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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 13 — Jun. 27, 2005
  • pp: 5030–5039
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Backscattered speckle size as a function of polarization: influence of particle-size and -concentration

Y. Piederrière, F. Boulvert, J. Cariou, B. Le Jeune, Y. Guern, and G. Le Brun  »View Author Affiliations


Optics Express, Vol. 13, Issue 13, pp. 5030-5039 (2005)
http://dx.doi.org/10.1364/OPEX.13.005030


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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

Speckle field measurement is, now, a usual tool to characterize the dynamic behavior of scattering media like, for example, the flow or Brownian movement of scatterers. Indeed, well-known techniques such as Dynamic Light Scattering [1

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]

], Diffusing Wave Spectroscopy [2

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]

], LAser Speckle Contrast Analysis (LASCA) [3

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]

] based on the temporal characterization of fluctuations in speckle intensity are now widely investigated for further applications in biology and medicine [4

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).

].

Here, the issue being strongly-scattering media, e.g. milk, blood, skin,…. we chose a backscattering configuration to investigate the effects of either circular, or linear, incident polarization on the size of backscattered speckles. We also analyzed the transmitted- or cross-polarization states so as to assess changes in speckle size according to the scattering parameters. Though speckle polarization analysis has often been used to study metal surfaces or turbid media [7

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

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

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]

], the investigations reported here are of a different nature since they use the spatial properties of speckle. Thus, Section II will detail the polarization analysis we made and describe our experimental conditions. Section III will report on the experimental data collected from different media before discussing them. Our conclusions will be drawn in section IV.

2. Experimental method

The size of a speckle can be determined from calculations of the normalized autocovariance function of the intensity speckle pattern got in the observation plane (x,y). This function, denoted cIx, Δy), 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

10. 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).

]; cIx, Δy) 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]

]:

cI(Δx,Δy)=FT1[FT[I(x,y)]2]I(x,y)2I(x,y)2I(x,y)2
(1)

where FT is the Fourier Transform, < > is a spatial average, cIx,0) and cI (0, Δy) are the horizontal and the vertical profiles of cIx, Δy), respectively.

Let us term dx the width of cIx, 0) so that cI (dx /2, 0)=0.5 and dy the width of cI (0, Δy) such as cI (0, dy/2)=0.5.

Figure 1 illustrates the experimental set-up. The 7-mW HeNe laser used emits a 1.12 mm-wide polarized (linear) beam at I0 /e 2 where I0 is the maximum laser intensity at the 632.8 nm wavelength with a coherence length of about 20 cm.

A CCD camera records the medium-produced speckle field. The CCD imager contains 788×268 pixels of size 8 µm×8 µm. When a newly acquired image is digitized, the analog-to-digital converter assigns an intensity value (gray level) in the range of 1 to 1024 (10-bit precision).

To record the speckle, one should be aware of the Brownian motion of particles in the medium. These movements induce a random agitation of the speckle, which is termed “boiling speckle”. The time scale of the speckle intensity fluctuations is given by the correlation time, which must be longer than the image acquisition time to avoid recording a blurred speckle [4

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).

]. The correlation times measured for our samples exceeded 0.1 ms; we also used a CCD camera with a time exposure in the range 0.1–60 ms to acquire images at 0.1 ms.

Another consideration of importance in recording the speckle data is the size of speckle on the CCD array: the speckles must be large as compared to the pixel size so as to resolve variations in speckle intensity [11

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]

]. Moreover, for a meaningful statistical evaluation each image must contain many speckles. These conditions were fulfilled by setting the surface of the medium under study at 15 cm (D) from the CCD camera.

These considerations led us to place the CCD camera so that we got the highest number of pixels, 788, along the vertical direction.

Fig. 1. Top view of the experimental set-up, P1 and P2 are linear polarizers, QWP1 and QWP2 are quarter-wave plates. Sample dimensions are 1×1×4 cm.

Table 1. Scattering coefficients of polystyrene-microspheres measured and anisotropy coefficient calculated (Mie calculation).

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From two monodisperse solutions of 0.20- and 1.44-µm microspheres, whose concentrations had been adjusted so that both exhibited the same µs , 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.

Each of these samples was, first, illuminated by a linearly polarized laser beam, then by a circularly polarized one. As stated by Morgan and Ridgway, Fig. 2 shows that, with a linear polarization, the light emerging from a medium is composed of photons in mixture; some of them have still their original polarization state because of the little number of scattering events they have undergone, whereas the other ones have a random polarization further to numerous scattering events [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]

]. On the other hand, a scattering medium illuminated with a circularly-polarized light gives rise to three types of photons: some of them are helicity-flipped by mirror reflection, others keep their original polarization state as previously and the last ones are depolarized by many scattering events [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]

].

Fig. 2. Different types of photons emerging from a scattering medium for an incident light linearly or circularly polarized [15].

