We propose a nonlinear method for the analysis of the time series for the spatial position of a bead trapped in optical tweezers, which enables us to reconstruct its dynamical equation of motion. The main advantage of the method is that all the functions and parameters of the dynamics are determined directly (non-parametrically) from the measured series. It also allows us to determine, for the first time to our knowledge, the spatial-dependence of the diffusion coefficient of a bead in an optical trap, and to demonstrate that it is not in general constant. This is in contrast with the main assumption of the popularly-used power spectrum calibration method. The proposed method is validated via synthetic time series for the bead position with spatially-varying diffusion coefficients. Our detailed analysis of the measured time series reveals that the power spectrum analysis overestimates considerably the force constant.
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