar 

  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).

    ADS  Google Scholar 

  6. P. Laven, “Simulation of Rainbows, Coronas and Glories by Use of Theory Mie,” Appl. Opt. 42, 436–444 (2003).

    Article  ADS  Google Scholar 

  7. P. Laven, “Atmospheric Glories: Simulations and Observations,” Appl. Opt. 44, 5667–5675 (2005).

    Article  ADS  Google Scholar 

  8. P. Laven, “Noncircular Glories and Their Relationship to Cloud Droplet Size,” Appl. Opt. 47, H25–H30 (2008).

    Article  ADS  Google Scholar 

  9. P. Laven, “Effects of Refractive Index on Glories,” Appl. Opt. 47, H133–H142 (2008).

    Article  ADS  Google Scholar 

  10. H. M. Nussenzveig, “Does the Glory Have a Simple Explanation?” Opt. Lett. 27, 1379–1381 (2002).

    Article  ADS  Google Scholar 

  11. P. Laven, “How Are Glories Formed?” Appl. Opt. 44, 5675–5683 (2005).

    Article  ADS  Google Scholar 

  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. 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.

  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. S. T. Shipley and J. A. Weinman, “A Numerical Study of Scattering by Large Dielectric Spheres,” J. Opt. Soc. Am. 68, 130–134 (1978).

    Article  ADS  Google Scholar 

  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. N. P. Romanov, “Study of Methods and Errors in Riccatti-Bessel Functions Computations,” Opt. Atmosf. Okeana 20, 701–709 (2007).

    Google Scholar 

  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).

    Article  Google Scholar 

  19. G. S. Landsberg, Optics (Fizmatgiz, Moscow, 1976) [in Russian].

    Google Scholar 

  20. D. Deirmendjan, Electromagnetic Scattering on Spherical Polydispersion (Elsevier, New York, 1962; Mir, Moscow, 1971).

    Google Scholar 

  21. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).

    Google Scholar 

  22. P. Debye, “Der Lichtdruck Auf Kugeln Von Beliebigem Material,” Ann. Phys. IV Folge, 30, 57–136 (1909).

    Article  ADS  Google Scholar 

  23. Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (Dover, New York, 1965; Nauka, Moscow, 1979).

    Google Scholar 

  24. Tables of Bessel Functions Zeros (VTs AN SSSR, Moscow, 1967) [in Russian].

  25. M. Vollmer, “Effects of Absorbing Particles on Coronas and Glories,” Appl. Opt. 44, 5658–5666 (2005).

    Article  ADS  Google Scholar 

  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).

    Article  Google Scholar 

  27. A. Nevzorov, “Glory on Clouds: What Hides Behind It,” Nauka Zhizn’, No. 1, 58–61 (2010).

Download references

Author information

Authors and Affiliations


Additional information

Original Russian Text © N.P. Romanov, S.O. Dubnichenko, 2010, published in Optica Atmosfery i Okeana.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Romanov, N.P., Dubnichenko, S.O. Physics of formation and analytical description of glory properties. Atmos Ocean Opt 23, 508–522 (2010).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI:


  • Phase Function
  • Oceanic Optic
  • Refraction Index
  • Geometric Optic
  • Light Ring