INTENSITY FLUCTUATING PATTERN OF LIGHT SCATTERED ON MICROPARTICLES
INTENSITY FLUCTUATING PATTERN OF LIGHT SCATTERED ON
MICROPARTICLES
I. Turcu * , Cristian V. L. Pop, Silvia Neamtu
National Institute of R &D for Isotopic and Molecular
Technologies, P.O.Box 700, RO-3400, Cluj-Napoca 5,
Romania
Abstract
Our results characterize the time dependent speckle pattern obtained by stochastic interference of light, coherently scattered by microparticles.
The information is obtained by capturing images by a CCD camera and also by measuring the intensity of scattered light by a photodetector.
The image analysis is done in statistic terms the relevant parameters being the maximum value and the area of local light intensity maxima.
The measured electric signal is a fluctuating current that captures the microparticles dynamics. There are two processes controlling the dynamics: the sedimentation in gravitational field, and additionally, a random Brownian motion.
The measured currents were separated conventionally in two components: a dc component corresponding to the average current, and an ac time dependent component describing the fluctuations. The experimental dependence of the mean light intensity scattered at small angle on scattering centers density is a peak-type curve.
The fluctuations of the scattered light intensity are very important in the maximum neighborhood becoming comparable to the mean scattered light intensity. The characteristic time scale of the fluctuating component becomes shorter as the cell density increases.
The detection process has important effects on current fluctuations and it is important to discriminate between intrinsic dynamic characteristics of the interference pattern and artifacts coming from the experimental setup. The artifacts are mainly due to the averaging effect of the detectors. In the far field experiments, the photo-detector captures a single interference speckle and gives the correct fluctuating dynamics. By decreasing the distance between the sample and detector, the detecting process switches from the single speckle to many speckles detection.
INTRODUCTION
Light-scattering techniques are often used to investigate static or dynamic properties of microparticles. Low power lasers with various wavelengths in the visible or IR domains are the usual light sources used in experiments. The literature in the field covers a diversity of aspects ranging from fundamental problems related to rigorous or approximate theoretical approaches [1,2] to medical
* E-mail: iturcu@L40.itim-cj.ro

I. TURCU, CRISTIAN V. L. POP, SILVIA NEAMTU applications with diagnostic purposes [3-5] (see reference 6 for a comprehensive review).
Laser light scattered coherently by microparticles located at random positions, having random orientation, and moving in a complex manner in suspensions give a time-varying speckled interference pattern. The scattering phenomenon is a stochastic interference process providing information on both static and dynamic parameters of the investigated system.
In a light-scattering experiments there are, basically, two ways to obtain information:
 capturing images by a CCD camera;
 measuring the intensity of scattered light and converting the light intensity into an electric signal by a photo-detector.
Sample
Photo-detector Amplifier
He-Ne
Laser
CCD
Camera
A/D
Converter
Fig. 1 The experimental set-up
As the speckle pattern is only partially captured by a photo-detector, the received information is incomplete. The detected current features fluctuations that contain encrypted information about the static and dynamic properties of the scatterers.
The purpose of the paper is to develop the appropriate experimental set-up and to investigate the static and dynamic properties of the scattered light upon interaction with suspensions of human red blood cells.
The human red blood cells are used as model microparticles but the results are similar for a wide variety of microparticles: yeast, bacteria, milk, natural juices, molecular aggregates in suspensions etc.

INTENSITY FLUCTUATING PATTERN OF LIGHT SCATTERED ON MICROPARTICLES
METHODS
For all experiments, blood was obtained from healthy male donors, was collected on natrium citrate 3.8% and was used after one or two hours. The erythrocytes were separated from the blood plasma by centrifugation at 4000 rpm for 10 min and were washed three times in an isotonic saline buffer (145 mM
NaCl, 5 mM KCl, 5mM Hepes, pH 7.4). The red blood cells were diluted in isotonic saline with haematocrit (volume fraction) values in the range 10 -6 – 0.4.
The used light source was a 633 nm linearly polarized continuous-wave
He-Ne laser (Uniphase model 1125P) with a power of 5 mW. The beam diameter at 1/e 2 was 0.81 mm and the beam divergence 1 mrad. The laser beam was directed onto a 1 mm thick quartz cuvette containing the blood sample.
The intensity of the light scattered at small angles was captured as a digitized image by a CCD camera and also was converted in an electric signal by a photodiode. The typical distance between photodetector and the cuvette was D = 1 m, but in order to capture single and multiple speckles, measurements were performed also at 5 and 0.5 m respectively. The sensitive area of the photodiode is
A ≈ 0.2 cm 2 corresponding to a solid angle ΔΩ ≈ 2
×
10 -5 sr. The detector measuring the scattered light is positioned in the forward direction at 2 o off-axis. Measured value was corrected for the refractive index mismatch on the water/air interface.
The detected current is amplified and transferred to a PC by an A/D 12-bits converter having ν = 20 Hz sampling rate. The measurements at each haematocrit took less than 4 minutes (until 2 12 data are accumulated) and no significant sedimentation was observed during this time.
The current signals were separated conventionally in two components: a dc component corresponding to the average current, and an ac time dependent component describing the fluctuations: i ( t )
 i dc
 i ac
( t ) ; i dc
 i ; i ac
( t )
 i ( t )
 i
The bracket denotes the time averaging operator over the measuring time T : i

T
1

T
 n


1 i ( n /

)
(1)
(2)
If the fluctuations are very fast, a rigorous approach is to consider also the averaging effect of the photo-detector. At the moment we focus only on fluctuations with characteristic times longer than 50 ms and the averaging effect of the detector can be neglected.
RESULTS AND DISCUSSION
In the following, we present the experimental results and we propose some mechanisms able to explain the effect of different parameters on the investigated phenomena. The relevant parameters are of two types: sample-related characteristics (microparticles density, optical and molecular properties of

