Abstract

Total scattering by a homogeneous sphere with projections is compared with that of the smooth homogeneous sphere of equal total volume and refractive index. The sphere sizes examined are x = 2πa/λ = 0.03 − 1200, n = 1.05. Scattered light from randomly oriented particles is predicted numerically with the Rayleigh-Gans-Debye approximation for small and intermediate particles and with van de Hulst’s anomalous diffraction approximation for intermediate and large ones. The results indicate moderate effects on total scattering of projection (spine) formation at the expense of the particle core. Spine formation does not change scattering by small (Rayleigh) particles; it decreases total scattering when x = 0.1 − 45 more or less in proportion to the total mass of the spines, and it increases scattering for x > 45 by somewhat more.

© 1984 Optical Society of America

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References

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  1. W. A. Farone, M. J. Robinson, Appl. Opt. 7, 643 (1968).
    [CrossRef] [PubMed]
  2. D. M. Moore, F. D. Bryant, P. Latimer, J. Opt. Soc. Am. 58, 281 (1968).
    [CrossRef]
  3. M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 427.
  4. D. A. Cross, Dissertation, Auburn U., Ala. (1971).
  5. P. Latimer, P. BarberJ. Coll. Interface Sci. 63, 310 (1978).
    [CrossRef]
  6. P. Latimer, Appl. Opt. 19, 3039 (1980).
    [CrossRef] [PubMed]
  7. P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
    [CrossRef]
  8. A. Brunsting, Ph.D. Dissertation, U. New Mexico, Albuquerque (1972).
  9. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), pp. 99, 107.
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 85, 172.
  11. A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
    [CrossRef]
  12. F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
    [CrossRef] [PubMed]
  13. P. Latimer, J. Theor. Biol. 51, 1 (1975).
    [CrossRef] [PubMed]
  14. P. Latimer, J. Theor. Biol. 102, 249 (1983).
    [CrossRef]
  15. A. Brunsting, P. F. Mullaney, Appl. Opt. 11, 675 (1972).
    [CrossRef] [PubMed]
  16. P. Latimer, Appl. Opt. 17, 2162 (1978).
    [CrossRef] [PubMed]
  17. F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
    [CrossRef] [PubMed]
  18. P. Latimer, F. Wamble, Appl. Opt. 21, 2447 (1982).
    [CrossRef] [PubMed]
  19. P. Latimer, Appl. Opt. 22, 1136 (1983).
    [CrossRef] [PubMed]
  20. H. E. Stanley, F. Family, H. Gould, J. Polym. Sci. (1983); in press.

1983 (2)

P. Latimer, J. Theor. Biol. 102, 249 (1983).
[CrossRef]

P. Latimer, Appl. Opt. 22, 1136 (1983).
[CrossRef] [PubMed]

1982 (1)

1980 (1)

1978 (2)

P. Latimer, P. BarberJ. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

P. Latimer, Appl. Opt. 17, 2162 (1978).
[CrossRef] [PubMed]

1977 (1)

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
[CrossRef]

1975 (1)

P. Latimer, J. Theor. Biol. 51, 1 (1975).
[CrossRef] [PubMed]

1972 (1)

1969 (2)

F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
[CrossRef] [PubMed]

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
[CrossRef] [PubMed]

1968 (2)

1951 (1)

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Aden, A. L.

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Barber, P.

P. Latimer, P. BarberJ. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

Born, G. V. R.

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
[CrossRef]

Brunsting, A.

A. Brunsting, P. F. Mullaney, Appl. Opt. 11, 675 (1972).
[CrossRef] [PubMed]

A. Brunsting, Ph.D. Dissertation, U. New Mexico, Albuquerque (1972).

Bryant, F. D.

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
[CrossRef] [PubMed]

F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
[CrossRef] [PubMed]

D. M. Moore, F. D. Bryant, P. Latimer, J. Opt. Soc. Am. 58, 281 (1968).
[CrossRef]

Cross, D. A.

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

Family, F.

H. E. Stanley, F. Family, H. Gould, J. Polym. Sci. (1983); in press.

Farone, W. A.

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), pp. 99, 107.

Gould, H.

H. E. Stanley, F. Family, H. Gould, J. Polym. Sci. (1983); in press.

Kerker, M.

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 427.

Latimer, P.

P. Latimer, Appl. Opt. 22, 1136 (1983).
[CrossRef] [PubMed]

P. Latimer, J. Theor. Biol. 102, 249 (1983).
[CrossRef]

P. Latimer, F. Wamble, Appl. Opt. 21, 2447 (1982).
[CrossRef] [PubMed]

P. Latimer, Appl. Opt. 19, 3039 (1980).
[CrossRef] [PubMed]

P. Latimer, P. BarberJ. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

P. Latimer, Appl. Opt. 17, 2162 (1978).
[CrossRef] [PubMed]

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
[CrossRef]

P. Latimer, J. Theor. Biol. 51, 1 (1975).
[CrossRef] [PubMed]

F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
[CrossRef] [PubMed]

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
[CrossRef] [PubMed]

D. M. Moore, F. D. Bryant, P. Latimer, J. Opt. Soc. Am. 58, 281 (1968).
[CrossRef]

Michal, F.

