Abstract

Two-dimensional angular optical scattering (TAOS) patterns from clusters of polystyrene latex spheres are measured in the near-forward and near-backward directions. In both cases, the scattering pattern contains a rich and complicated structure that is the result of the interaction and interference of light among the primary particles. Calculations are made for aggregates that are similar to those generated experimentally and also demonstrate the rich structure in the scattering pattern. A comparison of the experimental and theoretical TAOS patterns gives good qualitative agreement.

© 2000 Optical Society of America

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  1. R. H. Zerull, B. Å S. Gustafson, K. Schulz, E. Thiele-Corbach, “Scattering by aggregates with and without an absorbing mantle: microwave analog experiments,” Appl. Opt. 32, 4088–4100 (1993).
    [PubMed]
  2. G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
    [CrossRef]
  3. S. Holler, Y.-L. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. 23, 1489–1491 (1998).
    [CrossRef]
  4. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994).
    [CrossRef]
  5. D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
    [CrossRef]
  6. D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
    [CrossRef]
  7. G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
    [CrossRef]
  8. D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
    [CrossRef]
  9. E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).
  10. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  11. D. R. Huffman, “Interstellar grains. The interaction of light with a small particle system,” Adv. Phys. 26, 129–230 (1977).
    [CrossRef]
  12. C. M. Sorensen, J. Cai, N. Lu, “Light scattering measurements of monomer size, monomers per aggregate and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
    [CrossRef] [PubMed]
  13. R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
    [CrossRef]
  14. P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Science 312, 529–531 (1984).
  15. P. L. Marston, “Cusp diffraction catastrophe from spheroids: generalized rainbows and inverse scattering,” Opt. Lett. 10, 588–590 (1985).
    [CrossRef] [PubMed]
  16. J. P. Barton, “Light scattering calculations for irregularly shaped axisymmetric particles of homogeneous and layered compositions,” Meas. Sci. Technol. 9, 151–160 (1998).
    [CrossRef]
  17. J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering,” Appl. Opt. 37, 3339–3344 (1998).
    [CrossRef]
  18. G. Mie, “Beitrage zur optik trüber medien speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [CrossRef]
  19. J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  20. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  21. P. C. Waterman, “Symmetry, unitary, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
    [CrossRef]
  22. A.-K. Hamid, “Electromagnetic scattering by an arbitrary configuration of dielectric spheres,” Can. J. Phys. 68, 1419–1428 (1990).
    [CrossRef]
  23. Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres: far field,” Appl. Opt. 36, 9496–9508 (1997).
    [CrossRef]
  24. W. C. Chew, Waves and Field in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1990).
  25. J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).
  26. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  27. J.-C. Auger, Laboratoire d’Optiques des Solides, Unité Mixte de Recherche 7601, Université Pierre et Maríe Curie, Paris, France, and G. Videen, are preparing a manuscript to be called “Spatial light scattering and sphere clusters.”
  28. S. Stein, “Addition theorems for spherical wave function,” Q. Appl. Math. 19, 15–24 (1961).
  29. O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).
  30. B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3677 (1973).
    [CrossRef]
  31. W. J. Wiscombe, “Improve Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef] [PubMed]
  32. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
    [CrossRef]

1998 (7)

S. Holler, Y.-L. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. 23, 1489–1491 (1998).
[CrossRef]

G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

J. P. Barton, “Light scattering calculations for irregularly shaped axisymmetric particles of homogeneous and layered compositions,” Meas. Sci. Technol. 9, 151–160 (1998).
[CrossRef]

J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering,” Appl. Opt. 37, 3339–3344 (1998).
[CrossRef]

J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).

1997 (2)

Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres: far field,” Appl. Opt. 36, 9496–9508 (1997).
[CrossRef]

D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
[CrossRef]

1996 (2)

D. W. Mackowski, M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266–2278 (1996).
[CrossRef]

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1990 (1)

A.-K. Hamid, “Electromagnetic scattering by an arbitrary configuration of dielectric spheres,” Can. J. Phys. 68, 1419–1428 (1990).
[CrossRef]

1985 (1)

1984 (2)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Science 312, 529–531 (1984).

