Abstract

There are two widely accepted restrictions on the application of the discrete dipole approximation (DDA) in the study of light scattering by particles comparable to the wavelength: (1) when considering dielectric particles, the size of the cells must satisfy the condition kd|m|<0.5, where k is the wave number, d is the size of the cells, and m is the complex refractive index of the constituent material and (2) when considering conductive particles, the size of the cells must be small enough to reproduce sufficiently the evolution of the electromagnetic field in the skin layer. We examine both restrictions when the DDA is applied to irregularly shaped particles and show that its restrictions are not as strong as is widely accepted. For instance, when studying irregularly shaped particles averaged over orientations, even at kd|m|=1, the DDA provides highly accurate numerical results. Moreover, we show that the impact of using large constituent cells is similar to that produced by surface roughness; therefore, the replacement of the target particle by an array of large constituent cells has the same effect, qualitatively, as incorporating additional small-scale surface roughness on the particle. Such a modification of the target particle can be desirable in many practical applications of DDA when irregularly shaped particles are considered. When applying DDA to conductive, nonspherical particles, the insufficient description of the electromagnetic field in the skin layer does not lead to a violation of the Maxwell equations, although it has a visible but nonmajor influence on the light-scattering properties of the target.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  7. B. T. Draine and J. J. Goodman, “Beyond Clausius-Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697(1993).
    [CrossRef]
  8. B. T. Draine and P. J. Flatau, “The discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  9. B. T. Draine and P. J. Flatau, “User guide for the discrete dipole approximation code DDSCAT 6.1” (2004), available at http://arxiv.org/abs/astro-ph/0409262v2.
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    [CrossRef]
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    [CrossRef]
  12. E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.
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    [CrossRef]
  16. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).
  17. D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
    [CrossRef]
  18. D. Petrov, Y. Shkuratov, and G. Videen, “Analytical light-scattering solution for Chebyshev particles,” J. Opt. Soc. Am. A 24, 1103-1119 (2007).
    [CrossRef]
  19. D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
    [CrossRef]
  20. T. Nousiainen, “Optical modeling of mineral dust particles: a review,” J. Quant. Spectr. Rad. Trans. 110, 1261-1279(2009).
  21. E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
    [CrossRef]
  22. E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
    [CrossRef]
  23. E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
    [CrossRef]
  24. E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering and negative polarization of agglomerate particles,” Opt. Lett. 28, 1504-1506 (2003).
    [CrossRef] [PubMed]
  25. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  26. H. Okamoto, “Information content of the 95-GHz cloud radar signals: theoretical assessment of effects of nonsphericity and error evaluation of the discrete dipole approximation,” J. Geophys. Res. 107, 4628 (2002).
    [CrossRef]
  27. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” J. Opt. Soc. Am. A 23, 2578-2591 (2006).
    [CrossRef]
  28. G. Videen and W. S. Bickel, “Light scattering resonances in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
    [CrossRef] [PubMed]

2009 (1)

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

2008 (1)

D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
[CrossRef]

2007 (4)

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectr. Rad. Trans. 106, 546-557 (2007).
[CrossRef]

D. Petrov, Y. Shkuratov, and G. Videen, “Analytical light-scattering solution for Chebyshev particles,” J. Opt. Soc. Am. A 24, 1103-1119 (2007).
[CrossRef]

2006 (3)

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” J. Opt. Soc. Am. A 23, 2578-2591 (2006).
[CrossRef]

2003 (1)

2002 (1)

H. Okamoto, “Information content of the 95-GHz cloud radar signals: theoretical assessment of effects of nonsphericity and error evaluation of the discrete dipole approximation,” J. Geophys. Res. 107, 4628 (2002).
[CrossRef]

1994 (1)

1993 (1)

B. T. Draine and J. J. Goodman, “Beyond Clausius-Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697(1993).
[CrossRef]

1992 (1)

G. Videen and W. S. Bickel, “Light scattering resonances in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

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

1979 (1)

1978 (1)

1975 (1)

P. R. Shapiro, “Interstellar polarization: magnetite dust,” Astrophys. J. 201, 151-164 (1975).
[CrossRef]

1973 (1)

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

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Bickel, W. S.

G. Videen and W. S. Bickel, “Light scattering resonances in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

Bohren, C. F.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Cooke, D. D.

Draine, B.

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

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

Draine, B. T.

B. T. Draine and P. J. Flatau, “The discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine and J. J. Goodman, “Beyond Clausius-Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697(1993).
[CrossRef]

J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198-1200 (1991).
[CrossRef] [PubMed]

B. T. Draine and P. J. Flatau, “User guide for the discrete dipole approximation code DDSCAT 6.1” (2004), available at http://arxiv.org/abs/astro-ph/0409262v2.

Druger, S. D.

Eversole, J.

Flatau, P. J.

Goodman, J. J.

