Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events

Abstract

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

Shining Light in Mechanobiology: Optical Tweezers, Scissors, and Beyond

“…Quantitative measurement with optical tweezers has motivated the development of calibration techniques. Depending on the details of the problem, there are several requirements: precision and bandwidth − and coverage of large displacements and particle shape. − …”

“…Figure shows position traces demonstrating the difference between the random motion of the particle on its way to the center of the optical trap and its fit to a model of exponential approach to the equilibrium position. As a particle enters the optical trap, the behavior of an exponential approach to the stable trap position is apparent and measurable on a short time-scale ,, and thus the trap may be characterized quickly. This measurement may not be possible for various reasons ranging from sampling windows in detection, blurring, and limited ability to predict oncoming trapping events.…”

“…When particles accelerate over periods of time on the order of the exposure time the position of the particle is blurred. Blurring has to be accounted for to obtain valid calibration. , Thus, a measurement of position in a dynamic situation is not the true position and parameters such as trap stiffness must be corrected to account for this. Care must be taken in determining if the parallel tracking capability of camera detection is worth trading off the precision and accuracy afforded by detection with single probe beams.…”

Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap

“…Inferring naturally occurring energy landscapes or verifying artificially created potentials demands a method free of a priori assumptions on the potential’s shape. This requirement rules out many commonly used methods devised for harmonic systems ( Neuman and Block, 2004 ; Berg-Sørensen and Flyvbjerg, 2004 ; Jones et al., 2015 ; Gieseler et al., 2021 ) or alternative, otherwise-limited, methods to deduce potentials from data ( Reif, 2009 ; Türkcan et al., 2012 ; García et al., 2018 ; Wang et al., 2019 ; Frishman and Ronceray, 2020 ; Yang et al., 2021 ; Stilgoe et al., 2021 ). For example, some methods ( Reif, 2009 ; Türkcan et al., 2012 ) necessarily rely on binned data, relating potential energies to Boltzmann weights or average apparent force, thereby limiting the frequency of data in each bin and requiring that equilibrium be reached before data acquisition.…”