1980 (1)

1977 (2)

D. R. Huffman, “Interstellar grains. The interaction of light with a small particle system,” Adv. Phys. 26, 129–230 (1977).
[CrossRef]

D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
[CrossRef]

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 representation of E(3),” Phys. Rev. D 8, 3661–3677 (1973).
[CrossRef]

1970 (1)

P. C. Waterman, “Symmetry, unitary, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

1962 (1)

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

1961 (1)

S. Stein, “Addition theorems for spherical wave function,” Q. Appl. Math. 19, 15–24 (1961).

1908 (1)

G. Mie, “Beitrage zur optik trüber medien speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Auger, J.-C.

J.-C. Auger, Laboratoire d’Optiques des Solides, Unité Mixte de Recherche 7601, Université Pierre et Maríe Curie, Paris, France, and G. Videen, are preparing a manuscript to be called “Spatial light scattering and sphere clusters.”

Barton, J. P.

J. P. Barton, “Light scattering calculations for irregularly shaped axisymmetric particles of homogeneous and layered compositions,” Meas. Sci. Technol. 9, 151–160 (1998).
[CrossRef]

J. P. Barton, “Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering,” Appl. Opt. 37, 3339–3344 (1998).
[CrossRef]

Bohren, C. F.

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

Borghese, F.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Bottiger, J. R.

Boutou, V.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Bowes, D. R.

D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
[CrossRef]

Cai, J.

Chang, R. K.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

S. Holler, Y.-L. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. 23, 1489–1491 (1998).
[CrossRef]

Chen, G.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Field in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1990).

Cruzan, O. R.

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

Dalling, R.

D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
[CrossRef]

de Saeger, E.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Deluca, P. J.

J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).

Denti, P.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Frejafon, E.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Fu, Q.

G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Fuller, K. A.

Gustafson, B. Å S.

Hamid, A.-K.

A.-K. Hamid, “Electromagnetic scattering by an arbitrary configuration of dielectric spheres,” Can. J. Phys. 68, 1419–1428 (1990).
[CrossRef]

Hansen, J. E.

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

Hart, M. B.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Hill, S. C.

S. Holler, Y.-L. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. 23, 1489–1491 (1998).
[CrossRef]

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Hillis, D. B.

Holler, S.

Huffman, D. R.

D. R. Huffman, “Interstellar grains. The interaction of light with a small particle system,” Adv. Phys. 26, 129–230 (1977).
[CrossRef]

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

Kasparian, J.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Krämer, B.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Langer, A. M.

D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
[CrossRef]

Leisner, T.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Lu, N.

Mackowski, D. W.

Marston, P. L.

P. L. Marston, “Cusp diffraction catastrophe from spheroids: generalized rainbows and inverse scattering,” Opt. Lett. 10, 588–590 (1985).
[CrossRef] [PubMed]

P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Science 312, 529–531 (1984).

Mie, G.

G. Mie, “Beitrage zur optik trüber medien speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Mishchenko, M. I.

Nachman, P.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Ngo, D.

D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
[CrossRef]

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Ottobrini, B.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Pan, Y.-L.

Peterson, B.

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3677 (1973).
[CrossRef]

Pinnick, R. G.

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

Rairoux, P.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Rambaldi, P.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Rohl, A. N.

D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
[CrossRef]

Saija, R.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Schulz, K.

Sindoni, O. I.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Sorensen, C. M.

Stein, S.

S. Stein, “Addition theorems for spherical wave function,” Q. Appl. Math. 19, 15–24 (1961).

Stratton, J.

J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Ström, S.

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3677 (1973).
[CrossRef]

Stuebing, E. W.

J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).

Sun, W.

G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Thiele-Corbach, E.