B. T. Draine and J. J. Goodman, “Beyond Clausius-Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697(1993).
[CrossRef]

J. J. Goodman, B. T. Draine, and P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198-1200 (1991).
[CrossRef] [PubMed]

Hart, M.

Hoekstra, A. G.

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectr. Rad. Trans. 106, 546-557 (2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” J. Opt. Soc. Am. A 23, 2578-2591 (2006).
[CrossRef]

Huffman, D. R.

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

Kerker, M.

Kimura, H.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Kiselev, N. N.

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Lumme, K.

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

Maltsev, V. P.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectr. Rad. Trans. 106, 546-557 (2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” J. Opt. Soc. Am. A 23, 2578-2591 (2006).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Muinonen, K.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Nousiainen, T.

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

T. Nousiainen, “Optical modeling of mineral dust particles: a review,” J. Quant. Spectr. Rad. Trans. 110, 1261-1279(2009).

Okamoto, H.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

H. Okamoto, “Information content of the 95-GHz cloud radar signals: theoretical assessment of effects of nonsphericity and error evaluation of the discrete dipole approximation,” J. Geophys. Res. 107, 4628 (2002).
[CrossRef]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Pennypacker, C. R.

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

Penttilä, A.

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

Petrov, D.

D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
[CrossRef]

D. Petrov, Y. Shkuratov, and G. Videen, “Analytical light-scattering solution for Chebyshev particles,” J. Opt. Soc. Am. A 24, 1103-1119 (2007).
[CrossRef]

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Purcell, E. M.

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

Rahola, J.

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

Shapiro, P. R.

P. R. Shapiro, “Interstellar polarization: magnetite dust,” Astrophys. J. 201, 151-164 (1975).
[CrossRef]

Shkuratov, Y.

D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
[CrossRef]

D. Petrov, Y. Shkuratov, and G. Videen, “Analytical light-scattering solution for Chebyshev particles,” J. Opt. Soc. Am. A 24, 1103-1119 (2007).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

Shkuratov, Y. G.

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Shkuratov, Yu.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering and negative polarization of agglomerate particles,” Opt. Lett. 28, 1504-1506 (2003).
[CrossRef] [PubMed]

Synelnyk, E.

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Videen, G.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
[CrossRef]

D. Petrov, Y. Shkuratov, and G. Videen, “Analytical light-scattering solution for Chebyshev particles,” J. Opt. Soc. Am. A 24, 1103-1119 (2007).
[CrossRef]

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering and negative polarization of agglomerate particles,” Opt. Lett. 28, 1504-1506 (2003).
[CrossRef] [PubMed]

G. Videen and W. S. Bickel, “Light scattering resonances in small spheres,” Phys. Rev. A 45, 6008-6012 (1992).
[CrossRef] [PubMed]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Wang, D.-S.

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825-839 (1971).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Yamamoto, T.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Yung, Y. L.

Yurkin, M. A.

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectr. Rad. Trans. 106, 546-557 (2007).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. I. theoretical analysis,” J. Opt. Soc. Am. A 23, 2578-2591 (2006).
[CrossRef]

Zubko, E.

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

E. Zubko, Yu. Shkuratov, M. Hart, J. Eversole, and G. Videen, “Backscattering and negative polarization of agglomerate particles,” Opt. Lett. 28, 1504-1506 (2003).
[CrossRef] [PubMed]

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

Appl. Opt. (2)

Astrophys. J. (4)

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[CrossRef]

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[CrossRef]

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[CrossRef]

B. T. Draine and J. J. Goodman, “Beyond Clausius-Mossotti: wave propagation on a polarizable point lattice and the discrete dipole approximation,” Astrophys. J. 405, 685-697(1993).
[CrossRef]

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H. Okamoto, “Information content of the 95-GHz cloud radar signals: theoretical assessment of effects of nonsphericity and error evaluation of the discrete dipole approximation,” J. Geophys. Res. 107, 4628 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Quant. Spectr. Rad. Trans. (7)

D. Petrov, Y. Shkuratov, and G. Videen, “Influence of corrugation on light-scattering properties of capsule and finite-cylinder particles: Analytic solution using Sh-matrices,” J. Quant. Spectr. Rad. Trans. 109, 650-669 (2008).
[CrossRef]

A. Penttilä, E. Zubko, K. Lumme, K. Muinonen, M. A. Yurkin, B. Draine, J. Rahola, A. G. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectr. Rad. Trans. 106, 417-436(2007).
[CrossRef]

M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength,” J. Quant. Spectr. Rad. Trans. 106, 546-557 (2007).
[CrossRef]

D. Petrov, E. Synelnyk, Y. Shkuratov, and G. Videen, “The T-matrix technique for calculations of scattering properties of ensembles of randomly oriented particles with different size,” J. Quant. Spectr. Rad. Trans. 102, 85-110 (2006).
[CrossRef]

