Optical Trap Stiffness Research Articles

Aberration correction in holographic optical tweezers using a high-order optical vortex.

Holographic optical tweezers are a powerful optical trapping and manipulation tool in numerous applications such as life science and colloidal physics. However, imperfections in the spatial light modulator and optical components of the system will introduce detrimental aberrations to the system, thereby degrading the trapping performance significantly. To address this issue, we develop an aberration correction technique by using a high-order vortex as the correction metric. The optimal Zernike polynomial coefficients for quantifying the system aberrations are determined by comparing the distorted vortex and the ideal one. Efficiency of the proposed method is demonstrated by comparing the optical trap intensity distribution, trap stiffness, and particle dynamics in a Gaussian trap and an optical vortex trap, before and after aberration corrections.

Cooke-Triplet tweezers: more compact, robust, and efficient optical tweezers.

We present a versatile three-lens optical design to improve the overall compactness, efficiency, and robustness for optical tweezers based applications. The design, inspired by the Cooke-Triplet configuration, allows for continuous beam magnifications of 2-10×, and axial as well as lateral focal shifts can be realized without switching lenses or introducing optical aberrations. We quantify the beam quality and trapping stiffness and compare the Cooke-Triplet design with the commonly used double Kepler design through simulations and direct experiments. Optical trapping of 1 and 2μm beads shows that the Cooke-Triplet possesses an equally strong optical trap stiffness compared to the double Kepler lens design but reduces its lens system length by a factor of 2.6. Finally, we demonstrate how a Twyman-Green interferometer integrated in the Cooke-Triplet optical tweezers setup provides a fast and simple method to characterize the wavefront aberrations in the lens system and how it can help in aligning the optical components perfectly.

Optimizing phase to enhance optical trap stiffness

Phase optimization offers promising capabilities in optical tweezers, allowing huge increases in the applied forces, trap stiff-ness, or measurement sensitivity. One key obstacle to potential applications is the lack of an efficient algorithm to compute an optimized phase profile, with enhanced trapping experiments relying on slow programs that would take up to a week to converge. Here we introduce an algorithm that reduces the wait from days to minutes. We characterize the achievable in-crease in trap stiffness and its dependence on particle size, refractive index, and optical polarization. We further show that phase-only control can achieve almost all of the enhancement possible with full wavefront shaping; for instance phase control allows 62 times higher trap stiffness for 10 μm silica spheres in water, while amplitude control and non-trivial polarization further increase this by 1.26 and 1.01 respectively. This algorithm will facilitate future applications in optical trapping, and more generally in wavefront optimization.

Tunable nanophotonic array traps with enhanced force and stability.

A nanophotonic trapping platform based on on-chip tunable optical interference allows parallel processing of biomolecules and holds promise to make single molecule manipulation and precision measurements more easily and broadly available. The nanophotonic standing wave array trap (nSWAT) device [Nat. Nanotechnol. 9, 448 (2014); Nano Lett. 16, 6661 (2016)] represents such a platform and can trap a large array of beads by the evanescent field of the standing wave of a nanophotonic waveguide and reposition them using an integrated microheater. In this paper, by taking a systematic design approach, we present a new generation of nSWAT devices with significant enhancement of the optical trapping force, stiffness, and stability, while the quality of the standing wave trap is resistant to fabrication imperfections. The device is implemented on a silicon nitride photonic platform and operates at 1064 nm wavelength which permits low optical absorption by the aqueous solution. Such performance improvements open a broader range of applications based on these on-chip optical traps.

Fast Bayesian inference of optical trap stiffness and particle diffusion

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.

