## Backscattered speckle size as a function of polarization: influence of particle-size and -concentration

Optics Express, Vol. 13, Issue 13, pp. 5030-5039 (2005)

http://dx.doi.org/10.1364/OPEX.13.005030

Acrobat PDF (214 KB)

### Abstract

This report about backscattering measurements of the speckle produced by strongly-scattering liquid media shows that the size of the backscattered speckle depends on scattering and anisotropy coefficients. These measurements were aimed at assessing the effects of polarization characteristics of the incident laser beam and of the scattered light on speckle size. The samples under study consisted of monodisperse polystyrene microspheres in solutions, mixtures of different sized-microspheres, milk, blood and pig skin. Such measurements of speckle size in polarization give information on strongly scattering media, allow their discrimination and enable one to characterize the undergone changes.

© 2005 Optical Society of America

## 1. Introduction

1. K. Ishii, T. Iwai, S. Wada, and M. Miyakoshi, “Simultaneous viscometry and particle sizing on the basis of dynamic light scattering,” Proc. SPIE **4263**, 112–121 (2001). [CrossRef]

2. D.A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A **14**, 192–215 (1997). [CrossRef]

3. J.D. Briers, G. Richards, and X. W. He, “Capillary blood flow monitoring using laser speckle contrast analysis (LASCA),” J. Biomed. Opt. **4**, 164–175 (1999). [CrossRef]

*i.e.*the scattering, absorption and anisotropy coefficients denoted

*µ*

_{s},

*µ*

_{a}and

*g*, respectively [5]. So, in a previous study of transmission through weakly-scattering media, we showed that the speckle size is affected not only by

*µ*

_{s}, but also by the scatterer dimensions [6

6. Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express **12**, 176–188 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176 [CrossRef] [PubMed]

7. 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]

8. J. Li, G. Yao, and L.V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. **7**, 307–312 (2002). [CrossRef] [PubMed]

9. D.A. Zimnyakov, V.V. Tuchin, K.V. Larin, and A.A. Mishin, “Speckle patterns polarization analysis as an approach to turbid tissues structure monitoring,” Proc. SPIE **2981**, 172–180 (1997). [CrossRef]

## 2. Experimental method

*x*,

*y*). This function, denoted

*c*

_{I}(Δ

*x*, Δ

*y*), corresponds to the normalized autocorrelation function of the intensity; it has a zero base, and its width provides a reasonable measurement of the “average width” of a speckle [10];

*c*

_{I}(Δ

*x*, Δ

*y*) is calculated from the intensity distribution of the measured speckle,

*I*, as described in [6

6. Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express **12**, 176–188 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176 [CrossRef] [PubMed]

*FT*is the Fourier Transform, < > is a spatial average,

*c*

_{I}(Δ

*x*,0) and

*c*

_{I}(0, Δ

*y*) are the horizontal and the vertical profiles of

*c*

_{I}(Δ

*x*, Δ

*y*), respectively.

*c*

_{I}(Δ

*x*, 0) so that

*c*

_{I}(

*d*

_{x}/2, 0)=0.5 and

*dy*the width of

*c*

_{I}(0, Δ

*y*) such as

*c*

_{I}(0,

*dy*/2)=0.5.

*I*

_{0}/

*e*

^{2}where

*I*

_{0}is the maximum laser intensity at the 632.8 nm wavelength with a coherence length of about 20 cm.

11. Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, “Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,” Appl. Opt. **33**, 8240–8250 (1994). [CrossRef] [PubMed]

*D*) from the CCD camera.

