Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects
An optical tweezers technique is used for ultraprecise micromanipulation to measure positions of micrometer-scale objects with a precision down to the nanometer scale. It consists of a high-performance research microscope with a motorized scanning stage and a sensitive position detection system. Up...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Cite this: | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects / Rania Sayed // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 3. — С. 349-354. — Бібліогр.: 29 назв. — англ. |
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| citation_txt | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects / Rania Sayed // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 3. — С. 349-354. — Бібліогр.: 29 назв. — англ. |
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| description | An optical tweezers technique is used for ultraprecise micromanipulation to measure positions of micrometer-scale objects with a precision down to the nanometer scale. It consists of a high-performance research microscope with a motorized scanning stage and a sensitive position detection system. Up to 10 traps can be used quasisimultaneously. Non-photodamage optical trapping of Escherichia coli (E. coli) bacteria cells of 2 µm in length, as an example of motile bacteria, has been shown in this paper. Also, efficient optical trapping and rotation of polystyrene latex particles of 3 µm in diameter have been studied, as an optical handle for the pick and place of other tiny objects. A fast galvoscanner is used to produce multiple optical traps for the manipulation of micro-sized objects, and the optical forces of these trapped objects are quantified and measured according to the explanation of the ray optics regime. The diameter of the trapped particle is bigger than the wavelength of the trapping laser light. The force constant (k) has been determined in real time from the positional time series recorded from the trapped object that is monitored by a CCD camera through a personal computer.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 3. P. 349-354.
doi: https://doi.org/10.15407/spqeo20.03.349
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
349
PACS 42.15.Eq, 87.80.Fe, 87.85.Uv
Quantitative optical trapping and
optical manipulation of micro-sized objects
Rania Sayed
National Institute for Standards (NIS, Egypt), Metrology and Nanotechnology Lab,
Tersa Street, El Haram Giza, Egypt
P. O. Box: 136 Giza, Code No. 12211
E-mail: rsayed.nis@gmail.com, phone: 002 01005567106
Abstract. An optical tweezers technique is used for ultraprecise micromanipulation to
measure positions of micrometer scale objects with a precision down to the nanometer
scale. It consists of a high performance research microscope with motorized scanning
stage and sensitive position detection system. Up to 10 traps can be used quasi-
simultaneously. Non photodamage optical trapping of Escherichia coli (E. coli) bacteria
cells of 2 µm in length, as an example of motile bacteria, has been shown in this paper.
Also, efficient optical trapping and rotation of polystyrene latex particles of 3 µm in
diameter have been studied, as an optical handle for the pick and place of other tiny
objects. A fast galvoscanner is used to produce multiple optical traps for manipulation of
micro-sized objects and optical forces of these trapped objects quantified and measured
according to explanation of ray optics regime. The diameter of trapped particle is bigger
than the wavelength of the trapping laser light. The force constant (k) has been
determined in real time from the positional time series recorded from the trapped object
that is monitored by a CCD camera through a personal computer.
Keywords: optical tweezers, multiple traps, force calibration, nanometer displacement,
E. coli bacteria.
Manuscript received 15.03.17; revised version received 08.07.17; accepted for
publication 06.09.17; published online 10.10.17.
1. Introduction
Optical tweezers are commonly used for trapping and
manipulation with micro- and nanoparticles [1-4]. Since
their invention in 1986, the field of optical trapping has
become a hot-spot topic for research, and its applications
have extended from microfabrication [5] to drug deli-
very [6]. Furthermore, optical tweezers are considered as
a quantitative tool to analyze forces applied to trapped
objects and precisely determine these forces in the range
of pico-newton scale, with resolution at the femto-
newton, and nanometer scaled displacements. Many
experiments have been done by using these analytical
optical tweezers in many fields of research, namely:
physics, biology, nanotechnology, and materials science.
In recent time, manipulation, rotation and assembly of
different kinds of nanostructures [7, 8], such as carbon
nanotubes [9], nanowires [10, 11], and polymer
nanofibers [12], have been also done by using the optical
tweezers technique. Also, they have used to manipulate
living cells [13-16] and to investigate the motility and
flagellar rotation of single bacterial cells [17-19].
