Abstract

We consider two topics pertaining to light scattering by circular cylinders. (A) Scattering properties of cylinders with increasing aspect ratio are studied. It is shown that the solution for finite cylinders does not converge to the solution for infinitely long cylinders if the aspect ratio increases. This is due to differences in the treatment of diffraction for finite and infinite cylinders. (B) Finite cylinders have sharp edges, so their scattering properties differ from those of spheroids having the same aspect ratio. To illustrate these differences we present scattering matrix elements of cylinders and spheroids for a large set of aspect ratios. To handle the large amount of data, the scattering matrix elements as functions of aspect ratio and scattering angle are presented in so-called three-dimensional figures.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley,New York, 1957).
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), Chap. 15, p. 195.
  4. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988), Chap. 5, p. 155.
  5. P. W. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).
  6. P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  7. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, p. 79.
    [CrossRef]
  8. J. I. Hage, “The optics of porous particles and the nature of comets,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1991).
  9. J. I. Hage, J. M. Greenberg, R. T. Wang, “Scattering from arbitrarily shaped particles: theory and experiment,” Appl. Opt. 30, 1141–1152 (1991).
    [CrossRef] [PubMed]
  10. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [PubMed]
  11. S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  12. Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
    [CrossRef]
  13. Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
    [CrossRef]
  14. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  15. F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).
  16. P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
    [CrossRef]
  17. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [CrossRef]
  18. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  19. F. Kuik, J. F. De Haan, J. W. Hovenier, “Benchmark results for single scattering of light by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 47, 477–489 (1992).
    [CrossRef]
  20. A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
    [CrossRef]
  21. R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
    [CrossRef]
  22. P. Stammes, “Light scattering properties of aerosols and the radiation inside a planetary atmosphere,” Ph.D. dissertation (Free University, Amsterdam, 1989).
  23. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 8, p. 393.
  24. Y. Takano, M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2793 (1980).
    [CrossRef] [PubMed]
  25. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  26. Q. Cai, K.-N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
    [CrossRef] [PubMed]
  27. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.
  28. R. A. McClatchey, H.-J. Bolle, K. Ya Kondratyev, “A preliminary cloudless standard atmnosphere for radiation computation,” report on a standard atmosphere (World Meteorological Organization/International Association for Meteorology and Atmospheric Physics, Boulder, Colorado, 1982).
  29. C. Flesia, A. Mugnai, L. Stefanutti, “Depolarization effect by nonspherical particles on the lidar signal,” in Digest of the International Commission for Optics Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 573–576.
  30. M. I. Mishchenko, “Light scattering by nonspherical ice grains: an application to noctilucent cloud particles,” Earth Moon Planets 57, 203–211 (1992).
    [CrossRef]

1992 (2)

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

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)

1985 (1)

R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
[CrossRef]

1984 (1)

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

1982 (1)

1980 (2)

1979 (1)

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

1975 (2)

1974 (1)

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

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

1918 (1)

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

1881 (1)

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Asano, S.

Barber, P. W.

P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

P. W. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, p. 79.
[CrossRef]

Bohren, C. F.

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

Bolle, H.-J.

R. A. McClatchey, H.-J. Bolle, K. Ya Kondratyev, “A preliminary cloudless standard atmnosphere for radiation computation,” report on a standard atmosphere (World Meteorological Organization/International Association for Meteorology and Atmospheric Physics, Boulder, Colorado, 1982).

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 8, p. 393.

Cai, Q.

Cohen, A.

R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
[CrossRef]

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

Cohen, L. D.

R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
[CrossRef]

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

Colosi, J.

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

De Haan, J. F.

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

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

Flesia, C.

C. Flesia, A. Mugnai, L. Stefanutti, “Depolarization effect by nonspherical particles on the lidar signal,” in Digest of the International Commission for Optics Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 573–576.

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

Greenberg, J. M.

Hage, J. I.

J. I. Hage, J. M. Greenberg, R. T. Wang, “Scattering from arbitrarily shaped particles: theory and experiment,” Appl. Opt. 30, 1141–1152 (1991).
[CrossRef] [PubMed]

J. I. Hage, “The optics of porous particles and the nature of comets,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1991).

Hansen, J. E.

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

Haracz, R. D.

R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
[CrossRef]

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, p. 79.
[CrossRef]

Hovenier, J. W.

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

Huffman, D. R.

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

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), Chap. 15, p. 195.

Kondratyev, K. Ya

R. A. McClatchey, H.-J. Bolle, K. Ya Kondratyev, “A preliminary cloudless standard atmnosphere for radiation computation,” report on a standard atmosphere (World Meteorological Organization/International Association for Meteorology and Atmospheric Physics, Boulder, Colorado, 1982).

Kuik, F.

F. Kuik, J. F. De Haan, J. W. Hovenier, “Benchmark results for single scattering of light 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).

Liou, K.-N.

McClatchey, R. A.

R. A. McClatchey, H.-J. Bolle, K. Ya Kondratyev, “A preliminary cloudless standard atmnosphere for radiation computation,” report on a standard atmosphere (World Meteorological Organization/International Association for Meteorology and Atmospheric Physics, Boulder, Colorado, 1982).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

Mishchenko, M. I.

