Abstract

To determine the effects on total light scattering of deep holes in the scattering particles, the Rayleigh-Gans-Debye and anomalous difffraction equations were solved by numerical methods for x = 0.1–1200, n = 1.05. Scattering by randomly oriented spheres with holes was compared with that from homogeneous smooth ones of equal net volume and refractive index. The effects of hole formation are found to be similar to those of projection formation that were previously reported. They also resemble those of uniform particle swelling with no change in mass. The results indicate that the influence of detail formation on total scattering is caused primarily by changes in the overall radial distribution of the mass, not by the generation of scattering centers.

© 1984 Optical Society of America

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References

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  1. A. L. Aden, M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” J. Appl. Phys. 22, 1242 (1951).
    [Crossref]
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  4. D. Deirmendjian, Electromagnetic Scattering by Spherical Polydispersions (American Elsevier, New York, 1969).
  5. D. A. Cross, Dissertation, Auburn U. (1971).
  6. P. Latimer, P. Barber, “Scattering by Ellipsoids of Revolution—A Comparison of Theoretical Methods,” J. Colloid Interface Sci. 63, 310 (1978).
    [Crossref]
  7. P. Latimer, “Predicted Scattering by Spheroids: Comparison of Approximate and Exact Methods,” Appl. Opt. 19, 3039 (1980).
    [Crossref] [PubMed]
  8. P. Latimer, “Light Scattering by a Homogeneous Sphere with Radial Projections,” Appl. Opt. 23, 442 (1984).
    [Crossref] [PubMed]
  9. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), p. 107.
  10. P. Latimer, “The Influence of Photometer Design on Optical-Conformational Changes,” J. Theor. Biol. 51, 1 (1975).
    [Crossref] [PubMed]
  11. P. Latimer, “Photometric Assays of Cell Shrinkage—The Resolution of a Conflict,” J. Theor. Biol. 102, 249 (1983).
    [Crossref]
  12. F. D. Bryant, P. Latimer, “Optical Efficiences of Large Particles of Arbitrary Shape and Orientation,” J. Colloid Interface Sci. 30, 291 (1969).
    [Crossref]
  13. S. K. Friedlander, “The Characterization of Aerosols Distributed with Respect to Size and Chemical Composition,” Aerosol Sci. 1, 295 (1970).
    [Crossref]
  14. P. Latimer, “Light Scattering, Data Inversion, and Information Theory,” J. Colloid Interface Sci. 39, 497 (1972).
    [Crossref]
  15. B. E. Warren, X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1969), p. 9.

1984 (1)

1983 (1)

P. Latimer, “Photometric Assays of Cell Shrinkage—The Resolution of a Conflict,” J. Theor. Biol. 102, 249 (1983).
[Crossref]

1980 (1)

1978 (1)

P. Latimer, P. Barber, “Scattering by Ellipsoids of Revolution—A Comparison of Theoretical Methods,” J. Colloid Interface Sci. 63, 310 (1978).
[Crossref]

1975 (1)

P. Latimer, “The Influence of Photometer Design on Optical-Conformational Changes,” J. Theor. Biol. 51, 1 (1975).
[Crossref] [PubMed]

1972 (1)

P. Latimer, “Light Scattering, Data Inversion, and Information Theory,” J. Colloid Interface Sci. 39, 497 (1972).
[Crossref]

1970 (1)

S. K. Friedlander, “The Characterization of Aerosols Distributed with Respect to Size and Chemical Composition,” Aerosol Sci. 1, 295 (1970).
[Crossref]

1969 (1)

F. D. Bryant, P. Latimer, “Optical Efficiences of Large Particles of Arbitrary Shape and Orientation,” J. Colloid Interface Sci. 30, 291 (1969).
[Crossref]

1951 (1)

A. L. Aden, M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” J. Appl. Phys. 22, 1242 (1951).
[Crossref]

Aden, A. L.

A. L. Aden, M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” J. Appl. Phys. 22, 1242 (1951).
[Crossref]

Barber, P.

P. Latimer, P. Barber, “Scattering by Ellipsoids of Revolution—A Comparison of Theoretical Methods,” J. Colloid Interface Sci. 63, 310 (1978).
[Crossref]

Bryant, F. D.

F. D. Bryant, P. Latimer, “Optical Efficiences of Large Particles of Arbitrary Shape and Orientation,” J. Colloid Interface Sci. 30, 291 (1969).
[Crossref]

Cross, D. A.

D. A. Cross, Dissertation, Auburn U. (1971).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering by Spherical Polydispersions (American Elsevier, New York, 1969).

Friedlander, S. K.

S. K. Friedlander, “The Characterization of Aerosols Distributed with Respect to Size and Chemical Composition,” Aerosol Sci. 1, 295 (1970).
[Crossref]

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), p. 107.

Kerker, M.

A. L. Aden, M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” J. Appl. Phys. 22, 1242 (1951).
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Latimer, P.

