Download 1 Introduction 2 Theory of Optical Trapping

OPTICAL TWEEZERS: THE FORCE OF LIGHT
1 Introduction
1.1 Optical tweezers
Light can exert forces on small dielectric objects1,2. A tightly focused beam of light can
trap micron-sized objects, such as latex beads. This “optical trapping” principle has found
many applications in chemistry, physics and biology. It has found its most prominent use
in biophysics, because it allows the manipulation (like with a tweezers) of single
biomolecules. For example, “optical tweezers” have been used to measure the elasticity
of single DNA molecules3 and the forces induced by molecular motors such as kinesin4
that generate the forces in living cells.
1.2 About this practical
A simple optical tweezers setup is available in the undergraduate laboratory at LION. The
setup can be used to explore the possibilities of this technique. You will perform the
following experiments5,6:
• Setting up trapping
• Measuring Brownian motion of trapped particles, and characterizing the trap
strength and shape.
• Measurement of the viscous drag on trapped particles.
Before you can participate in the practical, you have to read this manual carefully, with
special emphasis on section 3.3, which deals with safety. Also you have to prepare the
assignments in section 4.1 and show them to the assistant on the first afternoon. Although
most essential information is contained within this manual, you are strongly encouraged
to consult the references and sources cited in this manual. Some of these are available in
printed form at the practical.
This setup is rather new, and is still being developed and improved. Therefore, not all
experiments described in this manual will be completely available. Please report any
malfunctioning of the setup to the responsible assistant.
2 Theory of Optical Trapping
2.1 Simple explanation of optical trapping
A basic and intuitive explanation of optical trapping can be given by a ray description.
Consider a transparent bead (whose index of refraction is larger than that of surrounding
medium), placed in an intensity gradient (Figure 1). A ray that travels through the bead is
refracted twice due to the change in index of refraction at the interfaces. The change in
direction of the ray is accompanied by a corresponding change in momentum of the ray,
and with an opposite change of momentum of the bead. The force the ray exerts on the
bead is proportional to the number of photons in the ray, and thus to the local intensity of
the beam. The resulting force of all the rays traveling through the bead is directed to
highest intensity: the focus of the beam. This force is called the “gradient force”, due to
the gradient in electric field which produces it.
A second important force which acts on the bead is called the “scattering force”.
Light that hits the bead is not only refracted but also reflected on, and scattered from the
bead. This generates radiation pressure on the bead, and results in a force in the direction
of propagation of the beam. The bead is therefore trapped slightly downstream of the
beam focus. In order to achieve trapping the gradient force has to be larger than the
scattering force. This can be achieved by using high NA (numerical aperture) objectives.
Figure 1 Ray optics description of the gradient force. A bead is illuminated by a beam of light with a
Gaussian intensity profile. Two representative rays of light of different intensities (represented by
lines of different thickness) from the beam are shown. The refraction of the rays by the bead changes
the momentum of the photons. The larger momentum change of the more intense rays results in a net
force toward the focus. [Image adapted from http://en.wikipedia.org/wiki/Optical_tweezers]
2.2 Energy considerations
Expressions for the trapping force can be derived by considering the Lorentz force on the
bead. The light induces a dipole moment, P, in the bead. The energy of the induced dipole
in the electric field is then:
r r
r r
(1)
U = − P • E = −α E • E ∝ − I ,
where α is the polarizibility of the bead, E is the electric field, and I is the intensity. The
force is then given by:
(2)
F ∝ ∇I ,
and depends on parameters such as the beam waist, particle size, the NA of the objective,
and the index of refraction.
A more complete, but still very basic theory is given by Bechoefer and Wilson5.
3 Optical Tweezers Setup
A schematic drawing of the undergraduate optical tweezers setup at LION is given in
Figure 2. The setup can be split in two parts: 1. trapping optics, which are used to set up
an optical trap in the sample and 2. imaging optics, which are used to image and view the
sample with a CCD camera and a microscope. These parts are discussed below, as well as
operating instructions for the setup.
Figure 2 Schematic overview of the undergraduate optical tweezers setup at LION. A laser beam (λ =
658 nm, 65 mW) is sent into the objective with a dichroic mirror. A steering lens placed at the right
position, allows for the manipulation of the trap position, while overfilling the back aperture of the
objective. The laser light can optionally be captured and imaged on a quadrant photodiode, to
monitor the bead position.
A bright LED is collimated on the bead sample. The light is collected with an oil immersion objective
(100X, NA = 1.2). After filtering out the reflections from the laser, the sample is imaged on a CCD
camera. Image processing can be used to monitor the bead position.
3.1 Trapping Optics
A red diode laser (Power Technology IQ1A70-LD1508-SG, λ = 658 nm, P = 65mW) is
used to set up the optical trap. A modulation voltage is used to control the laser intensity.