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Travis, L. D.

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

Trinh, E. H.

P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Science 312, 529–531 (1984).

Ulbricht, M.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

VanReenen, D. R.

J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).

Vezin, B.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Videen, G.

G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
[CrossRef]

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

J.-C. Auger, Laboratoire d’Optiques des Solides, Unité Mixte de Recherche 7601, Université Pierre et Maríe Curie, Paris, France, and G. Videen, are preparing a manuscript to be called “Spatial light scattering and sphere clusters.”

Waterman, P. C.

P. C. Waterman, “Symmetry, unitary, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

Weidauer, D.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Wiscombe, W. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Wolf, J. P.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Wöste, L.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Xu, Y.-L.

Yu, J.

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

Zerull, R. H.

Adv. Phys. (1)

D. R. Huffman, “Interstellar grains. The interaction of light with a small particle system,” Adv. Phys. 26, 129–230 (1977).
[CrossRef]

Aerosol Sci. Technol. (2)

R. G. Pinnick, S. C. Hill, P. Nachman, G. Videen, G. Chen, R. K. Chang, “Aesosol fluorescence spectrum analyzer for measurement of single micronsized airborne biological particles,” Aerosol Sci. Technol. 28, 95–104 (1998).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beitrage zur optik trüber medien speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (5)

Can. J. Phys. (1)

A.-K. Hamid, “Electromagnetic scattering by an arbitrary configuration of dielectric spheres,” Can. J. Phys. 68, 1419–1428 (1990).
[CrossRef]

Eur. J. Phys. D (1)

E. Frejafon, J. Kasparian, P. Rambaldi, B. Vezin, V. Boutou, J. Yu, M. Ulbricht, D. Weidauer, B. Ottobrini, E. de Saeger, B. Krämer, T. Leisner, P. Rairoux, L. Wöste, J. P. Wolf, “Laser applications for atmospheric pollution monitoring,” Eur. J. Phys. D 4, 231–238 (1998).

J. Aerosol Sci. (1)

J. R. Bottiger, P. J. Deluca, E. W. Stuebing, D. R. VanReenen, “An ink jet aerosol generator,” J. Aerosol Sci. 29(Suppl. 1), 965–966 (1998).

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

J. P. Barton, “Light scattering calculations for irregularly shaped axisymmetric particles of homogeneous and layered compositions,” Meas. Sci. Technol. 9, 151–160 (1998).
[CrossRef]

Opt. Commun. (2)

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

G. Videen, W. Sun, Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5–9 (1998).
[CrossRef]

Opt. Lett. (2)

Philos. Trans. R. Soc. London Ser. A (1)

D. R. Bowes, A. M. Langer, A. N. Rohl, “Nature and range of mineral dusts in the environment,” Philos. Trans. R. Soc. London Ser. A 286, 593–610 (1977).
[CrossRef]

Phys. Lett. A (1)

D. Ngo, G. Videen, R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227, 197–202 (1997).
[CrossRef]

Phys. Rev. D (2)

P. C. Waterman, “Symmetry, unitary, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
[CrossRef]

B. Peterson, S. Ström, “T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3),” Phys. Rev. D 8, 3661–3677 (1973).
[CrossRef]

Q. Appl. Math. (2)

S. Stein, “Addition theorems for spherical wave function,” Q. Appl. Math. 19, 15–24 (1961).

O. R. Cruzan, “Translation addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

Science (1)

P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Science 312, 529–531 (1984).

Space Sci. Rev. (1)

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

Other (5)

J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

J.-C. Auger, Laboratoire d’Optiques des Solides, Unité Mixte de Recherche 7601, Université Pierre et Maríe Curie, Paris, France, and G. Videen, are preparing a manuscript to be called “Spatial light scattering and sphere clusters.”

W. C. Chew, Waves and Field in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1990).

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Figures (9)

Fig. 1
Fig. 1

(a) Experimental setup used for the TAOS measurements, (b) the laboratory-coordinate system, (c) an illustration of the Abbé sine condition.

