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Optical Tweezers Microscope System


Optical Tweezers Microscope System
  • Available as Full System Including Microscope or Add-On System for an Existing Microscope
  • Sub-Piconewton Force Measurement and Nanometer Position Detection
  • Creates Multiple Computer-Controlled Traps in XYZ

 



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Sam Rubin
Sam Rubin
General Manager,
Thorlabs Imaging Systems

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DNA
Tweezers holding on to a probe bead can be used to measure forces acting on DNA strands.

Features

  • 1064 nm CW Power-Stabilized Laser
  • Optical Manipulation of Micro to Nanoscopic Particles
  • Dual Laser Paths Each with Galvo Steering Mirrors
  • Computer-Controlled Trap Locations in XYZ
  • High-Resolution Position and Force Measurements in the Back Focal Plane
  • 250 kHz Position Sensing Detector with Reverse Bias
  • Custom Configurations Available by Contacting ImagingSales@thorlabs.com
    • Other Laser Wavelengths and Powers
    • Add-On Version for Integration with Existing Microscopes

Optical Tweezers are a scientific tool generally used to spatially confine, translate, and measure properties of micro- to nanoscale objects. They provide a platform for ultra-sensitive observations of position changes of microscopic colloidal probes (such as silica or polystyrene spheres) which can then be used to calculate forces acting on the probe sphere. Thorlabs' full Optical Tweezers Microscope Systems are designed for users who desire an out-of-the-box optical tweezers solution. They are low-noise, low-drift systems that are suitable for a range of applications that probe elementary or complex environments. The system can also operate in conjunction with imaging modalities such as confocal microscopy and Raman spectroscopy.

A standard Thorlabs Optical Tweezer System includes a Nikon Eclipse Ti2-A inverted microscope, a 1064 nm trap-steering module, dual laser paths controlled by galvos, and a force/position measurement module. The system design interfaces with multiple ports on the Nikon Eclipse Ti2-A microscope, such as the side and epi-fluorescence ports. Alternatively, the system can be configured as an add-on for existing inverted microscopes, including those from other manufacturers. Other features, such as the laser wavelength and power, can also be customized based on the user’s requirements. Please contact ImagingSales@thorlabs.com for details and pricing.

Biological applications for tweezers systems include 2D surface patterning (such as the guiding of dendrite growth) and precise 3D micromanipulation of single cells (such as direct writing). Including a force module with the tweezer rig enables the acquisition of position and force measurements that are consistent with some popular assays found in published studies of molecular motors and single molecules such as DNA and proteins. Stress-strain relationships of cellular cytoskeleton networks (the viscoelastic properties related to the interior of single biological cells) can also be investigated. Calculations of a material’s mechanical storage and loss of moduli can be integrated into the tweezer control software upon request by contacting ImagingSales@thorlabs.com. Non-biological applications include droplet coalescence studies, microrheology, crystal growth studies, multi-body colloid science interaction measurements, and patterning of surface chemistry via photo-stimulation from a tweezer focus. See the Suggested Reading tab for a collection of journal articles illustrating the use of optical tweezers in these applications.

Thorlabs recognizes that each optical tweezers application has unique requirements.
If you have any feedback, questions, or need a quotation, please contact ImagingSales@thorlabs.com or call (703) 651-1700.

Components
Complete Optical Tweezers Microscope System Add-On Optical Tweezers Microscope System
  • Nikon Eclipse Ti2-A Inverted Microscope
  • 1064 nm Trapping Module, Dual Beam Path
  • Galvos for Each Path, or for a Single Path
  • Force Measurement Module for Dual or Single Beam Paths
  • High-Resolution XYZ Piezo Stage
  • Trapping Objective and Condenser
  • CMOS Camera (Options Available)
  • Software Package with Force Module Option
  • Computer and Dual Monitor
  • 1064 nm Trapping Module, Dual Beam Path
  • Force Measurement Module for Dual or Single Beam Paths (Optional Only)
  • Trapping Objective (Options Available with Consideration to Aberration Correction and Transmission)
  • CMOS Camera (Options Available)
  • Beam Dump Module
  • Software Package
  • Computer and Dual Monitor
Specifications
Optical Trap Specifications
Center Wavelength 1064 nm 
Emission Bandwidth <0.25 nm
Laser Head Output Power 5 W
Laser Power Noise (RMS) <0.2% (Under Optimal Environmental Conditions)
Beam Diameter at Objective Back Aperture 8 mm
Trap Scan Area 80 μm x 80 μm (With 1.3 NA)
Number of Independent Trap Beam Paths 2
Maximum Number of Stable Traps per Beam Path 15
Microscope Specifications
Inverted Microscope Nikon Eclipse Ti2-A
Focusing Via Nosepiece, Manual or Motorized
Condenser LWD 0.52 NA
Objective 1.3 NA , Oil Immersion (Other Options Available)
Force Module Specifications
Travel Range 200 µm x 200 µm x 200 µm
Stage Resolution (Closed Loop) 1 nm
Detection Dual Path Position Sensing Detector Module with Reverse Bias
Data Acquisition 16 Bits, 10 ns Timing Resolution
Computer Specifications
Operating System Windows® 10 Professional (English Version)
Disk Space 500 GB SSD + 1TB SSD
Monitor Dual Screen, 21.5" (54.6 cm)
RAM 32 GB
Video RAM 512 GB

A Tight Laser Beam Focus Traps Particles


About 400 years ago, in approximately 1619, Kepler reported comet tail deflection as a result of sunlight. Humans then spent the last several centuries suggesting that light can exert a force on matter, but only in the last half-century have the forces created by light at or below the microscopic level1-5 been measured with high resolution1,6-13. Optical tweezers have measured particle interactions in colloid science14 as well as the forces involved in the chemistry of single-molecules6-8,10,11. Optical tweezers, or optical traps, are both used commonly to connote a focused laser beam achieved with a high numerical aperture objective. Often, aberration correction and percent transmission of the objective at the laser wavelength is critical to the success of an optical trap. The diffraction-limited focal volume of the laser provided by the objective is where a particle with micron-scale dimensions can experience a force from the laser in the range of pico- to nanonewtons.

In the late 1960s, Arthur Ashkin at Bell Labs originally discovered that optical dipole forces can isolate and manipulate particles. Ashkin then began experimenting with optical traps with Steven Chu and other collaborators such as Joseph Dziedzic, John Bjorkholm and Alex Cable (the founder and current CEO of Thorlabs)2-5. The technique of manipulating matter via radiation pressure and gradient forces gained significant attention in physics and chemistry research all around the world. In 1997, Chu, along with Claude Cohen-Tannoudji and William Phillips, went on to win a Nobel prize in physics for the “development of methods to cool and trap atoms with laser light.” In 2018, Ashkin was awarded the Nobel prize in physics for “optical tweezers and their application to biological systems.” The essence of the techniques by these early inventors have remained at the core of optical tweezer research to this day. Trapping objects with light has become an important tool in a wide range of fields such as bioengineering, biophysics, material science, and fundamental colloid physics. This is due to the ability of optical tweezers to manipulate many types of particles, and to measure forces in the sub-piconewton to nanonewton regime, while simultaneously measuring positions at the nanometer scale.


  1. Jones, P.H., Maragò, O.M. and Volpe, G., 2015. Optical tweezers: Principles and applications. Cambridge University Press.
  2. Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E. and Chu, S., 1986. Observation of a single-beam gradient force optical trap for dielectric particles. Optics letters, 11(5), pp.288-290.
  3. Chu, S., Hollberg, L., Bjorkholm, J.E., Cable, A. and Ashkin, A., 1985. Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure. Physical review letters, 55(1), p.48.
  4. Chu, S., Bjorkholm, J.E., Ashkin, A. and Cable, A., 1986. Experimental observation of optically trapped atoms. Physical review letters, 57(3), p.314.
  5. Raab, E.L., Prentiss, M., Cable, A., Chu, S. and Pritchard, D.E., 1987. Trapping of neutral sodium atoms with radiation pressure. Physical review letters, 59(23), p.2631.
  6. Greenleaf, W.J., Woodside, M.T. and Block, S.M., 2007. High-resolution, single-molecule measurements of biomolecular motion. Annu. Rev. Biophys. Biomol. Struct., 36, pp.171-190.
  7. Perkins, T., 2009. Optical traps for single molecule biophysics: a primer. Laser & Photonics Reviews, 3(1-2), pp.203-220.
  8. Svoboda, K. and Block, S.M., 1994. Biological applications of optical forces. Annual review of biophysics and biomolecular structure, 23(1), pp.247-285.
  9. Svoboda, K., Schmidt, C.F., Schnapp, B.J. and Block, S.M., 1993. Direct observation of kinesin stepping by optical trapping interferometry. Nature, 365(6448), p.721.
  10. Moffitt, J.R., Chemla, Y.R., Smith, S.B. and Bustamante, C., 2008. Recent advances in optical tweezers. Annu. Rev. Biochem., 77, pp.205-228.
  11. Neuman, K.C. and Block, S.M., 2004. Optical trapping. Review of scientific instruments, 75(9), pp.2787-2809.
  12. Perkins, T., 2009. Optical traps for single molecule biophysics: a primer. Laser & Photonics Reviews, 3(1-2), pp.203-220.
  13. Gittes, F. and Schmidt, C.F., 1998. Interference model for back-focal-plane displacement detection in optical tweezers. Optics letters, 23(1), pp.7-9.
  14. Grier, D.G., 2003. A revolution in optical manipulation. Nature, 424(6950), p.810.

Trapping Theory


Click to Enlarge

Figure 1: Particle Scale versus Wavelength Scattering Regime (Adapted from Ref. 8)

Optical trapping theory has evolved over the years with regard to modeling the physical interaction of matter with light. There are two major regimes of mathematical theory to describe optical trapping forces, Rayleigh and Mie (see figure 1). Rayleigh theory models scattering objects as very small electric dipoles, and the photons interact with those dipoles elastically1,2. This model works well if the scattering particle diameter is small compared to the wavelength of light and the scattering particle is non-absorbing. A Rayleigh scattering force derives from polarization of those electric dipoles by the incoming light field, and a subsequent re-radiation of the light. The approximate upper limit for success with a Rayleigh model is when the scattering particle has a diameter of about 1/10th the wavelength of light. Additionally, because the laser presents a spatial gradient of the electric field of the incoming light wave, a gradient force acting on the scattering particle can occur1,2. However, when the particles are bigger than about 1/10th of a wavelength, the light wave scattered from one point on the particle can be out of phase with the light wave scattered from another point on that particle. Those differing wave contributions can interfere with each other, and consequentially the scattered light may no longer have a symmetrical light-scatter distribution around the particle (as is typically seen in the Rayleigh model). At this point, Mie theory becomes a preferable model1,3.


Click to Enlarge

Figure 2: The Net Forces on an Optical Trap. In the geometrical optics model, light rays 1 and 2 (yellow arrows) apply F1 and F2 (black arrows), respectively. A particle located before the focus (left) will experience a net forward force, while a particle behind the focus will experience a net backward force.

Mie theory accounts for not only the size, but also the refractive index of the scattering particles and refractive index of the surrounding media. Originally applied to many size regimes of non-absorbing material, variants of Mie can now apply to absorbing material or hybrid particles with coatings. Mie scattering theory has no upper size limit and is consistent with geometrical optics for large particles (which will be described below). The Rayleigh model can be considered as a special case within Mie theory for particles much smaller than the wavelength.

For particle sizes comparable to the laser wavelength, i.e., near the boundary of the Mie and Rayleigh models, the approximations that can simplify the scattering equation for these models may not apply, so their electromagnetic field analysis is more
complex1,3-7. See the Suggested Reading tab for additional textbooks and journal articles detailing these theories.


Click to Enlarge

Figure 3: Gradient Force and Radiation Pressure from the Scattering Force Act on Particle in Optical Trap

Instead of confronting the computational challenges posed by using Mie theory, many trapping scenarios can be approximated using simple ray or geometrical optics1. If the diameter of a trapped particle is larger than the wavelength of light, then geometrical optics can be applied. In this model (see figure 2), rays of light (yellow arrows) are refracted as they pass through the particle, and each refraction event transfers momentum to the particle as momentum is conserved after the light rays change direction. When the particle is slightly off-center, yet only a few microns away from the focus of the laser beam, the refracted rays transfer momentum to the particle such that the particle moves toward the xyz focus. The particle, still driven by the surrounding fluid’s Brownian forces, then samples its equilibrium xyz positions very close (typically within a few hundred nanometers) to the xyz-center of the focused beam. 

The forces in the axial z direction (the direction of laser propagation through the objective lens, and typically perpendicular to the microscope xy-image plane) have additional considerations. As rays are backscattered within the particle (at the particle-solvent interface), the light can transfer momentum to the particle multiple times, leading to a net scattering force in the forward direction of the beam (for spherical particles). This scattering force, which always displaces the particle slightly above the exact z focal center of the beam, is often referred to as “radiation pressure” (see figure 3).

Hence, optical tweezers that are aligned to focus exactly at the image plane of an inverted microscope tend to trap particles slightly above the image plane. Therefore, the gradient forces acting in all three dimensions can compete with the scattering force. In practice, this competition is influenced by the quality of the objective lens that forms the optical trap; a higher NA and the highest degree of aberration correction help to facilitate a stable optical trap that favors a strong gradient force over the radiation pressure. Ultimately, after all these optical force components are imposed on a particle (suspended in fluid), the net force FNET still varies as a function of position, therefore the particle is never absolutely still. This is because the random thermal motion of the fluid is energetic enough to perturb the bead position slightly away from the exact center of the optical trap, even when dampened by the frictional fluid drag force acting on the bead surface.  

Force Analysis

The Thorlabs Force Module operates by of quantifying position changes Δx of a probe bead. If you want to measure a force acting on a colloidal probe bead of mass mB residing inside of an optical trap, you need to first measure its position change in time, which is related to the probe bead’s one-dimensional velocity and acceleration:

We then can easily link position change in time to a force via Newton's 2nd Law:

Since a bead in an optical trap experiences many nano- and micro-scale forces approaching from many directions at any instant in time, one needs a more sophisticated method to extract information about individual forces acting on a probe bead. Fortunately, popular methods exist that translate data on colloidal bead motion into individual forces. Examples include: equipartition, Maxwell-Boltzmann distribution, mean-squared-displacement, drag-force, autocorrelation, light momentum, and power spectrum distribution (PSD) analysis. The Thorlabs force module’s primary approach to calibration of force is to use Langevin equation formalism followed by PSD analysis. This approach allows users to address noise contamination from the instrument and the environment .

In our analysis, FL (x,t), sometimes called the Langevin force, is the net force on a trapped probe bead. It is equal to the sum of forces from the laser trap, the bead-fluid friction, and the fluid’s thermal motion. If γ is the bead drag coefficient (γ = 6πηa), η is the fluid viscosity, a is the bead radius, κ is the Hooke’s law force constant (the bead-laser interaction is approximated as a linear spring restoring force, FTRAP), and X(t) is a random force due to thermal motion of the fluid in time, then the total force FL for a probe bead in a trap is:

The net bead inertia FNET (x,t) is then coupled to other forces to create a Langevin equation for a bead in a trap:

Brownian motion and fluid drag conditions are assumed to dampen out bead inertia in a typical bead force experiment. Therefore, it is valid to assume the probe bead’s inertia is insignificant (zero relative to other terms in the equation) over the timescale of our force measurements. Thus, the overdamped Langevin equation becomes the focus of our force module’s calibration:

With a few more steps, this equation can be recast in terms of the bead's Stokes–Einstein diffusion constant D, the laser-bead interaction potential U, and a white noise function W(t), where:
Diffusion Constant Trapping Force Equation
Therefore,
Based on this equation of motion, the rate of change of probe bead position (in one dimension) is:

1)      independent of bead mass,
2)      inversely proportional to the bead frictional drag with the fluid,
3)      proportional to the rate of change of the laser-bead interaction potential energy, as a function of position,
4)      proportional to a linear spring constant (assuming bead motion within a Hooke’s law approximation), and
5)      proportional to the diffusion constant (which is a function of temperature, T).

A Fourier transform is then applied to the above equation of motion, and with some algebraic manipulation of the Fourier-transformed complex position data xk, a Lorentzian function is formed representing the bead motion as a function of frequency. The power spectrum expectation value Pfexp relates to curve-fitting parameters fc (corner frequency) and Stokes-Einstein expectation value Dexp that one can use to find the spring constant (K = 2πγfc), the free-diffusion constant D and other calibration parameters that represent the strength of the optical trap and information about the local environment around the bead:

The position changes recorded within the total time ttotal for the acquisition, converted to nanometers, are derived from detector voltages using a calibrated detector responsivity. A force in units of piconewtons then results by multiplying the calibrated spring constant with subsequent position changes x(t) of the probe bead under the influence of a new external force:


  1. Jones, P.H., Maragò, O.M. and Volpe, G., 2015. Optical tweezers: Principles and applications. Cambridge University Press.
  2. Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E. and Chu, S., 1986. Observation of a single-beam gradient force optical trap for dielectric particles. Optics letters, 11(5), pp.288-290.
  3. Bohren, C. F., and D. R. Huffman 1983. Absorption and Scattering of Light by Small Particles. Wiley, New York.
  4. Almaas, E. and Brevik, I., 1995. Radiation forces on a micrometer-sized sphere in an evanescent field. JOSA B, 12(12), pp.2429-2438.
  5. Barton, J.P., Alexander, D.R. and Schaub, S.A., 1988. Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam. Journal of Applied Physics, 64(4), pp.1632-1639.
  6. Zemánek, P., Jonáš, A. and Liška, M., 2002. Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave. JOSA A, 19(5), pp.1025-1034.
  7. Ren, K.F., Greha, G. and Gouesbet, G., 1994. Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects. Optics communications, 108(4-6), pp.343-354.
  8. Kostylev, V.I., 2007. Scattering Fundamentals. Bistatic Radar: Principles and Practice, pp.193-223.
  9. Berg-Sørensen, K. and Flyvbjerg, H., 2004. Power spectrum analysis for optical tweezers. Review of Scientific Instruments, 75(3), pp.594-612.
Click to Enlarge
Figure 1: ThorSync Position Acquisition Panel

Optical tweezers interact with colloidal particles and apply a force toward the focus of a laser beam with a magnitude proportional to the distance of the particle from the laser focus (assuming small displacements away from the center of the trap)1. As the trapped particle samples the optical force, the over-damped Brownian motion of the particle deflects the laser’s scatter which is projected onto a photodiode. This causes observable voltage changes in the photodiode which, after calibration, can be mathematically related to the nanoscopic position displacements of the trapped particle. In a Thorlabs tweezers system, this scattered beam is then collected by a force module where the beam interference pattern is converted to an electrical signal by a position sensing photodiode, thus establishing what is termed in the literature as back focal plane interferometry2-4. The time series of analog diode voltages from the force module, representing trapped-particle positions, is digitized and recorded by a National Instruments™ acquisition card. The ThorSync™ software then analyzes this data and calculates nanometer-scale positions and sub-piconewton forces. 

Thorlabs’ Optical Tweezers Microscope Systems allow the user to run force measurements in situ using conventional microscope slide sample chambers. The force module facilitates position detection of trapped probe particles in two dimensions (xy), whereas the CCD camera enables the user to independently explore three-dimensional (xyz) imaging. The panel to the right shows the x and y voltage acquisition representing the centroid motion of a trapped silica bead incident on the back-focal-plane force module detector. Underneath those two signal channels is a separate channel showing a laser power time series with consistent milliwatt-level noise (from a 5 W laser head), as well as near-zero laser power drift. Laser pointing and power stability in Thorlabs' tweezers system is a function of thermal and electro-mechanical properties of the system because the laser passes through lenses and other electro-optic components. When properly warmed-up, nanometer-scale trap stability on the timescale of minutes is achievable, and this makes our system amenable to studies of molecular motors, single molecules, or extended polymer networks with observation times on the scale of minutes1,2,5-10

Accurate force measurements depend on the responsivity of the position detection method and the calibration of the force constant, both of which is a function of laser power and pointing stability, as well as the particle and surrounding fluid properties (such as size, shape and composition of the particles, and the dielectric properties of the particle and the fluid). One can think of a tweezers position or force measurement system as somewhat analogous to tuning a guitar, amplifier, and speakers for a specific kind of music performance quality. For example, researchers typically tune parameters like bead size, fluid viscosity, or even the sample chamber dimensions, to maximize performance with regard to position and force resolution, or position dynamic range, or the stiffness of the trap. Calibration of the sample via our tweezers system plays a central role in collecting good data. A few common methods for calibrating the force constant are power spectrum analysis, equipartition theorem, and Stokes' drag1,6

The equipartition theorem method, a simple way to describe bead motion, underlies the thermodynamic basis of a stationary trap. The average potential energy of the particle in the Hookean trap equates to the thermal energy of the solvent (without assuming a value for the local viscosity): 

Potential Energy of Hookean Trap

The equipartition method does not afford a very good way to assess and eliminate systematic measurement noise, however. Typically experimenters turn to mathematical transform techniques for this purpose. 


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Figure 2: ThorSync Power Spectrum

One such transform technique, which is the cornerstone of our position analysis method, is the popular calibration based on a power spectrum11, a frequency distribution resulting from the discrete Fourier transform of a time series of trapped-particle positions (driven by Brownian motion). This is fit to the response of a harmonic spring with over-damping due to the viscosity of the solvent. The functional form of the power spectrum looks like this equation:

Functional Form of the Power Spectrum

Here, Pfexp represents the power spectrum amplitudes, fc is the characteristic corner frequency of the trap, and Dexp is the expectation value of the bead’s Stokes–Einstein diffusion constant after the detector responsivity is factored. A rough example of a power spectrum acquired over two minute timescale with an initial curve fit (without the benefit of power spectrum corrections) is shown to the left. Here, low-frequency noise below 15 Hz can be attributed to subtle environment vibrations that percolated into a measurement. This spectrum shows how experimental data can diagnose the hardware and environment (table isolation) before an experiment. 

In a third, yet also popular force calculation, the Stokes drag-force method, the sample stage (and thus fluid) or the trap itself is translated with a range of velocities. A force balance between viscous drag acting on the particle from the fluid velocity versus the optical trap force is then computed. Since both equipartition and Stokes-drag methods rely on slightly different approaches than power spectrum analysis, each with their own physical assumptions, a user-defined approach can provide a sufficient way to calibrate the instrument and sample for most standard tweezer experiments.  

For inquiries on current or custom implementations of various analysis methods in our software, please contact ImagingSales@thorlabs.com


References

  1. Jones, P.H., Maragò, O.M. and Volpe, G., 2015. Optical tweezers: Principles and applications. Cambridge University Press.
  2. Neuman, K.C. and Block, S.M., 2004. Optical trapping. Review of scientific instruments, 75(9), pp.2787-2809.
  3. Gittes, F. and Schmidt, C.F., 1998. Interference model for back-focal-plane displacement detection in optical tweezers. Optics letters, 23(1), pp.7-9.
  4. Svoboda, K., Schmidt, C.F., Schnapp, B.J. and Block, S.M., 1993. Direct observation of kinesin stepping by optical trapping interferometry. Nature, 365(6448), p.721.
  5. Tassieri, M. ed., 2016. Microrheology with Optical Tweezers: Principles and Applications. CRC Press.
  6. Wilson, L., Matsudaira, P.T. and Sheetz, M.P., 1997. Laser tweezers in cell biology (Vol. 55). Academic Press.
  7. Greenleaf, W.J., Woodside, M.T. and Block, S.M., 2007. High-resolution, single-molecule measurements of biomolecular motion. Annu. Rev. Biophys. Biomol. Struct., 36, pp.171-190.
  8. Moffitt, J.R., Chemla, Y.R., Smith, S.B. and Bustamante, C., 2008. Recent advances in optical tweezers. Annu. Rev. Biochem., 77, pp.205-228.
  9. Perkins, T., 2009. Optical traps for single molecule biophysics: a primer. Laser & Photonics Reviews, 3(1-2), pp.203-220.
  10. Perkins, T., 2014., Angstrom-Precision Optical Traps and Applications, Annu. Rev. Biophys., vol. 43, pp. 279.
  11. Berg-Sørensen, K. and Flyvbjerg, H., 2004. Power spectrum analysis for optical tweezers. Review of Scientific Instruments, 75(3), pp.594-612.

Optical tweezers microscopes can be used in a variety of applications, not just those that inquire about position or force. Biological applications for tweezers systems include 2D surface patterning (such as the guiding of dendrite growth)1 and precise 3D micromanipulation of single cells (such as direct writing)2,3. Including a force module with the Thorlabs tweezer rig enables the acquisition of position and force measurements that are consistent with some popular assays found in published studies of molecular motors4 and single molecules5,6 such as DNA and proteins. The stress-strain relationships of cellular cytoskeleton networks (the viscoelastic properties related to the interior of single biological cells)7,8 can also be investigated.

In order to anticipate applications in which optical tweezer measurements can be successful, it is helpful to first appreciate how the physics (from instrument-to-sample) of position, time, and force act collectively to set constraints on what can or cannot be physically observed confidently within a given sample. Optical tweezers measurements in liquids rely on the thermal motion to drive bead displacements in the trap, so the detection of position changes in tweezers measurements are limited by that thermal noise. Researchers can tune that inherent physical noise in the sample to optimize the resolution and stability of a given measurement. Careful tuning of sample and instrument parameters thus work to build confidence toward the physical interpretation of the data and to qualify specific applications. 

When designing an experiment on a Thorlabs' tweezers system, the user selects the physical aspects of the probe bead, the solvent viscosity, the laser configuration, and other parameters in order to optimize performance.


Timescale-Bandwidth Considerations

For a single trapped particle, one first considers the minimum timescale tmin required to statistically resolve (at one sigma of statistical confidence, commonly known as the thermal-limit of bead statistics) a given minimum displacement xmin within a trap region described by constant stiffness κ:

One typically takes acquisitions longer than tmin in order to build confidence that one is sufficiently tuned-in to probe bead physics. For a silica bead of radius r in a moderately stiff trap of pure water (κ = 100 pN/mm, η = 0.001 kg·m-1·s-1, r = 5 x 10-7 m) at room temperature, one can expect a minimum of 4 ms of acquisition (sampled at 10 kHz) is needed to resolve a 1 nm position change. The reason a 10 kHz sample rate was chosen here is that one desires a sample rate minimally sufficient to capture enough frequency information for good curve-fitting of the power spectrum during the calibration of the given spring constant, and with consideration to Nyquist rate sampling. Sometimes obtained via an autocorrelation function, the characteristic frequency fchar and the characteristic time τ of the trap are both related to the ratio of the spring constant to the bead drag coefficient:

Characteristic Frequency


Position-Force Implications

Beyond basic tuning parameters, all tweezers measurement systems have some inherent drift over long times, so it also helps to look at a parameter called Allan variance to determine signal drift in the instrument’s position and force data9. The position error (derived from the Allan variance of position) σx_Allan and force error σF_Allan is related to half the averaged squared mean of neighboring positions: 


Error Derived from Allan Variance of Position and Force

By plotting these quantitites versus acquisition time for a single extended acquisition, one can find a best acquisition duration that minimizes position error σx. Allan variance is always a non-negative number and should only be calculated when the total acquisition time is greater or equal to the twice the characteristic time:

Total Acquisition Time

Allan variance can then be compared to the thermal limits of the experiment9,10. For an acquisition time ttotal averaged over several independent measurements N, the number of independent measurements can be related to the trap stiffness and the drag coefficient9,10:

Number of Independent Measurements Related to Trap Stiffness and Drag Coefficient

That equation along with the equipartition theorem:

Equipartition Theorem

leads to a standard “thermal limit” of position error:

Standard Thermal Limit of Error

Note, one can also re-cast that equation in terms of bandwidth (or sampling rate) to show that decreasing bandwidth minimizes position error11. However, a rate slightly higher than the corner frequency of the trap helps to achieve good curve-fitting slightly beyond the corner frequency.


Successful Application of Tuning Parameters

After addressing drift and basic tuning considerations, the positions of a probe bead can build confidence that subsequent physical properties derived from the calibrated sample will be physically meaningful. For example, the viscosity of the local fluid around the bead can then be determined by the following:

Viscosity of the Local Fluid around the Bead

with the characteristic time τ, temperature T, bead radius r, and the average bead-position-squared (x2). This viscosity calculation can be compared to viscosity results obtained from a curve-fitting procedure of the power spectrum. Then experimenters can begin to look at more fundamental questions about the local environment around the probe bead. For example, the local temperature of the fluid near the trap may slightly increase due to heating by the laser12. Bead radius typically has small variance from bead to bead in a given commercial batch. The ionic strength of some environments near the probe bead may be hard to assess, and this may affect local viscosity. Hydrodynamic drag from other nearby objects can affect the determination of viscosity.

The question for researchers becomes: how much uncertainty in microscopic physical parameters can one accept during an experiment, and what approaches are best to address these uncertainties with experimental design? To address the local environment near the probe bead, a 1064 nm laser, such as the one used in our tweezer systems, is smart choice because of its relatively low absorption by water. In some cases, this allows one to completely ignore temperature affects due to the laser. Also, fluid dynamics is a bulk theory, and researchers are actively trying to scale it down to the molecular domain. Similarly, another area of research aims to probe the interior of biological cells with tweezer probe beads in order to model the interior of the cell as a molecular stress-strain network. With a viscoelastic approach, optical tweezer position data can be used to explain physical properties (other than force) pertaining to storage and loss of energy within the material surrounding the probe bead. 

Such viscoelastic material response functions can be calculated from the tweezers' position time-series data. For a thorough review of the modeling opportunities that viscoelastic approaches afford, we urge the reader to consult Tassieri’s textbook listed in the references below, along with other listed journal articles on that subject. Thorlabs is happy to work with Optical Tweezers Microscope System customers to achieve custom designs toward these pursuits. Contact us, and we can adapt a software platform to investigate most of the popular load forces applied to a probe bead.


