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05-02-2011, 11:43 AM
I am Karthik pursuing my B-Tech 3rd year in ECE.I would like to get some information about OPTICAL TWEEZERS.
Hoping a response from you at the earliest
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Joined: Feb 2011
21-03-2011, 09:33 AM
SHRAVAN PRAHLAD KULKARNI
32573647-Optical-Tweezers-Seminar-Report-Original.doc (Size: 1,005.5 KB / Downloads: 64)
The detection of optical scattering and gradient forces on micrometer sized particles was first reported in 1970 by Arthur Ashkin a scientist working at Bell Labs. Years later, Ashkin and colleagues reported the first observation of what is now commonly referred to as an optical trap: a tightly focused beam of light capable of holding microscopic particles stable in three dimensions.
One of the authors of this seminal 1986 paper, Steven Chu, would go on to use optical tweezing in his work on cooling and trapping neutral atoms. This research earned Chu the 1997 Nobel Prize in Physics.In an interview, Steven Chu described how Ashkin had first envisioned optical tweezing as a method for trapping atoms. Ashkin was able to trap larger particles (10 to 10,000 nanometers in diameter) but it fell to Chu to extend these techniques to the trapping of neutral atoms (0.1 nanometers in diameter) utilizing resonant laser light and a magnetic gradient trap (cf. Magneto-optical trap).
In the late 1980s, Arthur Ashkin and his colleagues first applied the technology to the biological sciences, using it to trap an individual tobacco mosaic virus andEscherichia coli bacterium. Throughout the 1990s and afterwards, researchers like Carlos Bustamante, James Spudich, and Steven Block pioneered the use of optical trap force spectroscopy to characterize molecular-scale biological motors. These molecular motors are ubiquitous in biology, and are responsible for locomotion and mechanical action within the cell. Optical traps allowed these biophysicists to observe the forces and dynamics of nanoscale motors at the single-molecule level; optical trap force-spectroscopy has since led to greater understanding of the stochastic nature of these force-generating molecules.
Optical tweezers have proven useful in other areas of biology as well. For instance, in 2003 the techniques of optical tweezers were applied in the field of cell sorting; by creating a large optical intensity pattern over the sample area, cells can be sorted by their intrinsic optical characteristics. Optical tweezers have also been used to probe the cytoskeleton, measure the visco-elastic properties of biopolymers, and study cell motility.
An optical tweezers is a scientific instrument that uses a focused laser beam to provide an attractive or repulsive force (typically on the order of piconewtons), depending on the refractive index mismatch to physically hold and move microscopic dielectric objects. Optical tweezers have been particularly successful in studying a variety of biological systems in recent years.
Optical tweezers are capable of manipulating nanometer and micrometer-sized dielectric particles by exerting extremely small forces via a highly focused laser beam. The beam is typically focused by sending it through amicroscope objective. The narrowest point of the focused beam, known as the beam waist, contains a very strong electric field gradient. It turns out that dielectric particles are attracted along the gradient to the region of strongest electric field, which is the center of the beam. The laser light also tends to apply a force on particles in the beam along the direction of beam propagation. It is easy to understand why if one considers light to be a group of particles, each impinging on the tiny dielectric particle in its path. This is known as the scattering force and results in the particle being displaced slightly downstream from the exact position of the beam waist, as seen in the figure.
Figure1: Dielectric objects are attracted to the center of the beam, slightly above the beam waist, as described in the text.
Optical traps are very sensitive instruments and are capable of the manipulation and detection of sub-nanometer displacements for sub-micrometre dielectric particles. For this reason, they are often used to manipulate and study single molecules by interacting with a bead that has been attached to that molecule. DNA and the proteins and enzymes that interact with it are commonly studied in this way.
For quantitative scientific measurements, most optical traps are operated in such a way that the dielectric particle rarely moves far from the trap center. The reason for this is that the force applied to the particle is linear with respect to its displacement from the center of the trap as long as the displacement is small. In this way, an optical trap can be compared to a simple spring, which follows Hooke's law.
Hooke’s Law:In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.
Mathematically, Hooke's law states that
x is the displacement of the end of the spring from its equilibrium position;
F is the restoring force exerted by the material; and
k is the force constant (or spring constant).
When this holds, the behavior is said to be linear.
Proper explanation of optical trapping behavior depends upon the size of the trapped particle relative to the wavelength of light used to trap it. In cases where the dimensions of the particle are much greater than the wavelength, a simple ray optics treatment is sufficient. If the wavelength of light far exceeds the particle dimensions, the particles can be treated as electric dipoles in an electric field. For optical trapping of dielectric objects of dimensions within an order of magnitude of the trapping beam wavelength, the only accurate models involve the treatment of either time dependent or time harmonic maxwell equations using appropriate boundary conditions.
