Abstract

We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm (in air). These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length/width ratio than measured.

© 1999 Optical Society of America

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  1. V.-M. Taavitsainen, J. -P. Jalava, “Soft and harder multivariate modeling in developing the properties of titanium dioxide pigments,” Chemom. Intell. Lab. Syst. 29, 307–319 (1995).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  4. J. -P. Jalava, “Precipitation and properties of TiO2 pigments in the sulfate process. 1. Preparation of the liquor and effects of iron(II) in isoviscous liquor,” Ind. Eng. Chem. Res. 31, 608–611 (1992).
    [CrossRef]
  5. H. Schnablegger, O. Glatter, “Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments,” J. Colloid Interface Sci. 158, 228–242 (1993).
    [CrossRef]
  6. H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
    [CrossRef]
  7. M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
    [CrossRef] [PubMed]
  8. J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).
  9. J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).
  10. J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices, a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
    [CrossRef]
  11. M. W. Ribarsky, “Titanium dioxide (TiO2) (rutile),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 795–804.
    [CrossRef]
  12. G. M. Hale, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  13. J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
    [CrossRef]
  14. J. W. Hovenier, “Measuring scattering matrices of small particles at optical wavelengths,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 355–365.
  15. P. Stammes, “Light scattering properties of aerosols and the radiation inside a planetary atmosphere,” Ph.D. dissertation (Free University, Amsterdam, The Netherlands, 1989).
  16. F. Kuik, P. Stammes, J. W. Hovenier, “Experimental determination of scattering matrices of water droplets and quartz particles,” Appl. Opt. 30, 4872–4881 (1991).
    [CrossRef] [PubMed]
  17. F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, The Netherlands, 1992).
  18. S. Sugihara, M. Kishino, N. Okami, “Backscattering of light by particles suspended in water,” Phys. Chem. Res. 76, 1–8 (1982).
  19. E. S. Fry, K. J. Voss, “Measurements of the Mueller matrix for phytoplankton,” Limnol. Oceanogr. 30, 1322–1326 (1985).
    [CrossRef]
  20. D. A. Cross, P. Latimer, “Angular dependence of scattering from Escherichia Coli cells,” Appl. Opt. 11, 1225–1228 (1972).
    [CrossRef] [PubMed]
  21. M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
    [CrossRef] [PubMed]
  22. K. D. Lofftus, M. S. Quinby-Hunt, A. J. Hunt, F. Livolant, M. Maestre, “Light scattering by Prorocentrum micans: a new method and results,” Appl. Opt. 31, 2924–2931 (1992).
    [CrossRef]
  23. G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [CrossRef]
  24. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]
  25. D. Miller, M. S. Quinby-Hunt, A. J. Hunt, “Laboratory studies of angle- and polarization-dependent light scattering in sea ice,” Appl. Opt. 36, 1278–1288 (1997).
    [CrossRef] [PubMed]
  26. M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
    [CrossRef]
  27. M. I. Mishchenko, 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]
  28. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]
  29. H. Haario, V. -M. Taavitsainen, Data Analysis Toolbox for use with Matlab (ProfMat Oy, Helsinki, Finland, 1997).
  30. E. M. Purcell, C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
  31. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  32. K. Lumme, J. Rahola, J. W. Hovenier, “Light scattering by dense clusters of spheres,” Icarus 126, 455–469 (1997).
    [CrossRef]

1998 (3)

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

M. I. Mishchenko, 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]

1997 (2)

1996 (2)

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices, a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

1995 (2)

V.-M. Taavitsainen, J. -P. Jalava, “Soft and harder multivariate modeling in developing the properties of titanium dioxide pigments,” Chemom. Intell. Lab. Syst. 29, 307–319 (1995).

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (2)

M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

H. Schnablegger, O. Glatter, “Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments,” J. Colloid Interface Sci. 158, 228–242 (1993).
[CrossRef]

1992 (2)

J. -P. Jalava, “Precipitation and properties of TiO2 pigments in the sulfate process. 1. Preparation of the liquor and effects of iron(II) in isoviscous liquor,” Ind. Eng. Chem. Res. 31, 608–611 (1992).
[CrossRef]

K. D. Lofftus, M. S. Quinby-Hunt, A. J. Hunt, F. Livolant, M. Maestre, “Light scattering by Prorocentrum micans: a new method and results,” Appl. Opt. 31, 2924–2931 (1992).
[CrossRef]

1991 (1)

1988 (1)

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

1986 (1)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

1985 (1)

E. S. Fry, K. J. Voss, “Measurements of the Mueller matrix for phytoplankton,” Limnol. Oceanogr. 30, 1322–1326 (1985).
[CrossRef]

1983 (1)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

1982 (1)

S. Sugihara, M. Kishino, N. Okami, “Backscattering of light by particles suspended in water,” Phys. Chem. Res. 76, 1–8 (1982).

1974 (1)

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

1973 (2)

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

G. M. Hale, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

1972 (1)

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Bohren, C. F.

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

Charlton, F.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Cross, D. A.

De Haan, J. F.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Dekker, A.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Draine, B. T.

