Abstract

The size distribution of semitransparent irregularly shaped mineral dust aerosol samples is determined using a commonly used laser particle-sizing technique. The size distribution is derived from intensity measurements of singly scattered light at various scattering angles close to the forward-scattering direction at a wavelength of 632.8  nm. We analyze the results based on various light-scattering models including diffraction theory, Mie calculations for spheres with various refractive indices, and T-matrix calculations for spheroidal particles. We identify systematic errors of the retrieved size distribution when the semitransparent and nonspherical properties of the particles are neglected. Synthetic light-scattering data for a variety of parameterized size distributions of spheres and spheroids are used to investigate the effect of simplifying assumptions made when the diffraction model or Mie theory is applied in the retrieval.

© 2006 Optical Society of America

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  1. M. Kocifaj and M. Drzík, "Retrieveing the size distribution of microparticles by scanning the diffraction halo with a mobile ring gap detector," J. Aerosol Sci. 28, 797-804 (1996).
    [CrossRef]
  2. R. Santer and M. Herman, "Particle size distributions from forward scattered light using the Chahine inversion scheme," Appl. Opt. 22, 2294-2301 (1983).
    [CrossRef] [PubMed]
  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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
    [CrossRef]
  4. J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
    [CrossRef]
  5. O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
    [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  7. D. R, Huffman, "The interaction of light with a small-particle system," Adv. Phys. 26, 129-130 (1977).
    [CrossRef]
  8. I. N. Sokolik and O. B. Toon, "Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths," J. Geophys. Res. 104, 9423-9444 (1999).
    [CrossRef]
  9. C. Klein, Manual of Mineral Science, 22nd ed. (Wiley, 2002).
  10. M. I. MishchenkoJ. W. Hovenier, and L. D. Travis, "T-matrix method and its applications," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 147-172.
    [CrossRef]
  11. M. I. Mishchenko and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transfer 60, 309-324 (1998).
    [CrossRef]
  12. B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
    [CrossRef]
  13. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  14. C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000).
    [CrossRef]
  15. D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Math. 9, 84-97 (1962).
    [CrossRef]
  16. A. N. Tikhonov, "On the solution of incorrectly stated problems and a method of regularization," Dokl. Acad. Nauk SSSR 151, 501-504 (1963).
  17. O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
    [CrossRef]
  18. C. D. Rodgers, "Characterization and error analysis of profiles retrieved from remote sounding measurements," J. Geophys. Res. 95, 5587-5595 (1990).
    [CrossRef]
  19. D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
    [CrossRef]
  20. T. F. Coleman and Y. Li, "An interior, trust region approach for non-linear minimization subject to bounds," SIAM J. Optim. 27, 960-967 (1970).
  21. M. Kocifaj and H. Horvath, "Inversion of extinction data for irregularly shaped particles," Atmos. Environ. 39, 1481-1495 (2005).
    [CrossRef]

2006 (1)

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[CrossRef]

2005 (1)

M. Kocifaj and H. Horvath, "Inversion of extinction data for irregularly shaped particles," Atmos. Environ. 39, 1481-1495 (2005).
[CrossRef]

2002 (1)

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

2000 (1)

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

1999 (1)

I. N. Sokolik and O. B. Toon, "Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths," J. Geophys. Res. 104, 9423-9444 (1999).
[CrossRef]

1998 (1)

M. I. Mishchenko and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transfer 60, 309-324 (1998).
[CrossRef]

1996 (1)

M. Kocifaj and M. Drzík, "Retrieveing the size distribution of microparticles by scanning the diffraction halo with a mobile ring gap detector," J. Aerosol Sci. 28, 797-804 (1996).
[CrossRef]

1990 (1)

C. D. Rodgers, "Characterization and error analysis of profiles retrieved from remote sounding measurements," J. Geophys. Res. 95, 5587-5595 (1990).
[CrossRef]

1983 (1)

1977 (1)

D. R, Huffman, "The interaction of light with a small-particle system," Adv. Phys. 26, 129-130 (1977).
[CrossRef]

1974 (1)

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

1970 (1)

T. F. Coleman and Y. Li, "An interior, trust region approach for non-linear minimization subject to bounds," SIAM J. Optim. 27, 960-967 (1970).

1963 (1)

A. N. Tikhonov, "On the solution of incorrectly stated problems and a method of regularization," Dokl. Acad. Nauk SSSR 151, 501-504 (1963).

1962 (1)

D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Math. 9, 84-97 (1962).
[CrossRef]

Blarel, L.

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

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).

Chatenet, B.

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Coleman, T. F.