Ray Optic Approach:
In cases where the diameter of a trapped particle is significantly greater than the wavelength of light, the trapping phenomenon can be explained using ray optics. As shown in the figure, individual rays of light emitted from the laser will be refracted as it enters and exits the dielectric bead. As a result, the ray will exit in a direction different from which it originated. Since light has a momentum associated with it, this change in direction indicates that its momentum has changed. Due to Newton's third law, there should be an equal and opposite momentum change on the particle.
Most optical traps operate with a Gaussian beam (TEM00 mode) profile intensity. In this case, if the particle is displaced from the center of the beam, as in (a) in the figure, the particle has a net force returning it to the center of the trap because more intense beams impart a larger momentum change towards the center of the trap than less intense beams, which impart a smaller momentum change away from the trap center. The net momentum change, or force, returns the particle to the trap center.
If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.
Figure2: When the bead is displaced from the beam center, as in (a), the larger momentum change of the more intense rays cause a net force to be applied back toward the center of the trap. When the bead is laterally centered on the beam, as in (b), the net force points toward the beam waist.
It must be noted that the standard tweezers works with the trapping laser propagated in the direction of gravity and the inverted tweezers works against gravity.
The electric dipole approximation:
In cases where the diameter of a trapped particle is significantly smaller than the wavelength of light, the conditions for Rayleigh scattering are satisfied and the particle can be treated as a point dipole in an inhomogenous electromagnetic field. The force applied on a single charge in an electromagnetic field is known as the Lorentz force.
The force on the dipole can be calculated by substituting two terms for the electric field in the equation above, one for each charge. The polarization of a dipole is P=q*d where d is the distance between the two charges. For a point dipole, the distance is infinitesimal, x1-x2. Taking into account that the two charges have opposite signs, the force takes the form
F = q(E1(x,y,z) - E2(x,y,z) + d(x1-x2)/dt*B)
F = q(E1(x,y,z) + ((x1-x2)∙Δ)E - E1(x,y,z) + d(x1-x2)/dt*B).
Notice that the E1 cancel out. Multiplying through by the charge, q, converts position, x, into polarization, P.
where in the second equality, it has been assumed that the dielectric particle is linear (i.e. p=άE).
F = (p.∆)E + dp/dt*B
F = ά[(E.∆)E + dE/dt*B].
In the final steps, two equalities will be used: (1) A Vector Analysis Equality, (2) One of Maxwell's Equations.
(E.∆)E = ∆(0.5*E2) - E*(∆*E).
∆*E = -∂B/∂t.
First, the vector equality will be inserted for the first term in the force equation above. Maxwell's equation will be substituted in for the second term in the vector equality. Then the two terms which contain time derivatives can be combined into a single term.
F = ά[0.5ΔE2 - E*(Δ*E) + dE/dt*B].
F=ά[0.5ΔE2 – E*(-dB/dt) + dE/dt*B].
F=ά[0.5E2 + d(E*B)/dt].
The second term in the last equality is the time derivative of a quantity that is related through a multiplicative constant to the Poynting vector, which describes the power per unit area passing through a surface. Since the power of the laser is constant when sampling over frequencies much shorter than the frequency of the laser's light ~1014 Hz, the derivative of this term averages to zero and the force can be written as
F = 0.5άΔE2
The square of the magnitude of the electric field is equal to the intensity of the beam as a function of position. Therefore, the result indicates that the force on the dielectric particle, when treated as a point dipole, is proportional to the gradient along the intensity of the beam. In other words, the gradient force described here tends to attract the particle to the region of highest intensity. In reality, the scattering force of the light works against the gradient force in the axial direction of the trap, resulting in an equilibrium position that is displaced slightly downstream of the intensity maximum. The scattering force depends linearly on the intensity of the beam, the cross section of the particle and the index of refraction of the trapping medium.
EXPERIMENTAL DESIGN, CONSTRUCTION AND OPERATION:
Optical Tweezers use light to manipulate microscopic objects as small as a single atom. The radiation pressure from a focused laser beam is able to trap small particles. In the biological sciences, these instruments have been used to apply forces in the pN-range and to measure displacements in the nm range of objects ranging in size from 10 nm to over 100 mm.
The most basic form of an optical trap is diagramed in Fig 1a. A laser beam is focused by a high-quality microscope objective to a spot in the specimen plane. This spot creates an "optical trap" which is able to hold a small particle at its center. The forces felt by this particle consist of the light scattering and
Figure 3: Optical Tweezers principles
gradient forces due to the interaction of the particle with the light (Fig 1b, see Details). Most frequently, optical tweezers are built by modifying a standard optical microscope. These instruments have evolved from simple tools to manipulate micron-sized objects to sophisticated devices under computer-control that can measure displacements and forces with high precision and accuracy.
