ISSN 0030�400X, Optics and Spectroscopy, 2011, Vol. 110, No. 3, pp. 438–441. © Pleiades Publishing, Ltd., 2011.

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1 INTRODUCTION

Polarimetry is a useful tool by which to analyze themodification in the shape and orientation of the fieldvectors of the electromagnetic radiation which propa�gates through scattering medium. Among the methodsavailable to analyze turbid media, the use of polarizedlight has attracted much attention recently, as it hasbeen discovered that multiply scattered photons stillmaintain partial polarization [1]. A typical experimententails launching a known polarization state in lightinto a turbid sample and measuring the polarizationproperties of the remitted light. The detected signaldepends on many variables, including the number andnature of scattering events, the incident polarizationstate, and the detection geometry [2]. In the past fewyears, several groups have shown how polarizationsensitive scattering measurements can be used to mea�sure certain properties of turbid medium such as theaverage particle size, scattering coefficient, anisotropyfactor of particle suspensions, optical material charac�terization, and the study of biological materials [3–7].An optical polarizer and retarder are rotated to provideadditional incident and analyzed polarization states toenable the reconstruction of the 2D Stokes vectors ofvarious biological sample [8]. The polarization of lighthas been used to extract quantitative information fromthe optical medium. Indeed, although the degree ofpolarization is significantly lowered after propagatingthrough thick turbid media, often it is not completelydestroyed. Polarization is well suited for measuringbirefringence and optical activity, which affect,

1 The article is published in the original.

respectively, the ellipticity and the orientation of thepolarization of the incident beam [9]. For instance, ithas been used in birefringence measurement, polar�ization�sensitive optical coherence tomography mea�surements, and characterization of scattering medium[10]. The experimental optical calculus (Stokes vec�tors) of transmitted intensity pattern and degree ofpolarization allows the complete characterization ofthe scattering matrix of a sample [11].

EXPERIMENTAL ARRANGEMENT

The experimental setup for Stokes vector polarim�etry is shown schematically in Fig. 1. A He–Ne laser( = 632.8 nm) and of spot size less than 2 mm passesthrough a Polarizer (P1) and quarter wave�plate(QWP1) and impinges on the sample. The scatteredlight which emerges from the sample passes through aanalyzer (P2) and quarter wave�plate (QWP2), and isthen recorded by the detector connected to lock inamplifier or CCD camera system (Pico Star, LabVision). The CCD resolution is 12 bit and the lab viewsoftware is used for data analysis. The scatteringmedium (soybean oil) is placed in a cylindrical thin�walled quartz cell (3 × 2 cm). Soybean oil is an inex�pensive, non�toxic liquid with dielectric propertiessimilar to very low�water�content fatty tissue [12].

The stokes parameters generally denoted by S0, S1,S2, and S3 from a sufficient set describing the ampli�tude, phase, and polarization of a light wave. To

λ

Stokes Vector Determination of Polarized Light Propagation in Turbid Medium1

S. Firdous, M. Atif, and M. NawazBiophotonics Laboratory, National Institute of Lasers and Optronics (NILOP),

P.O. Nilore 45650 Islamabad, Pakistane�mail: atifhull@gmail.com, shamaraz@gmail.com

Received August 24, 2010

Abstract—We report a two dimensional Stokes vector imaging technique for transamination measurementsof the polarization state of scattering medium. Measurement of the depth resolved Stokes parameters allowsdetermination of the degree of polarization, birefringence, retardation, optical activity and characterizationof the medium. The polarized light preserved and degree of polarization very with scatterer concentration.The transmitted intensity patterns by varying a polarization state of the incident laser light (λ = 632.8 nm)and changing analyzer configuration provides a useful information about concentration, orientation, andshape of the sample under investigation. The results are important for the understanding of polarization phe�nomenon in turbid media, like biological tissues.

DOI: 10.1134/S0030400X11030064

PHYSICAL OPTICS

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STOKES VECTOR DETERMINATION 439

express the Stokes vector S in term of our experimentaldata, the following relation is needed [10].

, (1)

where H, V, P, and R are the measured quantities ofhorizontal, vertical, 45° linear, and right�hand circu�lar polarization components, respectively. From eachStokes vector, the degree of linear polarization(DOLP), circular polarization (DOCP) and totalpolarization (DOP), were calculated as

(2)

RESULTS AND DISCUSSION

For purely polarized light, the degree of polariza�tion is unity, and the Stokes parameters obey the

equality , while for partially polar�ized light, the degree of polarization is smaller than

unity, leading to . An input beam canbe decomposed into purely polarized beams, afterpropagating through an optical system. The experi�mental Stokes vector images provide detailed informa�tion about the optical properties of the medium. InFig. 2 the transmitted and scattered Stokes polariza�

0

1

2

3

2

2

S H V

S H VS

S P H V

S R H V

+⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥−⎢ ⎥ ⎢ ⎥= =

− −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

22 231 2

0 0

2 2 21 2 3

0

, ,

.

