Abstract

We use the T-matrix method as described by Mishchenko and Mackowski [Opt. Lett. 19, 1604 (1994)] to compute light scattering by bispheres in fixed and random orientations extensively. For all our computations the index of refraction is fixed at a value 1.5 + 0.005i, which is close to the refractive index of mineral tropospheric aerosols and was used in previous extensive studies of light scattering by spheroids and Chebyshev particles. For monodisperse bispheres with touching components in a fixed orientation, electromagnetic interactions between the constituent spheres result in a considerably more complicated interference structure in the scattering patterns than that for single monodisperse spheres. However, this increased structure is largely washed out by orientational averaging and results in scattering patterns for randomly oriented bispheres that are close to those for single spheres with size equal to the size of the bisphere components. Unlike other nonspherical particles such as cubes and spheroids, randomly oriented bispheres do not exhibit pronounced enhancement of side scattering and reduction of backscattering and positive polarization at side-scattering angles. Thus the dominant feature of light scattering by randomly oriented bispheres is the single scattering from the component spheres, whereas the effects of cooperative scattering and concavity of the bisphere shape play a minor role. The only distinct manifestations of nonsphericity and cooperative scattering effects for randomly oriented bispheres are the departure of the ratio F 22/F 11 of the elements of the scattering matrix from unity, the inequality of the ratios F 33/F 11 and F 44/F 11, and nonzero linear and circular backscattering depolarization ratios. Our computations for randomly oriented bispheres with separated wavelength-sized components show that the component spheres become essentially independent scatterers at as small a distance between their centers as 4 times their radii.

© 1995 Optical Society of America

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  1. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971); P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Comment on recent criticism of the T-matrix method,” J. Acoust. Soc. Am. 84, 2280–2284 (1988).
    [Crossref] [PubMed]
  2. 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]
  3. 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]
  4. M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
    [Crossref]
  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]
  6. F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
    [Crossref] [PubMed]
  7. 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; J. Wiscombe, A. Mugnai, “Scattering from nonspherical Chebyshev particles. 2: Means of angular scattering patterns,” Appl. Opt. 27, 2405–2421 (1988).
    [Crossref] [PubMed]
  8. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
    [Crossref]
  9. K. Fuller, “Cooperative electromagnetic scattering by ensembles of spheres,” Ph.D. dissertation (Texas A&M University, College Station, Texas, 1987).
  10. R. A. West, “Optical properties of aggregate particles whose outer diameter is comparable to the wavelength,” Appl. Opt. 30, 5316–5324 (1991).
    [Crossref] [PubMed]
  11. A-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres,” IEE Proc. H 138, 565–572 (1991).
  12. K. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
    [Crossref] [PubMed]
  13. K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
    [Crossref]
  14. D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
    [Crossref]
  15. M. I. Mishchenko, D. W. Mackowski, “Light scattering by randomly oriented bispheres,” Opt. Lett. 19, 1604–1606 (1994).
    [Crossref] [PubMed]
  16. B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)*,” Phys. Rev. D 8, 3661–3678 (1973).
    [Crossref]
  17. D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
    [Crossref]
  18. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991); M. I. Mishchenko, J. Opt. Soc. Am. A, 9, 497(E) (1992).
    [Crossref]
  19. M. I. Mishchenko, D. W. Mackowski, “T-matrix computations of light scattering by randomly oriented bispheres: comparison with experiment and benchmark results,” submitted to J. Quant. Spectrosc. Radiat. Transfer.
  20. K. A. Fuller, G. W. Kattawar, R. T. Wang, “Electromagnetic scattering from two dielectric spheres: further comparisons between theory and experiment,” Appl. Opt. 25, 2521–2529 (1986).
    [Crossref] [PubMed]
  21. P. J. Flatau, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete-dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
    [Crossref] [PubMed]
  22. V. P. Tishkovets, “Light scattering by clusters of spherical particles. Cooperative effects under random orientation,” Kinem. Fiz. Nebes. Tel. 10, (2)58–63 (1994).
  23. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  24. 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]
  25. C. V. M. van der Mee, J. W. Hovenier, “Expansion coefficients in polarized light transfer,” Astron. Astrophys. 228, 559–568 (1990).
  26. J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
    [Crossref]
  27. G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols (Deepak, Hampton, Va., 1991).
  28. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [Crossref]
  29. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  30. K. Sassen, “The polarization radar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
    [Crossref]
  31. S. J. Ostro, “Planetary radar astronomy,” Rev. Mod. Phys. 65, 1235–1279 (1993).
    [Crossref]
  32. M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. (to be published).
  33. R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Beitr. Phys. Atmos. 49, 168–188 (1976); S. C. Hill, A. C. Hill, P. W. Barber, “Light scattering by size/shape distributions of soil particles and spheroids,” Appl. Opt. 23, 1025–1031 (1984); F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).
    [Crossref] [PubMed]
  34. 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]
  35. S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [Crossref] [PubMed]
  36. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [Crossref] [PubMed]