In general, optical trap is performed by using a
highly focused laser beam into a transparent particle
with a higher refractive index than that of its
surroundings, to generate a large electric field gradient
helps to attract the particle towards the focal spot
without any mechanical contact [20]. The infrared
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 3. P. 349-354.
doi: https://doi.org/10.15407/spqeo20.03.349
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
350
wavelength is commonly used for optical trapping
because of its low absorptivity in biological material and
low degree of optical photodamage on biological
samples. The precision of using the optical tweezers
instruments is crucial for accuracy of the calibration
method aimed at a trapped transparent object. A well-
known calibration procedure is recording the stochastic
movement of the trapped transparent particle and
comparing its statistical behaviour with the theory of the
Brownian motion in a harmonic potential [21].
2. Theory and overview
The kinetic force induced by light on matter relies on the
size of trapped transparent particle. In case of trapping
micro-sized particles, the ray optics approach is used to
describe the origin of this force as presented by Ashkin
[22]. The obtained results from Ashkin’s calculation are
valid only for particles with sizes larger than the
wavelength of the laser light. In this regime, the light
beam consists of individual rays. Each ray reflects and
refracts on the surface of the transparent particle. The
optical trapping force produced by each ray is simply
calculated by the exchange of momentum between light
and matter. This kinetic force is presented by the
momentum change per unit time. The total force is the
sum of the forces calculated for each ray.
The total force from a single ray is divided into two
components, F1 and F2 for vertical and horizontal
directions, respectively, and is presented by the
following simple formulae [23]:
( )[ ]
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
++
+−
−+=
rRR
RrT
R
c
nPF
2cos21
2cos22cos
2cos1
2
2
1
θθ
θ (1)
( )[ ]
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
++
+−
−=
rRR
RrT
R
c
nPF
2cos21
2sin22sin
2sin
2
2
2
θθ
θ , (2)
where n, r, P and c are the refractive index of surround-
ding medium, angle of refraction, power of a single ray
and the speed of light, respectively. R and T are the
Fresnel reflection and refraction coefficients of the
incident angle θ. The total force on the trapped particle is
the sum of these two components expressed by Eqs (1)
and (2) over individual rays of the laser beam. The force
is estimated from Stokes’ law based on the drag force
induced by moving surrounding medium.
An optical tweezers is generally achieved by tightly
focusing a laser beam in order to generate a high
intensity hotspot towards which the particles are
attracted. The resulting optical forces are typically
distinguished into scattering forces, due to the forward
radiation pressure, and gradient forces, generated by the
gradient of the light intensity. Successful trapping can be
obtained, when the gradient forces exceed the scattering
ones. In general, there are several requirements for
achieving stable optical trap such as trapping power,
particle size, particle shape, refractive index, surface
roughness, absorption, numerical aperture of the
objective and transverse intensity distribution of the
laser light [23]. The trapping beam has Gaussian focal
intensity distribution, so that the gradient force can be
expressed as a harmonic restoring force acting on the
particle:
( )0xxkF −= , (3)
where k is the spring constant describing the stiffness of
the potential, x – position of the particle, and x0 denotes
its equilibrium position.
Trap stiffness calibration (Drag force method).
Calibration of trapped object is essential for quantitative
force and displacement measurements, and it can be
done in several ways. In this experiment, Stokes drag
calibration method presented to measure the
displacement of a trapped micro-sphere and E. coli
bacterium cell from its equilibrium position. This
method depends on the response to viscous forces
produced by the medium, and it is given by
k x = 6πηrυ, (4)
where η is the viscosity of the liquid, r – diameter of the
trapped particle, and υ – velocity of the fluid.
Since nanoscale measurements of both force and
displacement require a well-calibrated system for
determining the position, high sensitive position
detection system is required to track microscopic
objects.
3. Experimental set-up
The schematic of optical trapping system is shown in
Fig. 1. The optical trap used for quantitative
measurements of the optical forces is implemented in a
Nikon inverted microscope to visualize the sample. As it
can be seen, the experimental setup consists of the
continuous wave laser beam (1064 nm, 8 W) with a
symmetrical intensity distribution around the beam axis.
It is strongly focused by a high numerical aperture
objective of a microscope (Plan Fluor 100x NA 1.3).
