Abstract

We propose a novel, to our knowledge, method for characterizing the optical properties of pigment particles or powders. Measurements of the diffuse and the total transmittance as well as the diffuse and the total reflectance are used to obtain effective scattering and absorption coefficients per unit length for the particles that are dispersed in a continuous matrix. For dilute dispersions in the single-scattering regime scattering and absorption cross sections of the particles were obtained. The method was applied to two pigments, namely, FeMnCuOx and black carbon. The data were obtained by use of pellets consisting of low concentrations of FeMnCuOx or black-carbon pigments dispersed in a KBr matrix. The pigment volume concentrations used to evaluate the scattering and the absorption coefficients ranged from 0.053% to 0.530% for FeMnCuOx and 0.076% to 0.310% for the black carbon. These ranges were found to exhibit the linear dependence of the coefficients as a function of volume fraction, as given by single-scattering theory.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
  2. G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co–Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
    [CrossRef]
  3. G. Mie, “Optics of turbid media,” Ann. Phys. 25, 377–445 (1908).
    [CrossRef]
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  5. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  6. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  7. G. A. Niklasson, “Comparison between four-flux theory and multiple scattering theory,” Appl. Opt. 23, 4034–4036 (1987).
    [CrossRef]
  8. A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).
  9. G. W. Kattawar, G. N. Plass, “Asymptomatic radiance and polarization in optically thick media: ocean and clouds,” Appl. Opt. 15, 3166–3178 (1976).
    [CrossRef] [PubMed]
  10. G. W. Kattwar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere–ocean system,” J. Phys. Ocean 3, 353–372 (1973).
    [CrossRef]
  11. A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. XXI, 1–22 (1905).
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  12. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” A. Tech. Phys. 12, 593–601 (1931).
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    [CrossRef]
  14. H. Reiss, Radiative Transfer in Nontransparent, Dispersed Media (Springer-Verlag, Heidelberg, Germany, 1988).
  15. C. C. Johnson, A. W. Guy, “Nonionizing electromagnetic wave effects in biological materials and systems,” Proc. IEEE 60, 692–718 (1972).
    [CrossRef]
  16. W. G. Egan, T. Hilgeman, J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 2. Experiment,” Appl. Opt. 12, 1816–1823 (1973).
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  17. P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485–1502 (1971).
    [CrossRef] [PubMed]
  18. D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka–Munk analysis,” J. Coat. Technol. 48, 30–36 (1976).
  19. Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka–Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
    [CrossRef]
  20. K. M. Gunde, Z. C. Orel, “Absorption and scattering of light by pigment particles in solar-absorbing paints,” Appl. Opt. 39, 622–628 (2000).
    [CrossRef]
  21. T. Tesfamichael, W. E. Vargas, E. Wäckelgård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997).
    [CrossRef]
  22. C. A. Arancibai-Bulnes, J. C. Ruiz-Suarez, “Spectral selectivity of cermets with large metallic inclusions,” J. Appl. Phys. 83, 5421–5426 (1998).
    [CrossRef]
  23. C. Sasse, “Development of an experimental system for optical characterization of large arbitrarily shaped particles,” Rev. Sci. Instrum. 64, 864–869 (1993).
    [CrossRef]
  24. C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
    [CrossRef]
  25. C. M. Lampert, “Coatings for enhanced photothermal energy collection,” Solar Energy Mater. 2, 1–17 (1979).
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  26. O. P. Agnihotri, B. K. Gupta, Solar Selective Surfaces (Wiley-Interscience, New York, 1981).
  27. R. J. H. Lin, P. B. Zimmer, “Optimization of coatings for flat plate solar collectors,” (Honeywell, Inc., Minneapolis, Minn., 1977).
  28. Z. C. Orel, “Preparation of high temperature resistant selective paints for solar absorbers,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIV, C. M. Lampert, S. K. Deb, C. G. Granqvist, eds., Proc. SPIE2531, 296–307 (1995).
    [CrossRef]
  29. K. M. Gunde, Z. C. Orel, J. K. Logar, B. Orel, “Flocculation gradient technique in terms of Kubelka–Munk coefficients: quantifying black-pigmented dispersions,” Appl. Spectrosc. 49, 1756–1761 (1995).
    [CrossRef]
  30. K. M. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996).
    [CrossRef]
  31. W. E. Vargas, G. Niklasson, “Applicability conditions of the Kubelka–Munk theory,” Appl. Opt. 36, 5580–5586 (1997).
    [CrossRef] [PubMed]
  32. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).
  33. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).
  34. W. Q. Hong, “Extraction of extinction coefficient of weak absorbing thin films from special absorption,” J. Phys. D. Appl. Phys. 22, 1384–1385 (1989).
    [CrossRef]
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    [CrossRef] [PubMed]
  37. A. Roos, “Use of an integrating sphere in solar energy research,” Solar Energy Mater. Solar Cells 30, 77–94 (1993).
    [CrossRef]
  38. A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
    [CrossRef] [PubMed]
  39. T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).
  40. I. Balberg, H. L. Pinch, “The optical absorption of iron oxide,” J. Magn. Magn. Mater. 7, 12–15 (1978).
    [CrossRef]
  41. F. Rouleau, P. G. Martin, “Shape and clustering effects on the optical properties of amorphous carbon,” Astrophys. J. 377, 526–540 (1991).
    [CrossRef]
  42. N. Savvides, B. Window, “Diamond-like amorphous carbon films prepared by magnetron sputtering of graphite,” J. Vac. Sci. Technol. A 3, 2386–2390 (1985).
    [CrossRef]
  43. V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
    [CrossRef]