1994 (8)

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, 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]

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[Crossref]

M. I. Mishchenko, D. W. Mackowski, “Light scattering by randomly oriented bispheres,” Opt. Lett. 19, 1604–1606 (1994).
[Crossref] [PubMed]

D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
[Crossref]

V. P. Tishkovets, “Light scattering by clusters of spherical particles. Cooperative effects under random orientation,” Kinem. Fiz. Nebes. Tel. 10, (2)58–63 (1994).

1993 (4)

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]

P. J. Flatau, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete-dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
[Crossref] [PubMed]

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

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[Crossref] [PubMed]

1991 (6)

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

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

A-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres,” IEE Proc. H 138, 565–572 (1991).

K. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[Crossref] [PubMed]

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

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[Crossref]

1990 (1)

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

1987 (1)

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 (1)

1984 (1)

1980 (1)

1978 (1)

1976 (1)

R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Beitr. Phys. Atmos. 49, 168–188 (1976); S. C. Hill, A. C. Hill, P. W. Barber, “Light scattering by size/shape distributions of soil particles and spheroids,” Appl. Opt. 23, 1025–1031 (1984); F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).
[Crossref] [PubMed]

1974 (1)

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

1973 (1)

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)*,” Phys. Rev. D 8, 3661–3678 (1973).
[Crossref]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971); P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Comment on recent criticism of the T-matrix method,” J. Acoust. Soc. Am. 84, 2280–2284 (1988).
[Crossref] [PubMed]

Asano, S.

Bohren, C. F.

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

Borghese, F.

Bottiger, J. R.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[Crossref]

Ciric, I. R.

A-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres,” IEE Proc. H 138, 565–572 (1991).

d’Almeida, G. A.

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

de Haan, J. F.

Denti, P.

Flatau, P. J.

Fry, E. S.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[Crossref]

Fuller, K.

K. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[Crossref] [PubMed]

K. Fuller, “Cooperative electromagnetic scattering by ensembles of spheres,” Ph.D. dissertation (Texas A&M University, College Station, Texas, 1987).

Fuller, K. A.

Hamid, A-K.

A-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres,” IEE Proc. H 138, 565–572 (1991).

Hamid, M.

A-K. Hamid, I. R. Ciric, M. Hamid, “Iterative solution of the scattering by an arbitrary configuration of conducting or dielectric spheres,” IEE Proc. H 138, 565–572 (1991).

Hansen, J. E.

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

Herb, P.

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]

Hovenier, J. W.

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

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

M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. (to be published).

Hu, C-R.

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]

Huffman, D. R.

Hunt, A. J.

Kattawar, G. W.

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]

K. A. Fuller, G. W. Kattawar, R. T. Wang, “Electromagnetic scattering from two dielectric spheres: further comparisons between theory and experiment,” Appl. Opt. 25, 2521–2529 (1986).
[Crossref] [PubMed]

Koepke, P.

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

Kuik, F.

Lumme, K.

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[Crossref]

Macke, A.

Mackowski, D. W.

