## Full characterization of anisotropic diffuse light.

Optics Express, Vol. 16, Issue 10, pp. 7435-7446 (2008)

http://dx.doi.org/10.1364/OE.16.007435

Acrobat PDF (338 KB)

### Abstract

We demonstrate a method for fully characterizing diffuse transport of light in a statistically anisotropic opaque material. Our technique provides a simple means of determining all parameters governing anisotropic diffusion. Anisotropy in the diffusion constant, the mean free path, and the extrapolation length are, for the first time, determined independently. These results show that the anisotropic diffusion model is effective for modeling transport in anisotropic samples, providing that the light is allowed to travel several times the transport mean free path from the source.

© 2008 Optical Society of America

## 1. Introduction

1. M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. **77**, 2233–2236 (1996). [CrossRef] [PubMed]

2. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved anisotropic multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. **83**, 4321–4324 (1999). [CrossRef]

3. A. Sviridov, V. Chernomordik, M. Hassan, A. Russo, A. Eidsath, P. Smith, and A. H. Gandjbakhche, “Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms,” J. Biomed. Opt. **10**, 014012 (9 pages) (2005). [CrossRef]

4. T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy “Anisotropic photon migration in human skeletal muscle,” Phys. Med. Biol. **51**, N79–N90 (2006). [CrossRef] [PubMed]

5. A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. **97**, 018104 (4 pages) (2006). [CrossRef] [PubMed]

6. S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. **45**, 2873–2886 (2000). [CrossRef] [PubMed]

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

8. C. Baravian, F. Caton, J. Dillet, G. Toussaint, and P. Flaud, “Incoherent light transport in an anisotropic random medium: A probe of human erythrocyte aggregation and deformation,” Phys. Rev. E **76**, 011409 (7 pages) (2007). [CrossRef]

9. P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, “Anisotropic Diffusion of Light in a Strongly Scattering Material,” Phys. Rev. Lett. **89**, 243901 (4 pages) (2002). [CrossRef] [PubMed]

10. B. P. J. Bret and A. Lagendijk, “Anisotropic enhanced backscattering induced by anisotropic diffusion,” Phys. Rev. E **70**, 036601 (5 pages) (2004). [CrossRef]

13. B. A. van Tiggelen, R. Maynard, and A. Heiderich, “Anisotropic light diffusion in oriented nematic liquid crystals,” Phys. Rev. Lett. **77**, 639–642 (1996). [CrossRef] [PubMed]

14. H. Stark and T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. **77**, 2229–2232 (1996). [CrossRef] [PubMed]

12. B. Kaas, B. van Tiggelen, and A. Lagendijk, “Anisotropy and interference in wave transport: An analytic theory,” Phys. Rev. Lett.100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.) [CrossRef]

15. L. Margerin, “Attenuation, transport and diffusion of scalar waves in textured random media,” Tectonophysics **416**, 229–244 (2006). [CrossRef]

16. A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. **58**, 2043–2046 (1987). [CrossRef] [PubMed]

17. A. Lagendijk, R. Vreeker, and P. de Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A **136**, 81–88 (1989). [CrossRef]

18. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A **44**, 3948–3959 (1991). [CrossRef] [PubMed]

19. L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, “Effects ofanisotropic optical properties on photon migration in structured tissues,” Phys. Med. Biol. **48**, 1361–1370 (2003). [CrossRef] [PubMed]

11. B. van Tiggelen and H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. **72**, 1017–1039 (2000). [CrossRef]

20. J. Heino, S. Arridge, J. Sikora, and E. Somersalo, “Anisotropic effects in highly scattering media,” Phys. Rev. E **68**, 031908 (8 pages) (2003). [CrossRef]

12. B. Kaas, B. van Tiggelen, and A. Lagendijk, “Anisotropy and interference in wave transport: An analytic theory,” Phys. Rev. Lett.100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.) [CrossRef]

20. J. Heino, S. Arridge, J. Sikora, and E. Somersalo, “Anisotropic effects in highly scattering media,” Phys. Rev. E **68**, 031908 (8 pages) (2003). [CrossRef]

21. A. Kienle, “Anisotropic light diffusion: An oxymoron?” Phys. Rev. Lett. **98**, 218104 (4 pages) (2007). [CrossRef] [PubMed]

