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.
Highlights
Optical tweezers are an important tool for measuring femto-to-nano newton forces in soft matter and biological systems [1,2,3]
We have devised a correction to force reconstruction via maximum likelihood estimation (FORMA), such that a calibration of the trap response can be performed for single trapping events over about ∼2 ms capture time with relative standard deviation, σω /ωc < 6%, where various equilibrium determinations will fail due to a combination of low signal-to-noise, blurring, and aliasing
The calibration is biased toward the first few points under extension at large displacements from the equilibrium due to the increase of optical force over Brownian motion
Summary
Optical tweezers are an important tool for measuring femto-to-nano newton forces in soft matter and biological systems [1,2,3]. There are alternatives to power spectrum calibration, including Bayesian inference [12,13], which does not depend on input parameters and it is less sensitive to systematic errors It infers the diffusion coefficient and the potential felt by a bead trapped optically. It uses comparatively larger amount of the information stored in the recorded bead trajectory than the standard calibration approaches. Another alternative method is force reconstruction via maximum likelihood estimation (FORMA) [14], in which one retrieves the force field acting on a Brownian particle from the analysis of its observed motion within the macroscopic force field. FORMA is an attractive alternative to many of the other techniques, as it only consists of determining the ratio of two sums that arise from analysis of the occupation probability within the trap
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