Abstract

Our previous theory for calculating the scattering pattern from single spheres in the vicinity of a dielectric substrate [J. Opt. Soc. Am. A 14, 1505 (1997)] is extended to the case of aggregated spheres. This extension preserves our main result that a nonvanishing field, though somewhat attenuated when the substrate is absorptive, can propagate along the interface; this feature is apparent in the patterns from all the aggregates that we considered. The effects that can be expected when scattering particles on the dielectric surface either aggregate or undergo some kind of subdivision are investigated by comparing the pattern from a sphere containing a chosen volume V of a given refractive material with the pattern from the aggregate of two such spheres and with the pattern from two aggregated spheres of the same material, each of volume V/2.

© 1999 Optical Society of America

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  1. I. V. Lindell, E. Alanen, “Exact image theory for the Sommerfeld half-space problem. III. General formulation,” IEEE Trans. Antennas Propag. AP-32, 1027–1032 (1984).
    [CrossRef]
  2. T. Takemori, M. Inoue, K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
    [CrossRef]
  3. 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]
  4. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); errata 9, 844–845 (1992).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. E. Jakeman, “Scattering by particles on an interface,” J. Phys. D 27, 198–210 (1994).
    [CrossRef]
  7. G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115, 1–7 (1995).
    [CrossRef]
  8. E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
    [CrossRef]
  9. R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. (Bellingham) 15, 516–520 (1976).
    [CrossRef]
  10. P. Lilienfeld, “Optical detection of particle contamination on surfaces: a review,” Aerosol. Sci. Technol. 5, 145–165 (1986).
    [CrossRef]
  11. D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” Appl. Opt. 27, 4019–4026 (1988).
    [CrossRef] [PubMed]
  12. E. J. Bawolek, E. D. Hirleman, “Light scattering by submicron spherical particles on semiconductor surfaces,” in Detection, Adhesion, and Removal, K. L. Mittal, ed., Vol. 3 of Particles on Surfaces (Plenum, New York, 1991), pp. 91–105.
    [CrossRef]
  13. 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]
  14. F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light scattering photometer using a CCD camera,” in Proceedings of the 5th International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota, Minneapolis, Minn., 1998), pp. 229–232.
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    [CrossRef]
  17. 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]
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    [CrossRef]
  21. 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]
  22. 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]
  23. 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. 45, 868–875 (1997).
    [CrossRef]
  24. 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]
  25. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
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    [CrossRef]
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    [CrossRef]
  30. F. Borghese, P. Denti, G. Toscano, O. I. Sindoni, “An addition theorem for vector Helmholtz harmonics,” J. Math. Phys. 21, 2754–2755 (1980).
    [CrossRef]
  31. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  32. H. Yousif, “Light scattering from parallel tilted fibers,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1987).
  33. E. M. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).

1997 (5)

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[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]

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]

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. 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]

1996 (1)

1995 (2)

1994 (1)

E. Jakeman, “Scattering by particles on an interface,” J. Phys. D 27, 198–210 (1994).
[CrossRef]

1993 (2)

1992 (2)

1991 (3)

1989 (1)

1988 (1)

1987 (1)

T. Takemori, M. Inoue, K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

1986 (2)

P. Lilienfeld, “Optical detection of particle contamination on surfaces: a review,” Aerosol. Sci. Technol. 5, 145–165 (1986).
[CrossRef]

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

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]

I. V. Lindell, E. Alanen, “Exact image theory for the Sommerfeld half-space problem. III. General formulation,” IEEE Trans. Antennas Propag. AP-32, 1027–1032 (1984).
[CrossRef]

1980 (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]

1976 (1)

R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. (Bellingham) 15, 516–520 (1976).
[CrossRef]

Alanen, E.

I. V. Lindell, E. Alanen, “Exact image theory for the Sommerfeld half-space problem. III. General formulation,” IEEE Trans. Antennas Propag. AP-32, 1027–1032 (1984).
[CrossRef]

Balescu, R.

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

Barakat, R.

Barber, P.

Bawolek, E. J.

E. J. Bawolek, E. D. Hirleman, “Light scattering by submicron spherical particles on semiconductor surfaces,” in Detection, Adhesion, and Removal, K. L. Mittal, ed., Vol. 3 of Particles on Surfaces (Plenum, New York, 1991), pp. 91–105.
[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.

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

Bosi, G.

G. Bosi, “Retarded treatment of substrate-related effects on granular films,” Physica A 190, 375–392 (1992).
[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.

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

Fucile, E.

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]

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[CrossRef]

Hirleman, E. D.

D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” Appl. Opt. 27, 4019–4026 (1988).
[CrossRef] [PubMed]

E. J. Bawolek, E. D. Hirleman, “Light scattering by submicron spherical particles on semiconductor surfaces,” in Detection, Adhesion, and Removal, K. L. Mittal, ed., Vol. 3 of Particles on Surfaces (Plenum, New York, 1991), pp. 91–105.
[CrossRef]

Iafelice, V. J.