2000 (1)

1998 (1)

C. A. Arancibai-Bulnes, J. C. Ruiz-Suarez, “Spectral selectivity of cermets with large metallic inclusions,” J. Appl. Phys. 83, 5421–5426 (1998).
[CrossRef]

1997 (3)

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka–Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

T. Tesfamichael, W. E. Vargas, E. Wäckelgård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997).
[CrossRef]

W. E. Vargas, G. Niklasson, “Applicability conditions of the Kubelka–Munk theory,” Appl. Opt. 36, 5580–5586 (1997).
[CrossRef] [PubMed]

1996 (2)

C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
[CrossRef]

K. M. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996).
[CrossRef]

1995 (1)

1993 (2)

A. Roos, “Use of an integrating sphere in solar energy research,” Solar Energy Mater. Solar Cells 30, 77–94 (1993).
[CrossRef]

C. Sasse, “Development of an experimental system for optical characterization of large arbitrarily shaped particles,” Rev. Sci. Instrum. 64, 864–869 (1993).
[CrossRef]

1991 (2)

F. Rouleau, P. G. Martin, “Shape and clustering effects on the optical properties of amorphous carbon,” Astrophys. J. 377, 526–540 (1991).
[CrossRef]

A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474 (1991).
[CrossRef] [PubMed]

1989 (1)

W. Q. Hong, “Extraction of extinction coefficient of weak absorbing thin films from special absorption,” J. Phys. D. Appl. Phys. 22, 1384–1385 (1989).
[CrossRef]

1988 (1)

1987 (1)

1985 (1)

N. Savvides, B. Window, “Diamond-like amorphous carbon films prepared by magnetron sputtering of graphite,” J. Vac. Sci. Technol. A 3, 2386–2390 (1985).
[CrossRef]

1984 (2)

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co–Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorentz–Mie parameters,” Appl. Opt. 23, 3353–3362 (1984).
[CrossRef]

1983 (1)

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

1981 (1)

1979 (1)

C. M. Lampert, “Coatings for enhanced photothermal energy collection,” Solar Energy Mater. 2, 1–17 (1979).
[CrossRef]

1978 (1)

I. Balberg, H. L. Pinch, “The optical absorption of iron oxide,” J. Magn. Magn. Mater. 7, 12–15 (1978).
[CrossRef]

1976 (2)

D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka–Munk analysis,” J. Coat. Technol. 48, 30–36 (1976).