Theory of optical-tweezers forces near a plane interface

Optical-tweezers experiments in molecular and cell biology often take place near the surface of the microscope slide that defines the bottom of the sample chamber. There, as elsewhere, force measurements require force-calibrated tweezers. In bulk, one can calculate the tweezers force from first principles, as recently demonstrated. Near the surface of the microscope slide, this absolute calibration method fails because it does not account for reverberations from the slide of the laser beam scattered by the trapped microsphere. Nor does it account for evanescent waves arising from total internal reflection of wide-angle components of the strongly focused beam. In the present work we account for both of these phenomena. We employ Weyl's angular spectrum representation of spherical waves in terms of real and complex rays and derive a fast-converging recursive series of multiple reflections that describes the reverberations, including also evanescent waves. Numerical simulations for typical setup parameters evaluate these effects on the optical force and trap stiffness, with emphasis on axial trapping. Results are in good agreement with available experimental data. Thus, absolute calibration now applies to all situations encountered in practice.

Identification of volume phase transition of a single microgel particle using optical tweezers

Poly (N-isopropyl acrylamide-co-acrylic acid) (PNIPAM-co-Aac) microgel particles are pH responsive and exhibit volume phase transition (VPT) upon variation of pH. Dynamic light scattering (DLS) is used conventionally to identify VPT and requires a dilute suspension with particle concentration ∼107 particles cm−3 and if particles are polydisperse in nature, DLS data interpretation is relatively difficult. Here we show that optical tweezers allow one to measure the VPT of a single microgel particle by measuring the optical trap stiffness, κ of trapped particle as a function of pH. We report here a sudden change in κ at VPT, which is shown to arise from a sudden decrease in particle diameter with a concomitant increase in the refractive index of the particle at VPT.

Two-Photon Fluorescence Tracking of Colloidal Clusters.

In situ dynamics of colloidal cluster formation from nanoparticles is yet to be addressed. Using two-photon fluorescence (TPF) that has been amply used for single particle tracking, we demonstrate in situ measurement of effective three-dimensional optical trap stiffness of nanoparticles and their aggregates without using any position sensitive detector. Optical trap stiffness is an essential measure of the strength of an optical trap. TPF is a zero-background detection scheme and has excellent signal-to-noise-ratio, which can be easily extended to study the formation of colloidal cluster of nanospheres in the optical trapping regime. TPF tracking can successfully distinguish colloidal cluster from its monomer.

Optical trapping performance of dielectric-metallic patchy particles.

We demonstrate a series of simulation experiments examining the optical trapping behavior of composite micro-particles consisting of a small metallic patch on a spherical dielectric bead. A full parameter space of patch shapes, based on current state of the art manufacturing techniques, and optical properties of the metallic film stack is examined. Stable trapping locations and optical trap stiffness of these particles are determined based on the particle design and potential particle design optimizations are discussed. A final test is performed examining the ability to incorporate these composite particles with standard optical trap metrology technologies.

Simulation and measurement of stiffness for dual beam laser trap using residual gravity method

Dual-beam optical trap is constituted by two beams of unfocused counter-propagating laser. It has advantages such as several equilibrium points, small optical power density, large capture range and easier integration with other technologies, which optical tweezers may not achieve. Dual-beam optical trap stiffness is an important parameter to describe its mechanical properties. On the basis of quartz-substrate dual-beam optical fibre trap unit, we demonstrate a simple method for measuring stiffness. Residual gravity offset by buoyancy may provide a tiny force for the optical trap. By measuring the relations between the captured particle's axial equilibrium position and residual gravity, we may calibrate the optical trap stiffness. This method simply requires measuring the relative position of the particle in the steady state of the optical trap, and dynamic measurement of the particles location is not needed, so we can get a high position accuracy by long time measuring, thus the accuracy of the stiffness calibration is improved. In this paper, we simulated and carried out experiments to measure the stiffness of a dual-beam fibre optical trap unit based on a quartz-substrate. We simulate the stiffness of several Mie particles with different materials and sizes in dual-beam optical trap as well as the relation between the waist radius of fundamental mode Gaussian beam and stiffness. Stiffness measurement experiment is conducted using the residual gravity method. Stiffness values measured in experiments are consistent with the simulation results, which verify the validity and accuracy of the method.

