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Applied Optics

Applied Optics


  • Vol. 42, Iss. 21 — Jul. 20, 2003
  • pp: 4389–4395

Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase

Ping Yang, Heli Wei, George W. Kattawar, Yong X. Hu, David M. Winker, Chris A. Hostetler, and Bryan A. Baum  »View Author Affiliations

Applied Optics, Vol. 42, Issue 21, pp. 4389-4395 (2003)

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The Mueller matrix (M) corresponding to the phase matrix in the backscattering region (scattering angles ranging from 175° to 180°) is investigated for light scattering at a 0.532-µm wavelength by hexagonal ice crystals, ice spheres, and water droplets. For hexagonal ice crystals we assume three aspect ratios (plates, compact columns, and columns). It is shown that the contour patterns of the backscattering Mueller matrix elements other than M11, M44, M14, and M41 depend on particle geometry; M22 and M33 are particularly sensitive to the aspect ratio of ice crystals. The Mueller matrix for spherical ice particles is different from those for nonspherical ice particles. In addition to discriminating between spherical and nonspherical particles, the Mueller matrix may offer some insight as to cloud thermodynamic phase. The contour patterns for large ice spheres with an effective size of 100 µm are substantially different from those associated with small water droplets with an effective size of 4 µm.

© 2003 Optical Society of America

OCIS Codes
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(290.1350) Scattering : Backscattering
(290.5850) Scattering : Scattering, particles

Original Manuscript: January 30, 2003
Revised Manuscript: April 21, 2003
Published: July 20, 2003

Ping Yang, Heli Wei, George W. Kattawar, Yong X. Hu, David M. Winker, Chris A. Hostetler, and Bryan A. Baum, "Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase," Appl. Opt. 42, 4389-4395 (2003)

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  1. G. W. Kattawar, M. J. Rakovic, “Virtues of Mueller matrix imaging for underwater target detection,” Appl. Opt. 38, 6431–6438 (1999). [CrossRef]
  2. B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, G. L. Cote, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998). [CrossRef]
  3. T. Gehrels, ed., Planets, Stars and Nebulae (University of Arizona, Tucson, Ariz., 1974).
  4. K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991). [CrossRef]
  5. S. R. Pal, A. I. Carswell, “Polarization anisotropy in lidar multiple scattering from atmospheric clouds,” Appl. Opt. 24, 3464–3471 (1985). [CrossRef] [PubMed]
  6. M. J. Rakovic, G. W. Kattawar, B. D. Cameron, M. Mehrubeoglu, S. Rastegar, L. V. Wang, G. L. Cot, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999). [CrossRef]
  7. M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998). [CrossRef]
  8. Y. X. Hu, D. Winker, P. Yang, B. A. Baum, L. Poole, L. Vann, “Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study,” J. Quant. Spectrosc. Radiat. Transfer 70, 569–579 (2001). [CrossRef]
  9. Y. X. Hu, P. Yang, B. Lin, C. Hostetler, “Discriminating between spherical and non-spherical scatters with lidar using circular component: a theoretical study,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 757–764 (2003). [CrossRef]
  10. D. M. Winker, B. A. Wielicki, “The PICASSO-CENA mission,” in Sensors, Systems, and Next-Generation Satellites III, H. Fujisada, J. B. Lurie, eds., Proc. SPIE3870, 26–36 (1999). [CrossRef]
  11. A. Ben-David, “Mueller matrices and information derived from linear polarization lidar measurements: theory,” Appl. Opt. 37, 2448–2463 (1998). [CrossRef]
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  13. S. Chandrasekhar, Radiative Transfer (Oxford U. Press, London, 1950).
  14. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  15. M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
  16. K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, San Diego, Calif., 2002).
  17. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984). [CrossRef] [PubMed]
  18. 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]
  19. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
  20. Q. M. Cai, K. N. Liou, “Theory of polarized light scattering by hexagonal ice crystals,” Appl. Opt. 21, 3569–3580 (1982). [CrossRef] [PubMed]
  21. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989). [CrossRef]
  22. A. Macke, J. Muller, E. Rascke, “Single-scattering properties of atmopsheric crystals,” J. Atmos. Sci. 53, 2813–2825 (1996). [CrossRef]
  23. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974). [CrossRef]
  24. M. D. King, “Determination of the scaled optical thickness of clouds from reflected solar radiation measurements,” J. Atmos. Sci. 44, 1734–1751 (1987). [CrossRef]
  25. J. W. Hovenier, “Structure of a general pure Mueller matrix,” Appl. Opt. 33, 8318–8324 (1994). [CrossRef] [PubMed]
  26. C. R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrix for light scattering from a nonspherical dielectric scatter,” Appl. Opt. 26, 4159–4173 (1987). [CrossRef] [PubMed]

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