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
[CrossRef]

Moore, D. M.

Mullaney, P. F.

Robinson, M. J.

Seiber, B. A.

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
[CrossRef] [PubMed]

F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
[CrossRef] [PubMed]

Stanley, H. E.

H. E. Stanley, F. Family, H. Gould, J. Polym. Sci. (1983); in press.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 85, 172.

Wamble, F.

Appl. Opt. (6)

Appl. Phys. (1)

A. L. Aden, M. Kerker, Appl. Phys. 22, 1242 (1951).
[CrossRef]

Arch. Biochem. Biophy. (1)

P. Latimer, G. V. R. Born, F. Michal, Arch. Biochem. Biophy. 180, 151 (1977).
[CrossRef]

Arch. Biochem. Biophys. (2)

F. D. Bryant, P. Latimer, B. A. Seiber, Arch. Biochem. Biophys. 135, 109 (1969).
[CrossRef] [PubMed]

F. D. Bryant, B. A. Seiber, P. Latimer, Arch. Biochem. Biophys. 135, 97 (1969).
[CrossRef] [PubMed]

J. Coll. Interface Sci. (1)

P. Latimer, P. BarberJ. Coll. Interface Sci. 63, 310 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Theor. Biol. (2)

P. Latimer, J. Theor. Biol. 51, 1 (1975).
[CrossRef] [PubMed]

P. Latimer, J. Theor. Biol. 102, 249 (1983).
[CrossRef]

Other (6)

H. E. Stanley, F. Family, H. Gould, J. Polym. Sci. (1983); in press.

M. Kerker, The Scattering of Light (Academic, New York, 1969), p. 427.

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

A. Brunsting, Ph.D. Dissertation, U. New Mexico, Albuquerque (1972).

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1959), pp. 99, 107.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 85, 172.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagrams of spheres with cylindrical projections or spines. On the left is a sphere with short (u = 0.5) and thin (g = 0.1) spines; the six spines comprise ~2.2% of the total particle volume. On the right is a sphere of equal total volume with spines which comprise 15.3% of the total particle volume: u = 1.0, g = 0.2. The particle axes x′, y′, and z′ have been rotated (see α and β in text) away from x (out of paper), y (to right of page), and z (to top of page).

Fig. 2
Fig. 2

Ratio of total scattering cross sections: R(spiny)/R(smooth) for particles of equal volumes and refractive index (n = 1.05) as a function of the size parameter x = 2πa/λ of the smooth sphere. The points marked x show effects of small spine formation (see left part of Fig. 1); the circles show effects of large spine formation (see right part of Fig. 1). The smaller points were calculated by the RGD equations, the larger ones with the AD ones. Also calculated but not shown are RGD points for the large spines at x = 0.03 (−0.001) and 0.053 (−0.004).

Fig. 3
Fig. 3

Ratio of total scattering cross sections of a coated sphere to that of a homogeneous sphere of smaller overall size but of equal total mass. Calculations were with the equations of Aden and Kerker. As in Fig. 2, the volume of the core of the coated sphere is 97.8% and 84.7% of the homogeneous sphere particle volume for the two respective curves. The refractive index of the core is that of the homogeneous sphere. The inner and outer radii of the coat are those of the spines in Fig. 2. The refractive indices of the coats were chosen so that the total mass in each coat is equal to that of the spines in the spiny sphere counterpart.

Fig. 4
Fig. 4

Separate total scattering efficiencies K sc of nonabsorbing particles from AD theory for spheres (sphere body) and spines (cylinders). Efficiencies are plotted as functions of sphere size (x = 2πa/λ), where a is the radius of the spiny sphere body. Note that this x is slightly different from that in Fig. 2. To approximate effects of random orientation, the cylinder axes were oriented for calculations at 57.3° to the direction of the beam.

Tables (1)

Tables Icon

Table I Effects of the Production of an Outer Layer of the Particle, Spines or Coat, at the Expense of the Main Body Thereof on Total Scattering a

Equations (5)

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4 π r 3 / 3 = 4 π r b 3 / 3 + 6 π g 2 u r b 3 .
I ( θ ) = [ 1 + cos 2 ( θ ) ] m - 1 2 V 2 w 2 ,
w = ( 1 / V ) b min b max { B exp [ - i k b 2 sin ( θ / 2 ) ] } d b ,
total scattered flux = 2 π 0 π I ( θ ) sin ( θ ) d ( θ ) .
K s c = 2 - ( 2 / A ) cos ( ϕ ) d A ,

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