Brownian motion in a non-homogeneous force field and photonic force microscope

TL;DR

This paper enhances the Photonic Force Microscope (PFM) technique to accurately measure and reconstruct non-homogeneous, possibly rotational force fields acting on microscopic probes, expanding its applicability beyond conservative force assumptions.

Contribution

The authors develop a theoretical framework and analysis workflow to reconstruct complex force fields, including rotational components, from PFM measurements.

Findings

Successfully reconstructed conservative force fields.

Validated the method with rotational force field experiments.

Extended PFM capabilities to non-homogeneous force environments.

Abstract

The Photonic Force Microscope (PFM) is an opto-mechanical technique based on an optical trap that can be assumed to probe forces in microscopic systems. This technique has been used to measure forces in the range of pico- and femto-Newton, assessing the mechanical properties of biomolecules as well as of other microscopic systems. For a correct use of the PFM, the force field to measure has to be invariable (homogeneous) on the scale of the Brownian motion of the trapped probe. This condition implicates that the force field must be conservative, excluding the possibility of a rotational component. However, there are cases where these assumptions are not fulfilled Here, we show how to improve the PFM technique in order to be able to deal with these cases. We introduce the theory of this enhanced PFM and we propose a concrete analysis workflow to reconstruct the force field from the experimental time-series of the probe position. Furthermore, we experimentally verify some particularly important cases, namely the case of a conservative or rotational force-field.