21. A. Kienle, “Anisotropic light diffusion: An oxymoron?” Phys. Rev. Lett. **98**, 218104 (4 pages) (2007). [CrossRef] [PubMed]

2. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved anisotropic multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. **83**, 4321–4324 (1999). [CrossRef]

22. J. Taniguchi, H. Murata, and Y. Okamura, “Light diffusion model for determination of optical properties of rectangular parallelepiped highly scattering media,” Appl. Opt. **46**, 2649–2655 (2007). [CrossRef] [PubMed]

## 2. Theory

*L*. The dimensions of the sample are

*d*,

*w*

_{1}, and

*w*

_{2}where the image plane dimensions are

*w*

_{1}×

*w*

_{2}and the input plane dimensions are

*d*×

*w*

_{2}.

11. B. van Tiggelen and H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. **72**, 1017–1039 (2000). [CrossRef]

12. B. Kaas, B. van Tiggelen, and A. Lagendijk, “Anisotropy and interference in wave transport: An analytic theory,” Phys. Rev. Lett.100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.) [CrossRef]

*U*is the energy density,

*D̅*is the anisotropic diffusion tensor,

*S*is the function describing the source of diffuse light, and

*l̅*is the anisotropic mean free path tensor. We assume the symmetry of the sample to be such that the diffusion and mean free path tensors are diagonalized in the sample coordinate system. I.e.

*l*inside the material [25

_{yy}25. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent Backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. **56**, 1471–1474 (1986). [CrossRef] [PubMed]

*e*from the boundary [17

_{x,y,z}17. A. Lagendijk, R. Vreeker, and P. de Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A **136**, 81–88 (1989). [CrossRef]

18. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A **44**, 3948–3959 (1991). [CrossRef] [PubMed]

*x*-

*z*plane is

*l*+

_{yy}*e*.

_{y}*x*′=(

*D*/

_{yy}*D*)

_{xx}^{1/2}

*x*,

*y*′=

*y*+

*e*,

_{y}*z*′=(

*D*/

_{yy}*D*)

_{zz}^{1/2}(

*z*+

*e*),

_{z}*L*′=(

*D*/

_{yy}*D*)

_{zz}^{1/2}(

*L*+

*e*), and

_{z}*D*′=(

*D*/

_{xx}*D*)

_{zz}^{1/2}, the anisotropic diffusion equation can be rewritten as an isotropic diffusion equation:

*U*=0 at

*x*′=±∞,

*y*′=0,+∞, and

*z*′=0,+∞.

*I*(

*x*,

*y*,0) through the

*z*=0 surface for light governed by Eq. 5 has been solved analytically by Kienle in his treatment of isotropic media [24

24. A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A **22**, 1883–1888 (2005). [CrossRef]

*l*′/

*L*′≪1,

*e*/

_{y}*L*′≪1,

*L*/

*d*≪1, and

*L*/

*w*

_{1,2}≪1, the flux through the

*z*=0 surface may be approximated as:

*I*(

*x*,

*y*,0) may be integrated over the image plane to yield the total intensity exiting the side of the sample:

*l*+

_{yy}*e*)/(

_{y}*L*+

*e*). This result is similar to the result for total transmission through an optically thick infinite slab, which is a well known measurement for determining the mean free path from a series of the sample of different thicknesses [16

_{z}16. A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. **58**, 2043–2046 (1987). [CrossRef] [PubMed]

*single*sample and the sample may be anisotropic.

*β*=(

*D*/

_{xx}*D*)

_{yy}^{1/2}and

*A*,

*β*,

*e*,and

_{y}*L*′ define the measured image completely. After fitting an image,

*I*is calculated from the four parameters analytically. The parameters

_{tot}*I*,

_{tot}*β*,

*e*,and

_{y}*L*′ describe qualitatively different aspects of the image, namely the overall intensity, the rescaling factor in the

*x*-

*y*plane, the

*I*=0 line of the function (at

*y*=-

*e*, outside of the image), and the extent (size) of the image, respectively. It should be emphasized that

_{y}*e*can be determined directly from the fit with no assumptions about the surface reflectitivity and no knowledge of the incoming intensity, a considerable advantage over escape function measurements [26