P. Latimer, “Light Scattering by a Homogeneous Sphere with Radial Projections,” Appl. Opt. 23, 442 (1984).
[Crossref] [PubMed]

P. Latimer, “Photometric Assays of Cell Shrinkage—The Resolution of a Conflict,” J. Theor. Biol. 102, 249 (1983).
[Crossref]

P. Latimer, “Predicted Scattering by Spheroids: Comparison of Approximate and Exact Methods,” Appl. Opt. 19, 3039 (1980).
[Crossref] [PubMed]

P. Latimer, P. Barber, “Scattering by Ellipsoids of Revolution—A Comparison of Theoretical Methods,” J. Colloid Interface Sci. 63, 310 (1978).
[Crossref]

P. Latimer, “The Influence of Photometer Design on Optical-Conformational Changes,” J. Theor. Biol. 51, 1 (1975).
[Crossref] [PubMed]

P. Latimer, “Light Scattering, Data Inversion, and Information Theory,” J. Colloid Interface Sci. 39, 497 (1972).
[Crossref]

F. D. Bryant, P. Latimer, “Optical Efficiences of Large Particles of Arbitrary Shape and Orientation,” J. Colloid Interface Sci. 30, 291 (1969).
[Crossref]

van de Hulst, H. C.

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

Warren, B. E.

B. E. Warren, X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1969), p. 9.

Aerosol Sci. (1)

S. K. Friedlander, “The Characterization of Aerosols Distributed with Respect to Size and Chemical Composition,” Aerosol Sci. 1, 295 (1970).
[Crossref]

Appl. Opt. (2)

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” J. Appl. Phys. 22, 1242 (1951).
[Crossref]

J. Colloid Interface Sci. (3)

P. Latimer, “Light Scattering, Data Inversion, and Information Theory,” J. Colloid Interface Sci. 39, 497 (1972).
[Crossref]

P. Latimer, P. Barber, “Scattering by Ellipsoids of Revolution—A Comparison of Theoretical Methods,” J. Colloid Interface Sci. 63, 310 (1978).
[Crossref]

F. D. Bryant, P. Latimer, “Optical Efficiences of Large Particles of Arbitrary Shape and Orientation,” J. Colloid Interface Sci. 30, 291 (1969).
[Crossref]

J. Theor. Biol. (2)

P. Latimer, “The Influence of Photometer Design on Optical-Conformational Changes,” J. Theor. Biol. 51, 1 (1975).
[Crossref] [PubMed]

P. Latimer, “Photometric Assays of Cell Shrinkage—The Resolution of a Conflict,” J. Theor. Biol. 102, 249 (1983).
[Crossref]

Other (6)

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), p. 107.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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

D. Deirmendjian, Electromagnetic Scattering by Spherical Polydispersions (American Elsevier, New York, 1969).

D. A. Cross, Dissertation, Auburn U. (1971).

B. E. Warren, X-Ray Diffraction (Addison-Wesley, Reading, Mass., 1969), p. 9.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagrams of the homogeneous sphere with holes. These computer drawings are equatorial projections of the 3-D particle without foreshortening. The edges of the holes, which pass through the center of the sphere, are shown as dashed lines. However, no attempt was made to accurately depict the region near the center of the sphere where the holes meet. The sphere on the left has small holes (q = 0.1) and it is oriented at α = 25°, β = 20°. The sphere on the right has larger holes (q = 0.2). It is oriented at α = 35° and β = 35°. The creation of the holes increases the gross sphere volumes by 4.4% and 18.9%, respectively.

Fig. 2
Fig. 2

Influence of hole formation on total scattering as a function of the size parameter x = 2πa/λ of the original smooth sphere. Plotted is the ratio of scattering cross sections for the systems in Fig. 1 as calculated with the RGD relations (small points) and the AD relations (large points). For Rayleigh particles, the effects of the holes are negligible. For intermediate particles, the holes decrease total scattering while for larger particles they increase total scattering.

Fig. 3
Fig. 3

Influence of particle swelling, with no change in mass, on total scattering as predicted by the AD and RGD approximations. The refractive-index increment varies inversely with particle volume. The volumes of the swollen spheres were, respectively, 4.4% and 18.9% larger than those of their normal counterparts. Swelling increases A, increases particle thickness t, decreases (n − 1), and decreases ϕ. The net effect is to either increase or decrease K and also R depending on particle size.

Fig. 4
Fig. 4

Comparison of the curves of Figs. 2 and 3 for the sphere with large holes and for the fully swollen sphere. Insofar as the curves agree, the effects of hole production have the same influence on total scattering as does simple swelling. The results indicate that the effects on total scattering of structure formation are caused mainly by the inherent change in the radial distribution of the mass involved in hole formation, not by the details of the structure as such.

Equations (1)

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4 / 3 π r s 3 = 4 / 3 π r h 3 - 6 π q 2 r h 2 ( r h - q ) - π 3 / 2 r h 3 q 3 .

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