Before entering the microscope objective, a beam
expander (two convex lenses) is used to expand the
diameter of the laser beam for achieving a tiny beam
spot size on the trapping region. An extremely sensitive
position detector, quadrant photodiode, is used to
measure 3D position of micrometer scale objects with a
precision down to the nanometer scale. The position of
the trapped micro-sized object is traced by back focal
plan interferometry. The sample chamber mounted on a
motorized scanning stage to properly navigate and
provide positional control of the trap inside the chamber
with nanometer resolution. For achieving the optimal
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 3. P. 349-354.
doi: https://doi.org/10.15407/spqeo20.03.349
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
351
Fig. 1. Layout of the experimental setup. L – lenses, FL – focus lens, GS – galvoscanner, BS – beam splitter, A – analyser, S –
sample, P – polarizer, LS – light source, DM – dichroic mirror, F – infrared fillter, QPD – quadrant photodiode, M – mirror,
CCD – charge couple device camera to image the sample.
conditions of trapping, immersion oil with a refractive
index of 1.54 is used with the large numerical objective
to minimize spherical aberrations. A very rapid galvanic
scanner system is used in the path of the laser beam to
create multiple quasi-simultaneous traps, up to 10 traps,
and to move them in the field of view. Groups of trapped
objects can be rotated around their center or scaled up
and down. In this experiment, multiple trapping is easily
achieved by scanning the laser beam rapidly to prevent
escaping the particle from the trapping region before the
next beam scan take places. White light source
illuminates the sample that is imaged in a CCD camera
for videomicroscopy. Finally, the optical tweezers
instrument is mounted on an anti-vibration table to
eliminate the mechanical vibrations.
4. Results and discussion
Quantifying optical trapping forces for micro-sized
objects is done by using the high-tech optical tweezers
instrument for ultra-precise micromanipulation. This
study has been performed in a liquid environment using
polystyrene micro-spheres of 3 µm (Sigma, UK, LB30)
and E. coli bacteria of 2 µm in length (Strain No.
ATCC25922). All measurements were made at room
temperature (22 °C). In this experiment, the single
microscopic object was trapped in three dimensions with
efficient detection of position. The calibration procedure
was performed by converting the detected voltage signal
to displacement units, and the forces exerted on the
trapped object displaced from its equilibrium position
was defined by tracking and analysing its dynamics.
Trapping of E. coli bacteria. In general, E. coli
bacteria cells in the aqueous environment can swim, run,
tumble, and move anywhere inside the sample chamber.
It is considered as an example of motile bacteria.
Bacterial dynamics are directly related to bacterial
motility, and it can be observed in the trapping process
[19, 24]. The single cell level of E. coli can be damage-
free trapped in the focus without any mechanical contact
and tends to align itself along the optical axis [25]. This
type of bacteria has two kinds of movements: Brownian
motion and flagella-mediated propulsion. The positional
signal recorder from trapped bacterium cell contains of
both movements, so it has unreasonable information
about force constant. Also, trapping more than one
E. coli bacterium cell in the trap shows a complicating
noise in to the recorded positional signal. In this work,
very diluted sample is prepared to avoid bacterial
accumulation at the trap during measurements. Fig. 2
shows the calibration of optical tweezers by measuring
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 3. P. 349-354.
doi: https://doi.org/10.15407/spqeo20.03.349
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
352
Fig. 2. Calibration of optical forces on an E. coli bacterium cell of 2 µm in length. (a) Image of E. coli bacterium (white arrow
pointed to the trapped cell). (b) Voltage signal of trapped cell in x and y as recorded from a quadrant photodiode. (c) Trajectory of
trapped cell. (d) Two position histograms of trapped single E. coli bacterium cell (blue one) and trapped two E. coli bacteria cells
(red one) for the trapping power 0.86 W.
the Brownian motion of the trapped E. coli bacterium
cell. Fig. 2a shows the image of E. coli bacteria. The
voltage signal from the quadrant photodiode is detected
as shown in Fig. 2b, and the trajectory has shown in
Fig. 2c. As the optical trap is exerting a harmonic
potential on the trapped particle, the position distribution
is well described by a Gaussian distribution as shown in
Fig. 2d. During the experiment, the trapped single
bacterium cell showed different dynamics. It can be
trapped, arrested for a while, and then escaped away
from trapping region. This behaviour is happened
because of the energy stored in the trapped cell released
and converted into kinetic energy leading to escape away
from the trap [19].
