Abstract

In this paper a detailed investigation, based on simulations and experiments of polarized light propagation through textile material, is presented. The fibers in textile material are generally anisotropic with axisymmetric structure. The formalism of anisotropic fiber scattering (AFS) at oblique incidence is first deduced and then, based on this formalism and considered multiscattering, a polarization-dependent Monte Carlo method is employed to simulate the propagation of polarized light in textile material. Taking cotton fiber assemblies as samples, the forward-scattering Mueller matrices are calculated theoretically through the AFS-based simulations and measured experimentally by an improved Mueller matrix polarimeter. Their variations according to sample thickness are discussed primarily. With these matrices polar-decomposed, a further discussion on the optical polarization properties of cotton fiber assemblies (i.e., depolarization Δ, diattenuation D, optical rotation ψ and linear retardance δ) versus the thickness is held. Simultaneously, a meaningful comparison of both the matrices and their polar decomposition, generated from the simulations based on isotropic fiber scattering (IFS), with those simulated based on AFS is made. Results show that the IFS-derived values are strikingly different from those that are AFS-derived due to ignoring the fiber anisotropy. Furthermore, all the AFS-derived results are perfectly consistent with those obtained experimentally, which suggests that the Monte Carlo simulation based on AFS has potential applications for light scattering and propagation in textile material.

© 2012 Optical Society of America

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References

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  1. R. A. Taylor, “Absorption and scatter corrections for transflectance measurements in nonhomogeneous fiber samples,” J. Near Infrared Spectrosc. 6, A35–A44 (1998).
    [CrossRef]
  2. M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
    [CrossRef]
  3. J. A. Thomasson, S. Manickavasagam, and M. P. Menguc, “Cotton fiber quality characterization with light scattering and Fourier transform infrared techniques,” Appl. Spectrosc. 63, 321–330 (2009).
    [CrossRef]
  4. S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
    [CrossRef]
  5. A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
    [CrossRef]
  6. B. D. Cameron, M. J. Rakovic, M. Mehrubeoglu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Cote, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23, 485–487 (1998).
    [CrossRef]
  7. H. H. He, N. Zeng, W. Li, T. L. Yun, R. Liao, Y. H. He, and H. Ma, “Two-dimensional backscattering Mueller matrix of sphere-cylinder scattering medium,” Opt. Lett. 35, 2323–2325 (2010).
    [CrossRef]
  8. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18, 10200–10208 (2010).
    [CrossRef]
  9. 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]
  10. T. L. Yun, N. Zeng, W. Li, D. Z. Li, X. Y. Jiang, and H. Ma, “Monte Carlo simulation of polarized photon scattering in anisotropic media,” Opt. Express 17, 16590–16602 (2009).
    [CrossRef]
  11. W. D. Yu and C. Y. Chu, Textile Physics, 2nd ed. (Donghua, 2009), pp. 175–197.
  12. R. B. Wu and C. H. Chen, “Variational reaction formulation of scattering problem for anisotropic dielectric cylinders,” IEEE Trans. Antennas Propag. 34, 640–645 (1986).
    [CrossRef]
  13. J. C. Monzon, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder a spectral approach,” IEEE Trans. Antennas Propag. 35, 670–682 (1987).
    [CrossRef]
  14. X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
    [CrossRef]
  15. 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]
  16. A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29, 2617–2619 (2004).
    [CrossRef]
  17. T. Linder and T. Lofqvist, “Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium,” Appl. Phys. B: Lasers Opt. 105, 659–664 (2011).
    [CrossRef]
  18. X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
    [CrossRef]
  19. H. H. He, N. Zeng, R. Liao, T. L. Yun, W. Li, Y. H. He, and H. Ma, “Application of sphere-cylinder scattering model to skeletal muscle,” Opt. Express 18, 15104–15112 (2010).
    [CrossRef]
  20. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), p. 530.
  21. L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef]
  22. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: Part I,” Opt. Express 13, 4420–4438(2005).
    [CrossRef]
  23. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, “Laser light scattering in turbid media Part II: Spatial and temporal analysis of individual scattering orders via Monte Carlo simulation,” Opt. Express 17, 13792–13809 (2009).
    [CrossRef]
  24. K. M. Twietmeyer and R. A. Chipman, “Optimization of Mueller matrix polarimeters in the presence of error sources,” Opt. Express 16, 11589–11603 (2008).
    [CrossRef]
  25. M. Mujat and A. Dogariu, “Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transfer 70, 555–567 (2001).
    [CrossRef]
  26. S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
    [CrossRef]
  27. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
    [CrossRef]