Optical Trap Stiffness Online Measurement System Based on FPGA

For investigating the mechanical properties of optical tweezers, a data collection/process/control system based on FPGA is designed and developed to measure the optical trap stiffness. A four quadrant detector is used to track the positions of the trapped microsphere, the digital data converted by a high precision ADC is transferred through the USB interface into PC for processing and displaying, and the PC controls an electronically controlled platform to realize zero alignment of the four quadrant detector. Experiments show that this system could be effectively used for on-line optical trap stiffness measurement.

Measurements of the force fields within an acoustic standing wave using holographic optical tweezers

Direct measurement of the forces experienced by micro-spheres in an acoustic standing wave device have been obtained using calibrated optical traps generated with holographic optical tweezers. A micro-sphere, which is optically trapped in three dimensions, can be moved through the acoustic device to measure forces acting upon it. When the micro-sphere is subjected to acoustic forces, it's equilibrium position is displaced to a position where the acoustic forces and optical forces are balanced. Once the optical trapping stiffness has been calibrated, observation of this displacement enables a direct measurement of the forces acting upon the micro-sphere. The measured forces are separated into a spatially oscillating component, attributed to the acoustic radiation force, and a constant force, attributed to fluid streaming. As the drive conditions of the acoustic device were varied, oscillating forces (>2.5 pN pp ) and streaming forces (<0.2 pN) were measured. A 5 μm silica micro-sphere was used to characterise a 6.8 MHz standing wave, λ = 220 μm, to a spatial resolution limited by the uncertainty in the positioning of the micro-sphere (here to within 2 nm) and with a force resolution on the order of 10 fN. The results have application in the design and testing of acoustic manipulation devices.

Plasmonic Optical Trapping in Biologically Relevant Media

We present plasmonic optical trapping of micron-sized particles in biologically relevant buffer media with varying ionic strength. The media consist of 3 cell-growth solutions and 2 buffers and are specifically chosen due to their widespread use and applicability to breast-cancer and angiogenesis studies. High-precision rheological measurements on the buffer media reveal that, in all cases excluding the 8.0 pH Stain medium, the fluids exhibit Newtonian behavior, thereby enabling straightforward measurements of optical trap stiffness from power-spectral particle displacement data. Using stiffness as a trapping performance metric, we find that for all media under consideration the plasmonic nanotweezers generate optical forces 3–4x a conventional optical trap. Further, plasmonic trap stiffness values are comparable to those of an identical water-only system, indicating that the performance of a plasmonic nanotweezer is not degraded by the biological media. These results pave the way for future biological applications utilizing plasmonic optical traps.

Trapping red blood cells in living animals using optical tweezers

The recent development of non-invasive imaging techniques has enabled the visualization of molecular events underlying cellular processes in live cells. Although microscopic objects can be readily manipulated at the cellular level, additional physiological insight is likely to be gained by manipulation of cells in vivo, which has not been achieved so far. Here we use infrared optical tweezers to trap and manipulate red blood cells within subdermal capillaries in living mice. We realize a non-contact micro-operation that results in the clearing of a blocked microvessel. Furthermore, we estimate the optical trap stiffness in the capillary. Our work expands the application of optical tweezers to the study of live cell dynamics in animals.

Positioning Accuracy in Optical Trap Assisted Nanostructuring

The well-known optical diffraction limit prevents laser radiation from being focused to arbitrary small spots. Utilizing spherical micro-particles as near-field lenses provides an easy and robust way to overcome this limitation and to generate nanoscale surface structures. To achieve this, microspheres are positioned and translated with an optical trap and then used to focus pulsed laser radiation. The paper at hand presents the factors which influence the positioning accuracy in optical trap assisted nanostructuring. Theoretical considerations are backed up with experimentally obtained values of the surface structure accuracy in dependence of optical trap stiffness and particle position.