Trapping of polystyrene spheres (The optical
handles). Optical tweezers are commonly used to
perform force measurements in the range of femto- to
pico-newton scale and to detect nanometer scaled
displacements. The stiffness constant, k, can be
evaluated from the Stokes drag calibration method by
monitoring the Brownian motion of an optically trapped
polystyrene latex sphere. This kind of micro-spheres can
be used as an optical handle to grab and manipulate
other tiny objects, such as DNA [26, 27], viruses [28]
and molecules [29] by attaching them to the surface of
spherical bead. This could be useful for biological
studies and for optically assisted self-assembly
processes. The stiffness constants of trapped bead
perpendicular to the propagation direction of the
trapping laser (kx and ky) measured directly against
trapping power as shown in Fig. 3a, and they are nearly
identical. A laser trap is dragged across 3-µm
polystyrene latex particles exerting optical force to trap
objects in a potential well formed by light as shown in
Fig. 3b. In this experiment, multiple trapping is created
by rapid scanning of laser beam with galvoscanner to
prevent the trapped particle from escaping from the trap
before the next beam scan occurs. It is fairly easy to trap
and manipulate two or more particles of almost the same
size independently at the same time by using the same
number of laser beams as particles. Fig. 4 shows three
trapped particles placed in a triangle shape and rotated
around their center without affecting on each others by
reflected or scattered light.
5. Conclusions
To conclude, optical tweezers are very attractive
techniques for trapping and manipulation of microscopic
objects without any mechanical contact. Here, damage
free trapping of E. coli bacterium cell and trap
characterization and calibration of polystyrene spheres
are described. These micro-spheres can be used alone or
as optical handles attached to extremely small objects,
such as virus and DNA, to apply the calibrated force.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 3. P. 349-354.
doi: https://doi.org/10.15407/spqeo20.03.349
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
353
Fig. 3. Calibration of optical forces on a polystyrene sphere. (a) Estimated optical force constant on 3-µm polystyrene bead as a
function of the trapping power in x and y directions. (b) Potential energy and position histogram of 3-µm polystyrene bead at
trapping power 1.2 W.
Fig. 4. Rotation of the optical handles (Polystyrene particles of 3-µm diameter) around their centres.
This experiment may be extended and developed for
studying bacterium drug interactions and cell-cell
interactions.
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© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
354
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|
| id | nasplib_isofts_kiev_ua-123456789-214946 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:45:27Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Sayed, Rania 2026-03-05T12:02:01Z 2017 Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects / Rania Sayed // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 3. — С. 349-354. — Бібліогр.: 29 назв. — англ. 1560-8034 PACS: 42.15.Eq, 87.80.Fe, 87.85.Uv https://nasplib.isofts.kiev.ua/handle/123456789/214946 https://doi.org/10.15407/spqeo20.03.349 An optical tweezers technique is used for ultraprecise micromanipulation to measure positions of micrometer-scale objects with a precision down to the nanometer scale. It consists of a high-performance research microscope with a motorized scanning stage and a sensitive position detection system. Up to 10 traps can be used quasisimultaneously. Non-photodamage optical trapping of Escherichia coli (E. coli) bacteria cells of 2 µm in length, as an example of motile bacteria, has been shown in this paper. Also, efficient optical trapping and rotation of polystyrene latex particles of 3 µm in diameter have been studied, as an optical handle for the pick and place of other tiny objects. A fast galvoscanner is used to produce multiple optical traps for the manipulation of micro-sized objects, and the optical forces of these trapped objects are quantified and measured according to the explanation of the ray optics regime. The diameter of the trapped particle is bigger than the wavelength of the trapping laser light. The force constant (k) has been determined in real time from the positional time series recorded from the trapped object that is monitored by a CCD camera through a personal computer. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects Article published earlier |
| spellingShingle | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects Sayed, Rania |
| title | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects |
| title_full | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects |
| title_fullStr | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects |
| title_full_unstemmed | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects |
| title_short | Quantitative Optical Trapping and Optical Manipulation of Micro-Sized Objects |
| title_sort | quantitative optical trapping and optical manipulation of micro-sized objects |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214946 |
| work_keys_str_mv | AT sayedrania quantitativeopticaltrappingandopticalmanipulationofmicrosizedobjects |