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).
[CrossRef]

Moeller, K.

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

Mugnai, A.

C. Flesia, A. Mugnai, L. Stefanutti, “Depolarization effect by nonspherical particles on the lidar signal,” in Digest of the International Commission for Optics Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 573–576.

Rayleigh, Lord

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Sato, M.

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988), Chap. 5, p. 155.

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.

C. Flesia, A. Mugnai, L. Stefanutti, “Depolarization effect by nonspherical particles on the lidar signal,” in Digest of the International Commission for Optics Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 573–576.

Takano, Y.

Tanaka, M.

Tomaselli, V.

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

Travis, L. D.

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

van de Hulst, H. C.

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

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Wang, R. T.

Waterman, P. C.

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 8, p. 393.

Yamamoto, G.

Yeh, C.

Appl. Opt. (6)

Can. J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

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]

J. Appl. Phys. (3)

P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
[CrossRef]

A. Cohen, L. D. Cohen, R. D. Haracz, V. Tomaselli, J. Colosi, K. Moeller, “Angular scattering distribution by long copper and brass cylinders: experiment and theory,” J. Appl. Phys. 56, 1329–1332 (1984).
[CrossRef]

R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

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

Philos. Mag. (2)

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Lord Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[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 (13)

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

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 8, p. 393.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 10, p. 14.

R. A. McClatchey, H.-J. Bolle, K. Ya Kondratyev, “A preliminary cloudless standard atmnosphere for radiation computation,” report on a standard atmosphere (World Meteorological Organization/International Association for Meteorology and Atmospheric Physics, Boulder, Colorado, 1982).

C. Flesia, A. Mugnai, L. Stefanutti, “Depolarization effect by nonspherical particles on the lidar signal,” in Digest of the International Commission for Optics Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 573–576.

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

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

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

N. G. Jerlov, Marine Optics (Elsevier, Amsterdam, 1976), Chap. 15, p. 195.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988), Chap. 5, p. 155.

P. W. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1973).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, p. 79.
[CrossRef]

J. I. Hage, “The optics of porous particles and the nature of comets,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

I1 and I2 as functions of scattering angle for cylinders with their symmetry axes perpendicular to the scattering plane and with 2πb/λ = 2.75.

Fig. 2
Fig. 2

Scattering matrix elements as functions of scattering angle for H2O ice cylinders (m = 1.31) with their symmetry axes perpendicular to the scattering plane.

Fig. 3
Fig. 3

Same as Fig. 2 but for strongly absorbing H2O ice cylinders (m = 1.31 − 0.1i).

Fig. 4
Fig. 4

Scattering matrix elements as functions of scattering angle for ensembles of randomly oriented H2O ice cylinders with m = 1.31 and 2πb/λ = 2.75.

Fig. 5
Fig. 5

Same as Fig. 4 but for dirty H2O ice with m = 1.31 − 0.1i.

Fig. 6
Fig. 6

I(θ)/I0 for randomly oriented cylinders with kb = 100. The solid curve pertains to infinitely long cylinders, and the dashed curve has been computed from Eq. (9) and integral (11). The solid and the dashed vertical lines indicate the positions of the minima in the diffraction pattern for the infinitely long cylinders and for the cylinders with a/b = 100, respectively.

Fig. 7
Fig. 7

F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Fig. 8
Fig. 8

F22/F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Fig. 9
Fig. 9

F33/F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Fig. 10
Fig. 10

F44/F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Fig. 11
Fig. 11

F12/F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Fig. 12
Fig. 12

F3/F11 as functions of θ and a/b for ensembles of randomly oriented finite (top) cylinders and (bottom) spheroids.

Equations (11)

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

E inc ( k r ) = E 0 ν = 1 D ν [ a ν M ν 1 ( k r ) + b ν N ν 1 ( k r ) ] ,
E sca ( k r ) = E 0 ν = 1 D ν [ f ν M ν 3 ( k r ) + g ν N ν 3 ( k r ) ] ,
( f ν g ν ) = T ( a ν b ν ) ,
1 2 1 1 I j ( θ ) d ( cos θ ) = 1 ( j = 1 , 2 ) .
S = [ S 2 S 3 S 4 S 1 ] .
S M = [ S 2 S 3 S 4 S 1 ] .
[ F 11 F 12 0 0 F 12 F 11 0 0 0 0 F 33 F 34 0 0 F 34 F 33 ] .
I 1 ( θ = 0 ° , a / b = 5.0 ) I 1 ( θ = 0 ° , a / b = 3.0 ) I 2 ( θ = 0 ° , a / b = 5.5 ) I 2 ( θ = 0 ° , a / b = 3.0 ) 2.5 ,
I ( θ ) I 0 = k 2 4 π 2 R 2 G 2 D 2 ( θ , φ ) ,
D 2 = sin 2 ( k b θ cos φ ) ( k b θ cos φ ) 2 sin 2 ( k a θ sin γ sin φ ) ( k a θ sin γ sin φ ) 2 ,
0 2 π 0 π sin 2 ( k b θ cos ψ ) ( k b θ cos ψ ) 2 sin 2 ( k a θ sin γ sin ψ ) ( k a θ sin γ sin ψ ) 2 sin 3 γ d γ d ψ ,

Metrics