Abstract

I describe results of numerical calculations of the optical properties (extinction efficiency, single-scattering albedo, phase function, and linear polarization) of aggregate particles whose outer diameter is comparable with the wavelength. Results are presented for two types of particle, one composed of monomers whose radius is small compared with the wavelength and a second containing monomers with larger radii. The shape of the forward-scattered lobe of the phase function is diagnostic of the mean projected area (but differs from that for an equal-area sphere), while the linear polarization, phase function at large scattering angles, and single-scattering albedo depend on the monomer diameter. The wavelength dependence of the extinction efficiency differs markedly from that for equal-area spheres. These results can be used to infer particle properties from remotely sensed data.

© 1991 Optical Society of America

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References

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  1. M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
    [Crossref]
  2. J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
    [Crossref]
  3. M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
    [Crossref]
  4. R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).
  5. E. L. Wright, “Fractal dust grains around R Coronae Borealis stars,” Astrophys. J. Lett. 346, L89–L91 (1989).
    [Crossref]
  6. D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.
  7. A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
    [Crossref]
  8. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  9. R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus, 90, 330–333 (1991).
    [Crossref]
  10. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [Crossref]
  11. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [Crossref]
  12. T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47, 1400–1403 (1981).
    [Crossref]
  13. T. A. Witten, L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27, 5686–5697 (1983).
    [Crossref]
  14. P. Meakin, “Diffusion-controlled cluster formation in 2–6 dimensional space,” Phys. Rev. A 27, 1495–1507 (1983).
    [Crossref]
  15. F. Hausdorff, “Dimension und äusseres Mass,” Math. Ann. 78, 157–179 (1919).
  16. B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
    [Crossref]
  17. G. Yamamoto, M. Tanaka, “Determination of aerosol size distributions from spectral attenuation measurements,” Appl. Opt. 8, 447–453 (1969).
    [Crossref] [PubMed]
  18. H. Grassl, “Determination of aerosol size distributions from spectral attenuation measurements,” Appl. Opt. 10, 2534–2538 (1971).
    [Crossref] [PubMed]
  19. A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. 1: Multispectral extinctions in the anomalous diffraction approximation,” Appl. Opt. 17, 1675–1676 (1978).
  20. M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
    [Crossref]
  21. A. Deepak, “Inversion of solar aureole measurements for determining aerosol characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, ed. (Academic, New York, 1977), pp. 265–291.
  22. C. F. Bohren, G. Koh, “Forward-scattering corrected extinction by nonspherical particles,” Appl. Opt. 24, 1023–1029 (1985).
    [Crossref] [PubMed]
  23. B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

1991 (1)

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus, 90, 330–333 (1991).
[Crossref]

1989 (2)

E. L. Wright, “Fractal dust grains around R Coronae Borealis stars,” Astrophys. J. Lett. 346, L89–L91 (1989).
[Crossref]

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

1988 (2)

A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

1986 (2)

J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
[Crossref]

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

1985 (1)

1984 (1)

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

1983 (2)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27, 5686–5697 (1983).
[Crossref]

P. Meakin, “Diffusion-controlled cluster formation in 2–6 dimensional space,” Phys. Rev. A 27, 1495–1507 (1983).
[Crossref]

1981 (1)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47, 1400–1403 (1981).
[Crossref]

1978 (3)

A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. 1: Multispectral extinctions in the anomalous diffraction approximation,” Appl. Opt. 17, 1675–1676 (1978).

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

1973 (1)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

1971 (1)

1969 (1)

1919 (1)

F. Hausdorff, “Dimension und äusseres Mass,” Math. Ann. 78, 157–179 (1919).

Arakawa, E. T.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

Ball, R. C.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

Bar-Nun, A.

A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
[Crossref]

Berry, M. V.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Bohren, C. F.

Byrne, D. M.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Callcott, T. A.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

Corbach, E.

B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

Deepak, A.

A. Deepak, “Inversion of solar aureole measurements for determining aerosol characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, ed. (Academic, New York, 1977), pp. 265–291.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Felske, J. D.

J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
[Crossref]

Flasar, F. M.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Fymat, A. L.

Ganor, E.

A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
[Crossref]

Giese, R. H.

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

Grassl, H.

Gustafson, B. A. S.

B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

Hausdorff, F.

F. Hausdorff, “Dimension und äusseres Mass,” Math. Ann. 78, 157–179 (1919).

Herman, B. M.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Hsu, P.-F.

J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
[Crossref]

Hunten, D. M.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Kerker, M.

