Abstract

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T-matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.

© 1996 Optical Society of America

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    [CrossRef] [PubMed]
  2. M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
    [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]
  4. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  5. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
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    [CrossRef]
  7. J. F. de Haan, “Effects of aerosols on the brightness and polarization of cloudless planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1987).
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  11. W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  21. M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  26. C. -R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
    [CrossRef] [PubMed]
  27. M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
    [CrossRef] [PubMed]
  28. E. S. Fry, G. W. Kattawar, “Relationships between the elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
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  30. C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).
  31. 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]
  32. M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
    [CrossRef]
  33. M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
    [CrossRef]
  34. W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2440–2451 (1976).
    [CrossRef]
  35. S. F. Marshall, D. S. Covert, R. J. Charlson, “Relationship between asymmetry parameter and hemispheric backscatter ratio: implications for climate forcing by aerosols,” Appl. Opt. 34, 6306–6311 (1995).
    [CrossRef] [PubMed]
  36. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.
  37. G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 laser wavelengths. 1: aerosol properties, modeling techniques, and associated problems,” Appl. Opt. 22, 1655–1665 (1983).
    [CrossRef] [PubMed]
  38. Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
    [CrossRef] [PubMed]
  39. V. Srivastava, M. A. Jarzembski, D. A. Bowdle, “Comparison of calculated aerosol backscatter at 9.1- and 2.1-μm wavelengths,” Appl. Opt. 31, 1904–1906 (1992).
    [CrossRef] [PubMed]
  40. G. L. Stephens, Remote Sensing of the Lower Atmosphere (Oxford U. Press, New York, 1994).
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    [CrossRef] [PubMed]
  42. R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
    [CrossRef] [PubMed]
  43. K. Sassen, K. -N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice-crystal clouds. Part I: angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
    [CrossRef]
  44. M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
    [CrossRef]
  45. K. Sassen, “The polarization radar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
    [CrossRef]
  46. W. L. Eberhard, “Ice-cloud depolarization of backscatter for CO2 and other infrared lidars,” Appl. Opt. 31, 6485–6490 (1992).
    [CrossRef] [PubMed]
  47. S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235–1279 (1993).
    [CrossRef]
  48. L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
    [CrossRef]
  49. R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Contrib. Atmos. Phys./Beitr. Phys. Atmos. 49, 168–188 (1976).
  50. K. -N. Liou, H. Lahore, “Laser sensing of cloud composition: a backscattered depolarization technique,” J. Appl. Meteorol. 13, 257–263 (1974).
    [CrossRef]
  51. M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
    [CrossRef]

1996 (2)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

1995 (6)

1994 (4)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

1993 (3)

W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
[CrossRef]

M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235–1279 (1993).
[CrossRef]

1992 (4)

W. L. Eberhard, “Ice-cloud depolarization of backscatter for CO2 and other infrared lidars,” Appl. Opt. 31, 6485–6490 (1992).
[CrossRef] [PubMed]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Benchmark results for single scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
[CrossRef]

V. Srivastava, M. A. Jarzembski, D. A. Bowdle, “Comparison of calculated aerosol backscatter at 9.1- and 2.1-μm wavelengths,” Appl. Opt. 31, 1904–1906 (1992).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
[CrossRef]

1991 (3)

K. Sassen, “The polarization radar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[CrossRef]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991); “Erratum,” 9, 497 (1992).
[CrossRef]

1990 (1)

C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).

1989 (1)

1988 (1)

1987 (2)

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

C. -R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
[CrossRef] [PubMed]

1986 (2)

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 1: cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction,” Appl. Opt. 25, 1235–1244 (1986).
[CrossRef] [PubMed]

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

1983 (2)

G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 laser wavelengths. 1: aerosol properties, modeling techniques, and associated problems,” Appl. Opt. 22, 1655–1665 (1983).
[CrossRef] [PubMed]

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

1981 (1)

1980 (1)

1979 (1)

K. Sassen, K. -N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice-crystal clouds. Part I: angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

1978 (1)

1976 (2)

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2440–2451 (1976).
[CrossRef]

R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Contrib. Atmos. Phys./Beitr. Phys. Atmos. 49, 168–188 (1976).

1974 (2)

K. -N. Liou, H. Lahore, “Laser sensing of cloud composition: a backscattered depolarization technique,” J. Appl. Meteorol. 13, 257–263 (1974).
[CrossRef]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1955 (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Asano, S.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bosma, P. B.

