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.