Fig. 2
Fig. 2

Fraction of the 227 clusters that contain N sph spheres plotted versus N sph. The solid curve represents a Poisson distribution, given that the most probable number of spheres is 18.

Fig. 3
Fig. 3

(a) SEM image of a typical cluster for which TAOS measurements were performed. (b) Mathematica default representation of the cluster used in the numerical calculations. The primary particle coordinates are given in Table 1. (c) Representation of the unrotated (τ = 0°) theoretical cluster viewed along the z axis of the calculation frame, i.e., the cluster as seen from the incident plane wave. (d) Realization of the theoretical cluster rotated by 45° and viewed along the z axis of the calculation frame.

Fig. 4
Fig. 4

Forward and backward TAOS calculations transformed into the laboratory coordinates for three cluster orientations: 0°, top; 5°, middle; 45° bottom.

Fig. 5
Fig. 5

Eight representative TAOS measurements in the near-forward scattering direction.

Fig. 6
Fig. 6

Near-forward TAOS calculations, showing qualitative features found in the experiments.

Fig. 7
Fig. 7

Eight representative TAOS measurements in the near-backward scattering direction.

Fig. 8
Fig. 8

Near-backward TAOS calculations, showing qualitative features found in the experiments.

Fig. 9
Fig. 9

Forward TAOS calculations for two clusters of the same size that comprise primary particles with different sizes: (a) cluster containing 2.0-µm-diameter spheres, (b) cluster containing 2.26-µm-diameter spheres.

Tables (1)

Tables Icon

Table 1 Coordinates of the Spheres Used for the Cluster Calculation

Equations (43)

