A general method is presented for determining and correcting
nonlinear position detector responses in single particle tracking as
used in three-dimensional scanning probe microscopy based on optical
tweezers. The method uses locally calculated mean square displacements
of a Brownian particle to detect spatial changes in the sensitivity of
the detector. The method is applied to an optical tweezers setup, where
the position fluctuations of a microsphere within the optical trap are
measured by an interferometric detection scheme with nanometer
precision and microsecond temporal resolution. Detector sensitivity
profiles were measured at arbitrary positions in solution with a
resolution of approximately 6 nm and 20 nm in the lateral and axial
directions, respectively. Local detector sensitivities are used to
reconstruct the real positions of the particle from the measured
position signals.