Abstract

Our previous theory for calculating the scattering pattern from a single aggregate of spheres deposited on a dielectric substrate is extended to deal with a dispersion of identical aggregates onto the substrate with a random distribution of their orientations. To this end the definition of the transition matrix of an aggregate is generalized to take account of the presence of the substrate; then the transformation properties under rotation of the newly defined transition matrix are used to perform analytically the required orientational averages. When the patterns calculated with this theory are compared with the calculations for a single aggregate, it can easily be seen that the features that reveal the anisotropy of the scatterers are not canceled by the averaging procedure.

© 1999 Optical Society of America

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  1. E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
    [CrossRef]
  2. E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
    [CrossRef]
  3. P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
    [CrossRef]
  4. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
    [CrossRef]
  5. B. R. Johnson, “Calculation of light scattering from a spherical particle on a surface by a multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
    [CrossRef]
  6. T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
    [CrossRef]
  7. I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
    [CrossRef]
  8. K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
    [CrossRef]
  9. G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
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    [CrossRef]
  11. H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
    [CrossRef]
  12. F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.
  13. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
  14. 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]
  15. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
    [CrossRef]
  16. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
    [CrossRef]
  17. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
    [CrossRef]
  18. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
    [CrossRef]
  19. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
    [CrossRef]
  20. K. A. Fuller, “Optical resonances of two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
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  21. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A 12, 881–892 (1995).
    [CrossRef]
  22. M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
    [CrossRef] [PubMed]
  23. 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]
  24. P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  25. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  26. F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
    [CrossRef] [PubMed]
  27. F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
    [CrossRef]
  28. F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
    [CrossRef]
  29. V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
    [CrossRef]
  30. E. M. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).
  31. M. Hammermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962).
  32. F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
    [CrossRef]

1999 (1)

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

1998 (1)

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

1997 (4)

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

1996 (2)

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]

B. R. Johnson, “Calculation of light scattering from a spherical particle on a surface by a multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
[CrossRef]

1995 (3)

1993 (1)

1992 (1)

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

1991 (4)

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

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

1989 (1)

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

1987 (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

1986 (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

1984 (3)

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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[CrossRef]

1980 (2)

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

1971 (1)

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

Balescu, R.

R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).

Barber, P.

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

Bickel, W. S.

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Borghese, F.

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Chac, S.

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

Denti, P.

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Doicu, A.

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Fucile, E.

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
[CrossRef]

Fuller, K. A.

Galbraith, L. K.

G. L. Wojcik, D. K. Vaughan, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, D. J. Ehrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

González, F.

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

Hammermesh, M.

M. Hammermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962).

Iafelice, V. J.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Johnson, B. R.

Lee, H. S.

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

Lindell, I. V.

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

Lumme, K. A.

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

Mackowski, D. W.

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, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

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, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

Moreno, F.

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

Muinonen, K. O.

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

Neri, F.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.

Pizzi, P.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.

Pui, D. Y. H.

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

Romeo, G.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.

Rose, E. M.

E. M. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).

Saija, R.

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.

Saiz, J. M.

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

Sihvola, A. H.

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

Sindoni, O. I.

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Resonance suppression in the extinction spectrum of single and aggregated hemispheres on a reflecting surface,” Appl. Opt. 36, 4226–4234 (1997).
[CrossRef] [PubMed]

F. Borghese, P. Denti, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of model anisotropic particles on or near a perfectly reflecting surface,” J. Opt. Soc. Am. A 12, 530–540 (1995).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[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]

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of the electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

Turner, M. G.

Valle, P. J.

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

Varadan, V. K.

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Varadan, V. V.

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Vaughan, D. K.

G. L. Wojcik, D. K. Vaughan, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, D. J. Ehrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Waterman, P. C.

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

Wojcik, G. L.

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

G. L. Wojcik, D. K. Vaughan, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, D. J. Ehrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

Wolfe, W. L.

Wriedt, T.

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

Ye, Y.