T. F. Coleman and Y. Li, "An interior, trust region approach for non-linear minimization subject to bounds," SIAM J. Optim. 27, 960-967 (1970).

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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Drzík, M.

M. Kocifaj and M. Drzík, "Retrieveing the size distribution of microparticles by scanning the diffraction halo with a mobile ring gap detector," J. Aerosol Sci. 28, 797-804 (1996).
[CrossRef]

Dubovik, O.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

Eck, T. F.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

Hansen, J. E.

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Herman, M.

Holben, B. N.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Horvath, H.

M. Kocifaj and H. Horvath, "Inversion of extinction data for irregularly shaped particles," Atmos. Environ. 39, 1481-1495 (2005).
[CrossRef]

Hovenier, J. 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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

M. I. MishchenkoJ. W. Hovenier, and L. D. Travis, "T-matrix method and its applications," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 147-172.
[CrossRef]

Huffman, D. R

D. R, Huffman, "The interaction of light with a small-particle system," Adv. Phys. 26, 129-130 (1977).
[CrossRef]

Huffman, D. R.

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

Kahnert, M.

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[CrossRef]

Karnieli, A.

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Kaufman, Y. J.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

King, M. D.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

Klein, C.

C. Klein, Manual of Mineral Science, 22nd ed. (Wiley, 2002).

Kocifaj, M.

M. Kocifaj and H. Horvath, "Inversion of extinction data for irregularly shaped particles," Atmos. Environ. 39, 1481-1495 (2005).
[CrossRef]

M. Kocifaj and M. Drzík, "Retrieveing the size distribution of microparticles by scanning the diffraction halo with a mobile ring gap detector," J. Aerosol Sci. 28, 797-804 (1996).
[CrossRef]

Lavenu, F.

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Li, Y.

T. F. Coleman and Y. Li, "An interior, trust region approach for non-linear minimization subject to bounds," SIAM J. Optim. 27, 960-967 (1970).

Mishchenko, M. I.

M. I. Mishchenko and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transfer 60, 309-324 (1998).
[CrossRef]

M. I. MishchenkoJ. W. Hovenier, and L. D. Travis, "T-matrix method and its applications," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 147-172.
[CrossRef]

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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Muñoz, O.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Nousiainen, T.

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Phillips, D. L.

D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Math. 9, 84-97 (1962).
[CrossRef]

Remer, L. A.

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Rodgers, C. D.

C. D. Rodgers, "Characterization and error analysis of profiles retrieved from remote sounding measurements," J. Geophys. Res. 95, 5587-5595 (1990).
[CrossRef]

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000).
[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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Santer, R.

Slutsker, I.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

Smirnov, A.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Sokolik, I. N.

I. N. Sokolik and O. B. Toon, "Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths," J. Geophys. Res. 104, 9423-9444 (1999).
[CrossRef]

Tanré, D.

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

Tikhonov, A. N.

A. N. Tikhonov, "On the solution of incorrectly stated problems and a method of regularization," Dokl. Acad. Nauk SSSR 151, 501-504 (1963).

Toon, O. B.

I. N. Sokolik and O. B. Toon, "Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths," J. Geophys. Res. 104, 9423-9444 (1999).
[CrossRef]

Travis, L. D.

M. I. Mishchenko and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transfer 60, 309-324 (1998).
[CrossRef]

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

M. I. MishchenkoJ. W. Hovenier, and L. D. Travis, "T-matrix method and its applications," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 147-172.
[CrossRef]

van der Zande, W. J.

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[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 particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Veihelmann, B.

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[CrossRef]

Volten, H.

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

Wolf, E.

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

Adv. Phys. (1)

D. R, Huffman, "The interaction of light with a small-particle system," Adv. Phys. 26, 129-130 (1977).
[CrossRef]

Appl. Opt. (1)

Atmos. Environ. (1)

M. Kocifaj and H. Horvath, "Inversion of extinction data for irregularly shaped particles," Atmos. Environ. 39, 1481-1495 (2005).
[CrossRef]

Dokl. Acad. Nauk SSSR (1)

A. N. Tikhonov, "On the solution of incorrectly stated problems and a method of regularization," Dokl. Acad. Nauk SSSR 151, 501-504 (1963).