G. W. Kattawar, G. N. Plass, “Asymptomatic radiance and polarization in optically thick media: ocean and clouds,” Appl. Opt. 15, 3166–3178 (1976).
[CrossRef] [PubMed]

1973 (2)

W. G. Egan, T. Hilgeman, J. Reichman, “Determination of absorption and scattering coefficients for nonhomogeneous media. 2. Experiment,” Appl. Opt. 12, 1816–1823 (1973).
[CrossRef] [PubMed]

G. W. Kattwar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere–ocean system,” J. Phys. Ocean 3, 353–372 (1973).
[CrossRef]

1972 (1)

C. C. Johnson, A. W. Guy, “Nonionizing electromagnetic wave effects in biological materials and systems,” Proc. IEEE 60, 692–718 (1972).
[CrossRef]

1971 (1)

1931 (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” A. Tech. Phys. 12, 593–601 (1931).

1908 (1)

G. Mie, “Optics of turbid media,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

1905 (1)

A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. XXI, 1–22 (1905).
[CrossRef]

Agnihotri, O. P.

O. P. Agnihotri, B. K. Gupta, Solar Selective Surfaces (Wiley-Interscience, New York, 1981).

Arancibai-Bulnes, C. A.

C. A. Arancibai-Bulnes, J. C. Ruiz-Suarez, “Spectral selectivity of cermets with large metallic inclusions,” J. Appl. Phys. 83, 5421–5426 (1998).
[CrossRef]

Balberg, I.

I. Balberg, H. L. Pinch, “The optical absorption of iron oxide,” J. Magn. Magn. Mater. 7, 12–15 (1978).
[CrossRef]

Billmeyer, F. W.

D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka–Munk analysis,” J. Coat. Technol. 48, 30–36 (1976).

Bohren, C. F.

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

Bringi, V. N.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Dröse, G.

C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
[CrossRef]

Egan, W. G.

Gouesbet, G.

Granqvist, C. G.

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co–Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981).
[CrossRef] [PubMed]

Guinn, J. A.

G. W. Kattwar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere–ocean system,” J. Phys. Ocean 3, 353–372 (1973).
[CrossRef]

Gunde, K. M.

Gunde, M. K.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka–Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

Gupta, B. K.

O. P. Agnihotri, B. K. Gupta, Solar Selective Surfaces (Wiley-Interscience, New York, 1981).

Guy, A. W.

C. C. Johnson, A. W. Guy, “Nonionizing electromagnetic wave effects in biological materials and systems,” Proc. IEEE 60, 692–718 (1972).
[CrossRef]

Hilgeman, T.

Hilgeman, T. W.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Hoel, A.

T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

Hong, W. Q.

W. Q. Hong, “Extraction of extinction coefficient of weak absorbing thin films from special absorption,” J. Phys. D. Appl. Phys. 22, 1384–1385 (1989).
[CrossRef]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Huffman, D. R.

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

Hunderi, O.

Ishimaru, A.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, New York, 1997).

Johnson, C. C.

C. C. Johnson, A. W. Guy, “Nonionizing electromagnetic wave effects in biological materials and systems,” Proc. IEEE 60, 692–718 (1972).
[CrossRef]

Kattawar, G. W.

Kattwar, G. W.

G. W. Kattwar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere–ocean system,” J. Phys. Ocean 3, 353–372 (1973).
[CrossRef]

Kerker, M.

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

Kubelka, P.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” A. Tech. Phys. 12, 593–601 (1931).

Lampert, C. M.

C. M. Lampert, “Coatings for enhanced photothermal energy collection,” Solar Energy Mater. 2, 1–17 (1979).
[CrossRef]

Letoulouzan, J. N.

Lin, R. J. H.

R. J. H. Lin, P. B. Zimmer, “Optimization of coatings for flat plate solar collectors,” (Honeywell, Inc., Minneapolis, Minn., 1977).

Logar, J. K.

K. M. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996).
[CrossRef]

K. M. Gunde, Z. C. Orel, J. K. Logar, B. Orel, “Flocculation gradient technique in terms of Kubelka–Munk coefficients: quantifying black-pigmented dispersions,” Appl. Spectrosc. 49, 1756–1761 (1995).
[CrossRef]

Maheu, B.

