Abstract

A method is proposed to estimate the optical parameters in a fluorescing turbid medium with strong absorption for which traditional Kubelka–Munk theory is not applicable, using a model for the radiative properties of optically thick fluorescent turbid media of finite thickness proposed in 2009[J. Opt. Soc. Am. A 26, 1896 (2009)]. The method is successfully applied to uncoated papers with different thicknesses. It is found that the quantum efficiency of fluorescent whitening agents (FWAs) is nearly independent of the fiber type, FWA type, FWA concentration, and filler additive concentration used in this study. The results enable an estimation of the model parameters as function of the FWA concentration and substrate composition. This is necessary in order to use the model for optimizing fluorescence in the paper and textile industries.

© 2011 Optical Society of America

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    [CrossRef]
  3. D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
    [CrossRef]
  4. M. Sormaz, T. Stamm, S. Mourad, and P. Jenny, “Stochastic modeling of light scattering with fluorescence using a monte carlo-based multiscale approach,” J. Opt. Soc. Am. A 26, 1403–1413 (2009).
    [CrossRef]
  5. L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H.Niskanen and J.Hämäläinen, eds. (Kuopio, 2009).
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    [CrossRef]
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    [CrossRef]
  8. T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4–14(2003).
    [CrossRef]
  9. L. Fukshansky and N. Kazarinova, “Extension of the Kubelka-Munk theory of light propagation in intensely scattering materials to fluorescent media,” J. Opt. Soc. Am. 70, 1101–1111(1980).
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  13. American Society for Testing and Materials (ASTM), “Standard practice for obtaining bispectral photometric data for evaluation of fluorescent color,” ASTM E2153-01 (ASTM, 2006).
  14. International Organization for Standardization (ISO), “Paper and board—determination of CIE whiteness, d65/10 (outdoor daylight),” ISO 11475(ISO, 2004).
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    [CrossRef]
  19. P. Turunen, J. Kinnunen, and J. Mutanen, “Modeling of fluorescent color mixing by regression analysis,” in Fourth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science (Society for Imaging Science and Technology, 2010), pp. 94–100.
  20. International Organization for Standardization (ISO), Determination of light scattering and absorption coefficients (using Kubelka-Munk theory),” ISO 9416 (ISO, 1994).
  21. M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. i. theory,” J. Opt. Soc. Am. A 27, 1032–1039 (2010).
    [CrossRef]
  22. M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. ii. measurements,” J. Opt. Soc. Am. A 27, 1040–1045 (2010).
    [CrossRef]

2010

2009

2003

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4–14(2003).
[CrossRef]

J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, “Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues,” J. Opt. Soc. Am. A 20, 714–727 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

1999

J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the national research council of canada for high-accuracy fluorescence measurements,” Acta Chim. Slov. 380, 193–209 (1999).
[CrossRef]

1986

J. E. Bonham, “Fluorescence and Kubelka-Munk theory,” Color Res. Appl. 11, 223–230 (1986).
[CrossRef]

1980

1972

E. Allen, “Fluorescent colorants: true reflectance, quantum efficiency and match formulation,” J. Color Appearance 1, 28–32 (1972).

1964

1954

1948

Allen, E.

E. Allen, “Fluorescent colorants: true reflectance, quantum efficiency and match formulation,” J. Color Appearance 1, 28–32 (1972).

E. Allen, “Fluorescent white dyes: calculation of fluorescence from reflectivity values,” J. Opt. Soc. Am. 54, 506–515 (1964).
[CrossRef]

Andersson-Engels, S.

Bonham, J. E.

J. E. Bonham, “Fluorescence and Kubelka-Munk theory,” Color Res. Appl. 11, 223–230 (1986).
[CrossRef]

Churmakov, D. Y.

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

Coppel, L. G.

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H.Niskanen and J.Hämäläinen, eds. (Kuopio, 2009).

Donaldson, R.

R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210–214 (1954).
[CrossRef]

Edström, P.

M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. i. theory,” J. Opt. Soc. Am. A 27, 1032–1039 (2010).
[CrossRef]

M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. ii. measurements,” J. Opt. Soc. Am. A 27, 1040–1045 (2010).
[CrossRef]

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H.Niskanen and J.Hämäläinen, eds. (Kuopio, 2009).

Enejder, A. M. K.

Fukshansky, L.

Gauthier, F.

