Ann A. M. Bui

Calibration of nonspherical particles in optical tweezers using only position measurement

Nonspherical probe particles are an attractive choice for optically-trapped scanning probe microscopy. We show that it is possible to calibrate a trap with a nonspherical particle using only position measurements, without requiring measurement of orientation, using a pseudopotential based on the position occupation probability. It is not necessary to assume the force is linear with displacement.

Determination of motility forces on isolated chromosomes with laser tweezers

Quantitative determination of the motility forces of chromosomes during cell division is fundamental to understanding a process that is universal among eukaryotic organisms. Using an optical tweezers system, isolated mammalian chromosomes were held in a 1064 nm laser trap. The minimum force required to move a single chromosome was determined to be ≈0.8–5 pN. The maximum transverse trapping efficiency of the isolated chromosomes was calculated as ≈0.01–0.02. These results confirm theoretical force calculations of ≈0.1–12 pN to move a chromosome on the mitotic or meiotic spindle. The verification of these results was carried out by calibration of the optical tweezers when trapping microspheres with a diameter of 4.5–15 µm in media with 1–7 cP viscosity. The results of the chromosome and microsphere trapping experiments agree with optical models developed to simulate trapping of cylindrical and spherical specimens.

Escape forces and trajectories in optical tweezers and their effect on calibration

Whether or not an external force can make a trapped particle escape from optical tweezers can be used to measure optical forces. Combined with the linear dependence of optical forces on trapping power, a quantitative measurement of the force can be obtained. For this measurement, the particle is at the edge of the trap, away from the region near the equilbrium position where the trap can be described as a linear spring. This method provides the ability to measure higher forces for the same beam power, compared with using the linear region of the trap, with lower risk of optical damage to trapped specimens. Calibration is typically performed by using an increasing fluid flow to exert an increasing force on a trapped particle until it escapes. In this calibration technique, the particle is usually assumed to escape along a straight line in the direction of fluid-flow. Here, we show that the particle instead follows a curved trajectory, which depends on the rate of application of the force (i.e., the acceleration of the fluid flow). In the limit of very low acceleration, the particle follows the surface of zero axial optical force during the escape. The force required to produce escape depends on the trajectory, and hence the acceleration. This can result in variations in the escape force of a factor of two. This can have a major impact on calibration to determine the escape force efficiency. Even when calibration measurements are all performed in the low acceleration regime, variations in the escape force efficiency of 20% or more can still occur. We present computational simulations using generalized Lorenz-Mie theory and experimental measurements to show how the escape force efficiency depends on rate of increase of force and trapping power, and discuss the impact on calibration.

Theory and practice of simulation of optical tweezers

Computational modelling has made many useful contributions to the field of optical tweezers. One aspect in which it can be applied is the simulation of the dynamics of particles in optical tweezers. This can be useful for systems with many degrees of freedom, and for the simulation of experiments. While modelling of the optical force is a prerequisite for simulation of the motion of particles in optical traps, non-optical forces must also be included; the most important are usually Brownian motion and viscous drag. We discuss some applications and examples of such simulations. We review the theory and practical principles of simulation of optical tweezers, including the choice of method of calculation of optical force, numerical solution of the equations of motion of the particle, and finish with a discussion of a range of open problems.

Optical tweezers escape forces

With suitable calibration, optical tweezers can be used to measure forces. If the maximum force that can be exerted is of interest, calibration can be performed using viscous drag to remove a particle from the trap, typically by moving the stage. The stage velocity required to remove the particle then gives the escape force. However, the escape force can vary by up to 30% or more, depending on the particle trajectory. This can have significant quantitative impact on measurements. We describe the variation of escape force and escape trajectory, using both experimental measurements and simulations, and discuss implications for experimental measurement of forces.

Optical trapping of isolated mammalian chromosomes

We have estimated the mitotic forces exerted on individual isolated mammalian chromosomes using optical trapping. The chromosomes were trapped by an optical tweezers system created by a continuous wave ytterbium laser at 1064 nm. Individual chromosomes were trapped at different in situ powers in the range of ≈20-50 mW. The corresponding trapping forces were determined by a viscous drag method. In the range of laser powers used, the preliminary data show a linear relationship between the chromosome trapping forces and in situ powers. We have calculated the dimensionless trapping efficiency coefficient (Q) of the chromosomes at 1064 nm and the corresponding effects of trapping power on Q. The value of Q in our experiments was determined to be ≈0.01. The results of this study validate optical tweezers as a non-invasive and precise technique to determine intracellular forces in general, and specifically, the spindle forces exerted on the chromosomes during cell division.

Calibration of force detection for arbitrarily shaped particles in optical tweezers

Force measurement with an optical trap requires calibration of it. With a suitable detector, such as a position-sensitive detector (PSD), it is possible to calibrate the detector so that the force can be measured for arbitrary particles and arbitrary beams without further calibration; such a calibration can be called an “absolute calibration”. Here, we present a simple method for the absolute calibration of a PSD. Very often, paired position and force measurements are required, and even if synchronous measurements are possible with the position and force detectors used, knowledge of the force–position curve for the particle in the trap can be highly beneficial. Therefore, we experimentally demonstrate methods for determining the force–position curve with and without synchronous force and position measurements, beyond the Hookean (linear) region of the trap. Unlike the absolute calibration of the force and position detectors, the force–position curve depends on the particle and the trapping beam, and needs to be determined in each individual case. We demonstrate the robustness of our absolute calibration by measuring optical forces on microspheres as commonly trapped in optical tweezers, and other particles such a birefringent vaterite microspheres, red blood cells, and a deformable “blob”.

Optically driven rotating micromachines

We review the basic theory and principles of optically driven micromachines, and present a series of simple heuristic principles for designing such micromachines. We discuss the relationship between symmetry and optical torque, and consider techniques to enhance or reduce reflection. Finally, we briefly survey some applications, and present a prototypical optically driven micromachine for use in microfluidic devices.

Measurements of particle-wall interaction forces using simultaneous position and force detection (Conference Presentation)

Particle–wall interactions are important in biology, micromachining, coagulation studies, and many other areas of science. As a contactless tool, optical tweezers are ideal for measuring these kind of interactions. Here we will present a new method for calculating the non-optical forces acting on a trapped particle using simultaneous position and force detection. Analysis of the particles Brownian motion when trapped gives a measure of all the forces experienced by the particle. In contrast, measuring only the lights momentum change directly gives the solely optical force. This is achieved measuring the changes in the scattered light. The difference between the forces recorded by the two techniques reveals the external forces acting on the trapped particle. Therefore, by trapping the particle close to a wall, one can study the particle-wall interaction force in details. The simulation were done using the optical tweezer toolbox [1] to find the optical force acting on a particle. The net force was calculated from a Brownian motion’s statistics of a trapped particle in the presence of the exponential external force. By using the proposed method, we were able to successfully reconstruct the external force. The experiment was done on a trapped spherical PMMA particle (d=2.2um) close to the 3D-printed wall. For the particle-wall distance ~0.7um the non-optical force is ~100fN . The experiment and simulation results confirm the efficiency of the proposed method for an external force measurements. [1] Nieminen et al., J. Opt. A 9, S196-S203 (2007).