_{y}26. M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E **53**, 3215–3224 (1996). [CrossRef]

22. J. Taniguchi, H. Murata, and Y. Okamura, “Light diffusion model for determination of optical properties of rectangular parallelepiped highly scattering media,” Appl. Opt. **46**, 2649–2655 (2007). [CrossRef] [PubMed]

*z*axis with respect to the other (see Fig. 1). We refer to the orientation with the beam entering along the fast axis of diffusion as the parallel orientation and the orientation with the beam along the slow axis of diffusion as the perpendicular orientation with parameters along these beam axes subscripted with the symbols ‖ and ⊥ respectively. Thus for example,

*D*

_{‖}>

*D*

_{⊥}. The symmetry of the scatterers is such that the sample may be assumed to be uniaxial, therefore the parameters

*D*

_{‖,⊥},

*l*

_{‖,⊥}, and

*e*

_{‖,⊥}will be sufficient to fully characterize the sample.

*S*

_{0}, and

*D*, are the same for both orientations, the ratio of the plots of

_{zz}*I*vs.

_{tot}*L*+

*e*will yield

_{z}*L*≪

*d*is pushed at the largest depth measured in the experiments presented here for which

*L*=0.45

*d*. However the approximation of an infinite sample is nearly valid, even at these depths, affecting the value of

*β*by several percent and the total intensity by 10%. At

*L*=0.25

*d*, the approximation is nearly perfect. For the measurements of total intensity in this paper it is sufficient to make a second order correction in

*L*/

*d*for the larger values of

*L*, using the function

*f*(

*L*/

*d*)=(4(

*L*/

*d*)

^{2}-1)/(4(

*L*/

*d*)

^{2}-3), where

## 3. Experiment

27. J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, “Experimental evaluation of an anisotropic scattering model of a slab geometry,” Opt. Lett. **29**, 2518–2520 (2004). [CrossRef] [PubMed]

27. J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, “Experimental evaluation of an anisotropic scattering model of a slab geometry,” Opt. Lett. **29**, 2518–2520 (2004). [CrossRef] [PubMed]

*µ*m and a density of 0.37 g/cm

^{3}, as listed by the manufacturer. This corresponds to a volume fraction of polymer of roughly 30% or less, depending on the exact density of the polymer (which was unknown).

*w*

_{1}×

*w*

_{2}=(12×42) mm

^{2}and (42×12) mm

^{2}for the beam oriented parallel and perpendicular to the fibers respectively. For both ordinations,

*d*=5 mm.

*µ*m onto on the input side sample (Fig. 1). The sample was mounted on a two-axis translation stage so that several locations on the sample could be probed for each value of

*L*, via translation along the

*x*axis, in order to determine the measurement statistics. The value of

*L*was adjusted by hand in 250

*µ*m increments. The light escaping the image plane was imaged using peltier-cooled CCD (Andor iXon DV885JCS) equipped with a short range (3 cm) camera lens. By varying the the input beam intensity as well as the exposure time a wide dynamic range of measurements could be detected, allowing for a wide range of

*L*values to be measured. Iso-intensity plots of these images are shown in Fig. 3 for orientations of the sample with the fibers parallel and perpendicular to the incoming beam.

*A*,

*β*,

*e*,and

_{y}*L*′, from which

*I*was calculated. An examples of the data and fit for a single value of

_{tot}*L*can be seen in Fig. 3. The overlap of the fit with the data is excellent.

*L*yielded values for the parameters for all thicknesses. This process allowed us to determine the validity of the diffusion approximation as function of

*L*.

28. F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science **284**, 141–143 (1999). [CrossRef] [PubMed]

^{2}with thicknesses of 5 mm and 2.5 mm for the incoming beam parallel and perpendicular to the fibers respectively.

## 4. Results

*L*>0.75 mm, the data is in strong agreement with the diffusion model. Fig. 3 shows an iso-intensity plot for the data and the fit to the diffusion model for both the parallel and perpendicular orientations for one sample thickness (

*L*=2.0 mm). Fig. 4 is a 1d slice of the same data along the

*y*axis at the

*x*=0 (source) position. Both of these representations convey the high quality of the fit. The residual is zero over the entire area of the fit showing only a random deviation due to surface roughness of the sample. Remarkably, the fit extends even to distances near the edge shorter than the mean free path.

