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Applied Optics

Applied Optics


  • Vol. 43, Iss. 22 — Aug. 1, 2004
  • pp: 4427–4435

Effect of particle asphericity on single-scattering parameters: comparison between Platonic solids and spheres

Ping Yang, George W. Kattawar, and Warren J. Wiscombe  »View Author Affiliations

Applied Optics, Vol. 43, Issue 22, pp. 4427-4435 (2004)

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The single-scattering properties of the Platonic shapes, namely, the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, are investigated by use of the finite-difference time-domain method. These Platonic shapes have different extents of asphericity in terms of the ratios of their volumes (or surface areas) to those of their circumscribed spheres. We present the errors associated with four types of spherical equivalence that are defined on the basis of (a) the particle’s geometric dimension (b) equal surface area (A), (c) equal volume (V), and (d) equal-volume-to-surface-area ratio (V/A). Numerical results show that the derivations of the scattering properties of a nonspherical particle from its spherical counterpart depend on the definition of spherical equivalence. For instance, when the Platonic and spherical particles have the same geometric dimension, the phase function for a dodecahedron is more similar than that for an icosahedron to the spherical result even though an icosahedron has more faces than a dodecahedron. However, when the nonspherical and spherical particles have the same volume, the phase function of the icosahedral particle essentially converges to the phase function of the sphere, whereas the result for the dodecahedron is quite different from its spherical counterpart. Furthermore, the present scattering calculation shows that the approximation of a Platonic solid with a sphere based on V/A leads to larger errors than the spherical equivalence based on either volume or projected area.

© 2004 Optical Society of America

OCIS Codes
(010.1110) Atmospheric and oceanic optics : Aerosols
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(290.1310) Scattering : Atmospheric scattering
(290.2200) Scattering : Extinction
(290.5850) Scattering : Scattering, particles

Original Manuscript: November 28, 2003
Revised Manuscript: May 11, 2004
Published: August 1, 2004

Ping Yang, George W. Kattawar, and Warren J. Wiscombe, "Effect of particle asphericity on single-scattering parameters: comparison between Platonic solids and spheres," Appl. Opt. 43, 4427-4435 (2004)

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  1. T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1998). [CrossRef]
  2. M. I. Mishchenko, W. J. Wiscombe, J. W. Hovenier, L. D. Travis, “Overview of scattering by nonspherical particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 29–60. [CrossRef]
  3. F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 775–824 (2003). [CrossRef]
  4. K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, San Diego, Calif., 2002).
  5. A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. I: cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction,” Appl. Opt. 25, 1235–1244 (1986). [CrossRef] [PubMed]
  6. W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2: Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1988). [CrossRef] [PubMed]
  7. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  8. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996). [CrossRef]
  9. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998). [CrossRef]
  10. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 33, 4716–4731 (1991). [CrossRef]
  11. D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994). [CrossRef]
  12. D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996). [CrossRef]
  13. K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: applications to climate research,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 417–1449. [CrossRef]
  14. G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998). [CrossRef]
  15. W. Sun, T. Nousiainen, K. Muinonen, Q. Fu, N. G. Loeb, G. Videen, “Light scattering by Gaussian particles: a solution with finite-difference time-domain technique,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1083–1090 (2003). [CrossRef]
  16. T. Wriedt, “Using the T-matrix method for light scattering computations by non-axisymmetric particles: superellipsoids and realistically shaped particles,” Part. Part. Syst. Charact. 4, 256–268 (2002). [CrossRef]
  17. P. J. Barrett, “The shape of rock particles, a critical review,” Sedimentology 27, 291–303 (1980). [CrossRef]
  18. L. Liu, M. I. Mishchenko, “Constraints on PSC particle microphysics derived from lidar observations,” J. Quant Spectrosc. Radiat. Transfer 70, 817–831 (2001). [CrossRef]
  19. G. M. McFarquhar, P. Yang, A. Macke, A. J. Baran, “A new parameterization of single-scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions,” J. Atmos. Sci. 59, 2458–2478 (2002). [CrossRef]
  20. P. Yang, B. A. Baum, A. J. Heymsfield, Y. X. Hu, H.-L. Huang, S.-C. Tsay, S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 1159–1180 (2003). [CrossRef]
  21. T. Nousiainen, G. M. McFarquhar, “Light scattering by small quasi-spherical ice crystals: preliminary results,” in Proceedings of the 7th Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Universitäts-Buchhandlung, Bremen, Germany, 2003), pp. 271–274.
  22. K. S. Yee, “Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas. Propag. AP-14, 302–307 (1966).
  23. P. R. Cromwell, Polyhedra (Cambridge U. Press, Cambridge, UK, 1997).
  24. L. A. Lyusternik, Convex Figures and Polyhedra (Heath, Boston, Mass., 1966).
  25. B. Grunbaum, Convex Polytopes (Wiley, London, 1967).
  26. M. J. Wenninger, Polyhedron Models (Cambridge U. Press, Cambridge, UK, 1970).
  27. L. Euler, “Elementa Doctrinae Solidorum,” Novi Commentarii Academiae Scientiarum Petropolitanae 4, 109–140 (1758).
  28. J. S. Foot, “Some observations of the optical properties of clouds. II: cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988). [CrossRef]
  29. P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994). [CrossRef]
  30. D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus cloud. II. Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994). [CrossRef]
  31. K. Wyser, P. Yang, “Average crystal size and bulk shortwave single scattering properties in ice clouds,” Atmos. Res. 49, 315–335 (1998). [CrossRef]
  32. Q. Fu, W. Sun, P. Yang, “On modeling of scattering and absorption by cirrus nonspherical ice particles at thermal infrared wavelengths,” J. Atmos. Sci. 56, 2937–2947 (1999). [CrossRef]
  33. 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]
  34. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948). [CrossRef]
  35. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  36. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
  37. S. Havemann, A. J. Baran, “Extension of T-matrix to scattering of electromagnetic plane waves by non-axisymmetric particles: application to hexagonal ice cylinders,” J. Quant. Spectrosc. Radiat. Transfer 70, 139–158 (2001). [CrossRef]
  38. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
  39. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for light calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
  40. A. Taflove, Advances in Computational Electromagnetics (Artech House, Boston, Mass., 1998).
  41. P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996). [CrossRef]
  42. P. Yang, K. N. Liou, M. I. Mishchenko, B. C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols,” Appl. Opt. 39, 3727–3737 (2000). [CrossRef]
  43. W. B. 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]
  44. J. P. Berenger, “A perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  45. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  46. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984). [CrossRef] [PubMed]
  47. M. I. Mischenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
  48. W. P. Arnott, Y. Y. Dong, J. Hallett, “Extinction efficiency in the infrared (2–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995). [CrossRef] [PubMed]
  49. P. Yang, K. N. Liou, W. P. Arnott, “Extinction efficiency and single-scattering albedo of ice crystals in laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997). [CrossRef]
  50. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997). [CrossRef]

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