Calibration of force detection for arbitrarily shaped particles in optical tweezers

Marie Anne Balanant,Timo A. Nieminen,Ann A. M. Bui,Alexander B. Stilgoe,Anatolii V. Kashchuk,Halina Rubinsztein-Dunlop

doi:10.1038/s41598-018-28876-y

Marie Anne Balanant, Timo A. Nieminen + Show 4 more

Open Access

https://doi.org/10.1038/s41598-018-28876-y

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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”.

Highlights

Calibration for force measurement is often performed per-particle, using methods that assume that the trap is Hookean, i.e., can be characterised by a spring constant, and depend on knowing the viscous drag acting on the particle, and depend on knowing the particle size and shape, and the viscosity of the surrounding medium
We evaluate force–position curves in the cases of: synchronised measurements of force and position, force and position measurements without synchronisation, and position-only measurements using a camera
We have introduced a method of absolute force calibration

Summary

Introduction

Calibration for force measurement is often performed per-particle, using methods that assume that the trap is Hookean, i.e., can be characterised by a spring constant, and depend on knowing the viscous drag acting on the particle, and depend on knowing the particle size and shape, and the viscosity (and temperature) of the surrounding medium. Smith et al.[9] used measured properties of the optical system delivering the transmitted beams to a pair of PSDs for a counter-propagating trap to determine an absolute calibration for force measurement. More recently[11], this has been extended to rod-shaped particles Another approach is to use back-focal-plane interferometry to measure the deflection of the transmitted trapping beam[12]. We add to this body of work by, first, demonstrating a simple method for the positioning and calibration of a PSD for force measurement through deflection of the trapping beam, which requires relatively little knowledge of the optical system, and second, enhancing the capabilities of an optical trapping system with such absolute force detection by using the force–position relationship of a trapped particle

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Conclusion