MatLab program for precision calibration of optical tweezers

Optical tweezers are used as force transducers in many types of experiments. The force they exert in a given experiment is known only after a calibration. Computer codes that calibrate optical tweezers with high precision and reliability in the (x, y)-plane orthogonal to the laser beam axis were written in MatLab (MathWorks Inc.) and are presented here. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum. First, cross-talk between channels in 2D position measurements is tested for, and eliminated if detected. Then, the Lorentzian power spectrum that results from the Einstein-Ornstein-Uhlenbeck theory, is fitted to the low-frequency part of the experimental spectrum in order to obtain an initial guess for parameters to be fitted. Finally, a more complete theory is fitted, a theory that optionally accounts for the frequency dependence of the hydrodynamic drag force and hydrodynamic interaction with a nearby cover slip, for effects of finite sampling frequency (aliasing), for effects of anti-aliasing filters in the data acquisition electronics, and for unintended "virtual" filtering caused by the position detection system. Each of these effects can be left out or included as the user prefers, with user-defined parameters. Several tests are applied to the experimental data during calibration to ensure that the data comply with the theory used for their interpretation: Independence of x- and y-coordinates, Hooke's law, exponential distribution of power spectral values, uncorrelated Gaussian scatter of residual values. Results are given with statistical errors and covariance matrix.