Abstract

Fiber orientation is an important structural property in paper and other fibrous materials. In this study we explore the relation between light scattering and in-plane fiber orientation in paper sheets. Light diffusion from a focused light source is simulated using a Monte Carlo technique where parameters describing the paper micro-structure were determined from 3D x-ray computed tomography images. Measurements and simulations on both spatially resolved reflectance and transmittance light scattering patterns show an elliptical shape where the main axis is aligned towards the fiber orientation. Good qualitative agreement was found at low intensities and the results indicate that fiber orientation in thin fiber-based materials can be determined using spatially resolved reflectance or transmittance.

© 2014 Optical Society of America

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  1. C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
    [Crossref]
  2. W. Blecha and H. Kent, “On-line fiber orientation distribution measurement,” (1990). US Patent 4,955,720.
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, 1983).
  4. A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
    [Crossref] [PubMed]
  5. A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29, 2617–2619 (2004).
    [Crossref] [PubMed]
  6. A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
    [Crossref] [PubMed]
  7. A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
    [Crossref] [PubMed]
  8. H. He, N. Zeng, R. Liao, T. Yun, W. Li, Y. He, and H. Ma, “Application of sphere-cylinder scattering model to skeletal muscle,” Opt. Express 18, 15104–15112 (2010).
    [Crossref] [PubMed]
  9. A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express 16, 9895–9906 (2008).
    [Crossref] [PubMed]
  10. B. Peng, T. Ding, and P. Wang, “Propagation of polarized light through textile material,” Appl. Opt. 51, 6325–6334 (2012).
    [Crossref] [PubMed]
  11. T. Linder and T. Löfqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B. 105, 659–664 (2011).
    [Crossref]
  12. T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Paper Res. J. 27, 500–506 (2012).
    [Crossref]
  13. T. Linder, T. Löfqvist, L. G. Coppel, M. Neuman, and P. Edström, “Lateral light scattering in fibrous media,” Opt. Express 21, 7835–7840 (2013).
    [Crossref] [PubMed]
  14. M. Axelsson, “Estimating 3d fibre orientation in volume images,” in “Pattern Recognition, 2008. ICPR 2008. 19th International Conference on,” (2008), pp. 1–4.
  15. T. Yun, N. Zeng, W. Li, D. Li, X. Jiang, and H. Ma, “Monte Carlo simulation of polarized photon scattering in anisotropic media,” Opt. Express 17, 16590–16602 (2009).
    [Crossref] [PubMed]
  16. C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, Stockholm, 1996).
  17. K. Saarinen and K. Muinonen, “Light scattering by wood fibers,” Appl. Opt. 40, 5064–5077 (2001).
    [Crossref]
  18. M. Deng and C. T. J. Dodson, Paper: An Engineered Stochastic Structure (Tappi Press, Atlanta, GA, 1994).

2013 (1)

2012 (2)

B. Peng, T. Ding, and P. Wang, “Propagation of polarized light through textile material,” Appl. Opt. 51, 6325–6334 (2012).
[Crossref] [PubMed]

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Paper Res. J. 27, 500–506 (2012).
[Crossref]

2011 (1)

T. Linder and T. Löfqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B. 105, 659–664 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

2006 (1)

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

2001 (1)

1987 (1)

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

Axelsson, M.

M. Axelsson, “Estimating 3d fibre orientation in volume images,” in “Pattern Recognition, 2008. ICPR 2008. 19th International Conference on,” (2008), pp. 1–4.

Bassi, A.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Blecha, W.

W. Blecha and H. Kent, “On-line fiber orientation distribution measurement,” (1990). US Patent 4,955,720.

Bohren, C. F.

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

Comelli, D.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Coppel, L. G.

Crosby, C. M.

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

D’Andrea, C.

Deng, M.

M. Deng and C. T. J. Dodson, Paper: An Engineered Stochastic Structure (Tappi Press, Atlanta, GA, 1994).

Diebolder, R.

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

Ding, T.

Dodson, C. T. J.

M. Deng and C. T. J. Dodson, Paper: An Engineered Stochastic Structure (Tappi Press, Atlanta, GA, 1994).

Edström, P.

Eusufzai, A. R. K.

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

Fellers, C.

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, Stockholm, 1996).

Forster, F. K.

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29, 2617–2619 (2004).
[Crossref] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

Foschum, F.

He, H.

He, Y.

Hibst, R.

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[Crossref] [PubMed]

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29, 2617–2619 (2004).
[Crossref] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

Huffman, D. R.

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

Jiang, X.

Kent, H.

W. Blecha and H. Kent, “On-line fiber orientation distribution measurement,” (1990). US Patent 4,955,720.

Kienle, A.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express 16, 9895–9906 (2008).
[Crossref] [PubMed]

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[Crossref] [PubMed]

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29, 2617–2619 (2004).
[Crossref] [PubMed]

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Li, D.

Li, W.

Liao, R.

Linder, T.

