Abstract

We show that the use of a matrix inversion scheme based on a special lower triangular–upper triangular factorization rather than on the standard Gaussian elimination significantly improves the numerical stability of T-matrix computations for nonabsorbing and weakly absorbing nonspherical particles. As a result, the maximum convergent size parameter for particles with small or zero absorption can increase by a factor of several and can exceed 100. We describe an improved scheme for evaluating Clebsch–Gordon coefficients with large quantum numbers, which allowed us to extend the analytical orientational averaging method developed by Mishchenko [J. Opt. Soc. Am. A 8, 871 (1991)] to larger size parameters. Comparisons of T-matrix and geometrical optics computations for large, randomly oriented spheroids and finite circular cylinders show that the applicability range of the ray-tracing approximation depends on the imaginary part of the refractive index and is different for different elements of the scattering matrix.

© 1997 Optical Society of America

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References

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  1. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  2. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quantum Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, M. I. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).
  4. P. W. Barber, “Resonance electromagnetic absorption by nonspherical dielectric objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373–381 (1977).
    [CrossRef]
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    [CrossRef]
  9. C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
    [CrossRef]
  10. S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
    [CrossRef]
  11. W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
    [CrossRef]
  12. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991); J. Opt. Soc. Am. A 9, 497(E) (1992).
  13. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  14. F. Y. Sid’ko, V. N. Lopatin, L. E. Paramonov, Polarization Characteristics of Suspensions of Biological Particles (Nauka, Novosibirsk, 1990), in Russian.
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).
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    [CrossRef]
  22. 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]
  23. D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
    [CrossRef]
  24. K. Schulten, R. G. Gordon, “Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta,” J. Math. Phys. 16, 1961–1970 (1975).
    [CrossRef]
  25. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  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).
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  27. 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]
  28. M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995).
    [CrossRef] [PubMed]
  29. 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).
  30. C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).
  31. M. I. Mishchenko, “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).
    [CrossRef]
  32. M. I. Mishchenko, “Scattering cross section for randomly oriented particles of arbitrary shape,” Kinem. Phys. Celest. Bodies 7(5) , 93–95 (1991).
  33. N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
    [CrossRef] [PubMed]
  34. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  35. 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]
  36. 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]
  37. J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
    [CrossRef]
  38. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  39. 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]
  40. A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).
  41. A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
    [CrossRef]
  42. A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
    [CrossRef] [PubMed]
  43. P. Yang, Q. Cai, “Light scattering phase matrices for spheroidal and cylindric large particles,” Chinese J. Atmos. Sci. 14, 345–358 (1991).
  44. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  45. 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]
  46. A. Doicu, T. Wriedt, “Extended boundary condition method with multipole sources localized in the complex plane,” Opt. Commun. (1997).

1997 (1)

A. Doicu, T. Wriedt, “Extended boundary condition method with multipole sources localized in the complex plane,” Opt. Commun. (1997).

1996 (6)

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quantum 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]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

1995 (2)

1994 (5)

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]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering by highly aspherical targets: EBCM coupled with reinforced orthogonalization,” Appl. Opt. 23, 3502–3504 (1994).

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. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (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]

1993 (1)

1992 (3)

N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (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]

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

1991 (3)

P. Yang, Q. Cai, “Light scattering phase matrices for spheroidal and cylindric large particles,” Chinese J. Atmos. Sci. 14, 345–358 (1991).

M. I. Mishchenko, “Scattering cross section for randomly oriented particles of arbitrary shape,” Kinem. Phys. Celest. Bodies 7(5) , 93–95 (1991).

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

1990 (3)

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

M. I. Mishchenko, “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).
[CrossRef]

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

1989 (1)

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

1987 (1)

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]

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).

1984 (2)

1977 (1)

P. W. Barber, “Resonance electromagnetic absorption by nonspherical dielectric objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373–381 (1977).
[CrossRef]

1975 (1)

K. Schulten, R. G. Gordon, “Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta,” J. Math. Phys. 16, 1961–1970 (1975).
[CrossRef]

1974 (1)

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]

Ackerman, T. P.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Arnott, W. P.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Barber, P. W.

P. W. Barber, “Resonance electromagnetic absorption by nonspherical dielectric objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373–381 (1977).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Cai, Q.

P. Yang, Q. Cai, “Light scattering phase matrices for spheroidal and cylindric large particles,” Chinese J. Atmos. Sci. 14, 345–358 (1991).

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]

A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Dalu, G.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

de Haan, J. F.

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]

Doicu, A.

A. Doicu, T. Wriedt, “Extended boundary condition method with multipole sources localized in the complex plane,” Opt. Commun. (1997).

Dong, Y. Y.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).

Fraser, R. S.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

Golub, G. H.