*θ*=45° between the CCD camera and the optical axis (see Fig. 1). The value of

*θ*was chosen to prevent the measurement from being spoilt by specular reflections from the surface of sample like skin. As previous measurements had taught us that varying

*θ*affected

*dy*(vertical speckle size) by slight changes contrarily to those undergone by

*dx*(horizontal speckle size), we decided to use

*dy*as the speckle size-characterizing parameter. It is worth noting that with a diffusing surface,

*dx*is increasing with

*θ*, while

*dy*remains constant between 0° and 90°. Indeed, for a circularly-illuminated surface, we have

*dy*=1.22λ

*D*/

*D*

_{e}and

*dx*=1.22

*λ D*/(

*D*

_{e}cos

*θ*), where

*λ*is the wavelength of the light source and

*D*

_{e}is the diameter of the circularly-illuminated area [12

12. Q.B. Li and F.P. Chiang, “Three-dimensional of laser speckle,” Appl. Opt. **31**, 6287–6291 (1992). [CrossRef] [PubMed]

*dx*and

*dy*mentioned above are roughly verified by applying these relations while considering that

*D*

_{e}corresponds to the diameter of the surface of the illuminated scattering volume as seen by the CCD camera.

*N*

_{0}, is known (see Table 1). We investigated three kinds of milk because of differences in their scattering properties after removal, by skimming, of large fat particles; furthermore, milk contains also small particles of casein (0.02 to 1 µm). The scattering coefficient,

*µ*

_{s}, being affected by any change in milk and solution of microspheres concentrations, it was measured with respect to the concentration of milk or microspheres solution in the medium,

*c*, expressed in percent. For solutions of polystyrene microspheres or milk, at the experimental wavelength, the absorption coefficient is insignificant compared to the scattering coefficient, and,

*µ*

_{s}versus

*c*is therefore determined from the Beer Lambert law in single scattering regime [13

13. N.L. Swanson, B.D. Billard, and T.L. Gennaro, “Limits of optical transmission measurements with application to particle sizing techniques,” Appl. Opt. **38**, 5887–5893 (1999). [CrossRef]

*c*in cm

^{-1}for skimmed, semi-skimmed, and whole milks, respectively. Table 1 gives the scattering coefficients of the polystyrene-microspheres measured with respect to

*c*, with a ±5% precision; it also lists the particle diameters,

*d*, as well as the anisotropy factor,

*g*, issued from Monte Carlo simulations;

*g*is the mean scattering cosine,

*g*=<cos

*α*> where

*α*is the scattering angle;

*g*=1 corresponds to total forward scattering, whereas

*g*=0 is indicative of isotropic scattering. The refractive indices used were 1.59 and 1.33 for the spheres and medium, respectively. One should note, that as already done in a previous report, we consider scatterers to be small when

*g*≤0.3 and large for

*g*≥0.7 [14

14. N. Ghosh, H.S. Patel, and P.K. Gupta, “Depolarization of light in tissue phantoms effect of a distribution in the size of scatterers,” Opt. Express **11**, 2198–2205 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2198 [CrossRef] [PubMed]

*µ*

_{s}, we prepared two scattering samples by mixing them at the ratios 1:1 and 1:5 corresponding to

*g*=0.676 and

*g*=0.851, respectively.

15. S.P. Morgan and M.E. Ridgway, “Polarization properties of light backscattered from a two layer scattering medium,” Opt. Express **7**, 395–402 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-12-395 [CrossRef] [PubMed]

15. S.P. Morgan and M.E. Ridgway, “Polarization properties of light backscattered from a two layer scattering medium,” Opt. Express **7**, 395–402 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-12-395 [CrossRef] [PubMed]

*dy*was measured four times under different incident polarizations and polarization analysis conditions:

*dy*

^{pl}was measured in the case of parallel linear polarizers, P

_{1}and P2; on the other hand, for crossed P1 and P2, the measured parameter was

*dy*

^{cl}.

*dy*

^{tc}was determined when the incident polarization was transmitted to the CCD, and

*dy*

^{fc}when the polarization transmitted to the CCD was circular and helicity-flipped. Whatever the experimental conditions, the values of

*dy*are given at the nearest 0.1 µm.