For each sample under study, dy was measured four times under different incident polarizations and polarization analysis conditions:

i) when the laser beam was linearly polarized (vertical polarization), the quarter wave plates were removed, and dypl was measured in the case of parallel linear polarizers, P1 and P2; on the other hand, for crossed P1 and P2, the measured parameter was dycl .

ii) with a circularly-polarized beam, the quarter-wave plates were kept and dytc was determined when the incident polarization was transmitted to the CCD, and dyfc 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.

In order to compare our measurements, we calculated the degree of polarization Dp . 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

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]

].

Dp can be determined from the measurement of the speckle mean intensity through the polarization analysis as follows:

Dp=IpIcIp+Ic
(2)

where Ip is the mean intensity measured at the CDD surface when the light of the incident polarization is fully transmitted, and Ic is the mean intensity when the light totally transmitted results from either a cross linear, or helicity-flipped circular polarization. Dpl and Dpc the linear and circular polarization degrees, respectively, were thus determined at the nearest 0.01.

3. Results and discussion

Table 2, where samples are ranked in the ascending order of g, lists the speckle sizes found for the three polystyrene-microspheres of diameters 0.20, 1.44 and 3.17 µm and the two mixtures. For the first two series of microspheres, the measurements were made at two different µs . Table 2 also gives the reduced scattering coefficient µs for all samples; µs=µs (1-g) is introduced as the equivalent isotropic scattering coefficient of an otherwise anisotropically-scattering medium.

Table 2. dy in µm and polarization degree obtained for all the samples. Mix (1:1): 1:1 volume ratio mixtures of 0.20-µm microspheres (µs =140 cm-1) and 1.44-µm microspheres (µs =140 cm-1), Mix (1:5): 1:5 volume ratio mixtures.

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At µs =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 dypl (d=0.20 µm) > dypl (d=1.44 µm).

Fig. 3. (a) and (b) illustrate the speckle produced by the 1.44-µm microspheres and 0.20-µm microspheres (linear polarization) when µs =140 cm-1.

Moreover, the values got at other scattering coefficients (µs =930 cm-1 for 1.44-µm microspheres and µs =42 cm-1 for 0.20-µm microspheres) highlight an increase in the speckle size with higher scattering coefficient.

When µs is kept constant, any decrease of the anisotropy coefficient g (Table 2) goes along with an increase of dytc . Finally, the speckle size is affected by the scattering and anisotropy coefficients. One should note that, whatever the sample under study, we always found dypl > dytc and dyfc > dytc for 0.20-µm microspheres, and dyfc < dytc for 1.44-µm microspheres. So for monodisperse polystyrene-microspheres, the comparison between dyfc and dytc gave information about the scatterer size when the scattering coefficient was unknown: dyfc < dytc means large-size scatterers, and dyfc > dytc indicates small ones. On the other hand, in linear polarization dypl was always greater than dycl , whatever the scatterer. Figure 4 summarizes the results produced by the 0.20- and 1.44-µm microspheres.

Fig. 4. Scheme summing about the evolution of data produced by small and large microspheres (g=0.323 and 0.928, respectively).

In a mixture of small and large scatterers, the latter decrease the size of speckle, even though the mixture behaves like the monodisperse sample composed of small scatterers with dyfc > dytc . 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 dyfc < dytc for the latter (large particles-like behavior) and dyfc > dytc for the former (small particles-like behavior).

As previously mentioned in section II, the polarization of photons emerging from the medium can be assessed from Dp : indeed, under circularly-polarized light conditions, Dpc >0 indicates that many photons have kept the same polarization state; when Dpc < 0 most of them are helicity-flipped (mirror effect: for a mirror, Dpc =-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 Dpc >0 and Dpl =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

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]

]. So, for small particles, we measured Dpc <0 and |Dpc | < Dpl .

Explaining how a speckle size will evolve according to the anisotropy and scattering coefficients is difficult. It is worth recalling that the size of speckle in reflection on a diffusing metal surface depends on the dimension of the light spot responsible for the surface illumination according to the Van Cittert and Zernike theorem [10

10. 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).

]; moreover, illumination of a small area produces a speckle of large size. Our experimental set-up permitted us to measure 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]

]. Particularly the speckle size depends on the surface of the backscattered-light spot 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 µs [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]

]. Consequently, as previously shown in this study for monodisperse-sized polystyrene-spheres and in agreement with the Van Cittert and Zernike theorem, the speckle size is becoming smaller for higher g and lower µs . Moreover, any increase of µs causes a reduction of the backscattered spot width [21

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]

]. The plot of dypl , dycl , dytc and dyfc evolution versus µs (Fig. 5) highlighted a roughly linear increase of dycl and dytc with µs in agreement with the Van Cittert and Zernike theorem. On the other hand, when µs=24.3 cm-1 and µs=66.9 cm-1 the evolution of dypl and dyfc versus µs shows drops in the values of dypl and dyfc . Indeed, µs=24.3 cm-1 and µs=66.9 cm-1 were respectively obtained with 3.17- and 1.44-µm microspheres and, in these two cases, contrarily to small microspheres and mixtures, dyfc was found to be less than dytc together with close values for dypl and dycl . In other words, dypl and dyfc are not governed by only µs since they are affected by the polarization analysis and, thus, by the size of particles.