Martin, P. G.

F. Rouleau, P. G. Martin, “Shape and clustering effects on the optical properties of amorphous carbon,” Astrophys. J. 377, 526–540 (1991).
[CrossRef]

Mie, G.

G. Mie, “Optics of turbid media,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Mudgett, P. S.

Muinonen, K.

C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
[CrossRef]

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” A. Tech. Phys. 12, 593–601 (1931).

Niklasson, G.

Niklasson, G. A.

T. Tesfamichael, W. E. Vargas, E. Wäckelgård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997).
[CrossRef]

G. A. Niklasson, “Comparison between four-flux theory and multiple scattering theory,” Appl. Opt. 23, 4034–4036 (1987).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co–Al2O3 composite films,” J. Appl. Phys. 55, 3382–3410 (1984).
[CrossRef]

G. A. Niklasson, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981).
[CrossRef] [PubMed]

T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

Orel, B.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka–Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

K. M. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996).
[CrossRef]

K. M. Gunde, Z. C. Orel, J. K. Logar, B. Orel, “Flocculation gradient technique in terms of Kubelka–Munk coefficients: quantifying black-pigmented dispersions,” Appl. Spectrosc. 49, 1756–1761 (1995).
[CrossRef]

Orel, Z. C.

K. M. Gunde, Z. C. Orel, “Absorption and scattering of light by pigment particles in solar-absorbing paints,” Appl. Opt. 39, 622–628 (2000).
[CrossRef]

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka–Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

K. M. Gunde, J. K. Logar, Z. C. Orel, B. Orel, “Optimum thickness determination to maximize the spectral selectivity of black pigmented coatings for solar collectors,” Thin Solid Films 277, 185–191 (1996).
[CrossRef]

K. M. Gunde, Z. C. Orel, J. K. Logar, B. Orel, “Flocculation gradient technique in terms of Kubelka–Munk coefficients: quantifying black-pigmented dispersions,” Appl. Spectrosc. 49, 1756–1761 (1995).
[CrossRef]

T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

Z. C. Orel, “Preparation of high temperature resistant selective paints for solar absorbers,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIV, C. M. Lampert, S. K. Deb, C. G. Granqvist, eds., Proc. SPIE2531, 296–307 (1995).
[CrossRef]

Phillips, D. G.

D. G. Phillips, F. W. Billmeyer, “Predicting reflectance and color of paint films by Kubelka–Munk analysis,” J. Coat. Technol. 48, 30–36 (1976).

Piironen, J.

C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
[CrossRef]

Pinch, H. L.

I. Balberg, H. L. Pinch, “The optical absorption of iron oxide,” J. Magn. Magn. Mater. 7, 12–15 (1978).
[CrossRef]

Plass, G. N.

G. W. Kattawar, G. N. Plass, “Asymptomatic radiance and polarization in optically thick media: ocean and clouds,” Appl. Opt. 15, 3166–3178 (1976).
[CrossRef] [PubMed]

G. W. Kattwar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere–ocean system,” J. Phys. Ocean 3, 353–372 (1973).
[CrossRef]

Reichman, J.

Reiss, H.

H. Reiss, Radiative Transfer in Nontransparent, Dispersed Media (Springer-Verlag, Heidelberg, Germany, 1988).

Ribbing, C. G.

Richards, L. W.

Roos, A.

Rouleau, F.

F. Rouleau, P. G. Martin, “Shape and clustering effects on the optical properties of amorphous carbon,” Astrophys. J. 377, 526–540 (1991).
[CrossRef]

Ruiz-Suarez, J. C.

C. A. Arancibai-Bulnes, J. C. Ruiz-Suarez, “Spectral selectivity of cermets with large metallic inclusions,” J. Appl. Phys. 83, 5421–5426 (1998).
[CrossRef]

Sasse, C.

