  We have developed a new in situ method to calibrate optical tweezers
experiments and simultaneously measure the size of the trapped particle or the
viscosity of the surrounding fluid. The positional fluctuations of the trapped
particle are recorded with a high-bandwidth photodetector. Next, we compute the
mean-square displacement, as well as the velocity autocorrelation function of
the sphere and compare it to the theory of Brownian motion including
hydrodynamic memory effects. A careful measurement and analysis of the time
scales characterizing the dynamics of the harmonically bound sphere fluctuating
in a viscous medium then directly yields all relevant parameters. Finally, we
test the method for different optical trap strengths, with different bead sizes
and in different fluids, and we find excellent agreement with the values
provided by the manufacturers. The proposed approach overcomes the most
commonly encountered limitations in precision when analyzing the power spectrum
of position fluctuations in the region around the corner frequency. These low
frequencies are usually prone to errors due to drift, limitations in the
detection and trap linearity as well as short acquisition times resulting in
poor statistics. Furthermore, the strategy can be generalized to Brownian
motion in more complex environments, provided the adequate theories are
available.