A pair of mirrors is used to align the beam. A lens (f=+35mm), which can be manipulated
in x, y, and z, is used to control the position of the trap in the sample. Simultaneously it
expands the beam so that it overfills the back aperture of the objective, to achieve the
minimum beam spot size at the focus (and maximum trap strength). A dichroic mirror
(reflects the laser, transmits other light) is placed behind the objective to couple in the
laser light. A beam stop blocks the transmitted beam. The oil immersion objective
(Edmund Optics NT38-344, 100X, NA = 1.25, DIN 160 mm) focuses the laser beam into
the sample of latex beads. The transmitted light is collected with a condenser lens and
imaged on a quadrant photodiode, which can be used to monitor the position of the bead
in the trap.
The beam path is at a constant height of 125 mm above the optical table, for safety
reasons and to facilitate easier alignment of the trap. Because of this, the sample and
objective are placed sideways; adverse effects of this configuration are sedimentation of
the beads to the bottom of the sample, and leaking of immersion oil.
3.2 Imaging Optics
The sample is held in a xyz-translation stage. The z axis can be used manually to place
the sample in focus. The x and y axes are motorized and can be used to look at different
areas of the sample. A green LED is used as a light source to illuminate the sample. A
collimator and condenser lens are use to collimate the light. The microscope objective
produces an image (see Figure 3 a.) of the sample at 150 mm from the microscope
shoulder. A CCD camera is placed at this position. A filter is used to suppress scattered
laser light. A computer is used to acquire and process the images.
Y- position (µm)
-1.05
5 µm
-1.10
-1.15
-1.20
0
a)
1
2
3
4 5 6
Time (s)
7
8
9
10
b)
Figure 3 Typical data acquired with the optical tweezers setup. a) Image of a 2 µm bead. Notice the
diffraction rings b) The y position of the bead as a function of time, determined by the maximum
correlation of a) with its mirror image.
3.3 Safety Considerations
The laser used in this experiment is a class 3B laser: it poses a serious eye hazard from
viewing the direct beam or specular reflections. In this case your eye will be damaged
before a blink reflex sets in.
Take the following precautions when working with the laser:
• always wear protection goggles (these attenuate the beam 1000X)
• never look directly into the beam, and keep the laser well below eye level
• prevent reflections (don’t wear rings, watches etc.)
• use minimal power when aligning the beam.
• consult laser safety instructions:
http://www.biophys.leidenuniv.nl/index.php?module=article&view=45
The LED is also dangerous to the eye. Never look directly into the light.
4 Assignments & Experiments
This chapter contains assignments and instructions to prepare you for the practical work.
Furthermore, possible experiments are described with some clues how to tackle them.
4.1 Preparatory Assignments
As a mandatory preparation for the experiments, answer the following questions. They
are not easy, but spend at least 1 hour on them:
• What is the diffraction limited spot size of a laser (λ = 658 nm) focused by an
objective with NA = 1.25?
•
•
•
•
Assume there is a latex bead in the focus of the previous question, which reflects
~ 1.5% of the incident light. Estimate the scattering force acting on the bead from
a 50 mW laser beam.
Each pixel in the image represents an area of 90x90 nm. The accuracy of the
position detection algorithm is 5 nm (see Figure 3). How is this possible?
Read §4.4.2. Assume a latex bead is trapped in an optical trap with spring
constant kx = 10 pN/µm. What will be the typical size of the position fluctuations
at room temperature?
Read §4.4.3. Write down the equation of motion for a bead in the trap. This
describes a damped oscillation. Is the system overdamped? What does it imply for
the motion of the bead?
4.2 Aligning and Operating the Setup
In this section, a number of procedures for aligning and operating the setup are given.
Please read them carefully. More detailed instructions will be given on the first day of the
practical.
• Never touch a mirror, lens, or filter with your fingers, since the fatty acids on your
skin may degrade the surface. If you accidentally touch a component, ask the
assistant to clean it.
• The objective is an oil immersion objective. This means that the objective will
only form a proper image if it is optically connected to the sample by a thin layer
of oil, whose index of refraction matches that of glass. Always apply a droplet of
oil on the sampleholder when loading it.
• To make a sample, inject ~ 0.01% 2 µm latex beads in a buffer of PBS (phosphate
buffered saline, pH 7.8) with 0.05% Tween-20 (a detergent to prevent aggregation
of beads) in the closed sampleholder via suction with a syringe.
• Screw the sampleholder on the microscope stage. Move the Z-axis toward the
objective until the oil makes contact. Do not crash the sample into the objective!
This could seriously damage it. The objective is spring-loaded, so you will still
have enough room to safely manipulate the sample. X and Y manipulation are
done with motorized spindles, operated from the computer. Do not move these out
of range.