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[CrossRef]

Aerosol Sci. Technol. (2)

H. S. Lee, S. Chac, Y. Ye, D. Y. H. Pui, G. L. Wojcik, “Theoretical and experimental particle size response of wafer surface scanners,” Aerosol Sci. Technol. 14, 177–192 (1991).
[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]

Aerosol Sci. Technol. (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Optical absorption coefficient of a dispersion of clusters composed of a large number of spheres,” Aerosol Sci. Technol. 6, 173–181 (1987).
[CrossRef]

Appl. Opt. (1)

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

E. Fucile, F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “General reflection rule for electromagnetic multipole fields on a plane interface,” IEEE Trans. Antennas Propag. AP-45, 868–875 (1997).
[CrossRef]

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

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

J. Aerosol Sci. (1)

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989).
[CrossRef]

J. Math. Phys. (1)

F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
[CrossRef]

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

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
[CrossRef]

J. Opt. Soc. Am. A (3)

E. Fucile, P. Denti, F. Borghese, R. Saija, O. I. Sindoni, “Optical properties of a sphere in the vicinity of a plane surface,” J. Opt. Soc. Am. A 14, 1505–1514 (1997).
[CrossRef]

P. Denti, F. Borghese, R. Saija, E. Fucile, O. I. Sindoni, “Optical properties of aggregated spheres in the vicinity of a plane surface,” J. Opt. Soc. Am. A 16, 167–175 (1999).
[CrossRef]

F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

J. Opt. Soc. Am. A (5)

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

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]

Nuovo Cimento B (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Macroscopic optical constants of a cloud of randomly oriented nonspherical scatterers,” Nuovo Cimento B 81, 29–50 (1984).
[CrossRef]

Opt. Commun. (2)

T. Wriedt, A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376–384 (1998).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, F. Moreno, “Multiple scattering in particulate surfaces. Cross-polarization ratios and shadowing effects,” Opt. Commun. 137, 359–366 (1997).
[CrossRef]

Phys. Rev. D (2)

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

V. V. Varadan, V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
[CrossRef]

Physica A (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Other (6)

G. L. Wojcik, D. K. Vaughan, L. K. Galbraith, “Calculation of light scatter from structures on silicon surfaces,” in Lasers in Microlithography, J. S. Batchelder, D. J. Ehrlich, J. Y. Tsao, eds., Proc. SPIE774, 21–31 (1987).
[CrossRef]

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light-scattering photometer using a CCD camera,” in Proceedings of the Fifth International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota Press, Minneapolis, 1998), pp. 229–234.

R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).

E. M. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).

M. Hammermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Geometry that we adopted in our theory. Only the αth sphere of the aggregate is shown for clarity.

Fig. 2
Fig. 2

Aggregation case: pattern of the scattered intensity from an assembly of randomly oriented binary aggregates of the spheres of radius ρ1. The quantity that is actually reported (in square micrometers) is (a) ℐ¯φφ, (b) ℐ¯ϑφ , (c) ℐ¯φϑ, and (d) ℐ¯ϑϑ.

Fig. 3
Fig. 3

Subdivision case: pattern of the scattered intensity from an assembly of randomly oriented binary aggregates of the spheres of radius ρ2. The quantity that is actually reported (in square micrometers) is (a) ℐ¯φφ, (b) ℐ¯ϑφ, (c) ℐ¯φϑ, and (d) ℐ¯ϑϑ.

Equations (43)