Inoue, M.

T. Takemori, M. Inoue, K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Jackson, J. D.

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

Jakeman, E.

E. Jakeman, “Scattering by particles on an interface,” J. Phys. D 27, 198–210 (1994).
[CrossRef]

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]

Lilienfeld, P.

P. Lilienfeld, “Optical detection of particle contamination on surfaces: a review,” Aerosol. Sci. Technol. 5, 145–165 (1986).
[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]

I. V. Lindell, E. Alanen, “Exact image theory for the Sommerfeld half-space problem. III. General formulation,” IEEE Trans. Antennas Propag. AP-32, 1027–1032 (1984).
[CrossRef]

Moreno, F.

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[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]

Muinonen, K. O.

Neri, F.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light scattering photometer using a CCD camera,” in Proceedings of the 5th International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota, Minneapolis, Minn., 1998), pp. 229–232.

Ohtaka, K.

T. Takemori, M. Inoue, K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Ortiz, E. M.

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[CrossRef]

Pizzi, P.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light scattering photometer using a CCD camera,” in Proceedings of the 5th International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota, Minneapolis, Minn., 1998), pp. 229–232.

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]

Rao, T. C.

Romeo, G.

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light scattering photometer using a CCD camera,” in Proceedings of the 5th International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota, Minneapolis, Minn., 1998), pp. 229–232.

Rose, E. M.

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

Saija, R.

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

F. Neri, P. Pizzi, G. Romeo, R. Saija, “Differential light scattering photometer using a CCD camera,” in Proceedings of the 5th International Congress on Optical Particle Sizing, P. H. McMurry, A. A. Naqwi, eds. (University of Minnesota, Minneapolis, Minn., 1998), pp. 229–232.

Saiz, J. M.

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[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]

Sihvola, A. H.

Sindoni, O. I.

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

Takemori, T.

T. Takemori, M. Inoue, K. Ohtaka, “Optical response of a sphere coupled to a metal substrate,” J. Phys. Soc. Jpn. 56, 1587–1602 (1987).
[CrossRef]

Taubenblatt, M. A.

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]

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

Tran, T. K.

Turner, M. G.

Valle, P. J.

E. M. Ortiz, P. J. Valle, J. M. Saiz, F. González, F. Moreno, “Multiscattering effects in the far-field region for two small particles on a flat conducting substrate,” Waves Random Media 7, 319–329 (1997).
[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]

van de Hulst, H. C.

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

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]

Weber, D. C.

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.

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]

Young, R. P.

R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. (Bellingham) 15, 516–520 (1976).
[CrossRef]

Yousif, H.

H. Yousif, “Light scattering from parallel tilted fibers,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1987).

Aerosol. Sci. Technol. (3)

P. Lilienfeld, “Optical detection of particle contamination on surfaces: a review,” Aerosol. Sci. Technol. 5, 145–165 (1986).
[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]

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]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (2)

I. V. Lindell, E. Alanen, “Exact image theory for the Sommerfeld half-space problem. III. General formulation,” IEEE Trans. Antennas Propag. AP-32, 1027–1032 (1984).
[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. 45, 868–875 (1997).
[CrossRef]

J. Math. Phys. (1)

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Figures (4)

Fig. 1
Fig. 1

Sketch of the geometry that we adopted in our theory. Only the αth sphere of the cluster is shown for the sake of clarity.

Fig. 2
Fig. 2

Pattern of the scattered intensity from the single sphere of radius ρ1. The quantity that is actually shown (in square micrometers) is (a) Iϕϕ, (b) Iθϕ, (c) Iϕθ, and (d) Iθθ.

Fig. 3
Fig. 3

Pattern of the scattered intensity from the binary aggregate of the spheres of radius ρ1. The quantity that is actually shown (in square micrometers) is (a) Iϕϕ, (b) Iθϕ, (c) Iϕθ, and (d) Iθθ.

Fig. 4
Fig. 4

Pattern of the scattered intensity from the binary aggregate of the spheres of radius ρ2. The quantity that is actually shown (in square micrometers) is (a) Iϕϕ, (b) Iθϕ, (c) Iϕθ, and (d) Iθθ.