J. Aerosol Sci. (1)

M. Kocifaj and M. Drzík, "Retrieveing the size distribution of microparticles by scanning the diffraction halo with a mobile ring gap detector," J. Aerosol Sci. 28, 797-804 (1996).
[CrossRef]

J. Assoc. Comput. Math. (1)

D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Math. 9, 84-97 (1962).
[CrossRef]

J. Atmos. Sci. (1)

O. Dubovik, B. N. Holben, T. F. Eck, A. Smirnov, Y. J. Kaufman, M. D. King, D. Tanré, and I. Slutsker, "Variability of absorption and optical properties of key aerosol types observed in worldwide locations," J. Atmos. Sci. 59, 590-608 (2002).
[CrossRef]

J. Geophys. Res. (5)

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17401 (2001).
[CrossRef]

I. N. Sokolik and O. B. Toon, "Incorporation of mineralogical composition into models of the radiative properties of mineral aerosol from UV to IR wavelengths," J. Geophys. Res. 104, 9423-9444 (1999).
[CrossRef]

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 20673-20696 (2000).
[CrossRef]

C. D. Rodgers, "Characterization and error analysis of profiles retrieved from remote sounding measurements," J. Geophys. Res. 95, 5587-5595 (1990).
[CrossRef]

D. Tanré, Y. J. Kaufman, B. N. Holben, B. Chatenet, A. Karnieli, F. Lavenu, L. Blarel, O. Dubovik, L. A. Remer, and A. Smirnov, "Climatology of dust aerosol size distribution and optical properties derived from remotely sensed data on the solar spectrum," J. Geophys. Res. 106, 18205-18217 (2001).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

M. I. Mishchenko and L. D. Travis, "Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers," J. Quant. Spectrosc. Radiat. Transfer 60, 309-324 (1998).
[CrossRef]

B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande, "Light scattering by small feldspar particles simulated using the discrete dipole approximation for Gaussian random spheres," J. Quant. Spectrosc. Radiat. Transfer 100, 393-405 (2006).
[CrossRef]

SIAM J. Optim. (1)

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Space Sci. Rev. (1)

J. E. Hansen and L. D. Travis, "Light scattering in planetary atmospheres," Space Sci. Rev. 16, 527-610 (1974).
[CrossRef]

Other (5)

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

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M. I. MishchenkoJ. W. Hovenier, and L. D. Travis, "T-matrix method and its applications," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 147-172.
[CrossRef]

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

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Optical setup of the laser particle sizer.

Fig. 2
Fig. 2

Phase function P(Θ) for diffraction (solid curves) and Mie scattering by strongly absorbing (dashed curves) and nonabsorbing spheres (dotted curves). The intensity is normalized to 1 at Θ = 0 ° . The sizes of the spheres are given in terms of the size parameter x = 2 π r / λ .

Fig. 3
Fig. 3

Scattering efficiency Q for diffraction (crosses), from Mie calculations for strongly absorbing spheres (solid circles), from nonabsorbing spheres (open circles), and from T-matrix calculations for nonabsorbing spheroids (open diamonds).

Fig. 4
Fig. 4

Representation of the Jacobian matrix of the linearized forward model based on (a) diffraction theory, Mie theory for (b) strongly absorbing spheres and (c) nonabsorbing spheres, and (d) T-matrix calculations for a mixture of nonabsorbing oblate and prolate spheroids. High values of the matrix elements K i j are depicted as dark gray; low values are depicted as light gray levels. Further explanations are given in the text.

Fig. 5
Fig. 5

Surface distributions for the feldspar, the quartz, and the red clay samples retrieved using diffraction theory (error bars); Mie scattering by strongly absorbing spheres (black dots); by weakly absorbing spheres (open circles) assuming refractive indices of 1.57 − 0.0005i (feldspar), 1.54 − 0i (quartz), and 1.52 − 0.001i (red clay); and T-matrix calculations for nonabsorbing spheroids (open diamonds).

Tables (1)

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Table 1 Effective Radius r eff (μm) and Effective Variance v eff of the Size Distributions Based on the Diffraction Model and the Spherical Model a

Equations (10)

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ν ( R ) = d N d log 10 ( r ) .
n i = 1 + ν  d R R i R i + 1 ν ( R ) d R .
s i = 1 + π r 2 ν  d R R i R i + 1 π r 2 ν ( R ) d R
y i = j Q j s j Ω i P j ( Θ ) d Ω const .
y = K s · const.
I F ( x , Θ ) x 2 { J 1 [ x   sin ( Θ ) ] x  sin ( Θ ) } 2 .
s = D y .
D = [ K T S y - 1 K + γ 0 L 0 T L 0 + γ 1 L 1 T L 1 ] 1 K T S y - 1 .
L 1 = ( 1 1 0 0 0 1 1 0 0 0 1 1 )
S s = ( K T S y - 1 K + γ 0 L 0 T L 0 + γ 1 L 1 T L 1 ) 1 .

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