• Test microscope alignment by looking at the various surfaces (oil-glass, glasssample, maybe sample-glass). Make use of reflections of the laser focus from the
surface.
• The entire setup will be pre-aligned by the assistant. Optimal trapping will be
achieved if the laser is centered and aligned along the optical axis of the objective.
Adjustments to the laser alignment can be done with the steering lens and the
normal mirror in front of it. Alignment can be checked by looking at the reflection
of the laser focus.
• The z-position of the trap can be manipulated by sliding the steering lens along a
rail. This also requires adjustment of the x and y position, since the axes are not
completely decoupled.
•
Trapping of a bead can be achieved by moving a bead to the vicinity of the trap.
The bead will be ‘sucked’ into the trap. There is a difference in trapping
efficiency if you approach the bead from below or from above.
4.3 Data Acquisition and Analysis Software
A Labview VI “Optical Tweezers” is used as the main program to operate the setup. This
program can be used to manipulate the sample in x and y, to look at the camera output, to
set measurement parameters such as the laser intensity, and to record and save data. It
contains a routine to extract the position of the bead (see Figure 3 b.): it finds the
maximum correlation of the image with its mirror image. The program communicates
with the setup through a number of PCI-cards: a NI framegrabber card for the camera, a
NI-DAQ card for acquisition and generation of voltages, and a Thorlabs motion card.
Data processing can be done with software such as Origin.
4.4 Description of Experiments
The following experiments can be performed on the setup. Start with the first two
experiments. The experiments marked with a * are not fully operational yet. Ask the
assistant for the current status.
4.4.1 Trapping a bead
Your first goal is to repeatedly trap a bead. This will allow you to get to know the setup:
sample preparation, operating the microscope, and aligning the trap. How do you
recognize trapping?
Time: 1 afternoon
4.4.2 Analysis of trap strength and shape
Trap a bead and perform data analysis on the Brownian motion of the bead in a trap.
Extract the spring constants kx, ky, and kz* of the trap, its dependence on the laser power,
and the shape of the trap. Use the equipartition theorem for a particle in a harmonic
potential:
1
1
k x x 2 = k BT ,
(3)
2
2
where x denotes the displacement along the x-axis, <…> averaging over all datapoints, kB
is Boltzmann’s constant, and T the absolute temperature. Does this mean you can extract
information from noise? Check reference 5 for more detail.
Time: 1-2 afternoons
4.4.3 Applying external forces: the effect of viscous drag
Apply a fluid flow and measure the corresponding bead displacement in the harmonic
potential as an alternative way of calibrating the trap. You can either apply a constant
velocity to the trapped bead, or oscillate the sample with a triangular wave. What will be
the response of the bead? Use the Stokes relation for the drag on the bead:
F = 6πηRv
(4)
where F is the force on the bead, η is the viscosity of the buffer, R is the bead radius, and
v is the velocity of the fluid. Check reference 6 for more detail.
Time: 1 afternoon
4.4.4 Investigating dominant noise sources
Perform some scientific detective-work and investigate noise sources, e.g. noise from the
environment, flaws in setup design, noise from image processing. Which sources can you
find, which is the dominant one, how do these affect/limit your measurements?
Time: 1 afternoon.
4.4.5 Measuring fast fluctuations: Quadrant Photodiode*
Measure the power spectrum of bead fluctuations, extract trap parameters.
Time: 1-2 afternoons
4.4.6 Characterizing biological samples*
Trap bacteria, cells, measure DNA elasticity.
5 Info, Tips & Tricks
5.1 Info
Assistant:
Wiepke Koopmans
Teacher:
Thijs Aartsma
[email protected]
5968/5745
k11.23/11.01
[email protected]
5967
k11.21b
5.2 Links
• General background:
http://en.wikipedia.org/wiki/Optical_tweezers
http://www.nbi.dk/%7Etweezer/introduction.htm
http://www.biop.dk/Research/Tweezers.htm
• Famous labs using optical tweezers:
• Block:
http://www.stanford.edu/group/blocklab/
• Bustamante: http://alice.berkeley.edu/
• Optical tweezers movies:
http://www.atsweb.neu.edu/mark/opticaltweezersmovies.html
http://www.cosmic.ed.ac.uk/Facilities/tweezers.htm
• Laser safety:
http://www.biophys.leidenuniv.nl/index.php?module=article&view=45
5.3 References
1
Ashkin et al., Opt. Lett. 11, 288 (1986)
Chu, Science 252, 861 (1991)
3
Smith et al., Science 271, 795 (1996)
4
Svoboda et al., Nature 365, 721 (1993)
5
Bechhoefer and Wilson, Am.J.Phys. 70, 393 (2002)
6
Smith et al., Am.J.Phys. 67, 26 (1999)
2