*D*

_{p}. It allows one to assess the predominant type of photons. It is worth recalling that the measurement of depolarization properties is a well known method of analysis to probe scattering media like, for example, skin [16

16. F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A: Pure Appl. Opt **7**, 21–28 (2005). [CrossRef]

17. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. **7**, 1–12 (2002). [CrossRef]

*D*

_{p}can be determined from the measurement of the speckle mean intensity through the polarization analysis as follows:

*I*

_{p}is the mean intensity measured at the CDD surface when the light of the incident polarization is fully transmitted, and

*I*

_{c}is the mean intensity when the light totally transmitted results from either a cross linear, or helicity-flipped circular polarization.

*D*

_{pl}and

*D*

_{pc}the linear and circular polarization degrees, respectively, were thus determined at the nearest 0.01.

## 3. Results and discussion

*µ*

_{s}. Table 2 also gives the reduced scattering coefficient

*µ*

_{s}(1-

*g*) is introduced as the equivalent isotropic scattering coefficient of an otherwise anisotropically-scattering medium.

*µ*

_{s}=140 cm

^{-1}, the speckle size measured for the small scatterers is larger than the one got for large scatterers. Figure 3 depicts the speckle pattern obtained for both sizes of scatterers in linear polarization analysis and clearly shows that

*dy*

^{pl}(

*d*=0.20 µm) >

*dy*

^{pl}(

*d*=1.44 µm).

*µ*

_{s}=930 cm

^{-1}for 1.44-µm microspheres and

*µ*

_{s}=42 cm

^{-1}for 0.20-µm microspheres) highlight an increase in the speckle size with higher scattering coefficient.

*µ*

_{s}is kept constant, any decrease of the anisotropy coefficient

*g*(Table 2) goes along with an increase of

*dy*

^{tc}. Finally, the speckle size is affected by the scattering and anisotropy coefficients. One should note that, whatever the sample under study, we always found

*dy*

^{pl}>

*dy*

^{tc}and

*dy*

^{fc}>

*dy*

^{tc}for 0.20-µm microspheres, and

*dy*

^{fc}<

*dy*

^{tc}for 1.44-µm microspheres. So for monodisperse polystyrene-microspheres, the comparison between

*dy*

^{fc}and

*dy*

^{tc}gave information about the scatterer size when the scattering coefficient was unknown:

*dy*

^{fc}<

*dy*

^{tc}means large-size scatterers, and

*dy*

^{fc}>

*dy*

^{tc}indicates small ones. On the other hand, in linear polarization

*dy*

^{pl}was always greater than

*dy*

^{cl}, whatever the scatterer. Figure 4 summarizes the results produced by the 0.20- and 1.44-µm microspheres.

*dy*

^{fc}>

*dy*

^{tc}. Nevertheless, the anisotropy coefficient shows that the light is forward scattered alike scattering by monodisperse large microspheres. Thus, depending on the distribution in the scatterer size, two samples with the same scattering and anisotropy coefficients may produce different speckle sizes. Indeed, a comparison of the experimental values got for the mixture 1:5 and the monodisperse 3.17-µm microsphere sample (similar scattering parameters) gives

*dy*

^{fc}<

*dy*

^{tc}for the latter (large particles-like behavior) and

*dy*

^{fc}>

*dy*

^{tc}for the former (small particles-like behavior).

*D*

_{p}: indeed, under circularly-polarized light conditions,

*D*

_{pc}>0 indicates that many photons have kept the same polarization state; when

*D*

_{pc}< 0 most of them are helicity-flipped (mirror effect: for a mirror,

*D*

_{pc}=-1). With large particles, the polarization of a circularly-polarized light was kept after scattering events more numerous than those undergone by linearly-polarized photons. Table 2 data agree with those available in the literature: for large particles: we, indeed, measured

*D*

_{pc}>0 and

*D*

_{pl}=0. With small particles, the light being scattered with the same probability in any direction, the linear polarization is favored contrary to the circular one; in this case, the linear character of linearly-polarized light is not affected by backscattering, which reverses the helicity of circularly-polarized light and randomizes it more rapidly [15

15. S.P. Morgan and M.E. Ridgway, “Polarization properties of light backscattered from a two layer scattering medium,” Opt. Express **7**, 395–402 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-12-395 [CrossRef] [PubMed]

18. F.C. Mackintosh, J.X. Zhu, D.J. Pine, and D.A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B **40**, 9342–9345 (1989). [CrossRef]

*D*

_{pc}<0 and |

*D*

_{pc}| <

*D*

_{pl}.

