Development of a New 3D Shear Stress Measurement Technique ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/02.3_1.pdf · with a light transmission through the test volume an optical

14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008

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Development of a New 3D Shear Stress Measurement Technique Using the

Birefringence

Torsten Schneider1, Leonid Goubergrits

1, Ulrich Kertzscher

1,

Christian Oliver Paschereit2

1: Biofluid Mechanics Laboratory, Charité, Germany, [email protected]

2: ISTA (HFI), Technical University Berlin, Germany, [email protected]

Abstract A new measurement technique allowing a direct assessment of a three-dimensional shear stress field is proposed. The method is based on liquids exhibiting the optical effect of streaming birefringence that is visualized using the apparatus called polariscope. Spherical reflecting particles are added into the birefringent fluid and illuminated with a polarized, monochromatic light sheet. Three kinds of the light sources were tested: CW-Laser diode, low-pressure sodium lamps and light emitting diodes. In order to resolve a 3D shear stress field, a test volume is scanned by a set of parallel light sheets. Each sheet is acquired by two identical synchronized cameras from opposite directions that results in two different images. The light intensity in each image is a measure of the optical effect of streaming birefringence on the way of the light from reflecting particles to the sensor chip of each camera. By a combination of two images for one light sheet and one final image with a light transmission through the test volume an optical effect of the birefringence on the way between light sheet and camera may be separated and a 3D resolution of the effect in a test volume may be solved. The method is a tomography, but without a use of multi-projectional line-of-sight measurements. This paper describes the first steps of the development of this new measurement technique. The study included a choice, development, calibration and analysis of the experimental setup: light source, particles, polariscope, camera and birefringent fluid. Furthermore, the method viability was tested in experiments using a simple 2D-setup of polyvinyl chloride (PVC) plates. Rotated PVC-plates simulate different fluid layers with different shear stress values. Experimental results indicate that the rotation of the PVC-plates can be recovered from camera measured gray values with a deviation of approximately 0.8°. These preliminary tests show that the proposed measurement technique may be successfully realized.

1. Introduction

Direct measurement and visualization of a three-dimensional (3D) shear stress field of a fluid flow

is of great interest for a wide range of the experimental fluid mechanics. Especially in the biofluid

mechanics the shear stress plays an important role because of the strong correlation between this

parameter and pathologic processes of blood coagulation or thrombus formation and blood damage

[1, 2]. Furthermore, the direct measurement of the 3D shear stress field would have an advantage

for the wall shear stress measurement in comparison with all other methods based on the assessment

of the velocity field [3, 4].

The effect of the optical birefringence (Maxwell effect) generated in the flow of certain colloidal

or polymer solutions (Milling Yellow or vanadium solution V2O5) is normally visualized with a

technique adopted from photo-elasticity using an apparatus called a polariscope [5]. Birefringence

is well known for a number of transparent solid materials, mainly crystals since 17th

century. An

incident light wave is separated in the birefringent fluid into two components, which are linearly

polarized with the planes of polarization being perpendicular to one other, and which propagate at

different phase velocities. They are out of phase when leaving the birefringent fluid and this

difference in optical phase ∆s is a function of the shear stress τ and linearly proportional to the fluid

thickness d and reversely proportional to the light wave length λ. This difference in optical phase


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can be visualized and measured. Using a polariscope, one produces interference between the two

separated light wave components. The resulting isochromatic fringe system carries information on

the difference of the refractive indices n1 and n2 that may be visualized. Figure 1 shows the effect of

streaming birefringence in a silicone model of the cerebral aneurysm of a basilaris artery using the

vanadium solution.

Fig. 1 Left hand side is a photo of the aneurysm model without flow and without polariscope. Right hand side is a photo

of the model with flowing V2O5 solution in a polariscope. A standard filament lamp was used as a light source.

In case of colloidal fluids a relationship between shear stress and the difference of the refractive

indices has been derived by Wayland [6, 7]. The relationship is a power series of shear stress τ, but

for practical application only the linear term is used:

( ) ,12 dnnb

⋅−⋅=λ

τ (1)

where constant b is a function of the used birefringent fluid. We refer also to the fundamental study

of the streaming birefringence published by Pindera and Krishnamurthy [8] and to the review paper

of Pih [9].

Most of the flow studies using streaming birefringence are devoted to two-dimensional flow

problems [10, 11]. An algorithm and experimental results of integrated streaming birefringence for

the axisymmetric flow cases were also published [12, 13]. In general case, the theory of integrated

streaming birefringence for 3D shear stress analysis is rather complicated. In the case of weak

birefringence one can reduce the integrals to the ordinary Radon transform [13, 14]. This technique

has become very well known due to advances in medical imaging, i.e. computerized tomography

(CT) [15]. Tomography allows the distribution of physical parameters of a 3D object to be

determined from multi-projectional line-of-sight measurements.