J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the national research council of canada for high-accuracy fluorescence measurements,” Acta Chim. Slov. 380, 193–209 (1999).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

Greenhalgh, D. A.

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

Jenny, P.

Kazarinova, N.

Kinnunen, J.

P. Turunen, J. Kinnunen, and J. Mutanen, “Modeling of fluorescent color mixing by regression analysis,” in Fourth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science (Society for Imaging Science and Technology, 2010), pp. 94–100.

Kokhanovsky, A. A.

Kubelka, P.

Lamperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

Lindquister, M.

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H.Niskanen and J.Hämäläinen, eds. (Kuopio, 2009).

Meglinski, I. V.

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

Mourad, S.

Mutanen, J.

P. Turunen, J. Kinnunen, and J. Mutanen, “Modeling of fluorescent color mixing by regression analysis,” in Fourth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science (Society for Imaging Science and Technology, 2010), pp. 94–100.

Neuman, M.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

Pifferi, A.

Piletsky, S. A.

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

Shakespeare, J.

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4–14(2003).
[CrossRef]

Shakespeare, T.

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4–14(2003).
[CrossRef]

Sormaz, M.

Stamm, T.

Swartling, J.

Turunen, P.

P. Turunen, J. Kinnunen, and J. Mutanen, “Modeling of fluorescent color mixing by regression analysis,” in Fourth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science (Society for Imaging Science and Technology, 2010), pp. 94–100.

Zwinkels, J. C.

J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the national research council of canada for high-accuracy fluorescence measurements,” Acta Chim. Slov. 380, 193–209 (1999).
[CrossRef]

Acta Chim. Slov.

J. C. Zwinkels and F. Gauthier, “Instrumentation, standards, and procedures used at the national research council of canada for high-accuracy fluorescence measurements,” Acta Chim. Slov. 380, 193–209 (1999).
[CrossRef]

Br. J. Appl. Phys.

R. Donaldson, “Spectrophotometry of fluorescent pigments,” Br. J. Appl. Phys. 5, 210–214 (1954).
[CrossRef]

Color Res. Appl.

J. E. Bonham, “Fluorescence and Kubelka-Munk theory,” Color Res. Appl. 11, 223–230 (1986).
[CrossRef]

T. Shakespeare and J. Shakespeare, “A fluorescent extension to the Kubelka-Munk model,” Color Res. Appl. 28, 4–14(2003).
[CrossRef]

J. Color Appearance

E. Allen, “Fluorescent colorants: true reflectance, quantum efficiency and match formulation,” J. Color Appearance 1, 28–32 (1972).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, “Analysis of skin tissues spatial fluorescence distribution by the Monte Carlo simulation,” J. Phys. D 36, 1722 (2003).
[CrossRef]

Other

L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, H.Niskanen and J.Hämäläinen, eds. (Kuopio, 2009).

P. Turunen, J. Kinnunen, and J. Mutanen, “Modeling of fluorescent color mixing by regression analysis,” in Fourth European Conference on Colour in Graphics, Imaging, and MCS/10 Vision 12th International Symposium on Multispectral Colour Science (Society for Imaging Science and Technology, 2010), pp. 94–100.

International Organization for Standardization (ISO), Determination of light scattering and absorption coefficients (using Kubelka-Munk theory),” ISO 9416 (ISO, 1994).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards, 1977).

American Society for Testing and Materials (ASTM), “Standard practice for obtaining bispectral photometric data for evaluation of fluorescent color,” ASTM E2153-01 (ASTM, 2006).

International Organization for Standardization (ISO), “Paper and board—determination of CIE whiteness, d65/10 (outdoor daylight),” ISO 11475(ISO, 2004).

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Figures (10)

Fig. 1
Fig. 1

Scattering coefficient versus wavelength for selected samples. XPM samples: s was obtained by optimization with the Kokhanovsky model. It is compared to a linear extrapolation in the UV region of the spectrum. Sheet former samples: s was obtained by applying KMT on undyed samples.

Fig. 2
Fig. 2

Absorption coefficient versus wavelength for the XPM samples estimated with method 1. The 40 g / m 2 samples have much lower k than the 80 g / m 2 samples at equal amounts of FWA added into the substrate prior to the paper-making process.