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e Ψ1mnkr, θ, ϕ=γmnimsin θ jnkrPnmcos θ×expimϕθˆ-jnkrθ Pnm×cos θexpimϕϕˆ,
e Ψ2mnkr, θ, ϕ=γmnnn+1kr jnkrPnmcos θ×expimϕrˆ+1krr rjnkrθ Pnmcos θ×expimϕθˆ+imkr sin θr rjnkrPnmcos θ×expimϕϕˆ,
γmn=2n+1n-m!4πnn+1n+m!
Einc=n=1n=m=-nm=na1mne Ψ1mn+a2mne Ψ2mn=σ,m,n aσmn e Ψσmn,  Hinc=1iη0n=1n=m=-nm=na2mne Ψ1mn+a1mneΨ2mn;
Esca=n=1n=m=-nm=nf1mn Ψ1mn+f2mn Ψ2mn=σ,m,n fσmne Ψσmn,  Hsca=1iη0n=1n=m=-nm=nf2mn Ψ1mn+f1mn Ψ2mn,
f=T¯a.
T1mn,1mn=-δmmδnn×jnk1r0k0r0jnk0r0-jnk0r0k1r0jnk1r0jnk1r0k0r0hnk0r0-hnk0r0k1r0jnk1r0,
T2mn,2mn=-δmmδnn×k12/k02jnk1r0k0r0jnk0r0-jnk0r0k1r0jnk1r0k12/k02jnk1r0k0r0hnk0r0-hnk0r0k1r0jnk1r0,
T1mn,2mn=T2mn,1mn=0,
a1mnTM=ζmn in+3msin θi Pnmcos θiexp-imϕi,
a2mnTM=ζmn in+3dd θ Pnmcos θiexp-imϕi,
a1mnTE=ζmn in+2ddθ Pnmcos θiexp-imϕi,
a2mnTE=ζmn in+2msin θi Pnmcos θiexp-imϕi,
ζmn=4π2n+1n-m!nn+1n+m!
Etot=e Ψk0|r-r0|a0+i=1N Ψk0|r-ri|fiN.
Eexci=E0+j=1j1NEscaj.
Escai=T¯i1eΨk0|r-r0|a0+j=1jiN Ψk0|r-ri|fjN.
fjN=T¯i1β¯i, 0a0+j=1jiN α¯i, jfjN,  i=1, , N,
fiN=T¯iNai=T¯iNβ¯i, 0a0.
fTN=i=1N β¯0, iT¯iNβ¯i, 0a0.
fTN=T¯TNa0,
T¯TN=i=1N β¯0, iT¯iNβ¯i, 0.
T¯N+1N+1β¯N+1, 0=Ī-T¯N+11i=1n α¯N+1, i×T¯iNβ¯i, 0α¯0, N+1-1×T¯N+11β¯N+1, 0+i=1n α¯N+1, iT¯iNβ¯i, 0,
T¯iN+1β¯i, 0=T¯iNβ¯i, 0Ī+α¯0, N+1×T¯N+1N+1β¯N+1,  0,  iN.
h=f sin γ,
θlab=cos-1sin θcalc cos ϕcalc,  ϕlab=ϕ0+-1j sin-1-sin θcalc sin ϕcalc,
e Ψ1mnkri, θi, ϕi=μνe Aμνmnrij, θij, ϕij×e Ψ1μνkrj, θj, ϕj+eBμνmnrij, θij, ϕij×e Ψ2μνkrj, θj, ϕj,  e Ψ2mnkri, θi, ϕi=μνeBμνmnrij, θij, ϕij×e Ψ2μνkrj, θj, ϕj+e Aμνmnrij, θij, ϕij×e Ψ2μνkrj, θj, ϕj.
Ψ1mnkri, θi, ϕi=μν Aμνmnrij, θij, ϕij×e Ψ1μνkrj, θj, ϕj+Bμνmnrij, θij, ϕij×e Ψ2μνkrj, θj, ϕj,  Ψ2mnkri, θi, ϕi=μν Bμνmnrij, θij, ϕij×e Ψ1μνkrj, θj, ϕj+Aμνmnrij, θij, ϕij×e Ψ2μνkrj, θj, ϕj.
Ψ1mnkri, θi, ϕi=μνe Aμνmnrij, θij, ϕij×Ψ1μνkrj, θj, ϕj+e Bμνmnrij, θij, ϕij×Ψ2μνkrj, θj, ϕj,  Ψ2mnkri, θi, ϕi=μνe Bμνmnrij, θij, ϕij×Ψ1μνkrj, θj, ϕj+e Aμνrij, θij, ϕij×Ψ2μνkrj, θj, ϕj.
Aμνmn=γmnγμν-1μ p am, n|-μ, ν|pan, ν, p×hpkaPpm-μcos θ0kexpim-μϕ0k,
Bμνmn=γmnγμν-1μ+1p am, n|-μ, ν|p, p-1bn, ν, phpkaPpm-μcos θ0k×expim-μϕ0k.
j1j2j3000,
am, n|μ, ν|p=-1m+μ2p+1n+m!ν+μ!p-m-μ!n-m!ν-μ!p+m+μ!1/2×nνp000nνpmμ-m-μ,
am, n|μ, ν|p, q=-1m+μ2p+1×n+m!ν+μ!p-m-μ!n-m!ν-μ!p+m+μ!1/2×nνq000nνpmμ-m-μ.
nνp000,
nνq000
ai=a0 expikincri.
e Aμνmnkr0i, θ0i, ϕ0i=δnνδμm exp-ikΔi,  e Bμνmnkr0i, θ0i, ϕ0i=0.
fTN=i=1N exp-ikΔifiN.
T¯N+1N+1=Ī-T¯N+11i=1n α¯N+1, iT¯iNα¯i, N+1-1T¯N+11Ī+i=1n α¯N+1, iT¯iN expikincrN+1-ri,
T¯iN+1=T¯iNĪ+α¯i, N+1T¯N+1N+1×expikincrN+1-ri,  i  N,
fN+1=i=1N+1fiN+1 exp-ikΔi,
fiN+1=T¯iN+1a0 expikincri.

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