An alternative method to resolve the effect of integrated streaming birefringence is proposed

[16]. This method is a tomography, too. However, one has to direct the light only in one direction

that allows avoiding a restriction to the weak birefringence existing in the case of CT reconstruction

based on the Radon transformation. The next section describes general principles of the new

technique. Further, first steps of the proposed technique development are described.

2. Principle of a new measurement technique The new measurement method uses liquids, which exhibit the effect of streaming birefringence

described in the introduction. The oldest used technique for visualizing the effect of streaming

birefringence is the polariscope. A linearly polarized light is directed through the test volume and

after having traversed a second polarizer (“analyzer”) acquired with a camera. The method is based


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on the idea to locate a source of the polarized light within the flowing birefringent fluid. This is

done by adding reflecting particles to the birefringent fluid and illumination of these particles by a

polarized, monochromatic light sheet. Hence, the new method is a part of the speckle photography

like particle image velocimetry, dynamic speckle methods or speckle tomography [15]. The light

sheet is acquired by two synchronized cameras from opposite directions. The light intensity in each

image is a measure of the optical effect of streaming birefringence on a way of the light from a light

source to the camera chip. Two images are obtained for each light sheet and a set of parallel sheets

scanning a test volume are acquired in order to investigate the 3D shear stress field. Finally the

optical effect of the streaming birefringence by the light transmission through the whole test volume

is measured. By a combination of two images for one light sheet and one final image with a light

transmission through the test volume, an optical effect of the streaming birefringence on the way

between light sheet and camera may be separated. Using a set of parallel light sheets a three-

dimensional resolution of the effect may be solved. Figure 2 shows a schematically draw of the new

measurement technique principle.

Fig. 2 Schematically draw of the measurement principle. P(P) is a polarizer working as polarizer and P(A) are

polarizers working as analyzer. A reflecting particle located in a light sheet is marked with p.

Consider some reflecting particle P in the light sheet (see fig. 2). This particle reflects the same

polarized light to both (left and right) cameras. This light is altered due to the passage of two

different ways s2 and s3, whereas the effect of streaming birefringence is integrated along these

ways. The challenge is that the initial condition (light intensity or polarization) of the light reflected

by the particle P is not known. The reason is that the light is also altered on the way s1 between light

source and particle P in the light sheet. Hence, the left camera acquires the effect of streaming

birefringence integrated along the path s1+s2, whereas the right camera acquires the effect integrated

along the path s1+s3. The difference between two acquired images supplies the information about

the difference between the information integrated along the path s2 and s3. Additionally, an optical

effect of the streaming birefringence by the light transmission through the whole test volume or in

other words along the path s1+s2 for the particle P has to be obtained (see fig. 3). By a combination

of two images for one light sheet and one final image with a light transmission through a test

volume an optical effect of the birefringence on the way between light sheet and each camera may

be simply separated by solution of a system of two linear equations. A set of parallel sheets has to

be acquired in order to investigate the test volume and to disintegrate the 3D optical effect of


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streaming birefringence. Finally, the relationship between optical effect (change of the light

intensity) and shear stress should be known in order to resolve three-dimensional shear stress field

in the test volume.

Fig. 3 Schematically draw of the measurement principle. Last step – the effect of streaming birefringence by the light

transmission through the test volume - is shown.

There is a set of requirements that should be satisfied realizing the proposed measurement

technique. These are:

• use of

polarized and monochromatic (follow eq. 1) light,

• use of

birefringent fluid,

• use of

particles reflecting the polarized light without altering the light polarization, and

• use of

two identical synchronized cameras mounted exactly on one optical axis.

Next sections describe the first steps by proving the method viability and experimental setup

development.

3. Experimental setup The development of an experimental setup was started with a fabrication of a polariscope. HN38

polarizer with an optimal operation in the wavelength range between 600 and 700 nm (ScreenLab,

Germany) are used. The transmission of a one polarizer is 38.0%. The transmission for two parallel

polarizers is 29.0%, whereas the transmission of two 90°-crossed polarizer is 0.04%. The first

polarizer is fixed. The second polarizer that will be used as an analyzer may be rotated with an

accuracy of 0.1°. Follow the theory the light intensity I is a function of an angle α between two

polarizes with 180° of periodicity [17] and the light intensity of a source I0:

)(cos 2

0 α⋅= II (2)

A high dynamic 14bit cooled CCD camera pco.1600 (PCO AG, Germany) is used in all

experiments. Note that follow equation 2 the use of the 14bit camera with a useable gray value


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range of about 15,000 means a resolution of approximately 0.25°. Full range of the camera cannot

be used since over-lighting of the sensor has to be avoided.

