Abstract

We employ the numerically exact superposition T-matrix method to perform extensive computations of electromagnetic scattering by small volume elements filled with 8 randomly distributed wavelength-sized spherical particles. The results of these computations are used to examine quantitatively the conditions of applicability of the single-scattering approximation (SSA). We show that one may need large inter-particle distances and low packing densities in order to make the SSA sufficiently accurate.

© 2007 Optical Society of America

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  1. M. P. Mengüç and S. Manickavasagam, "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," Int. J. Eng. Sci. 36, 1569-1593 (1998).
    [CrossRef]
  2. J. W. Hovenier, "Measuring scattering matrices of small particles at optical wavelengths," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 355-365.
  3. H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
    [CrossRef]
  4. O. Muñoz, H. Volten, H., J. F. de Haan, W. Vassen, and J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833-22844 (2001).
    [CrossRef]
  5. J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
    [CrossRef]
  6. E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
    [CrossRef]
  7. H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
    [CrossRef]
  8. Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
    [CrossRef]
  9. O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
    [CrossRef]
  10. D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
    [CrossRef]
  11. M. I. Mishchenko, J. W. Hovenier, and D. W. Mackowski, "Single scattering by a small volume element," J. Opt. Soc. Am. A 21, 71-87 (2004).
    [CrossRef]
  12. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, Cambridge, UK, 2006).
  13. D. W. Mackowski and M. I. Mishchenko, "Calculation of the T matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A 13, 2266-2278 (1996).
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  14. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002). http://www.giss.nasa.gov/~crmim/books.html.
  15. D. Mackowski, K. Fuller, and M. Mishchenko, "Codes for calculation of scattering by clusters of spheres." ftp://ftp.eng.auburn.edu/pub/dmckwski/scatcodes/index.html.
  16. M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, "Multiple scattering by random particulate media: exact 3D results," Opt. Express 15, 2822-2836 (2007).
    [CrossRef] [PubMed]
  17. M. I. Mishchenko and L. Liu, "Weak localization of electromagnetic waves by densely packed many-particle groups: exact 3D results," J. Quant. Spectrosc. Radiat. Transfer 106, 616-621 (2007).
    [CrossRef]

2007 (3)

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, "Multiple scattering by random particulate media: exact 3D results," Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

M. I. Mishchenko and L. Liu, "Weak localization of electromagnetic waves by densely packed many-particle groups: exact 3D results," J. Quant. Spectrosc. Radiat. Transfer 106, 616-621 (2007).
[CrossRef]

2006 (2)

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

2005 (2)

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

2004 (1)

2003 (1)

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

2001 (2)

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

O. Muñoz, H. Volten, H., J. F. de Haan, W. Vassen, and J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833-22844 (2001).
[CrossRef]

1998 (1)

M. P. Mengüç and S. Manickavasagam, "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," Int. J. Eng. Sci. 36, 1569-1593 (1998).
[CrossRef]

1996 (1)

André, J.-M.

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

Bondarenko, S.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Brun, G.

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

Cairns, B.

Daugeron, D.

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

de Haan, J. F.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Hadamcik, E.

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

Hiroi, T.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Hovenier, J. W.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, and D. W. Mackowski, "Single scattering by a small volume element," J. Opt. Soc. Am. A 21, 71-87 (2004).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Jalava, J. P.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

Lasue, J.

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

Levasseur-Regourd, A. C.

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

Liu, L.

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, "Multiple scattering by random particulate media: exact 3D results," Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

M. I. Mishchenko and L. Liu, "Weak localization of electromagnetic waves by densely packed many-particle groups: exact 3D results," J. Quant. Spectrosc. Radiat. Transfer 106, 616-621 (2007).
[CrossRef]

Mackowski, D. W.

Manickavasagam, S.

M. P. Mengüç and S. Manickavasagam, "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," Int. J. Eng. Sci. 36, 1569-1593 (1998).
[CrossRef]

Mengüç, M. P.

M. P. Mengüç and S. Manickavasagam, "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," Int. J. Eng. Sci. 36, 1569-1593 (1998).
[CrossRef]

Min, M.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

Mishchenko, M. I.

Muinonen, K.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Muñoz, O.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

O. Muñoz, H. Volten, H., J. F. de Haan, W. Vassen, and J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833-22844 (2001).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Nousiainen, T.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Ovcharenko, A.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Personne, P.

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

Pieters, C.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Renard, J.-B.