*D̅*,

*l̅*, and

*e*on the data and fit. 1) The anisotropy in the contours, lengthened for both orientations along the direction of the fibers, indicates the anisotropy in the diffusion constant tensor, i.e.

_{y}*D*

_{‖}>

*D*

_{⊥}. 2) The integrated intensity with the input beam parallel to the fibers is higher, indicating the anisotropy of the mean free path tensor along this direction, i.e.

*l*

_{‖}>

*l*

_{⊥}. 3) The data and fit extend off of the edge of the sample, into the

*y*<0 region (i.e. the lower intensity contours in Fig. 3 are not closed but come to an abrupt end at the edge of the sample, and the function in Fig. 4(inset) clearly has a

*y*<0 intercept) indicating the effect of the extrapolation length at the input plane, which is larger along the direction parallel to the fibers, i.e.

*e*

_{‖}>

*e*

_{⊥}.

*L*. These are plotted in Fig. 5 for all values of

*L*measured. Multiple points at each value of

*L*indicate multiple measurements at different translations in the

*x*direction. The reproducibility of these measurements for sufficiently large values of

*L*is evident from the overlap of multiple data points.

*β*

_{‖,⊥}and

*e*

_{‖,⊥}plateau at thicknesses greater than

*L*>

*L*where

_{min}*L*=0.75 mm. For values of

_{min}*L*≤

*L*, it is likely that a non-diffuse contribution from the incoming beam is still present that is not accounted for by the diffusion model. This result suggests a useful length scale for applicability of the diffusion approximation.

_{min}*β*

_{‖,⊥}and

*e*

_{‖,⊥}are taken from the plots in Fig. 5a and Fig. 5b by averaging the results for

*L*>0.75 mm. The uncertainty is the standard deviation of the data points. The values for

*β*

_{‖}, 1/

*β*

_{‖}, and

*β*

_{⊥}at

*L*>0.75 are 1.84±.04, 0.54±.01 and 0.53±.02 respectively. These values are consistent, to within the experimental uncertainty, to the simple relation 1/

*β*

_{‖}=

*β*

_{⊥}, and yield a value of

*D*

_{⊥}/

*D*

_{‖}=0.28±.01. The values for the extrapolation lengths

*e*

_{‖}and

*e*

_{⊥}are (0.34±.04) mm and (0.10±.01)mm respectively. Note that the ratio of the extrapolation lengths is

*e*

_{⊥}/

*e*

_{‖}=0.29±.03.

*d*=5 mm and the value for

*e*=

_{z}*e*

_{⊥}=(0.10±.01) mm

*D*

_{⊥}/

*D*

_{‖}=0.28±.01 determined from Fig. 5b. This yields the ratio (

*l*

_{⊥}+

*e*

_{⊥})/(

*l*

_{‖}+

*e*

_{‖})=0.28±.03. Inserting the values of

*e*

_{‖}and

*e*

_{⊥}gives

*l*

_{⊥}=(0.28±0.03)

*l*

_{‖}±0.01 mm, which, assuming that the mean free paths are not anomolously small, gives

*l*

_{⊥}/

*l*

_{‖}=0.28 to within 10%.

*l*

_{⊥}+

*e*

_{⊥}=(0.25±0.02) mm and

*l*

_{‖}+

*e*

_{‖}=(0.93±0.04) mm, yielding (

*l*

_{⊥}+

*e*

_{⊥})/(

*l*

_{‖}+

*e*

_{‖})=0.27±.03. Combining these results with the results for the extrapolation lengths gives

*l*

_{⊥}=0.15±0.02mm

*l*

_{‖}=(0.59±0.06) mm and

*l*

_{⊥}/

*l*

_{‖}=(0.25±0.03). These results are fully consistent with those using the imaging approach. Furthermore they allow us to express

*L*in term of the mean free path, namely,

_{min}*L*=5

_{min}*l*

_{⊥}=1.3

*l*

_{‖}.