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Bowdle, D. A.

Browell, E. V.

Carlson, B. E.

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]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Charlson, R. J.

Covert, D. S.

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols (Deepak, Hampton, Va., 1991).

David, C.

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

de Haan, J. F.

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
[CrossRef]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Benchmark results for single scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
[CrossRef]

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

J. F. de Haan, “Effects of aerosols on the brightness and polarization of cloudless planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1987).

Deepak, A.

Del Guasta, M.

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

Eberhard, W. L.

Farrukh, U. O.

Fry, E. S.

Gelfand, I. M.

I. M. Gelfand, R. A. Minlos, Z. Y. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon, Oxford, 1963).

Godin, S.

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

Grams, G. W.

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2440–2451 (1976).
[CrossRef]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Herb, P.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
[CrossRef] [PubMed]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
[CrossRef]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Benchmark results for single scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
[CrossRef]

C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Hu, C. -R.

Huffman, D. R.

Hunt, A. J.

Jarzembski, M. A.

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.

Kattawar, G. W.

Kent, G. S.

Koepke, P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols (Deepak, Hampton, Va., 1991).

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Kuik, F.

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Benchmark results for single scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
[CrossRef]

F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).

Lacis, A. A.

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

Lahore, H.

K. -N. Liou, H. Lahore, “Laser sensing of cloud composition: a backscattered depolarization technique,” J. Appl. Meteorol. 13, 257–263 (1974).
[CrossRef]

Liou, K. -N.

K. Sassen, K. -N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice-crystal clouds. Part I: angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

K. -N. Liou, H. Lahore, “Laser sensing of cloud composition: a backscattered depolarization technique,” J. Appl. Meteorol. 13, 257–263 (1974).
[CrossRef]

Macke, A.

Mackowski, D. W.

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

Marshall, S. F.

Minlos, R. A.

I. M. Gelfand, R. A. Minlos, Z. Y. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon, Oxford, 1963).

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

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]

M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
[CrossRef]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991); “Erratum,” 9, 497 (1992).
[CrossRef]

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.

Morandi, M.

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

Mugnai, A.

Muinonen, K.

Ostro, S. J.

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235–1279 (1993).
[CrossRef]

Parkin, M. E.

Perry, R. J.

Sasano, Y.

Sassen, K.

K. Sassen, “The polarization radar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

K. Sassen, K. -N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice-crystal clouds. Part I: angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

Sato, M.

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Shapiro, Z. Y.

I. M. Gelfand, R. A. Minlos, Z. Y. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon, Oxford, 1963).

Shettle, E. P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols (Deepak, Hampton, Va., 1991).

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Srivastava, V.

Stammes, P.

P. Stammes, “Light scattering properties of aerosols and the radiation inside a planetary atmosphere,” Ph.D. dissertation (Free University, Amsterdam, 1989).

Stefanutti, L.

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

Stephens, G. L.

G. L. Stephens, Remote Sensing of the Lower Atmosphere (Oxford U. Press, New York, 1994).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van der Mee, C. V. M.

C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Wauben, W. M. F.

W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
[CrossRef]

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.

Wiscombe, W. J.

Yue, G. K.

Zerull, R. H.

R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Contrib. Atmos. Phys./Beitr. Phys. Atmos. 49, 168–188 (1976).

Appl. Opt. (15)

M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

W. J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2: means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1988).
[CrossRef] [PubMed]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 1: cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction,” Appl. Opt. 25, 1235–1244 (1986).
[CrossRef] [PubMed]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

E. S. Fry, G. W. Kattawar, “Relationships between the elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
[CrossRef] [PubMed]

C. -R. Hu, G. W. Kattawar, M. E. Parkin, P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
[CrossRef] [PubMed]

S. F. Marshall, D. S. Covert, R. J. Charlson, “Relationship between asymmetry parameter and hemispheric backscatter ratio: implications for climate forcing by aerosols,” Appl. Opt. 34, 6306–6311 (1995).
[CrossRef] [PubMed]

G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 laser wavelengths. 1: aerosol properties, modeling techniques, and associated problems,” Appl. Opt. 22, 1655–1665 (1983).
[CrossRef] [PubMed]

Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
[CrossRef] [PubMed]