*dy*=90 µm for a metal surface of about 1 µm in roughness, and this speckle size is the largest one that we can measure. With scattering media, the expected mean speckle size in the far diffraction zone is determined by the characteristic size of the scattering volume [19

19. D.A. Zimnyakov, V.V. Tuchin, and A.A. Mishin, “Spatial speckle correlometry in applications to speckle structure monitoring,” Appl. Opt. **36**, 5594–5607 (1997). [CrossRef] [PubMed]

*i.e.*the surface of the scattering volume as seen by the CCD camera (in application of the Van Cittert and Zernike theorem). Moreover, from solutions of monodisperse-sized polystyrene spheres Hielscher, Mourant, and Bigio evidenced an increase of spatial pattern size of backscattered light with increasing

*g*and decreasing

*µ*

_{s}[20

20. A.H. Hielscher, J. R. Mourant, and I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. **36**, 125–135 (1997). [CrossRef] [PubMed]

*g*and lower

*µ*

_{s}. Moreover, any increase of

21. S-P Lin, L. Wang, S. L. Jacques, and F. K. Tittel, “Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry,” Appl. Opt. **36**, 136–143 (1997). [CrossRef] [PubMed]

*dy*

^{pl},

*dy*

^{cl},

*dy*

^{tc}and

*dy*

^{fc}evolution versus

*dy*

^{cl}and

*dy*

^{tc}with

^{-1}and

^{-1}the evolution of

*dy*

^{pl}and

*dy*

^{fc}versus

*µ*

_{s}

*’*shows drops in the values of

*dy*

^{pl}and

*dy*

^{fc}. Indeed,

^{-1}and

^{-1}were respectively obtained with 3.17- and 1.44-µm microspheres and, in these two cases, contrarily to small microspheres and mixtures,

*dy*

^{fc}was found to be less than

*dy*

^{tc}together with close values for

*dy*

^{pl}and

*dy*

^{cl}. In other words,

*dy*

^{pl}and

*dy*

^{fc}are not governed by only

*µ*

_{s}=140 cm

^{-1}) evidences that the incident polarization-maintaining light traveled nearer the surface than the depolarized light; the relation

*dy*

^{fc}>

*dy*

^{tc}indicates a flip in helicity for the circular polarization in agreement with the measurements of polarization degrees (Table 2).

*dy*

^{pl},

*dy*

^{cl},

*dy*

^{tc}and

*dy*

^{fc}) and the polarization degree in the case of skimmed, semi-skimmed and whole milk. Whatever the milk, the small particles of casein induce

*dy*

^{fc}>

*dy*

^{tc}. Moreover, when

*µ*

_{s}=42 cm

^{-1}, the more the milk is skimmed, the larger the speckle is; a higher concentration in large particles reduces the speckle size in agreement with the experimental data reported above for mixtures of small and large microspheres.

*dy*

^{pl},

*dy*

^{cl},

*dy*

^{tc}and

*dy*

^{fc}) versus

*µ*

_{s}and the polarization degree versus

*µ*

_{s}for semi-skimmed milk. As shown above, the speckle size is increasing with the scattering coefficient. Moreover, the evolution of the polarization degree is limited when the scattering coefficient is increasing (see Fig. 6 b). So, our experimental set-up highlighted that any change in scattering coefficient affected more the speckle size than the polarization degree.

