Abstract

A comparative study of statistical particle model theory of diffuse reflectance has been made. Theories have been applied to six particulate samples having different optical characteristics and average particle sizes that vary from 42 to 106 µm. We made an overall assessment of each theoretical model by determining the CIELAB color difference using experimentally measured and theoretically predicted diffuse reflectance spectra in the visible spectral range. We discuss the performance ratings of the models of other researchers and discovered numerous typographical errors in Fresnel reflection coefficient expressions. We provide the correct versions for these expressions.

© 1997 Optical Society of America

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  1. N. T. Melamed, “Optical properties of powders,” J. Appl. Phys. 34, 560–570 (1963).
    [CrossRef]
  2. E. L. Simmons, “An equation relating the diffuse reflectance of weakly absorbing powdered samples to fundamental optical parameters,” Opt. Acta 18, 59–68 (1971).
    [CrossRef]
  3. E. L. Simmons, “Modification of the particle model theory of diffuse reflectance properties of powdered samples,” J. Appl. Phys. 46, 344–349 (1975).
    [CrossRef]
  4. A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance spectroscopy of large powders: the Melamed model revisited,” Appl. Opt. 29, 2853–2860 (1990).
    [CrossRef] [PubMed]
  5. A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
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  6. A. Companion, G. H. Winslaw, “Diffuse reflectance measurement of bulk uranium dioxide,” J. Opt. Soc. Am. 50, 1043–1045 (1960).
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  7. P. D. Johnson, “Absolute optical absorption from diffuse reflectance,” J. Opt. Soc. Am. 42, 978–981 (1952).
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  8. H. G. Hecht, “The present status of diffuse reflectance theory,” in Proceedings of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 1.
  9. E. A. Bourdreux, J. P. Englert, “Diffuse reflectance spectroscopy: a quantitative technique for characterizing ligand field spectra,” in Proceeding of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 47.
  10. A. Mandelis, Department of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada (personal communication, 1994).
  11. F. W. Billmeyer, D. H. Alman, “Exact calculation of Fresnel reflection coefficient for diffuse light,” J. Color Appearance 2, 36–38 (1973).
  12. H. S. Shah, M. S. Roy, “Estimation of average particle size in particulate system from its reflectance spectra, Indian J. Phys. B 66, 389–395 (1992).
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    [CrossRef] [PubMed]
  14. H. S. Shah, M. S. Roy, “Determination of absorption index of particulate matter: a comparative study,” Indian J. Pure Appl. Phys. 29, 682–686 (1991).
  15. H. S. Shah, R. S. Gandhi, Instrumental Colour Measurement and Computer Aided Colour Matching in Textiles (Mahajan Book Distributors, India, 1990), Chap. 3, pp. 57, 77; Chap. 4, p. 100.
  16. F. W. Billmeyer, M. Saltzman, Principles of Color Technology, 2nd ed. (Wiley, New York, 1981), Chap. 2, pp. 47, 63; Chap. 3, p. 103.

1992 (1)

H. S. Shah, M. S. Roy, “Estimation of average particle size in particulate system from its reflectance spectra, Indian J. Phys. B 66, 389–395 (1992).

1991 (2)

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
[CrossRef]

H. S. Shah, M. S. Roy, “Determination of absorption index of particulate matter: a comparative study,” Indian J. Pure Appl. Phys. 29, 682–686 (1991).

1990 (1)

1975 (1)

E. L. Simmons, “Modification of the particle model theory of diffuse reflectance properties of powdered samples,” J. Appl. Phys. 46, 344–349 (1975).
[CrossRef]

1974 (1)

1973 (1)

F. W. Billmeyer, D. H. Alman, “Exact calculation of Fresnel reflection coefficient for diffuse light,” J. Color Appearance 2, 36–38 (1973).

1971 (1)

E. L. Simmons, “An equation relating the diffuse reflectance of weakly absorbing powdered samples to fundamental optical parameters,” Opt. Acta 18, 59–68 (1971).
[CrossRef]

1963 (1)

N. T. Melamed, “Optical properties of powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

1960 (1)

1952 (1)

Alman, D. H.

F. W. Billmeyer, D. H. Alman, “Exact calculation of Fresnel reflection coefficient for diffuse light,” J. Color Appearance 2, 36–38 (1973).

Billmeyer, F. W.

F. W. Billmeyer, D. H. Alman, “Exact calculation of Fresnel reflection coefficient for diffuse light,” J. Color Appearance 2, 36–38 (1973).

F. W. Billmeyer, M. Saltzman, Principles of Color Technology, 2nd ed. (Wiley, New York, 1981), Chap. 2, pp. 47, 63; Chap. 3, p. 103.

Boroumand, F.

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
[CrossRef]

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance spectroscopy of large powders: the Melamed model revisited,” Appl. Opt. 29, 2853–2860 (1990).
[CrossRef] [PubMed]

Bourdreux, E. A.

E. A. Bourdreux, J. P. Englert, “Diffuse reflectance spectroscopy: a quantitative technique for characterizing ligand field spectra,” in Proceeding of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 47.

