OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 30 — Oct. 20, 2000
  • pp: 5560–5568

Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns

Anthony J. Baran and Stephan Havemann  »View Author Affiliations

Applied Optics, Vol. 39, Issue 30, pp. 5560-5568 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (131 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The applicability of various approximations for computing the absorption efficiency and single-scattering albedo of a randomly oriented hexagonal column is tested versus electromagnetic theory. To calculate the absorption efficiency and single-scattering albedo of the hexagonal column from electromagnetic theory we used a generalization to the separation-of-variables method, which enables continuous calculation of optical properties up to size parameters of 86. We found that the asymptotic absorption efficiency is independent of particle shape, and that, as the size parameter increases, the hexagonal column tends to its asymptotic absorption value more quickly than Mie theory. The asymptotic absorption limit of the hexagonal column is calculated accurately (to within 1%) and rapidly by use of the complex-angular-momentum approximation, indicating that this approximation could be used to calculate the absorption limit of nonspherical particles. The equal-volume sphere best approximates the hexagonal column single-scattering albedo at a strongly absorbing wavelength (e.g., 11.9 µm for an ice particle). However, in the resonance region (e.g., 80 µm for an ice particle) Mie theory fails to approximate the single-scattering albedo of the hexagonal column, but as the size parameter exceeds 10 the error in the sphere approximation reduces to within 2%. At 80-µm wavelength there is a characteristic ripple structure superimposed on the hexagonal column absorption efficiency solutions between size parameters from approximately 1 to 4. The ripple structure is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicability of ray tracing for calculating the single-scattering albedo at absorbing wavelengths relevant to remote sensing of ice particles in the atmosphere and found it to be within 4% for size parameters between 3 and 42 at 3.7-µm wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 µm) ray tracing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anomalous diffraction theory by using the separation-of-variables method.

© 2000 Optical Society of America

OCIS Codes
(010.2940) Atmospheric and oceanic optics : Ice crystal phenomena
(080.2720) Geometric optics : Mathematical methods (general)
(260.2110) Physical optics : Electromagnetic optics
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(290.4020) Scattering : Mie theory

Original Manuscript: November 18, 1999
Revised Manuscript: July 10, 2000
Published: October 20, 2000

Anthony J. Baran and Stephan Havemann, "Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns," Appl. Opt. 39, 5560-5568 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Wiegner, P. Seifert, P. Schlussel, “Radiative effects of cirrus clouds in Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager channels,” J. Geophys. Res. 103, 23217–23230 (1998). [CrossRef]
  2. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996). [CrossRef] [PubMed]
  4. M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current fortran implementation of the T-matrix method for randomly oriented rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998). [CrossRef]
  5. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space. Sci. Rev. 16, 527–610 (1974). [CrossRef]
  6. A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995). [CrossRef] [PubMed]
  7. P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995). [CrossRef]
  8. P. Yang, K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996). [CrossRef] [PubMed]
  9. T. Rother, “Generalization of the separation of variables method for nonspherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998). [CrossRef]
  10. T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with non-circular cross-sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMV Publishing, Cambridge, Mass., 1999), pp. 79–105. [CrossRef]
  11. H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1493 (1980). [CrossRef]
  12. A. J. Baran, S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999). [CrossRef]
  13. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  14. F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969). [CrossRef]
  15. Y. Takano, K. N. Liou, “Solar radiation transfer in cirrus clouds. Part 1: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989). [CrossRef]
  16. S. Havemann, “Modelling of atmospheric, non-spherical scatterers and its application in radiative transfer studies,” Ph.D dissertation (University of Kiel, Kiel, Germany, 2000).
  17. W. Sun, Q. Fu, Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999). [CrossRef]
  18. Q. Fu, W. B. Sun, P. Yang, “Modeling of scattering and absorption by nonspherical cirrus ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999). [CrossRef]
  19. Q. Fu, P. Yang, W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998). [CrossRef]
  20. S. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984). [CrossRef] [PubMed]
  21. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948). [CrossRef]
  22. T. C. Grenfell, S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999). [CrossRef]
  23. A. Kokhanovsky, A. Macke, “The dependence of the radiative characteristics of optically thick media on the shape of particles,” J. Quant. Spectrosc. Radiat. Transfer 63, 393–407 (1999). [CrossRef]
  24. H. M. Nussenzveig, “Uniform approximation in scattering by spheres,” J. Phys. A 21, 81–109 (1988). [CrossRef]
  25. D. L. Mitchell, A. Macke, Y. G. Liu, “Modeling cirrus clouds. Part II: Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996). [CrossRef]
  26. D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited