基于卡尔曼滤波的真空光阱悬浮微球位移探测

在光阱实际测量中,过程噪声以及光电测量噪声严重影响微球位移实时探测的灵敏度,针对这一问题,提出基于卡尔曼滤波的方法对微球位移进行探测.将光阱中微球运动的谐振子模型改写成卡尔曼滤波的状态转移矩阵形式,获得具有高灵敏度和高信噪比的微球位移信号.仿真结果表明:1 MHz的采样频率下,101kPa气压下滤波后的真空光阱微球位移的探测均方根误差从1nm降到0.27nm.实验结果表明,在293K、101kPa气压下对实测的微球位移信号进行滤波,探测均方根误差从2.8nm降到1.1nm;其他参数不变,在1Pa气压下均方根误差从5.2nm降到2.1nm.该方法可应用于高真空下光阱微球质心运动的激光冷却反馈方案.

Displacement Detection of Optically Trapped Microsphere in Vacuum Based on Kalman Filter

Process noise and photoelectric measurement noise seriously affect the sensitivity when detecting the displacement of the microsphere in the actual measurement.Aiming at this problem,a method of detecting the displacement of the microsphere based on Kalman filter is proposed.In order to obtain the displacement of the microsphere with high sensitivity and high signal-to-noise ratio,the harmonic oscillator model which interprets the motion of the microsphere is transformed into the form of state transition matrix for Kalman filter.Simulated results show that the root-mean-square error of measured displacement is reduced from 1 nm to 0.27 nm after filtered at 101 kPa.Experimental results show that the proposed method reduces the detection root-mean-square error of measured displacement from 2.8 nm to 1.1 nm at 293 Kand 101 kPa.Other parameters remaining unchanged,the root mean square error is reduced from 5.2 nm to 2.1 nm at 293 K and 1 Pa.The proposed method can be applied to the laser cooling feedback scheme of the center-of-mass motion of a micro-particle optically trapped in high vacuum.