Abstract

We use the current advanced version of the T-matrix method to compute the optical cross sections, the asymmetry parameter of the phase function, and the scattering matrix elements of ice spheroids with aspect ratios up to 20 and surface-equivalent-sphere size parameters up to 12. We demonstrate that platelike and needlelike particles with moderate size parameters possess unique scattering properties: their asymmetry parameters and phase functions are similar to those of surface-equivalent spheres, whereas all other elements of the scattering matrix are typical of particles much smaller than the wavelength (Rayleigh scatterers). This result may have important implications for optical particle sizing and remote sensing of the terrestrial and planetary atmospheres.

© 2000 Optical Society of America

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  1. 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]
  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]
  3. M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” 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. 147–172.
  4. M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
    [CrossRef]
  5. F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
    [CrossRef] [PubMed]
  6. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
    [CrossRef]
  7. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
    [CrossRef]
  8. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  9. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  10. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” 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. 3–27.
    [CrossRef]
  11. M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
    [CrossRef] [PubMed]
  12. 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]
  13. R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
    [CrossRef] [PubMed]
  14. K. Sassen, “Lidar backscatter depolarization technique for cloud and aerosol 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. 393–416.
    [CrossRef]
  15. W. F. Tozer, D. E. Beeson, “Optical model of noctilucent clouds based on polarimetric measurements from two sounding rocket campaigns,” J. Geophys. Res. 79, 5607–5612 (1974).
    [CrossRef]
  16. G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
    [CrossRef]
  17. R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
    [CrossRef]
  18. M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
    [CrossRef]
  19. P. Smith, “The vertical structure of the Jovian atmosphere,” Icarus 65, 264–279 (1986).
    [CrossRef]

1999 (1)

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

1998 (2)

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]

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]

1996 (1)

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]

1995 (1)

1994 (1)

1992 (1)

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

1991 (2)

R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
[CrossRef] [PubMed]

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

1986 (1)

P. Smith, “The vertical structure of the Jovian atmosphere,” Icarus 65, 264–279 (1986).
[CrossRef]

1984 (1)

1978 (1)

M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
[CrossRef]

1976 (1)

G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
[CrossRef]

1974 (2)

W. F. Tozer, D. E. Beeson, “Optical model of noctilucent clouds based on polarimetric measurements from two sounding rocket campaigns,” J. Geophys. Res. 79, 5607–5612 (1974).
[CrossRef]

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

1948 (1)

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Beeson, D. E.

W. F. Tozer, D. E. Beeson, “Optical model of noctilucent clouds based on polarimetric measurements from two sounding rocket campaigns,” J. Geophys. Res. 79, 5607–5612 (1974).
[CrossRef]

Castillo, N. D.

M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
[CrossRef]

de Haan, J. F.

Dye, J. E.

G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
[CrossRef]

Hansen, J. E.

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

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]

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” 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. 3–27.
[CrossRef]

Kuik, F.

Macke, A.

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” 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. 147–172.

Mackowski, D. W.

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]

Mishchenko, M. I.

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]

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]

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, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
[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, L. D. Travis, A. Macke, “T-matrix method and its applications,” 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. 147–172.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” 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. 3–27.
[CrossRef]

Sassen, K.

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]

K. Sassen, “Lidar backscatter depolarization technique for cloud and aerosol 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. 393–416.
[CrossRef]

Schulz, F. M.

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

Smith, P.

P. Smith, “The vertical structure of the Jovian atmosphere,” Icarus 65, 264–279 (1986).
[CrossRef]

Smith, P. H.

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

Stamnes, J. J.

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

Stamnes, K.

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

Tomasko, M. G.

M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
[CrossRef]

Tozer, W. F.

W. F. Tozer, D. E. Beeson, “Optical model of noctilucent clouds based on polarimetric measurements from two sounding rocket campaigns,” J. Geophys. Res. 79, 5607–5612 (1974).
[CrossRef]

Travis, L. D.

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]

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]

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, A. Macke, “T-matrix method and its applications,” 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. 147–172.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” 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. 3–27.
[CrossRef]

Vouk, V.

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Warren, S. G.

West, R. A.

R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
[CrossRef] [PubMed]

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
[CrossRef]

Wilhelm, N.

G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
[CrossRef]

Witt, G.

G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
[CrossRef]

Appl. Opt. (3)

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. (1)

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]

Icarus (3)

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus 90, 330–333 (1991).
[CrossRef]

M. G. Tomasko, R. A. West, N. D. Castillo, “Photometry and polarimetry of Jupiter at large phase angles. I. Analysis of imaging data of a prominent belt and a zone from Pioneer 10,” Icarus 33, 558–592 (1978).
[CrossRef]

P. Smith, “The vertical structure of the Jovian atmosphere,” Icarus 65, 264–279 (1986).
[CrossRef]

J. Atmos. Terrestrial Phys. (1)

G. Witt, J. E. Dye, N. Wilhelm, “Rocket-borne measurements of scattered sunlight in the mesosphere,” J. Atmos. Terrestrial Phys. 38, 223–238 (1976).
[CrossRef]

J. Geophys. Res. (2)

W. F. Tozer, D. E. Beeson, “Optical model of noctilucent clouds based on polarimetric measurements from two sounding rocket campaigns,” J. Geophys. Res. 79, 5607–5612 (1974).
[CrossRef]

F. M. Schulz, K. Stamnes, J. J. Stamnes, “Shape dependence of the optical properties in size-shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. 104, 9413–9421 (1999).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

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]

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]

Nature (London) (1)

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Opt. Lett. (1)

Space Sci. Rev. (1)

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

Other (3)

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” 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. 147–172.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, “Concepts, terms, notation,” 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. 3–27.
[CrossRef]

K. Sassen, “Lidar backscatter depolarization technique for cloud and aerosol 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. 393–416.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Extinction efficiency factor, asymmetry parameter, and radiation pressure efficiency factor versus surface-equivalent-sphere size parameter for spheres and randomly oriented spheroids with various semiaxis ratios. Note that the asymmetry parameter curves for spheroids with a/ b = 0.5 and 2 almost coincide.

Fig. 2
Fig. 2

Phase function and normalized elements of the scattering matrix for spheres and surface-equivalent, randomly oriented spheroids with size parameters ranging from 0.1 to 12 (see color legend) and semiaxis ratios a/ b = 0.05 (first row), 0.5 (second row), 1 (third row), 2 (fourth row), and 20 (fifth row).

Fig. 3
Fig. 3

Normalized elements of the scattering matrix for spheres and surface-equivalent, randomly oriented spheroids with size parameters ranging from 0.1 to 12 (see color legend) and semiaxis ratios a/ b = 0.05 (first row), 0.5 (second row), 1 (third row), 2 (fourth row), and 20 (fifth row).

Tables (1)

Tables Icon

Table 1 Equal-Surface-Sphere Size Parameters xs (or xs,eff), Equal-Volume-Sphere Size Parameters xv (or xv,eff), and Size Parameters along the Horizontal, xa (or xa,eff), and Vertical, xb (or xb,eff), Spheroid Axes Used in the T-Matrix Computations

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

nrs=1rs,effνeffΓ1-2νeffνeffrsrs,effνeff1-3νeff/νeff×exp- rsrs,effνeff,
a1Θb1Θ00b1Θa2Θ0000a3Θb2Θ00-b2Θa4Θ,
1/2 0πdΘa1Θsin Θ=1.

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