2011

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

2010

2009

2008

2006

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

2005

2004

2003

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]

S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
[CrossRef]

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

2002

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

2001

M. Mujat and A. Dogariu, “Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transfer 70, 555–567 (2001).
[CrossRef]

1998

1997

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

1996

1995

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

1987

J. C. Monzon, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder a spectral approach,” IEEE Trans. Antennas Propag. 35, 670–682 (1987).
[CrossRef]

1986

R. B. Wu and C. H. Chen, “Variational reaction formulation of scattering problem for anisotropic dielectric cylinders,” IEEE Trans. Antennas Propag. 34, 640–645 (1986).
[CrossRef]

Antonelli, M. R.

Aslan, M.

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

Benali, A.

Berrocal, E.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), p. 530.

Cameron, B. D.

Chen, C. H.

R. B. Wu and C. H. Chen, “Variational reaction formulation of scattering problem for anisotropic dielectric cylinders,” IEEE Trans. Antennas Propag. 34, 640–645 (1986).
[CrossRef]

Chipman, R. A.

Chu, C.

S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
[CrossRef]

Chu, C. Y.

W. D. Yu and C. Y. Chu, Textile Physics, 2nd ed. (Donghua, 2009), pp. 175–197.

Cote, G. L.

D’Andrea, C.

De Martino, A.

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]

Dogariu, A.

M. Mujat and A. Dogariu, “Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transfer 70, 555–567 (2001).
[CrossRef]

Dupont, D.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

Elias, M.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

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]

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]

Foschum, F.

Gayet, B.

Ghosh, N.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

He, H. H.

He, Y. H.

Hibst, R.

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

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]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), p. 530.

Jacques, S. L.

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: Part I,” Opt. Express 13, 4420–4438(2005).
[CrossRef]

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Jiang, X. Y.

Kattawar, G. W.

Kienle, A.

Li, D. Z.

Li, W.

Liao, R.

Linder, T.

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

Linne, M. A.

Lofqvist, T.

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

Lu, S. Y.

Ma, H.

Manickavasagam, S.

Meglinski, I. V.

Mehrubeoglu, M.

Menguc, M. P.

J. A. Thomasson, S. Manickavasagam, and M. P. Menguc, “Cotton fiber quality characterization with light scattering and Fourier transform infrared techniques,” Appl. Spectrosc. 63, 321–330 (2009).
[CrossRef]

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

Monzon, J. C.

J. C. Monzon, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder a spectral approach,” IEEE Trans. Antennas Propag. 35, 670–682 (1987).
[CrossRef]

Moussa, A.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

Mujat, M.

M. Mujat and A. Dogariu, “Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transfer 70, 555–567 (2001).
[CrossRef]

Novikova, T.

Paciaroni, M. E.

Pierangelo, A.

Pifferi, A.

Prahl, S. A.

Rakovic, M. J.

Ramella-Roman, J. C.

Rastegar, S.

Sedarsky, D. L.

Steen, D.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

Taroni, P.

Taylor, R. A.

R. A. Taylor, “Absorption and scatter corrections for transflectance measurements in nonhomogeneous fiber samples,” J. Near Infrared Spectrosc. 6, A35–A44 (1998).
[CrossRef]

Thomasson, J. A.

J. A. Thomasson, S. Manickavasagam, and M. P. Menguc, “Cotton fiber quality characterization with light scattering and Fourier transform infrared techniques,” Appl. Spectrosc. 63, 321–330 (2009).
[CrossRef]

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

Twietmeyer, K. M.

Validire, P.

Vitkin, I. A.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

Wang, L. H.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Wang, L. H. V.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Wang, L. V.

Wang, X. D.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

Wood, M. F. G.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

Wu, R. B.

