Influence of Noise on Force Measurements

We demonstrate how the ineluctable presence of thermal noise alters the measurement of forces acting on microscopic and nanoscopic objects. We quantify this effect exemplarily for a Brownian particle near a wall subjected to gravitational and electrostatic forces. Our results demonstrate that the force-measurement process is prone to artifacts if the noise is not correctly taken into account.

Figure 1

(a) A Brownian particle (drawn not to scale) diffuses near a wall in the presence of gravitational and electrostatic forces. Its trajectory perpendicular to the wall is measured with TIRM. (b) Comparison of measured (bullets) and calculated (line) vertical diffusion coefficient as a function of the particle-wall distance. (c) Experimentally determined probability distribution of the local drift $dz$ for $dt=5\mathrm{ms}$ at $z=380\mathrm{nm}$ (grey). The dashed line is a Gaussian in excellent agreement with the experimental data.

Figure 2

Comparison of forces obtained from local drift-velocity measurements of a Brownian particle according to Eq. (1) (bullets) and measured from the equilibrium particle height distribution (squares). The solid line corresponds to a fit to Eq. (2).

Figure 3

Calculated noise-induced drift (lines) for different values of $\alpha$. The symbols correspond to the experimentally determined noise-induced drift.

Figure 4

Forces obtained from a drift-velocity experiment with added noise-induced drift [see Eq. (7) with $\alpha =1$ (open squares), $\alpha =0.5$ (open triangles), and $\alpha =0$ (open dots)]. The solid squares represent the forces obtained from an equilibrium measurement (same as in Fig. 2).