I. TURCU, CRISTIAN V. L. POP, SILVIA NEAMTU microparticles and of the suspending medium) and geometric parameters pertaining to the experimental set-up (distance between sample and photo-detectors, detection angle, detector area, etc.).
We will first analyze the properties of the light intensity speckle pattern. A typical image capturing the speckle pattern is given in Fig.2. The image analysis is done in statistic terms the relevant parameters being the maximum value and the area of local light intensity maxima. The probability distribution of speckle maximum intensity values is given in Fig.3. As one can observe the distribution is
Poissonian.
Fig. 2 Stochastic interference pattern Fig. 3 Amplitude probability distribution
The probability distribution of speckle area has similar properties. The difference is given by the dependence of the two distributions on scattering centers concentration. The mean area (and also its distribution) is almost insensitive to scatterer concentration while the mean intensity increase linearly in the single scattering domain (small concentrations), attend a maximum and then decrease in the multiple scattering domain.
We present in the following the effect of scattering centers density on the static and dynamic characteristics of the time dependent photocurrent.
The dependence of the dc component of i(t), on haematocrit is a peak function. Neglecting the noise, the photocurrent starts from zero, increases until a maximum value is reached at H m
, and then decreases asymptotically to a small saturation value characteristic for the isotropic scattering regime.
For very dilute suspensions (10 2 – 10 3 cells/mm 3 corresponding to very small haematocrit values of H = 10 -5 – 10 -4 ) and for a cuvette thickness d = 1 mm for example, the probability of double scattering events is very small, the scattering being essentially a single scattering process. The forward scattering anisotropy is very high and the light intensity scattered at small angle increases with increasing cell density.

INTENSITY FLUCTUATING PATTERN OF LIGHT SCATTERED ON MICROPARTICLES
When the concentration is high enough so that the rate of multiple scattering events becomes comparable with the rate of single scattering, the process switches to multiple scattering. The scattered light looses gradually its anisotropy and consequently the amount of light scattered at small angle decreases.
Nevertheless, the total scattered light continues to increase until all incident photons are scattered and their propagation directions are distributed almost isotropically.
Depending on the external suspending medium, different values for the erythrocytes scattering cross-section was reported: from 63.82
 m 2 in plasma up to values by about 25 – 50 % higher (95
 m 2 ; 81,24
 m 2 ) in osmotically balanced saline solution (0.9% NaCl). Usually the erythrocyte scattering cross-section is in the domain 60 <
 s
< 90
 m 2 (depending on the properties of the suspending medium) and the erythrocyte volume is v e

90
 m 3 . For a sample thickness d = 1 mm the upper value of the single scattering domain is somewhere in the range 10 -3
- 1.5·10 -3 (0.1 – 0.15%).
Fig. 4 Density dependence of the dc photocurrent for erythrocytes suspended in saline buffer. The fluctuations (given by the error bars) are comparable with the mean value.
One can observe in Fig. 4 that the fluctuations of the scattered light intensity are very important in the maximum neighborhood becoming comparable with the scattered light intensity mean values. The characteristic time scale of the fluctuating component becomes shorter as the cell density increases from very small values up to physiologic values.
The H dependence of dc current does not change significantly (up to an irrelevant rescaling effect) with distance D between sample and photo-detectors, as long as θ is kept unchanged. Changes are observed rather in the fluctuating

I. TURCU, CRISTIAN V. L. POP, SILVIA NEAMTU behavior of ac component. The explanation is related to the different number of speckles captured by the photo-detector. Since both the average number of speckles in a solid angle
ΔΩ
, and the sensing area A of the detector are constant, any change in D modifies the solid angle as
ΔΩ = A/D 2
. Consequently, the detector captures more or less speckles, depending on distance D .
Fig. 5 Photocurrent fluctuations for single (upper curve) or multiple speckles (lover curve) capturing limits. The same time dependent stochastic interference pattern gives different photocurrent fluctuations.
Fig. 5 show the typical fluctuating behavior of i(t) measured at two distances D for the same H value. For small distances, ΔΩ is large enough so that the electric signal is the sum of many interference speckles and the fluctuations are distributed almost symmetrically about to the mean value. By decreasing the distance D one increase the number of captured speckles and the ratio of ac to dc components of i(t) decreases.
For large distances, to the limit of single speckle, the scattered light captured by photo-detector is either a single bright light maximum or a dark spot, depending on constructive or destructive interference, respectively. The current fluctuations are asymmetric increasing from and decreasing to a baseline corresponding to the dark photocurrent. At intermediate distances one finds mixtures of the described limits.
Our results allow us to conclude that the most relevant parameter controlling the dynamics of scattering process is the density of erythrocytes suspension. The artifacts are mainly due to the averaging effect of the detectors. In

INTENSITY FLUCTUATING PATTERN OF LIGHT SCATTERED ON MICROPARTICLES the far field experiments, the photo-detector capture a single interference speckle and give the correct fluctuating dynamics. By decreasing the distance between the sample and detector, the detecting process switches from the single speckle to many speckles detection and the fluctuations amplitude of the measured photocurrent decrease by an artificial smoothing.
The effect of multiple scattering is easily observed in the dependence of scattered light intensity on the scatterer density. Both dc and ac components of the photocurrent have peak type dependencies. The maximum of the corresponding curves indicates the entrance into the multiple scattering regime.
ACKNOWLEDGMENTS
This research was supported by Romanian Education and Research
Ministry, BIOTECH Program, research project 01-8-CPD-042.
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