R. B. Wu and C. H. Chen, “Variational reaction formulation of scattering problem for anisotropic dielectric cylinders,” IEEE Trans. Antennas Propag. 34, 640–645 (1986).
[CrossRef]

Wu, X. B.

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

Yamada, J.

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

Yan, H.

S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
[CrossRef]

Yasumoto, K.

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

Yu, W. D.

W. D. Yu and C. Y. Chu, Textile Physics, 2nd ed. (Donghua, 2009), pp. 175–197.

Yun, T. L.

Zeng, N.

Zeng, X.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

Zheng, L. Q.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

Zhou, S.

S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
[CrossRef]

Appl. Phys. B: Lasers Opt.

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

Appl. Spectrosc.

Color Res. Appl.

A. Moussa, D. Dupont, D. Steen, X. Zeng, and M. Elias, “Experimental study of backscattering spectrum of textile structures,” Color Res. Appl. 31, 122–132 (2006).
[CrossRef]

Comput. Methods Programs Biomed.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “MCML—Monte-carlo modeling of light transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef]

IEEE Trans. Antennas Propag.

R. B. Wu and C. H. Chen, “Variational reaction formulation of scattering problem for anisotropic dielectric cylinders,” IEEE Trans. Antennas Propag. 34, 640–645 (1986).
[CrossRef]

J. C. Monzon, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder a spectral approach,” IEEE Trans. Antennas Propag. 35, 670–682 (1987).
[CrossRef]

J. Appl. Phys.

X. B. Wu and K. Yasumoto, “Three-dimensional scattering by an infinite homogeneous anisotropic circular cylinder: an analytical solution,” J. Appl. Phys. 82, 1996–2003 (1997).
[CrossRef]

J. Biomed. Opt.

X. D. Wang and L. H. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7, 279–290 (2002).
[CrossRef]

J. Near Infrared Spectrosc.

R. A. Taylor, “Absorption and scatter corrections for transflectance measurements in nonhomogeneous fiber samples,” J. Near Infrared Spectrosc. 6, A35–A44 (1998).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

M. Mujat and A. Dogariu, “Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers,” J. Quant. Spectrosc. Radiat. Transfer 70, 555–567 (2001).
[CrossRef]

J. Thermophys. Heat Transfer

M. Aslan, J. Yamada, M. P. Menguc, and J. A. Thomasson, “Characterization of individual cotton fibers via light-scattering experiments,” J. Thermophys. Heat Transfer 17, 442–449 (2003).
[CrossRef]

Opt. Commun.

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues,” Opt. Commun. 283, 1200–1208 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

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]

Text. Res. J.

S. Zhou, C. Chu, and H. Yan, “Backscattering of light in determining fiber orientation distribution and area density of nonwoven fabrics,” Text. Res. J. 73, 131–138 (2003).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), p. 530.

W. D. Yu and C. Y. Chu, Textile Physics, 2nd ed. (Donghua, 2009), pp. 175–197.

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Figures (5)

Fig. 1.
Fig. 1.

Phase function p(ζ,ϕ) of (a) anisotropy-considered cotton fiber, (b) of anisotropy-neglected cotton fiber, and (c) scattering coefficient μs(ζ) of both fibers. The anisotropy-neglected cotton fiber is an assumption of isotropy, with the axial refractive indices of cotton fiber replaced by its radial refractive index. The scattering coefficient μs(ζ) is determined by the formula in [10] using the values of a diameter 6 μm and a density 80mm2 (number per area).

Fig. 2.
Fig. 2.

(a) Schema of polarized light propagation in textile material and (b) a magnified single scattering of incident photon by a single textile fiber at oblique incidence in the cylindrical coordinate system ρ^ϕ^z^.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Simulated and measured forward-scattering Mueller matrices of cotton fiber assemblies versus layer thickness. The results of Monte Carlo simulations, based on the formalism of AFS (cotton fiber anisotropy considered) and IFS (cotton fiber anisotropy neglected) are plotted respectively by solid lines and dotted lines, while results of experiments are plotted by points. These Mueller matrices, generated from simulations and experiments, are determined by accumulating all the pixel values of the corresponding intensity images with 8mm×8mm in size.