E. Zubko, Yu. Shkuratov, N. N. Kiselev, and G. Videen, “DDA simulations of light scattering by small irregular particles with various structure,” J. Quant. Spectr. Rad. Trans. 101, 416-434 (2006).
[CrossRef]

E. Zubko, H. Kimura, Yu. Shkuratov, K. Muinonen, T. Yamamoto, H. Okamoto, and G. Videen, “Effect of absorption on light scattering by agglomerated debris particles,” J. Quant. Spectr. Rad. Trans. 110, 1741-1749 (2009).
[CrossRef]

E. Zubko, K. Muinonen, Yu. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectr. Rad. Trans. 106, 604-615(2007).
[CrossRef]

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T. Nousiainen, “Optical modeling of mineral dust particles: a review,” J. Quant. Spectr. Rad. Trans. 110, 1261-1279(2009).

E. Zubko, D. Petrov, Y. G. Shkuratov, H. Okamoto, K. Muinonen, H. Kimura, T. Yamamoto, and G. Videen, “Applicability of discrete-dipole approximation to conductive particles,” in Proceedings of the Eleventh Conference on Electromagnetic and Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (University of Hertfordshire, 2008), pp. 117-120.

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Figures (8)

Fig. 1
Fig. 1

Sample of agglomerated debris particles discretized in the initial matrices of different sizes (upper row) and the relevant spheres of the same volume (bottom row). The numbers represent the number of cells composing a side of the initial matrix.

Fig. 2
Fig. 2

Intensity (left) and degree of linear polarization (right) of a single sphere at x = 6.379 and m = 1.6 plotted as a function of phase angle for (a) fixed orientation and (b) semiaveraging over orientations.

Fig. 3
Fig. 3

Intensity (left) and degree of linear polarization (right) of a single sphere at x = 7.655 and m = 1.33 plotted as a function of phase angle for (a) fixed orientation and (b) semiaveraging over orientations.

Fig. 4
Fig. 4

Intensity (left) and degree of linear polarization (right) of an agglomerated debris particle at x cs = 10 and m = 1.6 plotted as a function of phase angle for (a) fixed orientation, (b) semiaveraging over orientations, and (c) full averaging over orientations.

Fig. 5
Fig. 5

Intensity (left) and degree of linear polarization (right) of an agglomerated debris particle at x cs = 12 and m = 1.33 plotted as a function of phase angle for (a) fixed orientation, (b) semiaveraging over orientations, and (c) full averaging over orientations.

Fig. 6
Fig. 6

(a) Distribution of energy of the induced field in spheres and (b) agglomerated debris particles consisting of different numbers of cells. The refractive index is m = 1.5 + 1.3 i . The size parameter of the sphere is x = 4.795 , whereas the size parameter of the circumscribing sphere of the agglomerated debris particle is x cs = 7.5 . In each panel, the directions of propagation and polarization of the incident beam are shown by white and blue lines in the upper-left corner, respectively. The upper row shows whole particles, whereas the bottom row shows their cross sections. When the particle is allocated in the matrix with a side composed of 32 cells, the parameter of a single cell k d | m | = 0.93 ; 64 cells corresponds to k d | m | = 0.47 ; and 128 cells corresponds to k d | m | = 0.23 .

Fig. 7
Fig. 7

Intensity (left) and degree of linear polarization (right) of a single sphere at x = 4.795 and m = 1.5 + 1.3 i plotted as a function of phase angle for (a) fixed orientation and (b) semiaveraging over orientations.

Fig. 8
Fig. 8

Intensity (left) and degree of linear polarization (right) of an agglomerated debris particle at x cs = 7.5 and m = 1.5 + 1.3 i plotted as a function of phase angle for (a) fixed orientation, (b) semiaveraging over orientations, and (c) full averaging over orientations.

Tables (4)

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Table 1 Fractional and Root-Mean-Square Errors in Intensity of Light Scattering by Dielectric Spheres Computed with the Discrete Dipole Approximation

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Table 2 Fractional and Root-Mean-Square Errors in Intensity of Light Scattering by Dielectric Agglomerated Debris Particles Computed with the Discrete Dipole Approximation

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Table 3 Fractional and Root-Mean-Square Errors in Intensity of Light Scattering by a Conductive Sphere Computed with the Discrete Dipole Approximation

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Table 4 Fractional and Root-Mean-Square Errors in Intensity of Light Scattering by a Conductive Agglomerated Debris Particle Computed with the Discrete Dipole Approximation

Equations (4)

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k d | m | < A .
Error i = | I i DDA I i exact | I i exact · 100 % .
w i = I i exact n I n exact ,
RMSE w = [ 1 1 n ( w n ) 2 i w i ( I i DDA I i exact I i exact ) 2 ] 1 / 2 .

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