References

  1. Graves, C.E., McAllister, R.G., Rosoff, W.J. and Urbach, J.S., 2009. Optical neuronal guidance in three-dimensional matrices. Journal of neuroscience methods, 179(2), pp.278-283.
  2. Odde, D.J. and Renn, M.J., 1999. Laser-guided direct writing for applications in biotechnology. Trends in biotechnology, 17(10), pp.385-389.
  3. Nahmias, Y., Schwartz, R.E., Verfaillie, C.M. and Odde, D.J., 2005. Laser-guided direct writing for three-dimensional tissue engineering. Biotechnology and bioengineering, 92(2), pp.129-136.
  4. Neuman, K.C. and Block, S.M., 2004. Optical trapping. Review of scientific instruments, 75(9), pp.2787-2809.
  5. Perkins, T., 2009. Optical traps for single molecule biophysics: a primer. Laser & Photonics Reviews, 3(1-2), pp.203-220.
  6. Pang, Y. and Gordon, R., 2011. Optical trapping of a single protein. Nano letters, 12(1), pp.402-406.
  7. Tassieri, M. ed., 2016. Microrheology with Optical Tweezers: Principles and Applications. CRC Press.
  8. Tanner, N.A. and van Oijen, A.M., 2010. Single Molecule Tools, Part B: Super-Resolution, Particle Tracking, Multiparameter, and Force Based Methods. Walter, NG., editor.
  9. Czerwinski, F., Richardson, A.C. and Oddershede, L.B., 2009. Quantifying noise in optical tweezers by allan variance. Optics express, 17(15), pp.13255-13269.
  10. Gibson, G.M., Leach, J., Keen, S., Wright, A.J. and Padgett, M.J., 2008. Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy. Optics Express, 16(19), pp.14561-14570.
  11. Moffitt, J.R., Chemla, Y.R., Smith, S.B. and Bustamante, C., 2008. Recent advances in optical tweezers. Annu. Rev. Biochem., 77, pp.205-228.
  12. Peterman, E.J., Gittes, F. and Schmidt, C.F., 2003. Laser-induced heating in optical traps. Biophysical journal, 84(2), pp.1308-1316.

Thorlabs' software is included for free when tweezers products are purchased. Tweezers system software can be customized to suit the client's analysis needs. Our software package consists of two core products that also integrate with an assortment of Thorlabs imaging and position acquisition modalities: Thorlmage®LS and ThorSync™. With ThorlmageLS, one can acquire camera images and move the stage simultaneously while acquiring position and force data via ThorSync. These modules are optimized to run on a high-performance rack-mountable architecture to address computation and memory load, which ensures that there is no system latency during force acquisitions. Images of standard layouts for ThorSync and ThorImageLS can be seen below.


Click to Enlarge

Figure 2: ThorImageLS - Optical Tweezer Microscope Module

Click to Enlarge

Figure 1: ThorSync - Optical Tweezer Microscope Module

Textbooks

Greulich, K.O., 2012. Micromanipulation by light in biology and medicine: the laser microbeam and optical tweezers. Springer Science & Business Media.
Jones, P.H., Maragò, O.M. and Volpe, G., 2015. Optical tweezers: Principles and applications. Cambridge University Press.
Tassieri, M. ed., 2016. Microrheology with Optical Tweezers: Principles and Applications. CRC Press.
Wilson, L., Matsudaira, P.T. and Sheetz, M.P., 1997. Laser tweezers in cell biology (Vol. 55). Academic Press.
Gennerich, A., 2017. Optical Tweezers: Methods and Protocols, vol. 1486 of. Methods Mol. Biol.
Peterman, E.J. and Wuite, G.J., 2018. Single Molecule Analysis. Springer.
Selvin, P.R. and Ha, T., 2008. Single-molecule techniques. Cold Spring Harbor Laboratory Press.
Spies, M. and Chemla, Y.R., 2017. Single-Molecule Enzymology: Nanomechanical Manipulation and Hybrid Methods (Vol. 582). Academic Press.
Tanner, N.A. and van Oijen, A.M., 2010. Single Molecule Tools, Part B: Super-Resolution, Particle Tracking, Multiparameter, and Force Based Methods. Walter, NG., editor.
Bohren, C. F., and D. R. Huffman 1983. Absorption and Scattering of Light by Small Particles. Wiley, New York.
Kostylev, V.I., 2007. Scattering Fundamentals. Bistatic Radar: Principles and Practice, pp.193-223.

Optical Tweezers

Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E. and Chu, S., 1986. Observation of a single-beam gradient force optical trap for dielectric particlesOptics letters, 11(5), pp.288-290.
Berg-Sørensen, K. and Flyvbjerg, H., 2004. Power spectrum analysis for optical tweezers. Review of Scientific Instruments, 75(3), pp.594-612.
Moffitt, J.R., Chemla, Y.R., Smith, S.B. and Bustamante, C., 2008. Recent advances in optical tweezersAnnu. Rev. Biochem., 77, pp.205-228.
Neuman, K.C. and Block, S.M., 2004. Optical trappingReview of scientific instruments, 75(9), pp.2787-2809.
Peterman, E.J., Gittes, F. and Schmidt, C.F., 2003. Laser-induced heating in optical traps. Biophysical journal, 84(2), pp.1308-1316.
Perkins, T., 2014., Angstrom-Precision Optical Traps and Applications. Annu. Rev. Biophys, vol. 43, pp. 279.
Gittes, F. and Schmidt, C.F., 1998. Interference model for back-focal-plane displacement detection in optical tweezersOptics letters, 23(1), pp.7-9.
Pesce, G., Volpe, G., Maragó, O.M., Jones, P.H., Gigan, S., Sasso, A. and Volpe, G., 2015. Step-by-step guide to the realization of advanced optical tweezersJOSA B, 32(5), pp.B84-B98.
Czerwinski, F., Richardson, A.C. and Oddershede, L.B., 2009. Quantifying noise in optical tweezers by allan varianceOptics express, 17(15), pp.13255-13269.
Preece, D., Warren, R., Evans, R.M.L., Gibson, G.M., Padgett, M.J., Cooper, J.M. and Tassieri, M., 2011. Optical tweezers: wideband microrheologyJournal of optics, 13(4), p.044022.
Gibson, G.M., Leach, J., Keen, S., Wright, A.J. and Padgett, M.J., 2008. Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy. Optics express, 16(19), pp.14561-14570.

Atomic Trapping

Chu, S., Hollberg, L., Bjorkholm, J.E., Cable, A. and Ashkin, A., 1985. Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressurePhysical review letters, 55(1), p.48.
Chu, S., Bjorkholm, J.E., Ashkin, A. and Cable, A., 1986. Experimental observation of optically trapped atomsPhysical review letters, 57(3), p.314.
Raab, E.L., Prentiss, M., Cable, A., Chu, S. and Pritchard, D.E., 1987. Trapping of neutral sodium atoms with radiation pressurePhysical review letters, 59(23), p.2631.
Yuyama, K.I., Sugiyama, T. and Masuhara, H., 2013. Laser trapping and crystallization dynamics of L-phenylalanine at solution surfaceThe journal of physical chemistry letters, 4(15), pp.2436-2440.

Biophysics

Greenleaf, W.J., Woodside, M.T. and Block, S.M., 2007. High-resolution, single-molecule measurements of biomolecular motionAnnu. Rev. Biophys. Biomol. Struct., 36, pp.171-190.
Perkins, T., 2009. Optical traps for single molecule biophysics: a primerLaser & Photonics Reviews, 3(1-2), pp.203-220.
Svoboda, K. and Block, S.M., 1994. Biological applications of optical forcesAnnual review of biophysics and biomolecular structure, 23(1), pp.247-285.
Svoboda, K., Schmidt, C.F., Schnapp, B.J. and Block, S.M., 1993. Direct observation of kinesin stepping by optical trapping interferometryNature, 365(6448), p.721.
Graves, C.E., McAllister, R.G., Rosoff, W.J. and Urbach, J.S., 2009. Optical neuronal guidance in three-dimensional matricesJournal of neuroscience methods, 179(2), pp.278-283.

Optical Forces

Almaas, E. and Brevik, I., 1995. Radiation forces on a micrometer-sized sphere in an evanescent field. JOSA B, 12(12), pp.2429-2438.
Zemánek, P., Jonáš, A. and Liška, M., 2002. Simplified description of optical forces acting on a nanoparticle in the Gaussian standing waveJOSA A, 19(5), pp.1025-1034.
Ren, K.F., Greha, G. and Gouesbet, G., 1994. Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects. Optics communications, 108(4-6), pp.343-354.
Barton, J.P., Alexander, D.R. and Schaub, S.A., 1988. Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam. Journal of Applied Physics, 64(4), pp.1632-1639.
Grier, D.G., 2003. A revolution in optical manipulation. Nature, 424(6950), p.810.

Nanoscale Trapping

Zehtabi-Oskuie, A., Bergeron, J.G. and Gordon, R., 2012. Flow-dependent double-nanohole optical trapping of 20 nm polystyrene nanospheres.Scientific reports, 2, p.966.
Pang, Y. and Gordon, R., 2011. Optical trapping of a single proteinNano letters, 12(1), pp.402-406.
Chen, K.Y., Lee, A.T., Hung, C.C., Huang, J.S. and Yang, Y.T., 2013. Transport and trapping in two-dimensional nanoscale plasmonic optical latticeNano letters, 13(9), pp.4118-4122.
Wheaton, S., Gelfand, R.M. and Gordon, R., 2015. Probing the Raman-active acoustic vibrations of nanoparticles with extraordinary spectral resolutionNature photonics, 9(1), pp.68-72.

Surface Patterning

Odde, D.J. and Renn, M.J., 1999. Laser-guided direct writing for applications in biotechnology. Trends in biotechnology, 17(10), pp.385-389.
Nahmias, Y., Schwartz, R.E., Verfaillie, C.M. and Odde, D.J., 2005. Laser-guided direct writing for three-dimensional tissue engineering. Biotechnology and bioengineering, 92(2), pp.129-136.
Hoogenboom, J.P., Vossen, D.L.J., Faivre-Moskalenko, C., Dogterom, M. and Van Blaaderen, A., 2002. Patterning surfaces with colloidal particles using optical tweezers. Applied physics letters, 80(25), pp.4828-4830.

This optical tweezer simulation was made by Physics Education Technology (PhET) based at the University of Colorado Boulder (CU). It provides a sense of how optical tweezers are used in actual experiments. The JAVA™ applet simulates how a focused electric field from light waves creates the force which then controls probe bead displacement. The field vector magnitudes and directions in this applet are physically correct, and therefore useful for visualizing how force is related to the position of a probe bead in the tweezers. This applet was designed and tested by experts in optical tweezers, including Tom Perkins (who has published/invented some of the most sensitive force and position resolution experiments with tweezers at JILA).

This simulator has three tabs at the top of the screen: Physics of Tweezers, Fun with DNA, and Molecular Motors. The Physics of Tweezers tab aids in visualizing how electric field gradients can cause a force with electrically polarizable objects. Toggles on this screen allow the user to display vectors associated with electric fields in both the probe particle and the laser, which can be used to visualize the force that results from induced dipoles in dielectric particles like the ones used in testing (e.g., silica or polystyrene). The user can use their mouse to grab the particle, place it anywhere, and impose a fluid flow.


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