Equations (46)

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Eext=EI+ER+ES+ERS,
iB=1k×E,
EηI=E0ηuˆIη exp(ikI·r),
EηR=E0ηuˆRη exp(ikR·r),
uˆI1×uˆI2=kˆI,uˆR1×uˆR2=kˆR,
E0η=Fη(θI)E0η,
F1(θI)=n2 cos θI-βn2 cos θI+β,F2(θI)=cos θI-βcos θI+β,
β=[(n2-1)+cos2 θI]1/2.
EηR=Fη(θI)E0ηuˆRη exp(ikR·r).
EηI=E0ηplmJlm(p)(r, nk)Wlm(p)(uˆIη, kˆI),
EηR=Fη(θI)E0ηplmJlm(p)(r, nk)Wlm(p)(uˆRη, kˆR),
Jlm(1)(r, K)=jl(Kr)Xlm(rˆ),
Jlm(2)(r, K)=1K×jl(Kr)Xlm(rˆ)
Wlm(p)(uˆ,Kˆ)=4πip+l-1(-)m+1Zl,-m(p)(Kˆ)·uˆ.
Zlm(1)(Kˆ)=Xlm(Kˆ),Zlm(2)(Kˆ)=Xlm(Kˆ)×Kˆ
Wηlm(p)(uˆRη, kˆR)=(-)η+p+l+mWηlm(p)(uˆIη, kˆI),
EηI=E0ηuˆIη exp[ikI·(Rα+rα)]=exp(ikI·Rα)E0ηplmJlm(p)(rα, nk)×Wlm(p)(uˆIη, kˆI),
EηR=Fη(θI)E0ηuˆRη exp[ikR·(Rα+rα)]=exp(ikR·Rα)Fη(θI)E0ηplmJlm(p)(rα, nk)×Wlm(p)(uˆRη, kˆR).
EηS=E0ηαplmHlm(p)(rα, nk)Aηαlm(p),
EηRS=E0ηαplmHlm(p)(rα, nk)A¯ηαlm(p),
A¯ηαlm(p)=plaα;l,l;m(p, p)Aηαlm(p).
aα;l,l;m(p, p)=pl(Hα-1)l,l;m(p, p)Fα;l,l;m(p, p),
Eηint=E0ηplmJlm(p)(rα, nαk)Cηαlm(p).
EηS=E0ηplmHlm(p)(rα, nk)Aηαlm(p)+Jlm(p)(rα, nk)×plmβαHlm,lm(p, p)(Rβα, nk)Aηβlm(p),
EηRS=E0ηplmJlm(p)(rα, nk)×plmHlm,lm(p, p)(R¯αα, nk)A¯ηαlm(p)+βαHlm,lm(p, p)(R¯βα, nk)A¯ηβlm(p),
EηRS=E0ηplmJlm(p)(rα, nk)plFα;l,l;m(p, p)Aηαlm(p)+βαplmQlm,lm(p, p)(R¯βα, nk)×Fβ;l,l;m(p, p)Aηβlm(p),
Qlm,lm(p, p)(R¯βα, nk)=plHlm,lm(p, p)(R¯βα, nk)×(Hβ-1)l,l;m(p, p).
βplm(M-1)αlm,βlm(p, p)Aηβlm(p)=-W ηαlm(p),
(M-1)αlm,βlm(p, p)
=(R-1)αl(p)δαβδppδllδmm
+Hlm,lm(p, p)(Rβα, nk)+Fα;l,l;m(p, p)δαβδmm
+plQlm,lm(p, p)(R¯βα, nk)Fβ;l,l;m(p, p),
Rαl(p)=(1+n¯αδp1)ul(nαkρα)ul(nkρα)-(1+n¯αδp2)ul(nαkρα)ul(nkρα)(1+n¯αδp1)ul(nαkρα)wl(nkρα)-(1+n¯αδp2)ul(nαkρα)wl(nkρα),
n¯α=nαn-1,ul(x)=xjl(x),wl(x)=xhl(x).
Wηαlm(p)=exp(ikI·Rα)Wlm(p)(uˆIη, kˆI)
+Fη(θI)exp(ikR·Rα)Wlm(p)(uˆRη, kˆR).
Eηobs=E0ηplmHlm(p)(r, nk)Aηlm(p),
Aηlm(p)=αplm[Jlm,lm(p, p)(-Rα, nk)Aηαlm(p)+Jlm,lm(p, p)(-Rα, nk)A¯ηαlm(p)],
Eηobs=exp(inkr)rE0η fη,
fη=1nkplm(-i)p+lZlm(p)(rˆ)Aηlm(p).
Iηη=1r2|E0η fηη|2=1r2I0η|fηη|2,
fηη=fη·uˆOη=-i4πnkplmWlm(p)*(uˆOη, kˆO)Aηlm(p).
exp(-ik·R)Wlm(p)*(uˆ, kˆ)=plmWlm(p)*(uˆ, kˆ)×Jlm,lm(p, p)(-R, nk),
fηη=-i4πnkαplmWlm(p)*(uˆOη, kˆO)
×[exp(-ikO·Rα)Aηαlm(p)
+exp(-ikO·Rα)A¯ηαlm(p)].

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