The Function of Myosin-10 In Vitro and Inside Filopodia

Myosin-10 is an actin based motor that localizes to actin rich areas within the cell and carries cargos including netrin receptors and β integrins. Using transient kinetic and single molecule assays, a number of groups have shown that myosin-10 can act as a processivemotor, capable of translocating along actin as a single molecule. However, both the mechanical and kinetic parameters are quite diverse amongst different groups (Kerber & Cheney 2011, J. Cell Sci. 124:3733-3741 and references therein). Negative stain electron microscopy and single particle image processing performed using a truncated myosin-10 construct (1 - 940 a.a.) containing a leucine-zipper at the C-terminal end confirmed dimerization of the molecule with a distance between motor domains of ∼50 nm. When bound to F-actin, the myosin-10 lever arm makes a shallower angle with respect to the filament axis than seen for acto-myosin-5 or acto-myosin-2. In vitro actin gliding assays showed myosin-10-HMM moved F-actin at ∼410 nm.s−1 similar to the speed of GFP-tagged, intact myosin-10 we observed moving within filopodia of live mammalian cells (∼600 nm.s−1) using TIRF microscopy. Optical trapping experiments revealed the average work-stroke size was ∼17 nm with a single actomyosin-10 stiffness of ∼0.4 pN.nm−1 and an ADP-release limited detachment rate of ∼13 s−1. In most raw data traces, we observed unitary displacements, however at low [ATP] (<500 nM) and low optical trap stiffness (<0.005 pN.nm−1) we observed staircase-like interactions with an average movement of ∼35 nm between steps; a behavior characteristic of a processive molecular motor. We will discuss these measurements in the context of structure, mechano-chemical coupling and the functional significance of this motor in the living cell.

Optical trapping of gold nanoparticles by cylindrical vector beam

Optical trapping of gold nanoparticles is experimentally demonstrated using radially and azimuthally polarized beams. The transverse optical trapping stiffness of gold nanoparticles is measured. The radially polarized beam exhibits a higher trapping efficiency than the azimuthally polarized beam and the Gaussian beam. The transverse stiffness of particles with different diameters is measured experimentally and calculated via the discrete-dipole approximation method, and good agreement between theory and experiment is found.

Optical trapping force reduction and manipulation of nanoporous beads.

We studied the interaction of infrared optical traps with controlled-pore glass (CPG) beads in aqueous medium. The lateral optical trapping force and stiffness were experimentally found considerably smaller than those of their solid counterparts. The simulation using an average refractive index revealed significant losses of effective trapping efficiency, which quantitatively agreed well with experimentally fitted curves. This effect was ascribed to the reduced relative refractive index of medium-filled CPG beads with respect to the medium. Combining optical trapping with mechanical confinements, we demonstrated a microfluidic platform allowing for the synthesis of multiple DNA oligonucleotide sequences on individual beads of interest.

Tunable optical tweezers for wavelength-dependent measurements

Optical trapping forces depend on the difference between the trap wavelength and the extinction resonances of trapped particles. This leads to a wavelength-dependent trapping force, which should allow for the optimization of optical tweezers systems, simply by choosing the best trapping wavelength for a given application. Here we present an optical tweezer system with wavelength tunability, for the study of resonance effects. With this system, the optical trap stiffness is measured for single trapped particles that exhibit either single or multiple extinction resonances. We include discussions of wavelength-dependent effects, such as changes in temperature, and how to measure them.

Calibration of optical tweezers using time of flight method

Conventional method of calibrating optical trap stiffness is applicable for microspheres whose diameters range from hundreds of nanometer to several micrometers, but only have a slight advantage for those microspheres with diameters lager than five micrometers. To compensate this, we experimentally develop a time of flight method for measuring optical trap stiffness with larger microspheres. By comparing the optical trap stiffness of microspheres with different sizes and different materials at different laser powers, the time of flight method is confirmed to be more accurate and practical for microspheres larger than 5 μm; the result is of the same order of magnitude as the results of Brownian noise based analysis of 5 μm polystyrene bead. The results are higher than theoretical values due to the limited bandwidth of the camera. In comparison, the time of flight method is superior to other methods and does make sense in the fast calibration of optical trap stiffness on cell level. This method can be applied to optical traps with special field distributions. In the measurement of mechanical properties of cells, it can avoid using microspheres as force probe, thus providing a novel approach to the study of sophisticated single molecule process on the membrane of cells.