Abstract

Here we are concerned with the systematic study of polarized light transport in thick, isotropic, homogeneous random media and of the associated inverse problem. An original spatial and intensity rescaling of the polarization transport allows one to account implicitly for the volume fraction. This parameter elimination permits a complete exploration, by means of Monte Carlo simulations of the dependence of polarized light transport on microscopic parameters. Analysis of the Mueller matrices obtained from the simulations show that additional correlations (with respect to scalar transport) are obtained between the microscopic parameters and the spatial distribution of specific elements of the Mueller matrix. As a consequence, using carefully chosen polarization states, one can determine an average particle size independently of the volume fraction of particles, with only the knowledge of the refractive-index ratio being required. This analysis is validated with experimental Mueller matrices obtained for emulsions of various size, concentration, and polydispersity.

© 2006 Optical Society of America

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  12. P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
    [CrossRef]
  13. P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
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    [CrossRef]
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    [CrossRef]
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2005 (1)

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

2004 (2)

C. Baravian, F. Caton, and J. Dillet, "Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions," Rheol. Acta 43, 427-432 (2004).
[CrossRef]

D. Lacoste, V. Rossetto, F. Jaillon, and H. Saint-Jalmes, "Geometric depolarization in patterns formed by backscattered light," Opt. Lett. 29, 2040-2042 (2004).
[CrossRef] [PubMed]

2003 (3)

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, "Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase," Appl. Opt. 42, 4389-4395 (2003).
[CrossRef] [PubMed]

2002 (3)

X. Wang, and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A Pure Appl. Opt. 2, 216-222 (2002).
[CrossRef]

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

A. D. Gopal and D. J. Durian, "Shear-induced "melting" of an aqueous foam," J. Colloid Interface Sci. 213, 169-178 (1999)
[CrossRef] [PubMed]

1998 (2)

1997 (5)

1996 (1)

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, "Monte Carlo modeling of transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

1994 (1)

1992 (1)

1991 (1)

R. R. Anderson, "Polarized light examination and photography of the skin," Arch. Dermatol. 127, 1000-1005 (1991).
[CrossRef] [PubMed]

Anderson, R. R.

R. R. Anderson, "Polarized light examination and photography of the skin," Arch. Dermatol. 127, 1000-1005 (1991).
[CrossRef] [PubMed]

Anumula, H.

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

Asakura, T.

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Baba, J. S.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Baravian, C.

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

C. Baravian, F. Caton, and J. Dillet, "Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions," Rheol. Acta 43, 427-432 (2004).
[CrossRef]

Bartel, S.

Baum, B. A.

Bigio, I. J.

Bohren, C. F.

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

Bonner, R. F.

Boreman, G.

Bueno, J. M.

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A Pure Appl. Opt. 2, 216-222 (2002).
[CrossRef]

Cameron, B. D.

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

B. D. Cameron, M. J. Rakovic, M. Mehrübeoǧlu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, "Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium," Opt. Lett. 23, 485-487 (1998).
[CrossRef]

Cariou, J.

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

Caton, F.

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

C. Baravian, F. Caton, and J. Dillet, "Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions," Rheol. Acta 43, 427-432 (2004).
[CrossRef]

Chung, J.-R.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Coté, G. L.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

B. D. Cameron, M. J. Rakovic, M. Mehrübeoǧlu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, "Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium," Opt. Lett. 23, 485-487 (1998).
[CrossRef]

DeLaughter, A. H.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

Dillet, J.

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

C. Baravian, F. Caton, and J. Dillet, "Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions," Rheol. Acta 43, 427-432 (2004).
[CrossRef]

Dogariu, A.

Dogariu, M.

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Durian, D. J.

A. D. Gopal and D. J. Durian, "Shear-induced "melting" of an aqueous foam," J. Colloid Interface Sci. 213, 169-178 (1999)
[CrossRef] [PubMed]

Eick, A. A.

Elies, P.

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

Eliès, P.

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

Feng, T.-C.

Freyer, J. P.

Gandjbakhche, A. H.

Gerligand, P. Y.

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

Gopal, A. D.

A. D. Gopal and D. J. Durian, "Shear-induced "melting" of an aqueous foam," J. Colloid Interface Sci. 213, 169-178 (1999)
[CrossRef] [PubMed]

Gutsche, A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

Haskell, R. C.

Hielscher, A. H.

Hostetler, C. A.

Hu, Y. X.

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, 1997).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, "Monte Carlo modeling of transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

Jaillon, F.

Kattawar, G. W.

Kienle, A.

Kutsche, C.

Lacoste, D.