G. H. Golub, C. F. van Loan, Matrix Computations, (Johns Hopkins U. Press, Baltimore, Md., 1989), Chap. 3.

Gordon, R. G.

K. Schulten, R. G. Gordon, “Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta,” J. Math. Phys. 16, 1961–1970 (1975).
[CrossRef]

Hallett, J.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Hansen, J. E.

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

Hart, W. D.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Herb, P.

Heymsfield, A. J.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hovenier, J. W.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (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]

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. 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).

Hu, C. R.

Iskander, M. F.

Kattawar, G. W.

Khersonskii, V. K.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
[CrossRef]

Khlebtsov, N. G.

Kinne, S.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

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

Lakhtakia, A.

Lopatin, V. N.

F. Y. Sid’ko, V. N. Lopatin, L. E. Paramonov, Polarization Characteristics of Suspensions of Biological Particles (Nauka, Novosibirsk, 1990), in Russian.

Lumme, K.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Macke, A.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[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]

A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Macke, M. I.

M. I. Mishchenko, L. D. Travis, M. I. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Mackowski, D. W.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (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, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quantum Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Mishchenko, M. I.

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. Quantum Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

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, “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 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, “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, “Scattering cross section for randomly oriented particles of arbitrary shape,” Kinem. Phys. Celest. Bodies 7(5) , 93–95 (1991).

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

M. I. Mishchenko, “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).
[CrossRef]

M. I. Mishchenko, L. D. Travis, M. I. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Moskalev, A. N.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Mugnai, A.

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]

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of calculations,” (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

Muinonen, K.

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]

A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Paramonov, L. E.

F. Y. Sid’ko, V. N. Lopatin, L. E. Paramonov, Polarization Characteristics of Suspensions of Biological Particles (Nauka, Novosibirsk, 1990), in Russian.

Parkin, M. E.

Platt, C. M. R.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Poelott, M. R.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Prabhakara, C.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).

Rahola, J.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Raschke, E.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Sassen, K.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Schulten, K.

K. Schulten, R. G. Gordon, “Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta,” J. Math. Phys. 16, 1961–1970 (1975).
[CrossRef]

Shin, R. T.

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

Sid’ko, F. Y.

F. Y. Sid’ko, V. N. Lopatin, L. E. Paramonov, Polarization Characteristics of Suspensions of Biological Particles (Nauka, Novosibirsk, 1990), in Russian.

Spinhirne, J. D.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

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

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, M. I. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

Tsang, L.

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

Valero, F. P. J.

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

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).

van Loan, C. F.

G. H. Golub, C. F. van Loan, Matrix Computations, (Johns Hopkins U. Press, Baltimore, Md., 1989), Chap. 3.

Varadan, V. K.

Varadan, V. V.

Varshalovich, D. A.

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).

Voshchinnikov, N. V.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Warren, S. G.

Waterman, P. C.

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

P. C. Waterman, “Numerical solution of electromagnetic scattering problems,” in Computer Techniques for Electromagnetics, R. Mitra, ed. (Pergamon, Oxford, 1973), pp. 97–157.
[CrossRef]

Wiscombe, W. J.

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]

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of calculations,” (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

Wriedt, T.

A. Doicu, T. Wriedt, “Extended boundary condition method with multipole sources localized in the complex plane,” Opt. Commun. (1997).

Yang, P.

P. Yang, Q. Cai, “Light scattering phase matrices for spheroidal and cylindric large particles,” Chinese J. Atmos. Sci. 14, 345–358 (1991).

Yoo, J.-M.

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

Appl. Opt. (10)

M. F. Iskander, A. Lakhtakia, “Extension of the iterative EBCM to calculate scattering by low-loss or lossless elongated dielectric objects,” Appl. Opt. 23, 948–953 (1984).
[CrossRef] [PubMed]

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[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]

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]

N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
[CrossRef] [PubMed]

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]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Scattering by highly aspherical targets: EBCM coupled with reinforced orthogonalization,” Appl. Opt. 23, 3502–3504 (1994).

Astron. Astrophys. (2)

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).

Astrophys. Space Sci. (1)

M. I. Mishchenko, “Extinction of light by randomly-oriented non-spherical grains,” Astrophys. Space Sci. 164, 1–13 (1990).
[CrossRef]

Chinese J. Atmos. Sci. (1)

P. Yang, Q. Cai, “Light scattering phase matrices for spheroidal and cylindric large particles,” Chinese J. Atmos. Sci. 14, 345–358 (1991).