V. Srivastava, M. A. Jarzembski, D. A. Bowdle, “Comparison of calculated aerosol backscatter at 9.1- and 2.1-μm wavelengths,” Appl. Opt. 31, 1904–1906 (1992).
[CrossRef] [PubMed]

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef] [PubMed]

W. L. Eberhard, “Ice-cloud depolarization of backscatter for CO2 and other infrared lidars,” Appl. Opt. 31, 6485–6490 (1992).
[CrossRef] [PubMed]

Astron. Astrophys. (4)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

J. F. de Haan, P. B. Bosma, J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Bull. Am. Meteorol. Soc. (1)

K. Sassen, “The polarization radar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

Contrib. Atmos. Phys./Beitr. Phys. Atmos. (1)

R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Contrib. Atmos. Phys./Beitr. Phys. Atmos. 49, 168–188 (1976).

Earth Moon Planets (1)

M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
[CrossRef]

Geophys. Res. Lett. (2)

L. Stefanutti, M. Morandi, M. Del Guasta, S. Godin, C. David, “Unusual PSCs observed by LIDAR in Antarctica,” Geophys. Res. Lett. 22, 2377–2380 (1995).
[CrossRef]

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

J. Appl. Meteorol. (1)

K. -N. Liou, H. Lahore, “Laser sensing of cloud composition: a backscattered depolarization technique,” J. Appl. Meteorol. 13, 257–263 (1974).
[CrossRef]

J. Atmos. Sci. (2)

K. Sassen, K. -N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice-crystal clouds. Part I: angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

W. J. Wiscombe, G. W. Grams, “The backscattered fraction in two-stream approximations,” J. Atmos. Sci. 33, 2440–2451 (1976).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (6)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

W. M. F. Wauben, J. F. de Haan, J. W. Hovenier, “Influence of particle shape on the polarized radiation in planetary atmospheres,” J. Quant. Spectrosc. Radiat. Transfer 50, 237–246 (1993).
[CrossRef]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Benchmark results for single scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
[CrossRef]

M. I. Mishchenko, “Reflection of polarized light by plane-parallel slabs containing randomly-oriented, nonspherical particles,” J. Quant. Spectrosc. Radiat. Transfer 46, 171–181 (1991).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

Opt. Commun. (1)

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Rev. Mod. Phys. (1)

S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235–1279 (1993).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Other (10)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

I. M. Gelfand, R. A. Minlos, Z. Y. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon, Oxford, 1963).

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols (Deepak, Hampton, Va., 1991).

J. F. de Haan, “Effects of aerosols on the brightness and polarization of cloudless planetary atmospheres,” Ph.D. dissertation (Free University, Amsterdam, 1987).

P. Stammes, “Light scattering properties of aerosols and the radiation inside a planetary atmosphere,” Ph.D. dissertation (Free University, Amsterdam, 1989).

F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dust-like tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” submitted to J. Geophys. Res.

G. L. Stephens, Remote Sensing of the Lower Atmosphere (Oxford U. Press, New York, 1994).

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Figures (16)

Fig. 1
Fig. 1

Comparison of the shape of spheroids and finite circular cylinders with horizontal-to-vertical dimension ratios of 1/2 (prolate particles), 1 (compact particles), and 2 (oblate particles).

Fig. 2
Fig. 2

Elements of the scattering matrix versus scattering angle Θ for randomly oriented, monodisperse cylinders with a diameter-to-length ratio of 1, an equal-surface-area-sphere size parameter of 70, and a refractive index of 1.53 + 0.008i.

Fig. 3
Fig. 3

Elements of the scattering matrix versus scattering angle Θ for randomly oriented, monodisperse, prolate cylinders with a diameter-to-length ratio of 1/2, an equal-surface-area-sphere size parameter of 3, and a refractive index of 1.53 + 0.008i.