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

Fry, E. S.

E. S. Fry, K. J. Voss, “Measurements of the Mueller matrix for phytoplankton,” Limnol. Oceanogr. 30, 1322–1326 (1985).
[CrossRef]

Glatter, O.

H. Schnablegger, O. Glatter, “Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments,” J. Colloid Interface Sci. 158, 228–242 (1993).
[CrossRef]

Haario, H.

J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

H. Haario, V. -M. Taavitsainen, Data Analysis Toolbox for use with Matlab (ProfMat Oy, Helsinki, Finland, 1997).

Hale, G. M.

Hansen, J. E.

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

Hoogenboom, H. J.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Hovenier, J. W.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

K. Lumme, J. Rahola, J. W. Hovenier, “Light scattering by dense clusters of spheres,” Icarus 126, 455–469 (1997).
[CrossRef]

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices, a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

F. Kuik, P. Stammes, J. W. Hovenier, “Experimental determination of scattering matrices of water droplets and quartz particles,” Appl. Opt. 30, 4872–4881 (1991).
[CrossRef] [PubMed]

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

J. W. Hovenier, “Measuring scattering matrices of small particles at optical wavelengths,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 355–365.

Huffman, D. R.

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

Hunt, A. J.

Jalava, J. -P.

J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

V.-M. Taavitsainen, J. -P. Jalava, “Soft and harder multivariate modeling in developing the properties of titanium dioxide pigments,” Chemom. Intell. Lab. Syst. 29, 307–319 (1995).

J. -P. Jalava, “Precipitation and properties of TiO2 pigments in the sulfate process. 1. Preparation of the liquor and effects of iron(II) in isoviscous liquor,” Ind. Eng. Chem. Res. 31, 608–611 (1992).
[CrossRef]

Kishino, M.

S. Sugihara, M. Kishino, N. Okami, “Backscattering of light by particles suspended in water,” Phys. Chem. Res. 76, 1–8 (1982).

Kuik, F.

F. Kuik, P. Stammes, J. W. Hovenier, “Experimental determination of scattering matrices of water droplets and quartz particles,” Appl. Opt. 30, 4872–4881 (1991).
[CrossRef] [PubMed]

F. Kuik, “Single scattering of light by ensembles of particles with various shapes,” Ph.D. dissertation (Free University, Amsterdam, The Netherlands, 1992).

Lamberg, L.

J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

Latimer, P.

Livolant, F.

Lofftus, K. D.

Lumme, K.

K. Lumme, J. Rahola, J. W. Hovenier, “Light scattering by dense clusters of spheres,” Icarus 126, 455–469 (1997).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

Maestre, M.

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Miller, D.

Mishchenko, M. I.

M. I. Mishchenko, 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. Mishchenko, D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683–694 (1996).
[CrossRef]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

Okami, N.

S. Sugihara, M. Kishino, N. Okami, “Backscattering of light by particles suspended in water,” Phys. Chem. Res. 76, 1–8 (1982).

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]

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]

Quinby-Hunt, M. S.

Rahola, J.

K. Lumme, J. Rahola, J. W. Hovenier, “Light scattering by dense clusters of spheres,” Icarus 126, 455–469 (1997).
[CrossRef]

Ribarsky, M. W.

M. W. Ribarsky, “Titanium dioxide (TiO2) (rutile),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 795–804.
[CrossRef]

Schnablegger, H.

H. Schnablegger, O. Glatter, “Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments,” J. Colloid Interface Sci. 158, 228–242 (1993).
[CrossRef]

Schreurs, R.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Stammes, P.

F. Kuik, P. Stammes, J. W. Hovenier, “Experimental determination of scattering matrices of water droplets and quartz particles,” Appl. Opt. 30, 4872–4881 (1991).
[CrossRef] [PubMed]

P. Stammes, “Light scattering properties of aerosols and the radiation inside a planetary atmosphere,” Ph.D. dissertation (Free University, Amsterdam, The Netherlands, 1989).

Sugihara, S.

S. Sugihara, M. Kishino, N. Okami, “Backscattering of light by particles suspended in water,” Phys. Chem. Res. 76, 1–8 (1982).

Taavitsainen, V. -M.

J. -P. Jalava, V. -M. Taavitsainen, L. Lamberg, H. Haario, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigment by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

H. Haario, V. -M. Taavitsainen, Data Analysis Toolbox for use with Matlab (ProfMat Oy, Helsinki, Finland, 1997).

Taavitsainen, V.-M.

V.-M. Taavitsainen, J. -P. Jalava, “Soft and harder multivariate modeling in developing the properties of titanium dioxide pigments,” Chemom. Intell. Lab. Syst. 29, 307–319 (1995).

Travis, L. D.

M. I. Mishchenko, 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. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

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

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

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

van der Mee, C. V. M.

J. W. Hovenier, C. V. M. van der Mee, “Testing scattering matrices, a compendium of recipes,” J. Quant. Spectrosc. Radiat. Transfer 55, 649–661 (1996).
[CrossRef]

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Vassen, W.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Volten, H.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Voss, K. J.

