Simulation of the Brownian motion of particle in an optical trap based on the auto-regressive model

An auto-regressive (AR) model is established by analysing the characteristic of the particle motion in an optical trap. In this paper, a new method based on the AR model is investigated to simulate the Brownian motion of the particle in an optical trap. When optical stiffness values are 10, 20, 50 pN/mu m respectively, the displacement signals of 1 mu m diameter particle in these optical traps are simulated with this method. Their simulative autocorrelation function of the motion of the particle accords with their theoretical autocorrelation function. In order to further clarify the validity of the model, the particle signals are respectively simulated with the AR model method and the Monte-Carlo method, then the stiffness values are calibrated with power spectrum density method. The results show that the stiffness value based auto-regressive simulation can have the same precision as that based the Monte-Carlo simulation, therefore, the AR method can simulate effectively the motion of the particle in the optical trap.