Le Jeune, B.

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

Le Roy-Brehonnet, F.

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

Li, Y.

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

Likamwa, P.

Lotrian, J.

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

McAdams, M. S.

Mehrübeoglu, M.

Moudgil, B.

Mougel, J.

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

Mourant, J. R.

Nezhuvingal, A. A.

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

Patterson, M. S.

Rakovic, M. J.

Rastegar, S.

Rossetto, V.

Saint-Jalmes, H.

Schmitt, J. M.

Schwartz, J. A.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

Shen, D.

Sun, C.-W.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Svaasand, L. O.

Tittel, F. K.

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

Tromberg, B. J.

Tsay, T.-T.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, "Monte Carlo modeling of transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

Wang, L. V.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang, and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

B. D. Cameron, M. J. Rakovic, M. Mehrübeoǧlu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, "Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium," Opt. Lett. 23, 485-487 (1998).
[CrossRef]

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

Wang, X.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang, and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

Wei, H.

Winker, D. M.

Yang, C.-C.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Yang, P.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, "Monte Carlo modeling of transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

Appl. Opt. (4)

Arch. Dermatol. (1)

R. R. Anderson, "Polarized light examination and photography of the skin," Arch. Dermatol. 127, 1000-1005 (1991).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, "Monte Carlo modeling of transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

J. Biomed. Opt. (3)

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, "Development and calibration of an automated Mueller matrix polarization imaging system," J. Biomed. Opt. 7, 341-349 (2002).
[CrossRef] [PubMed]

X. Wang, and L. V. Wang, "Propagation of polarized light in birefringent turbid media: a Monte Carlo study," J. Biomed. Opt. 7, 279-290 (2002).
[CrossRef] [PubMed]

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (1)

A. D. Gopal and D. J. Durian, "Shear-induced "melting" of an aqueous foam," J. Colloid Interface Sci. 213, 169-178 (1999)
[CrossRef] [PubMed]

J. Opt. A Pure Appl. Opt. (1)

J. M. Bueno, "Polarimetry using liquid-crystal variable retarders: theory and calibration," J. Opt. A Pure Appl. Opt. 2, 216-222 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. D (2)

P. Elies, B. Le Jeune, F. Le Roy-Brehonnet, J. Cariou, and J. Lotrian, "Experimental investigation of the speckle polarization for a polished aluminium sample," J. Phys. D 30, 29-39 (1997).
[CrossRef]

P. Eliès, B. Le Jeune, P. Y. Gerligand, J. Cariou, and J. Lotrian, "Analysis of the dispersion of speckle polarization on the Poincaré sphere," J. Phys. D 30, 1285-1292 (1997).
[CrossRef]

Opt. Eng. (1)

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (1)

C. Baravian, F. Caton, J. Dillet, and J. Mougel, "Steady light transport under flow: characterization of evolving dense random media," Phys. Rev. E 71, 066603 (2005).
[CrossRef]

Proc. SPIE (1)

A. A. Nezhuvingal, Y. Li, H. Anumula, and B. D. Cameron, "Mueller matrix optical imaging with application to tissue diagnostics," in Laser-Tissue Interaction XIV, S. L. Jacques, D. D. Duncan, S. J. Kirkpatrick, and A. Kriste, eds., Proc. SPIE 4961, 137-146 (2003).
[CrossRef]

Rheol. Acta (1)

C. Baravian, F. Caton, and J. Dillet, "Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions," Rheol. Acta 43, 427-432 (2004).
[CrossRef]

Other (3)

S. L. Jacques, A. Gutsche, J. A. Schwartz, L. V. Wang, and F. K. Tittel, "Video reflectometry to specify optical properties of tissue in vivo," in Medical Optical Tomography: Functional Imaging and Monitoring, G.J.Mueller, B.Chance, R.R.Alfano, S.R.Arridge, J.Beuthan, E.Gratton, M.F.Kaschke, B.R.Masters, S.Svanberg, and P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (SPIE Press, (1993), pp. 211-226.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, 1997).

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

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Figures (13)

Fig. 1
Fig. 1

Experimental setup: L.D., laser diode, 635 nm 5 mW; O., focusing optic, L., linear polarizer; R.1, R.2, R.3, R.4, liquid crystal retarders; M., polarization-maintaining mirror; M.S, polarization-maintaining semitransparent mirror; S, tested sample; C., CCD camera.

Fig. 2
Fig. 2

Example of LCR calibration for the right circularly polarized state of the generator.

Fig. 3
Fig. 3

Mastersizer X radii distribution for the six emulsions.