IEEE Trans. Microwave Theory Tech. (1)

P. W. Barber, “Resonance electromagnetic absorption by nonspherical dielectric objects,” IEEE Trans. Microwave Theory Tech. MTT-25, 373–381 (1977).
[CrossRef]

J. Appl. Meteorol. (1)

C. Prabhakara, J.-M. Yoo, G. Dalu, R. S. Fraser, “Deep optically thin cirrus clouds in the polar regions. Part I: Infrared extinction characteristics,” J. Appl. Meteorol. 29, 1313–1329 (1990).
[CrossRef]

J. Atmos. Sci. (1)

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

J. Geophys. Res. (2)

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

J. Math. Phys. (1)

K. Schulten, R. G. Gordon, “Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta,” J. Math. Phys. 16, 1961–1970 (1975).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (4)

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]

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, 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]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

J. Quantum Spectrosc. Radiat. Transfer (1)

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

Kinem. Phys. Celest. Bodies (1)

M. I. Mishchenko, “Scattering cross section for randomly oriented particles of arbitrary shape,” Kinem. Phys. Celest. Bodies 7(5) , 93–95 (1991).

Mon. Weather Rev. (1)

S. Kinne, T. P. Ackerman, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. D. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Opt. Commun. (2)

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

A. Doicu, T. Wriedt, “Extended boundary condition method with multipole sources localized in the complex plane,” Opt. Commun. (1997).

Opt. Lett. (2)

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[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 (12)

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

A. Macke, M. I. Mishchenko, B. E. Carlson, K. Muinonen, “Scattering of light by large spherical, spheroidal, and circular cylindrical scatterers: geometrical optics approximation versus T-matrix method,” in IRS ’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

M. I. Mishchenko, L. D. Travis, M. I. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium’96: Current Problems in Atmospheric Radiation, W. L. Smith, K. Stamnes, eds. (Deepak, Hampton, Va., 1996).

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of calculations,” (NASA Goddard Space Flight Center, Greenbelt, Md., 1986).

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
[CrossRef]

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

P. C. Waterman, “Numerical solution of electromagnetic scattering problems,” in Computer Techniques for Electromagnetics, R. Mitra, ed. (Pergamon, Oxford, 1973), pp. 97–157.
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

F. Y. Sid’ko, V. N. Lopatin, L. E. Paramonov, Polarization Characteristics of Suspensions of Biological Particles (Nauka, Novosibirsk, 1990), in Russian.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing (Cambridge U. Press, Cambridge, U.K., 1992).

G. H. Golub, C. F. van Loan, Matrix Computations, (Johns Hopkins U. Press, Baltimore, Md., 1989), Chap. 3.

NAG fortran Library Manual, Mark 15 (Numerical Algorithms Groups, Oxford, U. K., 1991).

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Figures (5)

Fig. 1
Fig. 1

Scattering matrix elements for randomly oriented, monodisperse oblate spheroids with aspect ratio 2, surface-equivalent-sphere size parameter 60, and refractive index 1.311 + i0.311 × 10-8.

Fig. 2
Fig. 2

T-matrix (solid curves) and GO (dashed curves) computations of the elements of the scattering matrix for Model 1.

Fig. 3
Fig. 3

Same as Fig. 2 but for Model 2.

Fig. 4
Fig. 4

Same as Fig. 2 but for Model 3.

Fig. 5
Fig. 5

Same as Fig. 2 but for Model 4.

Tables (1)

Tables Icon

Table 1 Scattering Matrix Elements for Randomly Oriented, Monodisperse Oblate Spheroidsa

Equations (15)

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

Clknmqp=AqClknmq-1p+BqClknmq-2p
Clknmqmin-1p=0,
Clknmqminp=Cqmin,
Clknmqp=DqClknmq+1p+EqClknmq+2p,
Clknmqmax+1p=0,
Clknmqmaxp=×2l!2n!l+n+k+m!l+n-k-m!2l+2n!l+k!l-k!n+m!n-m!1/2.
FΘ=F11ΘF12Θ00F12ΘF22Θ0000F33ΘF34Θ00-F34ΘF44Θ
Csca=2πk2n=1nmaxn=1nmaxm=-nnm=-nni=12j=12Tmnmnij2,
Cext=-2πk2 Ren=1nmaxm=-nnTmnmn11+Tmnmn22,
Tmnmnij=δmmTmnmnij,
Csca=2πk2n=1nmaxn=1nmaxm=-minn,nminn,ni=12j=12Tmnmnij2.
n=1nmaxn=1nmaxm=-minn,nminn,ni=12j=12Tmnmnij2 -Ren=1nmaxm=-nnTmnmn11+Tmnmn22,
ln1m1Tm1n1mnli*Tm1n1mnlj-12Tmnmnji*+Tmnmnij,
n=1nmaxn=1nmaxi=12j=12Tmnmnij2 -Ren=1nmaxTmnmn11+Tmnmn22, -minn,n  m  minn,n,
Tmnmnij=-1i+jTmnmnji.

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