Calibration of force detection for arbitrarily shaped particles in optical tweezers

Abstract

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”.

Optical Tweezers in Studies of Red Blood Cells

“…To calibrate the optical forces exerted on an arbitrarily (nonspherical) shaped particle (e.g., red blood cell and biological particles) by an arbitrary beam in a poorly known environment, another methodology known as "absolute calibration" has been established and shown great practical capability in complex biological applications [79]. This method focuses on the deflection of the transmitting beam itself, as illustrated in Figure 1d that a transverse displacement of the particle causes a lateral deflection of the laser beam.…”

Optical trapping in vivo: theory, practice, and applications

“…The majority of theories deal with the trapping of spherical objects. In practice and especially in many of the biologically significant applications, the objects that are being manipulated are not spherical; therefore, consideration should be given to the shape and refractive index variations throughout the object [50][51][52]. The gradient force is not the only force that an object would be exposed to within an optical trap.…”

“…If we assume that the microscope imaging the light scattered by a transparent object obeys the Abbe sine condition, then its centroid is proportional to the angular displacement of the light scattered by the particle and transmitted by the microscope, and this observation permits force quantification. This method is very powerful, as it can be used to determine forces on nonspherical and deformable objects [50,87]. It has some strict limitations of applicability due to the fact that the light collection angle of microscopes is limited and the light emitted and absorbed by the particle needs to be completely resolved for an exact determination of the force.…”

Optical Micromachines for Biological Studies

“…Then, the stiffness coefficient of the optical trap can be estimated by measuring the root mean square displacement of the particle from the centre of the trap induced by thermal fluctuations and using the equipartition theorem [51,52]. Other calibration methods for measurement of trap stiffness have been developed [53], and are popularly based on balancing a viscous drag imposed on the particle in the trap [54] or by performing power spectrum analysis [55]. The simplicity of the Hookean spring approximation, and the wealth of different methods for calibration hints at a limitation of this method: the effective spring constant is affected by fluctuations in experimental parameters such as viscosity and temperature, and so may require recalibration during long-running experiments.…”