Fig. 4
Fig. 4

(a) Adjustment of the diffusion model [Eq. (2)] to the radial intensity decrease in M 11 of Fig. 11(b). Emulsion 2, concentration of 2%; ∘, experiment; continuous curve, diffusion model with l TR = 0.52 mm. (b) Rescaling of experimental data from successive dilutions of emulsion 4: ∘, 1.1%; Δ, 1.6%, −, 2.4%; +, 3.7%; ♢, 5.5%. The continuous curve represents the diffusion model.

Fig. 5
Fig. 5

Conventions for the axes and angles in the Monte Carlo simulations.

Fig. 6
Fig. 6

Radial normalized intensity of M 11 in Monte Carlo simulations for various values of x and m. Solid curve, the diffusion model [Eq. (2)].

Fig. 7
Fig. 7

Normalized intensity variation for a simulation with m = 1.10 and x = 3.00: (a) M 11 and M 44, radial variation; (b)–(f) angular variation of intensity at a radius of l TR ± l TR∕10 for the other nonzero elements.

Fig. 8
Fig. 8

Information contained in element M 44. (a) Schematic radial variation of M 44, (b) radial variation of M 44 for x = 3.00 and m = 1.10; (d) correlation among x 2, x 2, and y 3; +, m = 0.75; ∘, m = 0.90; •, m = 1.10; ×, m = 1.20; Δ, m = 1.30; ♢, m = 1.50; □, m = 1.80.

Fig. 9
Fig. 9

Amplitudes and offsets for elements with angular variation in the normalized intensity: (a) amplitude of M 12; (b) offset of M 12; (c) amplitude of M 22; (d) offset of M 22; (e) amplitude of M 23; (f) offset of M 23; +, m = 0.75; ∘, m = 0.90; •, m = 1.10; ×, m = 1.20; Δ, m = 1.30; ♢, m = 1.50; □, m = 1.80.

Fig. 10
Fig. 10

Comparison between significant parameters in Fig. 9. (a), (b), (c) Comparison of pattern variation and (d) x 3 of M 44 versus offset of M 22: +, m = 0.75; ∘, m = 0.90; •, m = 1.10; ×, m = 1.20; Δ, m = 1.30; ♢, m = 1.50; □ , m = 1.80.

Fig. 11
Fig. 11

Comparison of simulated and experimental Mueller matrices in normalized representation. The image size is 10l TR. (a) Monte Carlo simulation m = 1.10 and x = 3.00 and (b) experimental Mueller matrix for emulsion 2 with a concentration of 2% and a mean radius of 220 nm.

Fig. 12
Fig. 12

Comparison of the angular intensity variations for each element of the experimental and simulated Mueller matrix: —, Monte Carlo simulation; •, experimental results for emulsion 2 with l TR = 0.52 mm and 220 nm and a concentration of 2%.

Fig. 13
Fig. 13

Size determination of (a) amplitude of M 12 versus particle radius; (b) offset of M 22 versus particle radius; •, Monte Carlo simulation; ×, emulsion 1; +, emulsion 2; Δ, emulsion 3; □, emulsion 4; ∘, emulsion 5; ♢, emulsion 6. (c) Amplitude of M 12 for emulsion 4 versus concentration. The line corresponds to x = 4 in the Monte Carlo simulation. (d) Offset of M 22 for emulsion 2 and emulsion 4 versus concentration. The line corresponds to x = 4 in Monte Carlo simulation.

Tables (2)

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Table 1 Emulsion Characteristics

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Table 2 Macroscopic Characteristics of the Studied Emulsions a

Equations (7)

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I = A M G = ( 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 ) M ( 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 ) .
R ( ρ ) = 1 l TR             2 ( 0.0398 [ 1 + ( ρ / l TR ) 2 ] 3 / 2 + 0.0928 [ 5.444 + ( ρ / l TR ) 2 ] 3 / 2 + 0.0597 { 1 [ 1 + ( ρ / l TR ) 2 ] 1 / 2 1 [ 5.444 + ( ρ / l TR ) 2 ] 1 / 2 } ) .
l TR ( x , m , ϕ ) = l s ( x , m , ϕ ) 1 g ( x , m ) = 4 π a 3 3 ϕ C scat ( x , m ) [ 1 g ( x , m ) ] ,
M 12 = M 21 = M 31 [ π / 4 ] = M 13 [ π / 4 ] ,                      
M 22 = M 33 [ π / 4 ] , M 32 = M 23 ,
M 34 = M 43 [ π / 2 ] = M 24 [ π / 4 ] = M 42 [ π / 4 ] ,
M 14 = M 41 = 0,

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