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

Rol, E.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Shkuratov, Y. G.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

Shkuratov, Yu.

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

van der Zande, W. J.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

Vassen, W.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Videen, G.

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, "Multiple scattering by random particulate media: exact 3D results," Opt. Express 15, 2822-2836 (2007).
[CrossRef] [PubMed]

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Volten, H.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

O. Muñoz, H. Volten, H., J. F. de Haan, W. Vassen, and J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833-22844 (2001).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

Waters, L. B. F. M.

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

Astron. Astrophys. (1)

O. Muñoz, H. Volten, J. W. Hovenier, M. Min, Y. G. Shkuratov, J. P. Jalava, W. J. van der Zande, and L. B. F. M. Waters, "Experimental and computational study of light scattering by irregular particles with extreme refractive indices: hematite and rutile," Astron. Astrophys. 446, 525-535 (2006).
[CrossRef]

Int. J. Eng. Sci. (1)

M. P. Mengüç and S. Manickavasagam, "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," Int. J. Eng. Sci. 36, 1569-1593 (1998).
[CrossRef]

J. Geophys. Res. (2)

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001).
[CrossRef]

O. Muñoz, H. Volten, H., J. F. de Haan, W. Vassen, and J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented fly ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833-22844 (2001).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (5)

M. I. Mishchenko and L. Liu, "Weak localization of electromagnetic waves by densely packed many-particle groups: exact 3D results," J. Quant. Spectrosc. Radiat. Transfer 106, 616-621 (2007).
[CrossRef]

J. W. Hovenier, H. Volten, O. Muñoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transfer 79/80, 741-755 (2003).
[CrossRef]

E. Hadamcik, J.-B. Renard, A. C. Levasseur-Regourd, and J. Lasue, "Light scattering by fluffy particles with the PROGRA2 experiment: mixtures of materials," J. Quant. Spectrosc. Radiat. Transfer 100, 143-156 (2005).
[CrossRef]

H. Volten, O. Muñoz, J. W. Hovenier, and L. B. F. M. Waters, "An update of the Amsterdam light scattering database," J. Quant. Spectrosc. Radiat. Transfer 100, 437-443 (2005).
[CrossRef]

Yu. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Muñoz, and G. Videen, "Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles," J. Quant. Spectrosc. Radiat. Transfer 100, 340-358 (2006).
[CrossRef]

Meas. Sci. Technol. (1)

D. Daugeron, J.-B. Renard, P. Personne, G. Brun, and J.-M. André, "Laboratory polarization nephelometer for measurements of optical properties of aerosols," Meas. Sci. Technol. 18, 632-638 (2007).
[CrossRef]

Opt. Express (1)

Other (4)

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002). http://www.giss.nasa.gov/~crmim/books.html.

D. Mackowski, K. Fuller, and M. Mishchenko, "Codes for calculation of scattering by clusters of spheres." ftp://ftp.eng.auburn.edu/pub/dmckwski/scatcodes/index.html.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, Cambridge, UK, 2006).

J. W. Hovenier, "Measuring scattering matrices of small particles at optical wavelengths," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 355-365.

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Figures (5)

Fig. 1.
Fig. 1.

Spherical volume elements filled with eight randomly positioned, identical particles.

Fig. 2.
Fig. 2.

Electromagnetic scattering by a small volume element.

Fig. 3.
Fig. 3.

Ratios defined by Eqs. (3) and (4). Also shown are the ρ and k 1d〉 values corresponding to k 1 R = 12, 24, 36, 48, 60, and 72.

Fig. 4.
Fig. 4.

Elements of the normalized Stokes scattering matrix.

Fig. 5.
Fig. 5.

Forward-scattering phase function and the quantity 1 2 [ a 1 ( Θ ) a 2 ( Θ ) ] .

Equations (5)

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[ I sca Q sca U sca V sca ] [ a 1 ( Θ ) b 1 ( Θ ) 0 0 b 1 ( Θ ) a 2 ( Θ ) 0 0 0 0 a 3 ( Θ ) b 2 ( Θ ) 0 0 b 2 ( Θ ) a 4 ( Θ ) ] [ I inc Q inc U inc V inc ] .
1 2 0 π d Θ sin Θ a 1 ( Θ ) = 1 .
C ext ( volume element ) 8 C ext ( one particle )
a 1 ( Θ = , volume element ) 8 a 1 ( Θ = , one particle ) .
1 2 [ a 1 ( Θ ) a 2 ( Θ ) ] .

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