Fig. 3
Fig. 3

Scattering and absorption coefficient at 360 nm versus feed FWA concentration estimated with constant, extrapolated, scattering coefficient (black) and optimization with the Kokhanovsky model (gray). Comparison of the absorption coefficient of samples made of sulphate pulp on the XPM pilot paper machine and samples made of another sulphate pulp with Formette Dynamique. The two pulps give similar s and k for undyed samples.

Fig. 4
Fig. 4

Total apparent spectral quantum efficiency for the opaque pads of XPM samples at different FWA concentrations. Markers show the values obtained with extrapolation of the scattering coefficient in the UV region of the spectrum. Curves show direct optimization of s, k, and Q with the Kokhanovsky model.

Fig. 5
Fig. 5

Total spectral quantum efficiency for the two FWA types mixed to different pulps at different concentrations. The spectral density of the D65 illuminant and the relative absorption coefficient of the tetrasulpho FWA shows in which region the quantum efficiency has the most impact on the fluorescence component in that specific illuminant.

Fig. 6
Fig. 6

Quantum efficiency at the 360 nm excitation wavelength for the two FWA types mixed to different pulps at different concentrations.

Fig. 7
Fig. 7

Predicted luminescent radiance factor of an opaque pad of XPM samples, using a constant Q calibrated for the 9 kg / T unfilled sample. s is estimated by extrapolation (method 1) and is constant with FWA concentration.

Fig. 8
Fig. 8

Predicted luminescent radiance factor of an opaque pad of the sheet former samples at two FWA concentrations and two FWA types, using a constant Q calibrated for the 9 kg / T unfilled XPM sample. s is estimated by extrapolation (method 1) and is constant with FWA concentration.

Fig. 9
Fig. 9

Predicted luminescence factor of the 9 kg / T unfilled XPM sample at 80 g / m 2 and for an opaque pad. s is estimated by extrapolation (method 1) and Q is calibrated for the opaque pad of samples. The model fails to predict β L for finite BW with method 1 as parameter estimation method.

Fig. 10
Fig. 10

Predicted luminescence factor of the 9 kg / T unfilled XPM sample at different BW. s is estimated by optimization (method 2) and Q is calibrated for the opaque pad of samples and the 80 g / m 2 sample. The model predicts well β L at 120 g / m 2 . At 40 g / m 2 , the same Q can be used, but k must be adjusted to account for the lower FWA adsorption at this low BW.

Tables (1)

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Table 1 Paper Sample Used in the Study: Forming Unit, BW, FWA Type, FWA Concentration, Filler Concentration, and Fiber Type

Equations (13)

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r ( λ 2 ) = c 1 + c 2 + A + B ( ξ 2 μ 2 ) ,
A = a 2 ( k 1 ) ϕ 12 ( ϵ 2 + s 2 ξ ) , B = b 2 k 1 ϕ 12 ( ϵ 2 + s 2 ξ ) ,
c 1 = q 1 + ( ϵ 2 + μ ) c 2 ϵ 2 + μ , , c 2 = q 1 ( ϵ 1 + μ ) 1 e 2 μ L q 2 e μ L 1 ( ϵ 2 μ ) ( ϵ 2 + μ ) 1 e 2 μ L ,
q 1 = A ( ϵ 2 + ξ ) + B ( ϵ 2 ξ ) ξ 2 μ 2 1 2 k 1 ϕ 12 ( a + b ) s 2 ,
q 2 = A e ξ L + B e ξ L ξ 2 μ 2 ,
a = 1 + r 1 1 r 1 2 e 2 ξ L , b = ( 1 + r 1 ) r 1 2 ξ L 1 r 1 2 e 2 ξ L ,
r 1 = s 1 ϵ 1 + ξ .
k 1 ϕ 12 = ( k 1 k 0 ) Q 12 ,
D ( λ 1 , λ 2 ) = r ( λ 2 ) β R ( λ 2 ) .
β L ( λ 2 | E ) = λ λ < λ 2 D ( λ 1 , λ 2 ) E ( λ 1 ) E ( λ 2 ) ,
r ( λ 2 ) = β R ( λ 2 ) + ( k 1 k 0 ) Q ( 1 + β r ( λ 1 ) ) ( 1 + β r ( λ 2 ) ) 2 ( ξ + μ ) ,
Q 12 = 2 ( ξ + μ ) D ( k 1 k 0 ) ( 1 + β R ( λ 1 ) ) ( 1 + β R ( λ 2 ) ) .
Q tot ( λ 1 ) = λ 2 Q 12 ( λ 1 , λ 2 ) .

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