*dy*

^{pl}-

*dy*

_{cl}versus the scattering coefficient for semi-skimmed milk and evidences the small and random fluctuations of

*dy*

^{pl}-

*dy*

^{cl}.; the difference between

*dy*

^{fc}and

*dy*

^{tc}was found to vary more than the one between

*dy*

^{pl}and

*dy*

^{cl}(data not shown). Thus, a variation of the scattering coefficient will have no effect on the difference between

*dy*

^{pl}and

*dy*

^{cl}only because it depends on the scatterer size-distribution. Table 2 exhibits similarity in the behaviors of the 0.2-µm microspheres at

*µ*

_{s}=42 cm

^{-1}and

*µ*

_{s}=140 cm

^{-1}(

*dy*

^{pl}-

*dy*

^{cl}=14.7 µm).

*dy*

^{pl}-

*dy*

^{cl}with increasing concentration of large scatterers. According to Table 2, for big scatterers (for example, 3.17-µm microspheres and the 1.44-µm ones at

*µ*

_{s}=140 cm

^{-1}and

*µ*

_{s}=930 cm

^{-1}), the differences between

*dy*

^{pl}and

*dy*

^{cl}are small and around 2 (2.4 and 2.1).

*λ*=633 nm are typically

*µ*

_{a}=25 cm

^{-1},

*µ*

_{s}=400 cm

^{-1}and

*g*=0.98 [5]. The high value of

*g*and the dominance of large scatterers in blood both explain why

*dy*

^{fc}is less than

*dy*

^{tc}in agreement with previous data. Conversely, the skin biopsies gave

*dy*

^{fc}>

*dy*

^{tc}because of the wide size distribution of scatterers.

## 4. Conclusion

*dy*

^{tc}) and the “flipped helicity circular” speckle size (denoted

*dy*

^{fc}) permitted us to discriminate the scattering media with respect to the size of scatterers, even in the case of an unknown scattering coefficient. Indeed, with large particles

*dy*

^{tc}>

*dy*

^{fc}, whereas for small ones,

*dy*

^{tc}<

*dy*

^{fc}.

*dy*

_{pl}and

*dy*

_{cl}, respectively) will remain constant when the scattering coefficient is varying, and will decrease at higher concentration of large scatterers. So, the measurement of a polarized speckle size should allow one to discriminate among media, even when the scattering coefficient is unknown.

## Acknowledgments

## References and links

1. | K. Ishii, T. Iwai, S. Wada, and M. Miyakoshi, “Simultaneous viscometry and particle sizing on the basis of dynamic light scattering,” Proc. SPIE |

2. | D.A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A |

3. | J.D. Briers, G. Richards, and X. W. He, “Capillary blood flow monitoring using laser speckle contrast analysis (LASCA),” J. Biomed. Opt. |

4. | D.A. Zimnyakov, J.D. Briers, and V.V. Tuchin, “Speckle technologies for monitoring and imaging of tissues and tissuelike phantoms,” Chap.18 in Handbook of biomedical diagnostics, Valery V. Tuchin, Ed. (SPIE press, Bellingham2002). |

5. | V.V. Tuchin, “Laser light scattering in biomedical diagnostics and therapy,” J. Las. Appl. 5, No.2&3, 43–60 (1993). |

6. | Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, “Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,” Opt. Express |

7. | 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. |

8. | J. Li, G. Yao, and L.V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. |

9. | D.A. Zimnyakov, V.V. Tuchin, K.V. Larin, and A.A. Mishin, “Speckle patterns polarization analysis as an approach to turbid tissues structure monitoring,” Proc. SPIE |

10. | J.W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in |

11. | Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, “Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,” Appl. Opt. |

12. | Q.B. Li and F.P. Chiang, “Three-dimensional of laser speckle,” Appl. Opt. |

13. | N.L. Swanson, B.D. Billard, and T.L. Gennaro, “Limits of optical transmission measurements with application to particle sizing techniques,” Appl. Opt. |