Fig. 5.
Fig. 5.

Optical polarization properties of cotton fiber assemblies versus. layer thickness. The simulated values of depolarization Δ, diattenuation D, optical rotation ψ, and linear retardance δ, based on the formalism of AFS for anisotropy-considered cotton fiber (represented by solid lines) and of IFS for isotropy-assumed cotton fiber (represented by dotted lines), are, respectively, exhibited in (a)–(d), where those that are measured are marked in the corresponding thickness by diamond, asterisk, circle, and square.

Tables (1)

Tables Icon

Table 1. Experimental Forward-scattering Mueller Matrix of Cotton Fiber Assemblies with the Thickness of 2.0 mm (Denoted by M(2.0)) and its Polar Decomposition

Equations (8)

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

{E||s=E0sinζ2πkρsinζejπ4ejk(ρsinζ+zcosζ)·ejnϕ{[ρ^cosζ+z^sinζ]·bnI+θ^·anI}Es=E0sinζ2πkρsinζejπ4ejk(ρsinζ+zcosζ)·ejnϕ{[ρ^cosζ+z^sinζ]·bnII+θ^·anII}{anI=2πτFn(2)Jn(ξ+)/{δHn(2)(τ)}bnI={2πτηFn(1)Jn(ξ)/δsinζJn(τ)}/Hn(2)(τ)anII={sinζJn(τ)2πτηFn(4)Jn(ξ+)/δ}/Hn(2)(τ)bnII=2πτFn(3)Jn(ξ)/{δHn(2)(τ)}δ=Fn(1)·Fn(4)Fn(2)·Fn(3){Fn(1)=jηsinζHn(2)(τ)Jn(ξ+)+gn(1)Jn(ξ+)Fn(2)=cosζ(μεμ0ε)aksin2ζ(μ0εμεcos2ζ)nHn(2)(τ)Jn(ξ)Fn(3)=cosζ(μεμ0ε)aksin2ζ(μ0εμεcos2ζ)nHn(2)(τ)Jn(ξ+)Fn(4)=j1ηsinζHn(2)(τ)Jn(ξ)gn(2)Jn(ξ){gn(1)=jμ0χ+ω(μ0εμεcos2ζ)·Hn(2)(τ)gn(2)=jεχω(μ0εμεcos2ζ)·Hn(2)(τ),
{χ+2=ω2(μ0εμεcos2ζ)χ2=ω2(μ0εμεcos2ζ)ε||/ε(ε||ε){χ+2=ω2(μ0εμεcos2ζ)ε||/εχ2=ω2(μ0εμεcos2ζ)(ε||<ε),
(E||sEs)=1sinζ2πkρsinζejπ4ejk(ρsinζ+zcosζ)(J1J3J4J2)(E||iEi)J1=ejnϕbnIJ3=ejnϕanIJ4=ejnϕbnIIJ2=ejnϕanII.
J(ζ,ϕ)=1sinζ2πkρsinζejπ4ejk(ρsinζ+zcosζ)(J1J3J4J2).
M(ζ,ϕ)=2πkρsin3ζ(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44),m11=12(|J1|2+|J2|2+|J3|2+|J4|2),m12=m21=12(|J1|2|J2|2+|J3|2|J4|2),m13=m31=Re(J1J4*+J3J2*),m14=m41=Im(J4J1*+J2J3*),m22=12(|J1|2+|J2|2|J3|2|J4|2),m23=m32=Re(J1J4*J2J3*),m24=m42=Im(J4J1*+J3J2*),m33=Re(J2J1*+J4J3*),m34=m43=Im(J2J1*+J4J3*),m44=Re(J1J2*J3J4*).
Sre=M·Sin(IreQreUreVre)=(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44)(IinQinUinVin),
(Is,Qs,Us,Vs)T=MnRnM2R2M1R1·(Ii,Qi,Ui,Vi)T(n0),
Δ=1|tr(MΔ)1|3,D=1mD11mD122+mD132+mD142,ψ=12tan1(mR32mR23mR22+mR33),δ=cos1((mR22+mR33)2+(mR32mR23)21),

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