SS S

S S

S S S

S

+= =

+ +=

DOLP DOCP

DOP

2 2 2 20 1 2 3S S S S= + +

2 2 2 20 1 2 3S S S S> + +

tion images are described for different scatterer con�centration. The intensity contrast depends upon scat�tering concentration, structure and orientation of themedium. The contrast reduces with optical depth andthe scattering is strongly related to optical activity,which rotates the electric vector of the incident light.The Stokes image the S0 shows total intensity of theilluminating beam and provides less information com�pared to others. The image S1 and S2 describe linearpolarization and play significant role for materialcharacterization being preserved for longer distance indense medium. These images clearly differentiatedense and light scatterer, as the circular polarized lightdepolarize and lose its polarization memory rapidly indense medium as compared to linearly polarized light[13]. The size of the scattering medium can be charac�terize through S3 if it is closer to 0 then the scatteringcross�section is smaller and the medium is related toRayleigh theory otherwise if S3 is close to 1 then thescatterer size can be measured through Mie theory[14]. So we can find concentration, size, shape andorientation of scatterer with detailed study of Stokesimages.

It is clearly seen by Stokes polarization transmitteddata of Fig. 3, that the intensity profiles is differentamong the four Stokes components and transmittedintensity for circular, parallel and perpendicular lightindicates that the polarization state changes are notdue to dichroism of the sample only. The transmittedintensity maintains the original polarization states atdifferent points in the total intensity pattern and statis�tically different from each other because both the ratioof amplitude and the phase between the orthogonalintensity patterns vary from point to point. The Stokes

12

3

4

5

6

7

8

9

Fig. 1. Experimental setup for the measurements of transmitted Stokes vector images of turbid medium: 1—He–Ne laser, 2—P1, 3—QWP1, 4—sample, 5—P2, 6—QWP2, 7—CCD/Detector, 8—lock�in amplifier, 9—PC.

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FIRDOUS et al.

vector for an area including more than one such pointis then determined by summing the Stokes vectors ofall of the points in the area. From Fig. 4 we see that,the DOP of the area is less than unity and decreases

statistically as the area is enlarged because more pointsare included in the enlarged area. It is worth notingthat, because of their statistical nature, polarizationstates and DOPs can be different even for detection

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S0 S1 S2 S3

(a)

(b)

(c)

0 1

Fig. 2. The transmitted Stokes components corresponding to polarized images of scattering medium, (a, b) represents (3D) pat�tern and (c) the direct intensity pattern for different optical concentration. The images are taken with the experimental setup inFig. 1. All displayed images are 3 × 2 cm.

2.41.60.80Optical depth, mm

0.8

0.4

0

S2

S3

S1

Stokes parameters

Fig. 3. Stokes normalized parameters S1 (linear horizon�tal), S2 (linear 45°) and S3 (circular) as a function of opti�cal depth of scattering medium.

20100Optical depth, mm

0.8

0.4

0

Degree of polarization

Fig. 4. Degrees of total linear and circular polarization(DGP, DOLP, and DOCP, respectively) measured throughStokes polarization parameters, vs. optical depth. Eachpoint is an average of three points.

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STOKES VECTOR DETERMINATION 441

areas of the same size. We conclude that the measuredDOP, DOLP, and DOCP in a intensity pattern that isgenerated by a scattering medium depend on the sizeof the detection area, they decrease with an increasingarea of detection, and only the DOP of an area muchsmaller than a coherence area is close to unity. Thisconclusion is important for the understanding ofpolarization phenomena in scattering medium, wherepolarized coherent light is applied and an intensityimages are generated. When the DOPs of an intensitypattern from a turbid medium such as biological tissueare measured, the above properties should be consid�ered, especially if the measurement is made from asmaller area in the field, for DOLP < DOCP themedium exhibit Rayleigh scattering for DOLP >DOCP medium exhibits Mie scattering and DOLP ~DOCP the medium corresponds Rayleigh Mie transi�tion region.

The pattern of the Stokes images is altered by thesize as well as the scattering coefficient of the particles.This can be seen in Figs. 2, 3 where the S1 element isaffected by particle size for the same scattering coeffi�cient. The lower particle sizes, which have dominantRayleigh scattering, have a dominant intensity patternand the particle size increases where Mie�type scatter�ing becomes dominant. For scattering medium ofRayleigh spheres, circularly polarized light is depolar�ized, more quickly than linearly polarized light. In thetransition region between Raleigh and Mie scattering,the polarized light propagation through a densemedium of (Mie scattering) spheres is similar to polar�ized light propagation through a medium of smaller(Rayleigh) particles. From Fig. 4, we observed that fordense concentrations, circularly polarized light wasdepolarized similarly to or more quickly than linearlypolarized light. This behavior corresponds to that seenfor scattering by medium of particles in the Rayleigh�Mie regions of dense concentrations [15].

CONCLUSIONS

The Stokes polarization images of transmittedintensity along with degree of polarization providesfingerprint of the turbid medium. Careful analysis ofimages in Figs. 2, 3 and degree of polarization in Fig. 4one can differentiate the scatterer in term of its con�centration, size, shape and orientation. The results arerelated to polarized light propagation, and thesedensely packed images are likely to exhibit dependedscattering and, therefore dependent polarizationeffects. The linear polarization preservation is domi�nant over circular due to scatterer density rather thensize of the particle in medium.

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