14. | N. Ghosh, H.S. Patel, and P.K. Gupta, “Depolarization of light in tissue phantoms effect of a distribution in the size of scatterers,” Opt. Express |

15. | S.P. Morgan and M.E. Ridgway, “Polarization properties of light backscattered from a two layer scattering medium,” Opt. Express |

16. | F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A: Pure Appl. Opt |

17. | S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. |

18. | F.C. Mackintosh, J.X. Zhu, D.J. Pine, and D.A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B |

19. | D.A. Zimnyakov, V.V. Tuchin, and A.A. Mishin, “Spatial speckle correlometry in applications to speckle structure monitoring,” Appl. Opt. |

20. | A.H. Hielscher, J. R. Mourant, and I. J. Bigio, “Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions,” Appl. Opt. |

21. | S-P Lin, L. Wang, S. L. Jacques, and F. K. Tittel, “Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry,” Appl. Opt. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(260.5430) Physical optics : Polarization

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 18, 2005

Revised Manuscript: May 27, 2005

Published: June 27, 2005

**Citation**

Y. Piederrière, F. Boulvert, J. Cariou, B. Le Jeune, Y. Guern, and G. Le Brun, "Backscattered speckle size as a function of polarization: influence of particle-size and- concentration," Opt. Express **13**, 5030-5039 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-5030

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### References

- K. Ishii, T. Iwai, S.Wada, and M. Miyakoshi, �??Simultaneous viscometry and particle sizing on the basis of dynamic light scattering,�?? Proc. SPIE 4263, 112-121 (2001). [CrossRef]
- D. A. Boas and A. G. Yodh, �??Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,�?? J. Opt. Soc. Am. A 14, 192-215 (1997). [CrossRef]
- J. D. Briers, G. Richards and X.W. He, �??Capillary blood flow monitoring using laser speckle contrast analysis (LASCA),�?? J. Biomed. Opt. 4, 164-175 (1999). [CrossRef]
- D.A. Zimnyakov, J.D. Briers, V.V. Tuchin, �??Speckle technologies for monitoring and imaging of tissues and tissuelike phantoms,�?? Chap.18 in Handbook of biomedical diagnostics, Valery V. Tuchin, Ed. (SPIE press, Bellingham 2002).
- V.V. Tuchin, �??Laser light scattering in biomedical diagnostics and therapy,�?? J. Las. Appl. 5, No.2&3, 43-60 (1993).
- Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, J. Lotrian, �??Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering,�?? Opt. Express 12, 176-188 (2004), <a href= �??http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176�??>http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-176</a>. [CrossRef] [PubMed]
- 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]
- J. Li, G. Yao, L.V. Wang, �??Degree of polarization in laser speckles from turbid media: implications in tissue optics,�?? J. Biomed. Opt. 7, 307-312 (2002). [CrossRef] [PubMed]
- D.A. Zimnyakov, V.V. Tuchin, K.V. Larin, A.A. Mishin, �??Speckle patterns polarization analysis as an approach to turbid tissues structure monitoring,�?? Proc. SPIE 2981, 172-180 (1997). [CrossRef]
- J.W. Goodman, �??Statistical Properties of Laser Speckle Patterns,�?? in Laser speckle and related phenomena, Vol.9 in series Topics in Applied Physics, J.C. Dainty, Ed., (Springer-Verlag, Berlin, Heidelberg New York Tokyo, 1984).
- Terri L. Alexander, James E. Harvey, and Arthur R. Weeks, �??Average speckle size as a function of intensity threshold level: comparison of experimental measurements with theory,�?? Appl. Opt. 33, 8240-8250 (1994). [CrossRef] [PubMed]
- Q.B. Li and F.P. Chiang , �??Three-dimensional of laser speckle,�?? Appl. Opt. 31, 6287-6291 (1992). [CrossRef] [PubMed]
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