M. I. Mishchenko, D. W. Mackowski, “Light scattering by randomly oriented bispheres,” Opt. Lett. 19, 1604–1606 (1994).
[Crossref] [PubMed]

D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
[Crossref]

P. J. Flatau, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete-dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
[Crossref] [PubMed]

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[Crossref]

M. I. Mishchenko, D. W. Mackowski, “T-matrix computations of light scattering by randomly oriented bispheres: comparison with experiment and benchmark results,” submitted to J. Quant. Spectrosc. Radiat. Transfer.

Mishchenko, M. I.

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, 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, D. W. Mackowski, “Light scattering by randomly oriented bispheres,” Opt. Lett. 19, 1604–1606 (1994).
[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, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991); M. I. Mishchenko, J. Opt. Soc. Am. A, 9, 497(E) (1992).
[Crossref]

M. I. Mishchenko, D. W. Mackowski, “T-matrix computations of light scattering by randomly oriented bispheres: comparison with experiment and benchmark results,” submitted to J. Quant. Spectrosc. Radiat. Transfer.

M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. (to be published).

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

Ostro, S. J.

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

Parkin, M. E.

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]

Perry, R. J.

Peterson, B.

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)*,” Phys. Rev. D 8, 3661–3678 (1973).
[Crossref]

Rahola, J.

K. Lumme, J. Rahola, “Light scattering by porous dust particles in the discrete-dipole approximation,” Astrophys. J. 425, 653–667 (1994).
[Crossref]

Saija, R.

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]

Sato, M.

Shettle, E. P.

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

Sindoni, O. I.

Ström, S.

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)*,” Phys. Rev. D 8, 3661–3678 (1973).
[Crossref]

Thompson, R. C.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregularly Shaped Particles, D. W. Schuerman, ed. (Plenum, New York, 1980), pp. 283–290.
[Crossref]

Tishkovets, V. P.

V. P. Tishkovets, “Light scattering by clusters of spherical particles. Cooperative effects under random orientation,” Kinem. Fiz. Nebes. Tel. 10, (2)58–63 (1994).

Toscano, G.

Travis, L. D.

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, “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]

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).

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).

Wang, R. T.

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971); P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975); V. V. Varadan, A. Lakhtakia, V. K. Varadan, “Comment on recent criticism of the T-matrix method,” J. Acoust. Soc. Am. 84, 2280–2284 (1988).
[Crossref] [PubMed]

West, R. A.

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

Zerull, R. H.

R. H. Zerull, “Scattering measurements of dielectric and absorbing nonspherical particles,” Beitr. Phys. Atmos. 49, 168–188 (1976); S. C. Hill, A. C. Hill, P. W. Barber, “Light scattering by size/shape distributions of soil particles and spheroids,” Appl. Opt. 23, 1025–1031 (1984); F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, 1992).
[Crossref] [PubMed]

Appl. Opt. (3)

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]

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

Appl. Opt. (9)

K. A. Fuller, G. W. Kattawar, R. T. Wang, “Electromagnetic scattering from two dielectric spheres: further comparisons between theory and experiment,” Appl. Opt. 25, 2521–2529 (1986).
[Crossref] [PubMed]

P. J. Flatau, K. A. Fuller, D. W. Mackowski, “Scattering by two spheres in contact: comparisons between discrete-dipole approximation and modal analysis,” Appl. Opt. 32, 3302–3305 (1993).
[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]

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

A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[Crossref] [PubMed]

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

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Figures (7)