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E ext = E I + E R + E S + E RS ,
E η I = E 0 η u ˆ I η   exp i k I · r ,
E η R = F η ϑ I E 0 η u ˆ R η   exp i k R · r ,
E η I = E 0 η plm J lm p r ,   n k W lm p u ˆ I η ,   k ˆ I ,   E η R = F η ϑ I E 0 η plm J lm p r ,   n k W lm p u ˆ R η ,   k ˆ R ,
J lm 1 r ,   K = j l Kr X lm r ˆ ,   J lm 2 r ,   K = 1 K   × j l Kr X lm r ˆ ,
W lm p u ˆ ,   K ˆ = 4 π i p + l - 1 - m + 1 Z l , - m p K ˆ · u ˆ .
Z lm 1 K ˆ = X lm K ˆ ,   Z lm 2 K ˆ = X lm K ˆ × K ˆ
W lm p u ˆ R η ,   k ˆ R = - η + p + l + m W lm p u ˆ I η ,   k ˆ I
E η I = E 0 η plm p l m J lm p r α ,   n k × J lm , l m p , p R α ,   n k W l m p u ˆ I η ,   k ˆ I , E η R = F η ϑ I E 0 η plm p l m J lm p r α ,   n k × J lm , l m p , p R α ,   n k W l m p u ˆ R η ,   k ˆ R ,
E η S = E 0 η α plm H lm p r α ,   n k A η α lm p ,
E η RS = E 0 η α plm H lm p r α ,   n k A ¯ η α lm p ,
A ¯ η α lm p = p l   a l , l ; m ; α p , p A η α l m p ,
a l , l ; m ; α p , p = p l α - 1 l , l ; m p , p α ; l , l ; m p , p ,
E η int = E 0 η plm J lm p r α ,   n α k C η α lm p .
E η S = E 0 η plm H lm p r α ,   n k A η α lm p + J lm p r α ,   n k × p l m α α   lm , l m p , p R α α ,   n k A η α l m p ,
E η RS = E 0 η plm J lm p r α ,   n k × p l m lm , l m p , p R ¯ α α ,   n k A ¯ η α l m p + α α   lm , l m p , p R ¯ α α ,   n k A ¯ η α l m p ,
E η RS = E 0 η plm J lm p r α ,   n k p l l , l ; m p , p A η α l m p + α α p l m   Q lm , l m p , p R ¯ α α ,   n k × α ; l , l ; m p , p A η α l m p ,
Q lm , l m p , p R ¯ α α ,   n k = p l   lm , l m p , p R ¯ α α ,   n k × α - 1 l , l ; m p , p .
α p l m - 1 α lm , α l m p , p A η α l m p = - W η α lm p ,
- 1 α lm , α l m p , p = R - 1 α l p δ α α δ pp δ ll δ mm + lm , l m p , p R α α ,   n k + α ; l , l ; m p , p δ α α + p l m   Q lm , l m p , p R ¯ α α α ; l , l ; m p , p ,
R α l p = 1 + n ¯ α δ p 1 u l n α k ρ α u l n k ρ α - 1 + n ¯ α δ p 2 u l n α k ρ α u l n k ρ α 1 + n ¯ α δ p 1 u l n α k ρ α w l n k ρ α - 1 + n ¯ α δ p 2 u l n α k ρ α w l n k ρ α ,   n ¯ α = n α n - 1 ,   u l x = xj l x ,   w l x = xh l x .
W η α lm p = p l m   J lm , l m p , p R α ,   n k W E η l m p ,
W E η lm p = W lm p u ˆ I η ,   k ˆ I 1 + - η + p + l + m F η ϑ I .
E η obs = plm H lm p r ,   n k A η lm p ,
A η lm p = α p l m J lm , l m p , p - R α ,   n k A η α l m p + J lm , l m p , p - R α ,   n k A ¯ η α l m p .
A η lm p = - p l m   S lm , l m p , p W E η l m p ,
A η α lm p = - α p l m   α lm , α l m p , p W η α l m p .
S lm , l m p , p = α α qLM q L M J lm , LM p , q - R α ,   n k × α LM , α L M q , q + J lm , LM p , q - R α ,   n k × q L   a L , L ; M ; α q , q α L M , α L M q , q × J L M , l m q , p R α ,   n k .
E η obs = exp in kr r   E 0 η f η ,
f η = 1 n k plm - i p + l Z lm p r ˆ A η lm p .
I η η = 1 r 2   | E 0 η f η η | 2 = 1 r 2   I 0 η | f η η | 2 ,
f η η = f η · u ˆ O η = - i 4 π n k plm   W O η lm p * A η lm p
W O η lm p = W lm p u ˆ O η ,   k ˆ O .
f η η = i 4 π n k pp ll mm   W O η lm p * × S lm , l m p , p W E η l m p .
I ¯ η η = N I η η = N     I η η R ,   Θ w R ,   Θ d R d Θ ,
I η η   I η η R ,   Θ w R R w Θ Θ d R d Θ   w R R d R     I η η 0 ,   Θ w Θ Θ d Θ =   I η η 0 ,   Θ w Θ Θ d Θ
  w R R d R = 1 .
f η η = i 4 π n k pp ll mm   W ¯ O η lm p * × S ¯ lm , l m p , p W ¯ E η l m p ,
f η η = i 4 π nk plm p l m μ μ   W O η lm p * D μ m l * Θ × S ¯ l μ , l μ p , p D μ m l Θ W E η l m p ,
D μ m l α ,   0 ,   0 = exp - i μ α δ μ m ,
f η η = i 4 π nk plm p l m   W O η lm p *   exp im α × S ¯ lm , l m p , p   exp - im α W E η l m p .
I ¯ η η = N 16 π 2 k 2 r 2   | E 0 | 2 mm m m   F η η mm * F η η m m m - m - m + m ,
F η η mm = pl p l   W O η lm p * S ¯ lm , l m p , p W E η l m p ,   μ = 0 2 π   exp - i α μ w α d α ,

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