Fig. 5. Evolution of speckle size versus the reduced scattering coefficient for all samples.

Thus, the speckle size is indicative of the scattering characteristics of a medium, and a polarization analysis evidences “the polarized scattering volume”, but this parameter depends on the type of polarization as well as on the scattering medium under analysis. For example, Fig. 2 shows that the incident polarization-keeping photons have traveled at a depth closer to the surface than the depolarized ones. This property induces a small polarized volume (large speckle size) for the former, and a large depolarized volume (small speckle size) for the latter. The noticeable difference observed with the 0.20-µm microspheres between the sizes of the cross linear and linear polarized speckles (46.3 and 61.0 µm, respectively, for µs =140 cm-1) evidences that the incident polarization-maintaining light traveled nearer the surface than the depolarized light; the relation dyfc > dytc indicates a flip in helicity for the circular polarization in agreement with the measurements of polarization degrees (Table 2).

Table 3 gives the size of speckles (dypl , dycl , dytc and dyfc ) and the polarization degree in the case of skimmed, semi-skimmed and whole milk. Whatever the milk, the small particles of casein induce dyfc > dytc . Moreover, when µs =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.

Table 3. dy in µm for different milks, µs =42 cm-1.

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Figure 6 illustrates the variations of speckle size (dypl , dycl , dytc and dyfc ) versus µs and the polarization degree versus µs 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.

Fig. 6. Evolution of speckle size a) and polarization degree b) versus scattering coefficient for semi-skimmed milk.

Figure 7 depicts the evolution of dypl - dycl versus the scattering coefficient for semi-skimmed milk and evidences the small and random fluctuations of dypl - dycl .; the difference between dyfc and dytc was found to vary more than the one between dypl and dycl (data not shown). Thus, a variation of the scattering coefficient will have no effect on the difference between dypl and dycl only because it depends on the scatterer size-distribution. Table 2 exhibits similarity in the behaviors of the 0.2-µm microspheres at µs =42 cm-1 and µs =140 cm-1 (dypl - dycl =14.7 µm).

Fig. 7. Variations of dypl - dycl versus the scattering coefficient for semi-skimmed milk.

Moreover, for the samples containing scatterers of different sizes (milk and mixtures of polystyrene-microspheres), Table 4 shows a decrease of dypl - dycl 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 µs =140 cm-1 and µs =930 cm-1), the differences between dypl and dycl are small and around 2 (2.4 and 2.1).

Table 4. dypl - dycl in µm for sample with distribution in size of scatterers. Mix (1:1): 1:1 volume ratio mixtures of 0.20-µm microspheres (µs =140 cm-1) and 1.44-µm microspheres (µs =140 cm-1), Mix (1:5): 1:5 volume ratio mixtures.

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Table 5. dy in µm for human whole blood and pig skin

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4. Conclusion

We studied the size of backscattered speckles produced by strong scattering media. We showed its dependence with scattering and anisotropy coefficients of the analyzed scattering medium. For a given anisotropy coefficient, any rise of the scattering coefficient widened the speckle size. Similarly, at a given scattering coefficient, the size of the speckle grew when the anisotropy coefficient was lowering.

We also investigated the effect of linearly-polarized laser beam on the speckle size by analyzing the linear, or cross linear, polarization as well as the circularly-polarized one through analysis of transmitted circular or helicity-flipped circular polarization. The comparison between the “transmitted circular” speckle size (denoted dytc ) and the “flipped helicity circular” speckle size (denoted dyfc ) 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 dytc > dyfc , whereas for small ones, dytc < dyfc .

The speckle measurements carried out on mixtures of large and small microspheres produced results similar to those of a monodisperse sample of small microspheres though the anisotropy coefficient of mixtures was found to be alike that of a sample of large monodisperse microspheres. These results agree with those reported by Gosh et al. further to experiments made in transmission [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]

]. These authors, indeed, concluded that the depolarization behavior of light in a medium containing scatterers of various sizes would differ from that of a matched monodisperse scattering sample of similar anisotropy and scattering coefficients.

Moreover for samples characterized by a scatterer size-distribution, the difference between the size of “linearly polarized” speckle and that of the “unpolarized” one (dypl and dycl , 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.

Further investigations are still required to gain much insight into our experimental data, and theoretical studies are needed on media of known optical parameters to understand the evolution of speckle size.

Such measurements of speckle size in polarization could be used to evidence any scattering change, i.e. modification in the number, size, shape or structure of scatterers, and applied to biomedical studies for gaining valuable information beneficial for diagnosis. We envision carrying out measurement on irradiated samples of skin.

Acknowledgments

The authors thank Dr. M.T. Blouch and Pr. J.F. Abgrall (Hematology Laboratory of Brest Hospital) for their collaboration.

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 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]

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 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]

10.

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).

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]

12.

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

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]

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]

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]

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]

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]

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]

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]

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]

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

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