Fig. 4
Fig. 4

Ratio of the extinction cross section for randomly oriented, polydisperse cylinders with diameter-to-length ratios D/L = 1, 1/1.4, 1.4, 1/2, and 2 relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 5
Fig. 5

Ratio of the scattering cross section for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 6
Fig. 6

Ratio of the absorption cross section for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 7
Fig. 7

Ratio of the single-scattering albedo for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 8
Fig. 8

Ratio of the asymmetry parameter of the phase function for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 9
Fig. 9

Ratio of the backscattered fraction for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 10
Fig. 10

Upper-left diagram shows the logarithm of the phase function versus scattering angle and effective size parameter for polydisperse spheres with a refractive index of 1.53 + 0.008i and an effective variance of νeff = 0.1. This diagram can be quantified by using the left-hand color bar at the bottom of the figure. The three lower diagrams of the left-hand column show the ratio of the phase function for polydisperse, randomly oriented cylinders with diameter-to-length ratios D/L = 1, 1/2, and 2 relative to that for surface-equivalent spheres. These diagrams can be quantified by using the middle color bar. The middle and the right-hand columns show ratios F33/F11 and F44/F11 of the elements of the scattering matrix for polydisperse, surface-equivalent spheres and randomly oriented cylinders. These diagrams can be quantified by using the right-hand color bar. Note that visible boundaries between discrete colors in the figures and color bars permit convenient and easy quantification of the respective diagrams by using the white color as the reference.

Fig. 11
Fig. 11

Phase function versus scattering angle for polydisperse, randomly oriented cylinders and surface-equivalent spheres with effective size parameters xeff = 5, 10, 15, and 25.

Fig. 12
Fig. 12

Ratio of the phase function at Θ = 180° for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 13
Fig. 13

Ratio of extinction-to-backscatter ratio Reb for randomly oriented polydisperse cylinders relative to that for surface-equivalent spheres versus effective size parameter.

Fig. 14
Fig. 14

Ratios F22/F11, −F21/F11, and F34/F11 of the elements of the scattering matrix for polydisperse, surface-equivalent spheres and randomly oriented cylinders with diameter-to-length ratios D/L = 1, 1/2, and 2. The diagrams in each column should be quantified by using the color bar below this column.

Fig. 15
Fig. 15

Linear backscattering depolarization ratio versus effective size parameter for randomly oriented polydisperse cylinders.

Fig. 16
Fig. 16

Circular backscattering depolarization ratio versus effective size parameter for randomly oriented polydisperse cylinders.

Tables (2)

Tables Icon

Table 1 Expansion Coefficients from Eqs. (3)(8) for Randomly Oriented, Monodisperse, Prolate Cylindersa

Tables Icon

Table 2 Elements of the Scattering Matrix Versus Scattering Angle Θ for Randomly Oriented, Monodisperse, Prolate Cylindersa

Equations (18)

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F ( Θ ) = [ F 11 ( Θ ) F 21 ( Θ ) 0 0 F 21 ( Θ ) F 22 ( Θ ) 0 0 0 0 F 33 ( Θ ) F 34 ( Θ ) 0 0 F 34 ( Θ ) F 44 ( Θ ) ] .
1 4 π 4 π d Ω F 11 ( Θ ) = 1 .
F 11 ( Θ ) = s = 0 s max α 1 s P 00 s ( cos Θ ) ,
F 22 ( Θ ) + F 33 ( Θ ) = s = 2 s max ( α 2 s + α 3 s ) P 22 s ( cos Θ ) ,
F 22 ( Θ ) F 33 ( Θ ) = s = 2 s max ( α 2 s α 3 s ) P 2 , 2 s ( cos Θ ) ,
F 44 ( Θ ) = s = 0 s max α 4 s P 00 s ( cos Θ ) ,
F 21 ( Θ ) = s = 0 s max β 1 s P 02 s ( cos Θ ) ,
F 34 ( Θ ) = s = 0 s max β 2 s P 02 s ( cos Θ ) ,
n ( x ) = { C for x x 1 C ( x 1 / x ) 3 for x 1 x x 2 , 0 for x x 2 ,
0 d x n ( x ) = 1 .
x eff = 1 G 0 d x π x 3 n ( x ) ,
ν eff = 1 G x eff 2 0 d x ( x x eff ) 2 π x 2 n ( x ) ,
G = 0 d x π x 2 n ( x ) ,
β = 1 2 π 0 π d Θ F 11 ( Θ ) Θ sin Θ .
R e b = C ext C sca P ( 180 ° ) .
δ L = F 11 ( 180 ° ) F 22 ( 180 ° ) F 11 ( 180 ° ) + F 22 ( 180 ° ) ,
δ C = F 11 ( 180 ° ) + F 44 ( 180 ° ) F 11 ( 180 ° ) F 44 ( 180 ° ) .
δ C = 2 δ L 1 δ L .

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