## 5. Discussion

26. M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E **53**, 3215–3224 (1996). [CrossRef]

2. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved anisotropic multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. **83**, 4321–4324 (1999). [CrossRef]

**83**, 4321–4324 (1999). [CrossRef]

11. B. van Tiggelen and H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. **72**, 1017–1039 (2000). [CrossRef]

## Acknowledgments

## References and links

1. | M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. |

2. | D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved anisotropic multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. |

3. | A. Sviridov, V. Chernomordik, M. Hassan, A. Russo, A. Eidsath, P. Smith, and A. H. Gandjbakhche, “Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms,” J. Biomed. Opt. |

4. | T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy “Anisotropic photon migration in human skeletal muscle,” Phys. Med. Biol. |

5. | A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. |

6. | S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, “Anisotropy of light propagation in human skin,” Phys. Med. Biol. |

7. | A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. |

8. | C. Baravian, F. Caton, J. Dillet, G. Toussaint, and P. Flaud, “Incoherent light transport in an anisotropic random medium: A probe of human erythrocyte aggregation and deformation,” Phys. Rev. E |

9. | P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, “Anisotropic Diffusion of Light in a Strongly Scattering Material,” Phys. Rev. Lett. |

10. | B. P. J. Bret and A. Lagendijk, “Anisotropic enhanced backscattering induced by anisotropic diffusion,” Phys. Rev. E |

11. | B. van Tiggelen and H. Stark, “Nematic liquid crystals as a new challenge for radiative transfer,” Rev. Mod. Phys. |

12. | B. Kaas, B. van Tiggelen, and A. Lagendijk, “Anisotropy and interference in wave transport: An analytic theory,” Phys. Rev. Lett.100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.) [CrossRef] |

13. | B. A. van Tiggelen, R. Maynard, and A. Heiderich, “Anisotropic light diffusion in oriented nematic liquid crystals,” Phys. Rev. Lett. |

14. | H. Stark and T. C. Lubensky, “Multiple light scattering in nematic liquid crystals,” Phys. Rev. Lett. |

15. | L. Margerin, “Attenuation, transport and diffusion of scalar waves in textured random media,” Tectonophysics |

16. | A. Z. Genack, “Optical transmission in disordered media,” Phys. Rev. Lett. |

17. | A. Lagendijk, R. Vreeker, and P. de Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A |

18. | J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A |

19. | L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, “Effects ofanisotropic optical properties on photon migration in structured tissues,” Phys. Med. Biol. |

20. | J. Heino, S. Arridge, J. Sikora, and E. Somersalo, “Anisotropic effects in highly scattering media,” Phys. Rev. E |

21. | A. Kienle, “Anisotropic light diffusion: An oxymoron?” Phys. Rev. Lett. |

22. | J. Taniguchi, H. Murata, and Y. Okamura, “Light diffusion model for determination of optical properties of rectangular parallelepiped highly scattering media,” Appl. Opt. |

23. | The effect of absorption has been treated for the isotropic case in reference [24]. For the samples studied here, the expressions given sufficiently described the data without the inclusion of absorption. |

24. | A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A |

25. | E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent Backscattering of light by disordered media: Analysis of the peak line shape,” Phys. Rev. Lett. |

26. | M. U. Vera and D. J. Durian, “Angular distribution of diffusely transmitted light,” Phys. Rev. E |

27. | J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, “Experimental evaluation of an anisotropic scattering model of a slab geometry,” Opt. Lett. |

28. | F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, “Strongly photonic macroporous gallium phosphide networks,” Science |

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: March 31, 2008

Revised Manuscript: May 3, 2008

Manuscript Accepted: May 6, 2008

Published: May 7, 2008

**Citation**

P. M. Johnson, Sanli Faez, and Ad Lagendijk, "Full characterization of anisotropic diffuse light," Opt. Express **16**, 7435-7446 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7435

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### References

- M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996). [CrossRef] [PubMed]
- D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999). [CrossRef]
- A. Sviridov, V. Chernomordik, M. Hassan, A. Russo, A. Eidsath, P. Smith, and A. H. Gandjbakhche, "Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms," J. Biomed. Opt. 10, 014012 (9 pages) (2005). [CrossRef]
- T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006). [CrossRef] [PubMed]
- A. Kienle and R. Hibst, "Light guiding in biological tissue due to scattering," Phys. Rev. Lett. 97, 018104 (4 pages) (2006). [CrossRef] [PubMed]
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