E. S. Fry, K. J. Voss, “Measurements of the Mueller matrix for phytoplankton,” Limnol. Oceanogr. 30, 1322–1326 (1985).
[CrossRef]

Wouts, R.

H. Volten, J. F. De Haan, J. W. Hovenier, W. Vassen, R. Schreurs, A. Dekker, H. J. Hoogenboom, F. Charlton, R. Wouts, “Laboratory measurements of angular distributions of light scattered by phytoplankton and silt,” Limnol. Oceanogr. 43, 1180–1197 (1998).
[CrossRef]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Appl. Opt. (8)

Astron. Astrophys. (2)

J. W. Hovenier, C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 157, 301–310 (1986).

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]

Chemom. Intell. Lab. Syst. (1)

V.-M. Taavitsainen, J. -P. Jalava, “Soft and harder multivariate modeling in developing the properties of titanium dioxide pigments,” Chemom. Intell. Lab. Syst. 29, 307–319 (1995).

Icarus (1)

K. Lumme, J. Rahola, J. W. Hovenier, “Light scattering by dense clusters of spheres,” Icarus 126, 455–469 (1997).
[CrossRef]

Ind. Eng. Chem. Res. (1)

J. -P. Jalava, “Precipitation and properties of TiO2 pigments in the sulfate process. 1. Preparation of the liquor and effects of iron(II) in isoviscous liquor,” Ind. Eng. Chem. Res. 31, 608–611 (1992).
[CrossRef]

J. Colloid Interface Sci. (1)

H. Schnablegger, O. Glatter, “Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments,” J. Colloid Interface Sci. 158, 228–242 (1993).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (4)

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Figures (8)

Fig. 1
Fig. 1

TEM image of rutile particles. The white bar at the bottom of the image denotes 500 nm.

Fig. 2
Fig. 2

Two-dimensional distribution of the width and the length/width of the rutile sample. The normalization is such that the sum of all values for 180 combinations of width and length/width equals unity. Solid curves, values determined by TEM; dashed curves, estimated values obtained by fitting results of the T-matrix calculations to measured angular distributions of scattering matrix elements (see Section 7).

Fig. 3
Fig. 3

Schematic of the experimental setup: P, polarizer; S, rutile sample in water; PM, photomultiplier; A, (optional) analyzer; Q, (optional) quarter-wave plate. The photomultipliers are mounted on a goniometer ring with an outer diameter of 1 m.

Fig. 4
Fig. 4

Correction function of scattering angle (solid line) to correct the measured flux for the changing scattering volume as seen by the detector. This function equals sin θ (dashed curve) for most of the scattering angle range.

Fig. 5
Fig. 5

Comparison of results of measurements on latex spheres in water (solid circles) with Mie calculations (solid curves) for angular distributions of F 11, F 22/F 11, F 33/F 11, F 44/F 11, -F 12/F 11, and F 34/F 11. Note that F 11 is plotted on a log scale.

Fig. 6
Fig. 6

Same as Fig. 5 but for F 13/F 11, F 14/F 11, F 23/F 11, and F 24/F 11.

Fig. 7
Fig. 7

Comparison of results of measurements on rutile particles in water with the results of T-matrix calculations for the angular distributions of F 11, F 22/F 11, F 33/F 11, F 44/F 11, -F 12/F 11, and F 34/F 11. The normalization of F 11(θ) is such that its average over three-dimensional space equals unity. Solid circles, measured values, dash–dot curves, functions calculated with the T-matrix method by using the width and the length/width distributions determined by TEM (see Fig. 2 and Table 2); solid curves, the same but for estimated values obtained by fitting the results of T-matrix calculations to measured angular distributions of scattering matrix elements (see Fig. 2 and Table 2).

Fig. 8
Fig. 8

Same as Fig. 7 but for F 13/F 11, F 14/F 11, F 23/F 11, and F 24/F 11. Results of calculations have been omitted for these element ratios since they are identically zero at all scattering angles.

Tables (2)

Tables Icon

Table 1 Matrix Elements Measured for Eight Combinations of the Orientation Angles γP, γM, γQ, and γA of the Polarizer, the Modulator, the Quarter-Wave Plate, and the Analyzera

Tables Icon

Table 2 Parameters Used in the T-Matrix Calculations Presented in Figs. 7 and 8a

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

IsQsUsVs=λ24π2D2F11F12F13F14F12F22F23F24-F13-F23F33F34F14F24-F34F44IiQiUiVi.
Idetθ=cDCθ+2J1ϕ0Sθsin ωt+2J2ϕ0Cθcos 2ωt+,
F14+F24F11+F12=F14/F11+F24/F111+F12/F11,
Fθ=Funcθ-rRFunc180°-θ+Func180°-θrR,
120π F11θsin θdθ=1,
SS=SS1+SS2
SS1=1Ni=1NF11θimeas/F11θicalc-12+j wjFj, measθi/F11, measθi-Fj, calcθi/F11,calcθi2,
SS2=dTEM-dcalc2+σTEM-σcalc2,

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