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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 11 — Nov. 1, 2003
  • pp: 2071–2080

Scattering matrices for large ice crystal particles

Anatoli G. Borovoi and Igor A. Grishin  »View Author Affiliations

JOSA A, Vol. 20, Issue 11, pp. 2071-2080 (2003)

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The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.

© 2003 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(280.3640) Remote sensing and sensors : Lidar
(290.1310) Scattering : Atmospheric scattering
(290.1350) Scattering : Backscattering

Original Manuscript: December 30, 2002
Revised Manuscript: July 14, 2003
Manuscript Accepted: July 21, 2003
Published: November 1, 2003

Anatoli G. Borovoi and Igor A. Grishin, "Scattering matrices for large ice crystal particles," J. Opt. Soc. Am. A 20, 2071-2080 (2003)

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  1. K. N. Liou, “Influence of cirrus clouds on weather and climate process: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986). [CrossRef]
  2. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, 2000).
  3. Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982). [CrossRef] [PubMed]
  4. Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985). [CrossRef] [PubMed]
  5. K. Muinonen, “Scattering of light by crystals: a modified Kirchhoff approximation,” Appl. Opt. 28, 3044–3050 (1989). [CrossRef] [PubMed]
  6. K. Muinonen, K. Lumme, J. Peltoniemi, W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989). [CrossRef] [PubMed]
  7. M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonalice crystals,” Appl. Opt. 33, 7740–7746 (1994). [CrossRef] [PubMed]
  8. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993). [CrossRef] [PubMed]
  9. A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996). [CrossRef]
  10. M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving δ-function transmission,” J. Geophys. Soc. 103, No. D2, 1799–1805 (1998). [CrossRef]
  11. V. Noel, G. Ledanois, H. Chepfer, P. H. Flamant, “Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space,” Appl. Opt. 40, 4365–4375 (2001). [CrossRef]
  12. A. Borovoi, I. Grishin, E. Naats, U. Oppel, “Backscattering peak of hexagonal ice columns and plates,” Opt. Lett. 25, 1388–1390 (2000). [CrossRef]
  13. A. Borovoi, I. Grishin, E. Naats, U. Oppel, “Light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf. 72, 403–417 (2002). [CrossRef]
  14. 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]
  15. 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]
  16. P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997). [CrossRef]
  17. A. Borovoi, “Light propagation in precipitation,” Izv. Vuzov. SSSR Radiofizi. 25, 391–400 (1982) (in Russian).
  18. A. Borovoi, “Light propagation in media with closely packed particles,” Opt. Spektrosk. 54, 757–759 (1983) (in Russian).
  19. C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 8, 1220–1224 (1978). [CrossRef]
  20. C. M. R. Platt, “Remote sensing of high cirrus clouds. III: Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981). [CrossRef]
  21. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1970).

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