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

Khare, B. N.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

King, M. D.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Klein, R.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

Kleinfeld, I.

A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
[Crossref]

Koh, G.

Ku, J. C.

J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
[Crossref]

Lin, M. Y.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

Lindsay, H. M.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

Meakin, P.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

P. Meakin, “Diffusion-controlled cluster formation in 2–6 dimensional space,” Phys. Rev. A 27, 1495–1507 (1983).
[Crossref]

Ono, T.

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Percival, I. C.

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

Reagan, J. A.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

Sagan, C.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

Samuelson, R. E.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Sander, L. M.

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27, 5686–5697 (1983).
[Crossref]

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47, 1400–1403 (1981).
[Crossref]

Schulz, K.

B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

Smith, P. H.

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus, 90, 330–333 (1991).
[Crossref]

Stevenson, D. J.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Strobel, D. F.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Suits, F.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

Tanaka, M.

Tomasko, M. G.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

Weiss, K.

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

Weitz, D. A.

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

West, R. A.

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus, 90, 330–333 (1991).
[Crossref]

Williams, M. W.

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

Witten, T. A.

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27, 5686–5697 (1983).
[Crossref]

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47, 1400–1403 (1981).
[Crossref]

Wright, E. L.

E. L. Wright, “Fractal dust grains around R Coronae Borealis stars,” Astrophys. J. Lett. 346, L89–L91 (1989).
[Crossref]

Yamamoto, G.

Zerull, R. H.

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

Appl. Opt. (4)

Astron. Astrophys. (1)

R. H. Giese, K. Weiss, R. H. Zerull, T. Ono, “Large fluffy particles: a possible explanation of the optical properties of interplanetary dust,” Astron. Astrophys. 65, 265–272 (1978).

Astrophys. J. (2)

E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Astrophys. J. Lett. (1)

E. L. Wright, “Fractal dust grains around R Coronae Borealis stars,” Astrophys. J. Lett. 346, L89–L91 (1989).
[Crossref]

Icarus (2)

R. A. West, P. H. Smith, “Evidence for aggregate particles in the atmospheres of Titan and Jupiter,” Icarus, 90, 330–333 (1991).
[Crossref]

B. N. Khare, C. Sagan, E. T. Arakawa, F. Suits, T. A. Callcott, M. W. Williams, “Optical constants of organic tholins produced in a simulated Titanian atmosphere: from soft x-ray to microwave frequencies,” Icarus 60, 127–137 (1984).
[Crossref]

J. Atmos. Sci. (1)

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distribution obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[Crossref]

J. Geophys. Res. (1)

A. Bar-Nun, I. Kleinfeld, E. Ganor, “Shape and optical properties of aerosols formed by photolysis of acetylene, ethylene, and hydrogen cyanide,” J. Geophys. Res. 93, 8383–8387 (1988).
[Crossref]

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

J. D. Felske, P.-F. Hsu, J. C. Ku, “The effect of soot particle optical inhomogeneity and agglomeration on the analysis of light scattering measurements in flames,” J. Quant. Spectrosc. Radiat. Transfer 35, 447–465 (1986).
[Crossref]

Math. Ann. (1)

F. Hausdorff, “Dimension und äusseres Mass,” Math. Ann. 78, 157–179 (1919).

Nature (London) (1)

M. Y. Lin, H. M. Lindsay, D. A. Weitz, R. C. Ball, R. Klein, P. Meakin, “Universality in colloid aggregation,” Nature (London) 339, 360–362 (1989).
[Crossref]

Opt. Acta (1)

M. V. Berry, I. C. Percival, “Optics of fractal clusters such as smoke,” Opt. Acta 33, 577–591 (1986).
[Crossref]

Phys. Rev. A (1)

P. Meakin, “Diffusion-controlled cluster formation in 2–6 dimensional space,” Phys. Rev. A 27, 1495–1507 (1983).
[Crossref]

Phys. Rev. B (1)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27, 5686–5697 (1983).
[Crossref]

Phys. Rev. Lett. (1)

T. A. Witten, L. M. Sander, “Diffusion-limited aggregation, a kinetic critical phenomenon,” Phys. Rev. Lett. 47, 1400–1403 (1981).
[Crossref]

Other (4)

A. Deepak, “Inversion of solar aureole measurements for determining aerosol characteristics,” in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, ed. (Academic, New York, 1977), pp. 265–291.