The light sensitivity to α is given by:

ααα dIdI ⋅⋅⋅⋅= )sin()cos(20 (3)

Follow equation 3 the optimal operation may be achieved if the angle between polarization plane

and the polarizer (“analyzer”) is in the range between 10° and 80°.

Two light sources were tested for use as a frontal illumination: the first light source consists of

three low-pressure sodium lamps (λ=589nm, 18W, OSRAM, Germany) with a white reflector (see

fig. 4 left) and the second light source being a lamp consisting of 56 Luxeon light emitting diodes

(LED) with a wavelength of λ=627nm and 3W power for each LED (Philips Lumileds Lighting,

USA) equally distributed over an area of 130mm x 110mm (LED panel) and cooled by an air (see

fig. 4 right). A stability of the light source operation was tested (see fig. 5). The results show that

the use of LED’s is favorable since the time dependence (variability) of the light intensity is

significantly lower for this light source. The optimal operation time is at least after 1 hour from the

start up. The temperature regulation is planned in order to reduce the start up period.

Fig. 4 Left hand side shows a photo of the used sodium lamps light source. Right hand side is a photo of the used LEDs

light source – LED panel cooled by air.

Fig. 5 Left graph shows a stability of light sources operation for a long period with start. Right graph shows a detailed

operation behavior for a short period. The gray values were normalized in order to compare two different light sources.


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Next, the second rotatable polarizer (“analyzer”) was calibrated – the zero point or degree was

defined. The analyzer was rotated in the range between -90° and 95° and each 5° a set of images

was acquired. Figure 6 shows the comparison between measured gray values averaged over image

(selected region of interest 100x100 pixels) and over 20 acquired images for each angle between

two polarizers with standard deviations and theoretical curve. The comparative analysis revealed

the best correlation for an angle of -0.24°.

Fig. 6 Theoretical and experimental curves for the light intensity after the passing two polarizers as a function of the

angle α between them.

4. Method viability: choice of particles One of the major requirements for the proposed technique, deciding whether the method is viable or

not, is a choice of particles reflecting the polarized light without altering the light polarization.

Following experiments were performed. Particles were added into the water sample and illuminated

by a light sheet generated by a laser diode (CW-Laser, λ=600 nm, 100 mW). Altogether ten

different types of particles were tested. The aim of the tests was to dim out the illuminated particles

by a change of the polarizer (“analyzer”) orientation (rotation) that was located between the test

sample and a camera. The results for two different particle kinds are shown in figure 7. For the first

kind of particles (two upper images) the experiment was not successful, since only a small part of

the particles was dimmed out. The analysis showed that about 34% of bright pixels are seen in the

second (right) image. Second pair of images shows the result that is successful for the proposed

measurement technique. Nearly all particles were dimmed out. Only 0.36% of bright pixels are

visible in the second (right) image. The difference between these two kinds of particles is that the

second particles are spheres. We suppose that particles, which were not dimmed out, are some few

mechanically destroyed particles.


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Particles 1:

Particles 2: Fig. 7 Left images show particles illuminated by a laser diode light sheet and acquired by a camera through a polarizer

with the same orientation as the polarization plane of the light sheet. Right images are acquired with a polarizer rotated

by 90° relatively to the orientation used for the left images.

5. 2D-tests with rotated PVC-plates In order to test the viability of the proposed measurement technique, the effect of birefringence was

studied in a 2D static model. Rotated polyvinyl chloride (PVC) plates of 1 mm thickness were used

to simulate different fluid layers with different shear stress values. The light intensity for the PVC-

plates is a function of the plate’s rotation angle β (angle between polarization plane and one of the

principle stresses) with a 90°-periodicity:

))(

(sin)2(sin 1222

0λ

πσσβ

⋅⋅−⋅⋅⋅⋅=

dCII

, (4)

where d is the PVC-plate thickness, C is the material dependent constant and σ1 with σ2 are two

principal stresses caused by a mechanical loading [17]. Since no loading to PVC-plates was applied,

this term can be neglected. Each PVC-plate was calibrated (zero point or degree) in a similar way as

it was done for the two polarizers. The transmission parameter of each plate was also measured. The

mean transmission coefficient with standard deviation measured for five PVC-plates was

0.85±0.0101. Figure 8 shows an experimental setup used for 2D static model with PVC-plates.

White Plexiglas® and a white reflecting surface were used in order to achieve an evenly distributed

light intensity. Circular PVC-plates contain a circular hole in the center of the plate, which was used

to measure a reference light intensity.