Companion, A.

Englert, J. P.

E. A. Bourdreux, J. P. Englert, “Diffuse reflectance spectroscopy: a quantitative technique for characterizing ligand field spectra,” in Proceeding of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 47.

Gandhi, R. S.

H. S. Shah, R. S. Gandhi, Instrumental Colour Measurement and Computer Aided Colour Matching in Textiles (Mahajan Book Distributors, India, 1990), Chap. 3, pp. 57, 77; Chap. 4, p. 100.

Hecht, H. G.

H. G. Hecht, “The present status of diffuse reflectance theory,” in Proceedings of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 1.

Johnson, P. D.

Laude, L. S.

Lindberg, J. D.

Mandelis, A.

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
[CrossRef]

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance spectroscopy of large powders: the Melamed model revisited,” Appl. Opt. 29, 2853–2860 (1990).
[CrossRef] [PubMed]

A. Mandelis, Department of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada (personal communication, 1994).

Melamed, N. T.

N. T. Melamed, “Optical properties of powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

Roy, M. S.

H. S. Shah, M. S. Roy, “Estimation of average particle size in particulate system from its reflectance spectra, Indian J. Phys. B 66, 389–395 (1992).

H. S. Shah, M. S. Roy, “Determination of absorption index of particulate matter: a comparative study,” Indian J. Pure Appl. Phys. 29, 682–686 (1991).

Saltzman, M.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology, 2nd ed. (Wiley, New York, 1981), Chap. 2, pp. 47, 63; Chap. 3, p. 103.

Shah, H. S.

H. S. Shah, M. S. Roy, “Estimation of average particle size in particulate system from its reflectance spectra, Indian J. Phys. B 66, 389–395 (1992).

H. S. Shah, M. S. Roy, “Determination of absorption index of particulate matter: a comparative study,” Indian J. Pure Appl. Phys. 29, 682–686 (1991).

H. S. Shah, R. S. Gandhi, Instrumental Colour Measurement and Computer Aided Colour Matching in Textiles (Mahajan Book Distributors, India, 1990), Chap. 3, pp. 57, 77; Chap. 4, p. 100.

Simmons, E. L.

E. L. Simmons, “Modification of the particle model theory of diffuse reflectance properties of powdered samples,” J. Appl. Phys. 46, 344–349 (1975).
[CrossRef]

E. L. Simmons, “An equation relating the diffuse reflectance of weakly absorbing powdered samples to fundamental optical parameters,” Opt. Acta 18, 59–68 (1971).
[CrossRef]

vanden Bergh, H.

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
[CrossRef]

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance spectroscopy of large powders: the Melamed model revisited,” Appl. Opt. 29, 2853–2860 (1990).
[CrossRef] [PubMed]

Winslaw, G. H.

Appl. Opt. (2)

Indian J. Phys. B (1)

H. S. Shah, M. S. Roy, “Estimation of average particle size in particulate system from its reflectance spectra, Indian J. Phys. B 66, 389–395 (1992).

Indian J. Pure Appl. Phys. (1)

H. S. Shah, M. S. Roy, “Determination of absorption index of particulate matter: a comparative study,” Indian J. Pure Appl. Phys. 29, 682–686 (1991).

J. Appl. Phys. (2)

E. L. Simmons, “Modification of the particle model theory of diffuse reflectance properties of powdered samples,” J. Appl. Phys. 46, 344–349 (1975).
[CrossRef]

N. T. Melamed, “Optical properties of powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

J. Color Appearance (1)

F. W. Billmeyer, D. H. Alman, “Exact calculation of Fresnel reflection coefficient for diffuse light,” J. Color Appearance 2, 36–38 (1973).

J. Opt. Soc. Am. (2)

Opt. Acta (1)

E. L. Simmons, “An equation relating the diffuse reflectance of weakly absorbing powdered samples to fundamental optical parameters,” Opt. Acta 18, 59–68 (1971).
[CrossRef]

Spectrochim. Acta Part A (1)

A. Mandelis, F. Boroumand, H. vanden Bergh, “Quantitative diffuse reflectance and transmittance spectroscopy of loosely packed powders,” Spectrochim. Acta Part A 47, 943–971 (1991).
[CrossRef]

Other (5)

H. G. Hecht, “The present status of diffuse reflectance theory,” in Proceedings of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 1.

E. A. Bourdreux, J. P. Englert, “Diffuse reflectance spectroscopy: a quantitative technique for characterizing ligand field spectra,” in Proceeding of the American Chemical Society Symposium on Reflectance Spectroscopy, W. W. Wendlandt, ed. (American Chemical Society, Washington, D.C., 1967), p. 47.

A. Mandelis, Department of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada (personal communication, 1994).

H. S. Shah, R. S. Gandhi, Instrumental Colour Measurement and Computer Aided Colour Matching in Textiles (Mahajan Book Distributors, India, 1990), Chap. 3, pp. 57, 77; Chap. 4, p. 100.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology, 2nd ed. (Wiley, New York, 1981), Chap. 2, pp. 47, 63; Chap. 3, p. 103.

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