D. M. Hunten, M. G. Tomasko, F. M. Flasar, R. E. Samuelson, D. F. Strobel, D. J. Stevenson, “Titan,” in Saturn, T. Gehrels, M. S. Matthews, eds. (U. Arizona Press, Tucson, Ariz., 1984), pp. 671–759.

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

B. A. S. Gustafson, R. H. Zerull, E. Corbach, K. Schulz, “Light scattering by open-structured and filamentary dust aggregates: experiment and theory,” in Fluffy Structures II, Proceedings of the Second Workshop on the Optics of Cometary and Interplanetary Particles, P. M. M. Jenniskens, J. I. Hage, eds. (Laboratory Astrophysics, University of Leiden, Leiden, The Netherlands, 1989), pp. 3–6.

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Figures (8)

Fig. 1
Fig. 1

Six views of the Type I particle corresponding to incident ray direction vectors whose (x, y, z) components are (1, 0, 0), (0,1, 0), (0, 0, 1), (1, 1, 1), (1, 0, −1), and (1, −2, 1), clockwise beginning with the upper left-hand corner. Each dipole element in the DDA representation is depicted as a small sphere.

Fig. 2
Fig. 2

Six views of the Type II particle having the same orientations as described in the Fig. 1 caption.

Fig. 3
Fig. 3

Extinction efficiency for Type I and Type II particles compared with that for spheres, as a function of equal-area size parameter Xa. The continuous curve is for spheres with refractive index (1.649, 0.0009). The square symbols show results for the Type II particle with refractive indices (1.700, 0.0229). Other symbols are for the Type I particle with refractive indices (1.649, 0.0009) (triangles), (1.700, 0.0229) (×'s), (1.629, 0.11) (diamonds), and (1.681, 0.21) (+'s).

Fig. 4
Fig. 4

Wavelength dependence of the extinction efficiency for particles with refractive index (1.700, 0.0229) for Type I (×'s) and Type II (squares) particles and for spheres with the indicated size parameters (X0 = 2πr0). Both types of aggregate particle have equal-volume size parameter Xυ,0 = 1. Corresponding equal-area size parameters are Xa,0 = 1.67 and Xa,0 = 1.163 for Type I and Type II particles, respectively. Q/Q0 is the ratio of extinction efficiency at wavelength λ to its value at λ0.

Fig. 5
Fig. 5

Size parameter (Xfit = 2πr/λ) of a sphere that best fits the shape of the aggregate particle phase function in the 10–30° scattering angle range shown as a function of aggregate particle equal-area size parameter Xa for Type I (× 's) and Type II (squares) particles. All particles have refractive indices (1.700, 0.0229). The straight line represents the equation Xfit = Xa.

Fig. 6
Fig. 6

(a) Phase functions for Type I particles with Xa = 1.67, 2.5, 3.3, 4.2, 5.0 in order of increasing value at 0° scattering angle. (b) Phase functions for Type II particles with Xa = 1.2, 1.17, 2.3, 2.9, 3.5 in order of increasing value at 0° scattering angle. (c) Phase functions for spheres that provide best fits for the shape of the phase function for Type I particles in the 10–30° scattering angle range. The corresponding size parameters are X = 2.1, 2.8, 3.6, 3.8, 4.4. (d) Phase functions for spheres that provide best fits for the shape of the phase function for Type II particles in the 10–30° scattering angle range. Corresponding size parameters are X = 1.7, 2.1, 2.8, 3.1, 3.7. All particles have refractive indices (1.700, 0.0229).

Fig. 7
Fig. 7

(a) Linear polarization for Type I particles with Xa = 1.67, 2.5, 3.3, 4.2, 5.0 in order of decreasing maximum polarization at 90° scattering angle, (b) Polarization for Type II particles with Xa = 1.2, 1.17, 2.3, 2.9, 3.5 in order of decreasing maximum polarization. (c) Polarization for spheres with X = 0.375, 1.510, 1.540, 1.576, 1.590 in order of decreasing maximum polarization. The maximum polarization for these cases is approximately the same for the Type II particles shown in (b). All particles have refractive indices of (1.700, 0.0229).

Fig. 8
Fig. 8

Single-scattering albedos for Type I and Type II particles compared with those for spheres. The symbols have the same meaning as in Fig. 3. The continuous curves are for spheres with the same refractive indices as the aggregate particles (single-scattering albedo is inversely related to the imaginary refractive index).

Equations (1)

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σ = [ 1 I i = 1 I ( Q i 2 Q ¯ 2 ) ] 1 / 2 ,

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