Optical tweezers and dynamic light scattering Introduction ...

ANNALS OF OPTICS - XXV ENFMC - 2002
Optical tweezers and dynamic light scattering
Nathan B. Viana * , Rodrigo T. S. Freire and Oscar N. Mesquita
*Departamento de Física, ICEX, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo
Horizonte, CEP 30123-970, MG, Brazil
nathan@fisica.ufmg.br
Abstract
In this work we study the Brownian motion of an optically trapped bead using the light intensity
correlation technique. By measuring backscattered profiles and temporal-intensityautocorrelation
functions (ACFs) we determine the trap stiffness using two different methods. As
an application we measure the Stokes friction coefficient of a trapped bead as a function of its
distance from a surface.
Introduction
Lasers can be used to trap small dielectric objects. This fact was first perceived by Ashkin and coworkers in their
pioneer works about pressure radiation [1].
They made a sample with polystyrene micro spheres in water and passed through it a laser in the TEM 00 mode.
They were interested in the study of laser action over the micro spheres observing their motion. For a typical
laser power 10 -3 W, a force in the pN range would act upon the micro sphere. They observed that when the laser
beam reached the spheres the spheres started to move towards the beam center where the light intensity is
maximum. When they focused the beam with a lens the micro spheres were trapped near its focus. This
apparatus has been named an optical tweezer.
In 1987 [2] an experiment with the Tobacco virus turned out to be one of the most important applications for the
optical tweezer. They were in trouble with the light scattering experiments and suspected that sample bacterial
contamination was the source of the problems. They mounted the optical tweezer in a microscope and
confirmed that contamination was present. In addition they observed that the bacteria were trapped and after few
seconds in the trap they died. Changing the argon laser by an infrared one, they could trap, manipulate and
isolate the bacteria E. Coli [3] for hours.
In this work we present a study of optical tweezers using as a sample polystyrene beads in water and as a tool the
light intensity correlation technique. The trap stiffness was measured from light intensity fluctuations caused by
the Brownian movement of the spheres. As an application we measure the parallel Stokes friction coefficient of a
trapped bead as function of its distance from a surface.
Experimental Setup
The basic setup used is shown in FIG. 1. An inverted optical microscope Nikon TE300 with an infinity corrected
objective (100X, N. A. = 1.4) is used to make the optical tweezer, observe the bead and collect the scattered
intensity. In one port of the microscope we use a CCD camera (CCD-72 DAGE-MTI) for visualization. In
another port we use a photo detector (EG&G-Photon Counting Module, SPCM-200-PQ-F500), with collection
diameter of 150 µm mounted in Newport XY-Stages to be precisely positioned. The EG&G photo detector
delivers TTL pulses ready to be fed into a Brookhaven BI-9000AT digital correlator. An IR-laser (SDL, 5422-
H1) operating at 832 nm, with maximum power of 150mW is used for the optical tweezer. The light of a He-Ne
laser (SP-127) is the scattering probe. A line filter for wavelength 632.8 nm is put in front of the photo detector
to eliminate the IR and any light other than the He-Ne laser light. A half-wave plate and polarizers are used to
control the intensity and polarization of the He-Ne incident and scattered light. A micro-motor (m) was
connected to the mirror (M1) that drives the IR laser on the objective. The purpose of this motor is to move the
IR beam and, consequently, move the trapped bead in relation to the fixed He-Ne laser beam to obtain the
backscattering profile as a function of time. From an accurate measurement of the bead speed, time is converted
into position and one gets backscattering profile as a function of position. The motion of the bead was recorded
with the CCD camera. Images were analyzed, and the bead speed was then extracted. The image pixel size was
measured by recording the motion of a bead stuck on the microscope slide and driven by one of the previous
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ANNALS OF OPTICS - XXV ENFMC - 2002
calibrated stages. Samples were made with polystyrene spheres of diameter 2.8 µm (Polysciences) in deionized
water. The setup was mounted on a homemade isolating table.
Figure 1: Experimental setup.
Results and Discussions
In FIG. 2 we show a typical intensity time auto-correlation function, ACF. In that figure we can see two decay
times. The shortest one is related to the bead Brownian movement in the direction perpendicular to the objective
axis and the largest is related to the axial Brownian movement. The decay time and the trap stiffness are related
by τ = γ/ k where τ is the decay time, k is the trap stiffness and γ is the Stokes friction coefficient on the bead.
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ANNALS OF OPTICS - XXV ENFMC - 2002
Figure 2: Typical ACF.
Another way to obtain the trap stiffness is measuring the backscattered profile. With the intensity versus position
profile we can relate intensity fluctuations to bead position fluctuations
depend of the trap stiffness as
x
2
kBT
= , then we can obtain k.
k
2
x
. The bead position fluctuations
For a bead of 1.4 µm radius positioned 10 µm above the microscope glass-slide and laser power in the bead of 6
mW , the trap stiffness obtained from the decay time is
5 .8 ± 5% mdyn/ cm and from amplitude
fluctuations 5 .9 ± 5% mdyn/ cm , in good agreement.
The method we are using has an important advantage over others. We can measure the trap stiffness and friction
coefficient independently. From the bead position fluctuations we get the trap stiffness. From the stiffness
obtained and the decay time measured we get the friction coefficient on the bead.
So as an application of this technique we measure the parallel γ
||
Stokes friction coefficient as a function of the
bead´s distance (h) from the glas-slide. The result is shown in the FIG. 3. The continuous curve is a fit of :
γ
γ
||
0
= 1
−
9
16
R 1 R
+ −
h 8 h
3
45
256
4
R
h
−
1
16
R
h
5
−1
,
where γ
0
is the friction far from the slide. There is a good agreement with theory [4] and our data.
Conclusions
Figure 3: Parallel Stokes friction coefficient.
We used the intensity correlation technique to measure the trap stiffness of an optical trap. In addition we
measure the Stokes coefficient friction as a function of the bead distance from a surface. Theory and
experiments are in good agreement indicating that the method developed here can be consistently used.
Acknowledgements
This work was supported by the Brazilian Agencies: Fundação de Amparo à Pesquisa do Estado de Minas
Gerais – FAPEMIG, Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq and FINEP-
PRONEX.
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References
[1] A. Ashkin, Proc. Natl. Acad. Sci. USA, 94, 4853 (1997).
[2] A. Ashkin, and J. M. Dziedzic, Science, 235, 1517 (1987).
[3] L. Stryer, Biochemistry, (W. H. Freeman and Company, New York, 1995).
[4] N. B. Viana, R. T. S. Freire, and O. N. Mesquita, to appear in PRE (2002).
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