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".

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.

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.

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.