Abstract

Three models have been developed to describe light scattering from a sphere in contact with a mirror. With two of the models the mirror was replaced with an image sphere. Light scattering from each sphere is assumed to follow the Mie theory: no further interaction between the sphere and mirror is assumed. The models differ in their consideration of the interaction of scattered fields from the spheres. The results of the models are compared to experimental values obtained for polystyrene spheres, 0.984 μm in diameter, with incident radiation λ = 0.6328 and 0.4416 μm. The comparison indicates that a best fit can be obtained by assuming that the real sphere and its image sphere are coherent light sources with a phase difference of π.

© 1987 Optical Society of America

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References

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  1. G. Mie, “Beitrage zur Optik trüber Meiden speziell kolloidaler Metallosüngen,” Ann. Phys. 25, 377 (1908).
    [CrossRef]
  2. J. H. Brunning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
    [CrossRef]
  3. J. H. Bruning, Y. H. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957, 1976).
  5. R. P. Young, “Low-Scatter Mirror Degradation by Particle Contamination,” Opt. Eng. 15, 516 (1976).
    [CrossRef]
  6. F. Nicodemus, “Reflectance Nomenclature and Directional Reflectance and Emissivity,” Appl. Opt. 9, 1474 (1970).
    [CrossRef] [PubMed]
  7. J. M. Elson, H. E. Bennet, J. M. Bennet, “Scattering from Optical Surfaces,” Applied Optics and Engineering, Vol. 7 (Academic, New York, 1979), p. 191.
    [CrossRef]
  8. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  9. L. D. Brooks, “Micro-processor Based Instrumentation for BRDF Measurement from Visible to FIR,” Ph.D. Dissertation, U. Arizona, Tucson (1982).
  10. R. A. Bowling, Author-insert affiliation; private communication.Also, “A Theoretical Review of Particle Adhesion,” in Proceedings, Fine Particle Society (1986) to be published.

1976

R. P. Young, “Low-Scatter Mirror Degradation by Particle Contamination,” Opt. Eng. 15, 516 (1976).
[CrossRef]

1971

J. H. Brunning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

1970

1908

G. Mie, “Beitrage zur Optik trüber Meiden speziell kolloidaler Metallosüngen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Bennet, H. E.

J. M. Elson, H. E. Bennet, J. M. Bennet, “Scattering from Optical Surfaces,” Applied Optics and Engineering, Vol. 7 (Academic, New York, 1979), p. 191.
[CrossRef]

Bennet, J. M.

J. M. Elson, H. E. Bennet, J. M. Bennet, “Scattering from Optical Surfaces,” Applied Optics and Engineering, Vol. 7 (Academic, New York, 1979), p. 191.
[CrossRef]

Bohren, C.

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

Brooks, L. D.

L. D. Brooks, “Micro-processor Based Instrumentation for BRDF Measurement from Visible to FIR,” Ph.D. Dissertation, U. Arizona, Tucson (1982).

Bruning, J. H.

J. H. Bruning, Y. H. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

Brunning, J. H.

J. H. Brunning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Elson, J. M.

J. M. Elson, H. E. Bennet, J. M. Bennet, “Scattering from Optical Surfaces,” Applied Optics and Engineering, Vol. 7 (Academic, New York, 1979), p. 191.
[CrossRef]

Huffman, D.

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

Lo, Y. H.

J. H. Bruning, Y. H. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

Lo, Y. T.

J. H. Brunning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Mie, G.

G. Mie, “Beitrage zur Optik trüber Meiden speziell kolloidaler Metallosüngen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Nicodemus, F.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957, 1976).

Young, R. P.

R. P. Young, “Low-Scatter Mirror Degradation by Particle Contamination,” Opt. Eng. 15, 516 (1976).
[CrossRef]

Ann. Phys.

G. Mie, “Beitrage zur Optik trüber Meiden speziell kolloidaler Metallosüngen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Appl. Opt.

IEEE Trans. Antennas Propag.

J. H. Brunning, Y. T. Lo, “Multiple Scattering of EM Waves by Spheres Part I—Multipole Expansion and Ray-Optical Solution,” IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Opt. Eng.

R. P. Young, “Low-Scatter Mirror Degradation by Particle Contamination,” Opt. Eng. 15, 516 (1976).
[CrossRef]

Other

J. M. Elson, H. E. Bennet, J. M. Bennet, “Scattering from Optical Surfaces,” Applied Optics and Engineering, Vol. 7 (Academic, New York, 1979), p. 191.
[CrossRef]

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

L. D. Brooks, “Micro-processor Based Instrumentation for BRDF Measurement from Visible to FIR,” Ph.D. Dissertation, U. Arizona, Tucson (1982).

R. A. Bowling, Author-insert affiliation; private communication.Also, “A Theoretical Review of Particle Adhesion,” in Proceedings, Fine Particle Society (1986) to be published.

J. H. Bruning, Y. H. Lo, “Multiple Scattering by Spheres,” Tech. Rep. 69-5 (Antenna Laboratory, U. Illinois, Urbana, 1969).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957, 1976).

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Figures (8)

Fig. 1
Fig. 1

Phase difference model. The sphere actually rests on the plane.

Fig. 2
Fig. 2

Double interaction model: (a) path difference 1 = efg. Path difference 2 = abc.

Fig. 3
Fig. 3

Area factor. The beam incident on the shaded area constitutes the secondary incidence beam on the sphere.

Fig. 4
Fig. 4

Instrument background profile: 0.6328 μm and s polarization.

Fig. 5
Fig. 5

BRDF vs scattering angle at 0.6328 μm, 0° incidence: (a) s polarization; (b) p polarization.

Fig. 6
Fig. 6

BRDF vs scattering angle at 0.6328 μm, 10° incidence: (a) s polarization; (b) p polarization.

Fig. 7
Fig. 7

BRDF vs scattering angle at 0.6328 μm, 30° incidence, s polarization: (a) forward direction; (b) backscattered.

Fig. 8
Fig. 8

BRDF vs scattering angle at 0.4416 μm, 10° incidence, s polarization, backscattered.

Equations (9)

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E θ = i kr exp [ i ( kr ω t ) ] cos ϕ S 2 ( θ ) ,
E ϕ = i kr exp [ i ( kr ω t ) ] sin ϕ S 1 ( θ ) ,
I p = 1 k 2 | S 2 ( θ ) | 2 .
I s = 1 k 2 | S 1 ( θ ) | 2 ,
δ = 2 π λ a cos θ s .
E s E 1 exp ( i δ ) + E 2 exp [ i ( π δ ) ] .
δ 1 = 2 π λ 2 h cos θ i ,
δ 2 = 2 π λ 2 h cos ( θ s + θ i ) .
BRDF = 1 P i d P s d Ω 1 cos θ ,

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