基于自回归模型的光阱中粒子运动模拟

通过分析光阱中颗粒位移信号特性, 建立描述粒子受限布朗运动过程的自回归模型, 进而提出了一种基于自回归模型的光阱中颗粒运动信号模拟的新方法. 对半径为1 μm的粒子处于光阱刚度分别为10, 20, 50 pN/μm 光阱时的位移信号进行了模拟, 得到的模拟位移信号的自相关函数与理论值相一致. 为了进一步阐明自回归模型的有效性, 在相同光阱参数下, 分别采用自回归模型与蒙特卡罗方法模拟光阱中微粒的位移信号, 采用功率谱法分别对两种模拟方法所得的微粒位移标定光阱刚度, 结果表明自回归模型方法能够取得和蒙特卡洛法相同的精度. 因此, 本文为分析光阱中粒子的随机运动提出了一种新的模拟方法, 可以用来对光阱中的噪声及特性进行分析. 关键词： 光阱 布朗运动 信号模拟 自回归模型

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/μm respectively, the displacement signals of 1 μm 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.
Keywords： optical trap Brownian motion signal simulation auto-regressive model