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Fig. 8 Schematically draw of the 2D experimental setup with PVC-plates, polariscope, camera and LED-light source.

Figure 9 shows five images of an experiment with the polariscope and one PVC-plate: image (a) is

done for two parallel polarizers (α=0°) without PVC-plate, image (b) is done for crossed polarizers

(α=90°) without PVC-plate, image (c) is done with two crossed polarizers and PVC-plate with

β=0°, image (d) is done with two crossed polarizers and PVC-plate with β=45° and image (e) is

done with two crossed polarizers and PVC-plate with β=22°. Using an information from first four

images (calibration images) the rotation angle of the PVC-plate in the last image was calculated

from the gray value with β=21.88°. The maximal grey value in the image (a) was 12500 averaged

for a selected ROI (50x50 px.). The minimal gray value in the image (b) was 108 averaged for the

same ROI.

Fig. 9 Images generated for a test with one PVC-plate. Dust and scratches were removed from images (d) and (e) using

a filter in the software Adobe Photoshop®. However, raw images were used for the analysis.

Tests with two PVC-plates were also successful. Table 1 shows total rotation angle of two PVC-

plates that were set during experiment and angles recovered based on gray values obtained from

acquired images. The results correlate well with the equation 3 – maximal error by recovering of the


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PVC-plate rotation angle is in the case, when the angle is about 0° or 45° that corresponds to the

maximal or the minimal intensity, respectively.

Table 1 Results of tests with two PVC-plates.

Test 1 Test 2 Test 3 Test 4 Test 5

Positioned β angles 15° 5° 0° 35° 45°

Calculated β angles 15.13° 4.77° 0.97° 34.8° 43.2°

Finally, tests were performed with four PVC-plates simulating image acquiring from two opposite

directions of different birefringent layers (plates) that represent the shifted light sheet. These tests

were performed with the angle α=0° between the two polarizers. Table 2 shows the acquired PVC-

plate configuration sets. Results of the calculation of PVC-plate rotation angles β based on

acquired images are shown in figure 10. The recovered angles are calculated using an iterative

algorithm according to the configuration of the acquired PVC-plates. The algorithm was realized

with MATLAB® taking into account the transmission coefficient of each plate. All PVC-plates

were rotated the same angle of 8° (fig. 10 left) or 10° (fig. 10 right). Tests with four plates have the

maximal error when the total rotation angle of the polarization plane is about 0° or 90° that is

similar to results obtained with two PVC-plates. The maximal error among all configurations was

found to be about 15% in configuration four of the test with 10° rotated plates (all four PVC-plates

with total 80° of rotation plane of polarization). This error is caused by the gray value sensitivity.

This sensitivity of the measurement procedure could be significantly improved (follow eq. 3) by 45°

rotation of the polarizer (“analyzer”). The mean error of a test with 8° rotated plates was 0.7°. The

mean errors for two tests with 10° rotated plates were 0.85° and 0.62°. Further improvement of the

measurement accuracy can be achieved by a better stabilization of the light source operation

(temperature dependence), spatial light homogeneity, elimination of reflections, and use of

collimators.

Table 2 Configuration sets for tests with four PVC-plates

Configuration 1 2 3 4 5 6 7

Acquired PVC-plates 1 1+2 1+2+3 1+2+3+4 2+3+4 3+4 4

Fig. 10 Results of tests with four PVC-plates.

Note that all experiments were performed under condition that the total rotation of polarization

plane is <90°.


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6. Conclusion A new tomography method measuring directly the 3D fields of shear stress in birefringent fluids without multi-projectional line-of-sight measurements was proposed. The major components of the measurement setup (polarizers, camera and light source) were built-on and calibrated. The use of LEDs with high operation stability is preferable for 2D studies without flowing fluid. Later, use of a laser light source is planned. Used reflecting particles should be spherical in order to reflect a polarized light without a change of polarization plane. Viability tests were performed with rotated PVC-plates. These tests showed that the proposed measurement technique may be successfully realized. The future work will be concentrated into two directions: 2D-experiments with PVC-plates and fluid sample with added particles located between PVC-plates with a laser light sheet illumination of the fluid sample and choice of the birefringent fluid including a calibration of the fluid birefringence in a Couette device (study of the relation between shear stress and change of the light intensity due to birefringence). We plan to test different birefringent fluids: V2O5 that is not favourable since it is toxic and does not allow any contact with metals, Milling Yellow [18], castor oil for high shear stress values and solution of sodium laurylether sulphate (aq.) with a small amount of NaCl [19]. Furthermore the software should be improved in order to take into account the case when the total angle of the polarization plane is larger as 90°.

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Development of a New 3D Shear Stress Measurement Technique ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/02.3_1.pdf · with a light transmission through the test volume an optical