C. Sasse, K. Muinonen, J. Piironen, G. Dröse, “Albedo measurements on single particles,” J. Quant. Spectrosc. Radiat. Transfer 55, 673–681 (1996).
[CrossRef]

C. Sasse, “Development of an experimental system for optical characterization of large arbitrarily shaped particles,” Rev. Sci. Instrum. 64, 864–869 (1993).
[CrossRef]

Savvides, N.

N. Savvides, B. Window, “Diamond-like amorphous carbon films prepared by magnetron sputtering of graphite,” J. Vac. Sci. Technol. A 3, 2386–2390 (1985).
[CrossRef]

Schuster, A.

A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. XXI, 1–22 (1905).
[CrossRef]

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Tesfamichael, T.

T. Tesfamichael, W. E. Vargas, E. Wäckelgård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997).
[CrossRef]

T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

van de Hulst, H. C.

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

Varadan, V. K.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Varadan, V. V.

V. K. Varadan, V. N. Bringi, V. V. Varadan, A. Ishimaru, “Multiple scattering theory for waves in discrete random media and comparison with experiments,” Radio Sci. 18, 321–327 (1983).
[CrossRef]

Vargas, W. E.

T. Tesfamichael, W. E. Vargas, E. Wäckelgård, G. A. Niklasson, “Optical properties of silicon pigmented alumina films,” J. Appl. Phys. 82, 3508–3513 (1997).
[CrossRef]

W. E. Vargas, G. Niklasson, “Applicability conditions of the Kubelka–Munk theory,” Appl. Opt. 36, 5580–5586 (1997).
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T. Tesfamichael, A. Hoel, G. A. Niklasson, E. Wäckelgård, M. K. Gunde, Z. C. Orel, “Optical characterization and modeling of black pigments used in thickness sensitive solar selective absorbing paints,” Solar Energy (to be published).

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Figures (8)

Fig. 1
Fig. 1

Collimated reflectance and transmittance of incident light of an intensity I i impinging along the z axis on a sufficiently transparent absorbing slab of thickness d and an extinction coefficient K + S per unit length.

Fig. 2
Fig. 2

Cross-sectional SEM photographs of (a) KBr, (b) FeMnCuO x , (c) black-carbon pellets. The length scales are shown in the insets in each micrograph together with values for the electron high tension (EHT) and the microscope working distance (WD).

Fig. 3
Fig. 3

Total reflectance R t and transmittance T t of a KBr pellet plotted as functions of the wavelength for different numbers of pressings: solid curve, 1 pressing; long-dashed curve, 2 pressings; intermediate-dashed curve, 3 pressings; dashed curve, 4 pressings.

Fig. 4
Fig. 4

Total (a) transmittance and (b) reflectance of the FeMnCuO x pigment in a KBr matrix plotted as functions of the wavelength for different volume fractions of the pigment: f = 0.053%–1.07%.

Fig. 5
Fig. 5

Total (a) transmittance and (b) reflectance of black-carbon pigment in a KBr matrix plotted as functions of the wavelength for different volume fractions of the pigment: f = 0.076%–1.52%.

Fig. 6
Fig. 6

Normalized effective absorption K/ f and scattering S/ f coefficients plotted as functions of the wavelength. The circles with dots represent FeMnCuO x , and the open squares represent the black-carbon pigments.

Fig. 7
Fig. 7

Volumetric absorption and scattering cross sections plotted as functions of the wavelength for the FeMnCuO x (f = 0.053%–0.53%) pigment compared with the corresponding values of the FeMnCuO x (f = 18%) TSSS paint.

Fig. 8
Fig. 8

Volumetric absorption and scattering cross sections plotted as functions of the wavelength for the black-carbon (f = 0.076%–0.31%) pigment compared with the corresponding values of the black-carbon (f = 20%) TSSS paint.

Equations (11)

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

Rt=Rc+Rd.
Tt=Tc+Td,
A=1-Rt+Tt.
E=Rd+Td+A.
E=1-Rc+Tc.
Tc1-Rc=1-R0exp-K+Sd1-R0 exp-2K+Sd.
Tc1-Rcexp-K+Sd.
Tt1-Rtexp-Kd
Cabsv=Kf,
Cscav=Sf,
f=11+ρpρm1-FF,

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