Fig. 1
Fig. 1

(a) Ratio −F 21/F 11 of the elements of the scattering matrix as a function of scattering angle and size parameter for monodisperse single spheres. (b) Ratio −Z 21/Z 11 of the elements of the Mueller matrix as a function of scattering angle and constituent-sphere size parameter for monodisperse bispheres with touching components and axes perpendicular to the direction of light incidence. (c) Ratio −Z 21/Z 11 of the elements of the Mueller matrix as a function of scattering angle and constituent-sphere size parameter for monodisperse bispheres with touching components and axes parallel to the direction of light incidence. (d) Ratio −F 21/F 11 of the elements of the scattering matrix as a function of scattering angle and size parameter for monodisperse randomly oriented bispheres with touching components. The vertical axis shows constituent-sphere size parameters. (e) Scattering phase function F 11 as a function of scattering angle and size parameter for monodisperse single spheres. (f) As in (e) but for monodisperse randomly oriented bispheres with touching components. The vertical axis shows constituent-sphere size parameters. (g) Ratio F 33/F 11 of the elements of the scattering matrix as a function of scattering angle and size parameter for monodisperse single spheres. (h) As in (g) but for monodisperse randomly oriented bispheres with touching components. The vertical axis shows constituent-sphere size parameters. (i) Ratio F 22/F 11 of the elements of the scattering matrix as a function of scattering angle and constituent-sphere size parameter for monodisperse randomly oriented bispheres with touching components. (j) Ratio F 44/F 11 of the elements of the scattering matrix as a function of scattering angle and constituent-sphere size parameter for monodisperse randomly oriented bispheres with touching components. (k) Ratio F 34/F 11 of the elements of the scattering matrix as a function of scattering angle and size parameter for monodisperse single spheres. (l) As in (k) but for monodisperse randomly oriented bispheres with touching components. The vertical axis shows constituent-sphere size parameters.

Fig. 2
Fig. 2

Phase function and degree of linear polarization for a single sphere (thin solid curves), randomly oriented bispheres with touching components (thick solid curves), and randomly oriented bispheres with distance between sphere centers equal to 3 (dotted curves) and 4 (dotted–dashed curves) times their radius. The size parameter of the single sphere and the bisphere components is equal to 5.

Fig. 3
Fig. 3

Phase function and degree of linear polarization for a single sphere (thin solid curves), randomly oriented bispheres with touching components (thick solid curves), and randomly oriented bispheres with the distance between sphere centers equal to 4 times their radius (dotted curves). The size parameter of the single sphere and the bisphere components is equal to 15.

Fig. 4
Fig. 4

Linear (solid curve) and circular (dotted curve) backscattering depolarization ratios versus constituent-sphere size parameter for randomly oriented monodisperse bispheres with touching components.

Fig. 5
Fig. 5

Ratios of extinction (solid curve), scattering (dotted curve), and absorption (dotted–dashed curve) cross sections versus size parameter for monodisperse randomly oriented bispheres with touching components and monodisperse single spheres. For bi-spheres the horizontal axis shows constituent-sphere size parameters.

Fig. 6
Fig. 6

Ratios of single-scattering albedos (dotted curve) and asymmetry parameters of the phase function (solid curve) versus size parameter for monodisperse randomly oriented bispheres with touching components and monodisperse single spheres. For bispheres the horizontal axis shows constituent-sphere size parameters.

Fig. 7
Fig. 7

Elements of the scattering matrix for polydisperse randomly oriented bispheres with touching components and effective constituent-sphere radius r eff = 1 μm (solid curves) and polydisperse single spheres with the same effective radius (dotted curves). The effective variance of the size distribution is v eff = 0.2 and the wavelength is 0.6283 μm. For comparison, dotted–dashed lines were computed for an equivalent power-law distribution of randomly oriented prolate spheroids with aspect ratio 2, effective variance v eff = 0.2, and effective equal-volume-sphere radius r eff = 1 μm.

Tables (1)

Tables Icon

Table 1 Total Optical Cross Sections C (in Square Micrometers), Single-Scattering Albedo ω, Asymmetry Parameter of the Phase Function 〈cos Θ〉, and Backscattering Depolarization Ratios for Polydisperse Randomly Oriented Bispheres with Touching Components and Effective Constituent-Sphere Radius r eff = 1 μm and Polydisperse Single Spheres with the Same Effective Radiusa

Equations (6)

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I sca = 1 R 2 Z ( Θ ) I inc ,
F ( Θ ) = 4 π C sca Z ( Θ ) ,
1 4 π 4 π d Ω F 11 ( Θ ) = 1.
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 ) ] ,
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 ° ) ,

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