Fig 1b shows a more detailed look at how an optical trap works. The basic principle behind optical tweezers is the momentum transfer associated with bending light. Light carries momentum that is proportional to its energy and in the direction of propagation. Any change in the direction of light, by reflection or refraction, will result in a change of the momentum of the light. If an object bends the light, changing its momentum, conservation of momentum requires that the object must undergo an equal and opposite momentum change. This gives rise to a force acting on the object.
In a typical optical tweezers setup the incoming light comes from a laser which has a "Gaussian intensity profile". Basically, the light at the center of the beam is brighter than the light at the edges. When this light interacts with a bead, the light rays are bent according the laws of reflection and refraction (two example rays are shown in Fig 1b). The sum of the forces from all such rays can be split into two components: Fscattering, the scattering force, pointing in the direction of the incident light (z, see axes in Fig 1b), and Fgradient, the gradient force, arising from the gradient of the Gaussian intensity profile and pointing in x-y plane towards the center of the beam (dotted line). The gradient force is a restoring force that pulls the bead into the center. If the contribution to Fscattering of the refracted rays is larger than that of the reflected rays then a restoring force is also created along the z-axis, and a stable trap will exist. Incidentally, the image of the bead can be project and implimentationed onto a quadrant photodiode to measure nm-scale displacements (see Further Reading).
Figure 4: Measurement of the 8-nm steps of kinesin.
When the bead is displaced from the center of the trap force felt by it is the restoring force of the optical trap works like an optical spring: the force is proportional to the displacement out of the trap. In practice, the bead is constantly moving with Brownian motion. But whenever it leaves the center of the optical trap the restoring force pulls it back to the center. If some external object, like a molecular motor, were to pull the bead away from the center of the trap, a restoring force would be imparted to the bead and thus to the motor. An example trace of a single kinesin motor taking 8 nm steps against a 5-pN force is shown in Fig 2.
Modern Optical Tweezers:
In practice, optical tweezers are very expensive, custom-built instruments. These instruments usually start with a commercial optical microscope but add extensive modifications. In addition, the capability to couple multiple lasers into the microscope poses another challenge. High power infrared laser beams are often used to achieve high trapping stiffness with minimal photo-damage to biological samples. Precise steering of the optical trap is accomplished with lenses, mirrors, and acousto/electro-optical devices that can be controlled via computer. The most basic optical tweezers setup will likely include the following components: a laser (usually Nd:YAG), a beam expander, some optics used to steer the beam location in the sample plane, a microscope objective and condenser to create the trap in the sample plane, a position detector (e.g. quadrant photodiode) to measure beam displacements and a microscope illumination source coupled to a CCD camera.
An Nd:YAG laser (1064 nm wavelength) is a common choice of laser for working with biological specimens. This is because such specimens (being mostly water) have a low absorption coefficient at this wavelength. A low absorption is advisable so as to minimise damage to the biological material, sometimes referred to as opticution. Perhaps the most important consideration in optical tweezers design is the choice of the objective. A stable trap requires that the gradient force, which is dependent upon the numerical aperture (NA) of the objective, be greater than the scattering force. Suitable objectives typically have an NA between 1.2 and 1.4.
While alternatives are available, perhaps the simplest method for position detection involves imaging the trapping laser exiting the sample chamber onto a quadrant photodiode. Lateral deflections of the beam are measured similarly to how its done using atomic force microscopy (AFM).
Expanding the beam emitted from the laser to fill the aperture of the objective will result in a tighter, diffraction-limited spot. While lateral translation of the trap relative to the sample can be accomplished by translation of the microscope slide, most tweezers setups have additional optics designed to translate the beam to give an extra degree of translational freedom. This can be done by translating the first of the two lenses labelled as "Beam Steering" in the figure. For example, translation of that lens in the lateral plane will result in a laterally deflected beam from what is drawn in the figure. If the distance between the beam steering lenses and the objective are chosen properly, this will correspond to a similar deflection before entering the objective and a resulting lateral translation in the sample plane. The position of the beam waist, that is the focus of the optical trap, can be adjusted by an axial displacement of the initial lens. Such an axial displacement causes the beam to diverge or converge slightly, the end result of which is an axially displaced position of the beam waist in the sample chamber.
Figure 5: A generic optical tweezers diagram with only the most basic components.
Visualization of the sample plane is usually accomplished through illumination via a separate light source coupled into the optical path in the opposite direction using dichroic mirrors. This light is incident on a CCD camera and can be viewed on an external monitor or used for tracking the trapped particle position via video tracking.
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