T. Linder, T. Löfqvist, L. G. Coppel, M. Neuman, and P. Edström, “Lateral light scattering in fibrous media,” Opt. Express 21, 7835–7840 (2013).
[Crossref] [PubMed]

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Paper Res. J. 27, 500–506 (2012).
[Crossref]

T. Linder and T. Löfqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B. 105, 659–664 (2011).
[Crossref]

Löfqvist, T.

T. Linder, T. Löfqvist, L. G. Coppel, M. Neuman, and P. Edström, “Lateral light scattering in fibrous media,” Opt. Express 21, 7835–7840 (2013).
[Crossref] [PubMed]

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Paper Res. J. 27, 500–506 (2012).
[Crossref]

T. Linder and T. Löfqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B. 105, 659–664 (2011).
[Crossref]

Ma, H.

Mark, R. E.

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

Muinonen, K.

Neuman, M.

Norman, B.

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, Stockholm, 1996).

Peng, B.

Pifferi, A.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express 16, 9895–9906 (2008).
[Crossref] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Saarinen, K.

Taroni, P.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express 16, 9895–9906 (2008).
[Crossref] [PubMed]

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Wang, P.

Wetzel, C.

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

Yang, C. F.

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

Yun, T.

Zeng, N.

Appl. Opt. (2)

Appl. Phys. B. (1)

T. Linder and T. Löfqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B. 105, 659–664 (2011).
[Crossref]

J. Appl. Polym. Sci. (1)

C. F. Yang, C. M. Crosby, A. R. K. Eusufzai, and R. E. Mark, “Determination of paper sheet fiber orientation distributions by a laser optical diffraction method,” J. Appl. Polym. Sci. 34, 1145–1157 (1987).
[Crossref]

Nord. Pulp Paper Res. J. (1)

T. Linder and T. Löfqvist, “Anisotropic light propagation in paper,” Nord. Pulp Paper Res. J. 27, 500–506 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Med. Biol. (1)

A. Kienle, F. K. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48, N7–N14 (2003).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97, 018104 (2006).
[Crossref] [PubMed]

Other (6)

A. Kienle, C. Wetzel, A. Bassi, D. Comelli, P. Taroni, and A. Pifferi, “Determination of the optical properties of anisotropic biological media using an isotropic diffusion model,” J. Biomed. Opt.12(2007).
[Crossref] [PubMed]

W. Blecha and H. Kent, “On-line fiber orientation distribution measurement,” (1990). US Patent 4,955,720.

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

M. Axelsson, “Estimating 3d fibre orientation in volume images,” in “Pattern Recognition, 2008. ICPR 2008. 19th International Conference on,” (2008), pp. 1–4.

C. Fellers and B. Norman, Pappersteknik, 3rd ed. (Department of Pulp and Paper Chemistry and Technology, Royal Institute of Technology, Stockholm, 1996).

M. Deng and C. T. J. Dodson, Paper: An Engineered Stochastic Structure (Tappi Press, Atlanta, GA, 1994).

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Figures (7)

Fig. 1
Fig. 1 Distribution functions of the fiber alignment estimated with x-ray computerized tomography for each paper sheet in (a). High resolution 2.6 × 2.4 mm2 color image of sample 3 from the reconstructed micro-tomography in (b), can be zoomed on a computer screen.

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Fig. 2
Fig. 2 Illustration of the experimental setup where light from the laser, L, is focused through the lens system, ls, and beam splitter, bs, onto the sample, s. The spatially resolved reflected and transmitted light is detected at camera positions C1 and C2 respectively.

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Fig. 3
Fig. 3 Ellipse where a and b are the major and minor axis respectively and θ is the angle between the ellipse major axis and the machine-direction.

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Fig. 4
Fig. 4 Iso-intensity curves for a measurement point on the paper sheet with the highest degree of fiber alignment, sample 5, in reflectance (a) and transmittance (c). Simulated iso-intensity curves for the corresponding sample is found in (b) and (d), respectively.

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Fig. 5
Fig. 5 Spatially resolved reflectance (a) and transmittance (b) along the x- and y-directions for sample 5. The measured and simulated reflectance is denoted Rm and Rs and the measured and simulated transmittance is denoted Tm and Ts.

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Fig. 6
Fig. 6 Area of the ellipses matched into iso-contour patterns at relative intensity levels 0.01 and 0.001 in (a) and the angle between the ellipse major axis and the machine-direction in (b). The area of the ellipse indicate sample thickness or density is and the major axis angle indicates the variability of the main fiber orientation.

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Fig. 7
Fig. 7 The x-axis show the tensile strength MD/CD ratio and the y-axis show the a/b ratio of the ellipse fitting where the bar is two standard deviation wide. The ratio a/b of 72 measurement points for each of the five paper sheets is taken at relative intensity level 0.001 for reflectance (a) and at relative intensity level 0.01 for transmittance (b).

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Tables (1)

Tables Icon

Table 1 Paper sheet data, area density, tensile strength in the machine-direction, tensile strength in the cross-direction and the ratio between them, all these values where provided by the paper manufacturer.

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Equations (3)

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C a = ρ s A ρ c ,
μ s ( ζ ) = C a d Q s ( ζ ) ,
A x 2 + B x y + C y 2 + D x + E y + F = 0 ,

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