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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.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.
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Keywords:
- optical trap /
- Brownian motion /
- signal simulation /
- auto-regressive model
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[1] Neuman K C, Nagy A 2008 Nat. Methods 5 491
[2] Dienerowitz M, Mazilu M, Dholakia K 2008 J. Nanophoton. 2 1
[3] Abbondanzieri E A, Greenleaf W J, Shaevitz J W, Landick R, Block S M 2005 Nature 438 460
[4] Gibson G M, Leach J, Keen S, Wright A J, Padgett M J 2008 Opt. Express 16 14561
[5] Bechhoefer J, Wilson S 2002 Am. J. Phys. 70 393
[6] Berg-Sorensen K, Flyvbjerg H 2004 Rev. Sci. Instrum. 75 594
[7] Jiang Y Q, Guo H L, Liu C X, Li Z L, Cheng B Y, Zhang D Z, Jia S T 2004 Acta Phys. Sin. 53 1721 (in Chinese) [降雨强, 郭红莲, 刘春香, 李兆霖, 程丙英, 张道中, 贾锁堂 2004 53 1721]
[8] Czerwinski F, Richardson A C, Oddershede L B 2009 Opt. Express 17 13255
[9] Ren Y X, Wu J G, Zhong M C, Li Y M 2010 Chin. Opt. Lett. 8 170
[10] Neuman K C, Block S M 2004 Rev. Sci. Instrum. 75 2787
[11] Alves P S, Rocha M S 2012 Appl. Phys. B: Lasers and Optics 107 375
[12] Qi L X, Jia Y L, Tang H C 2010 Ocean Technol. 29 60 (in Chinese) [齐立新, 贾云龙, 唐海川 2010 海洋技术 29 60]
[13] Wang Y J, Zheng G, Shen J, Tan B X, Cheng Y T 2009 Acta Opt. Sin. 28 91 (in Chinese) [王雅静, 郑刚, 申晋, 谭博学, 成艳亭 2009 光学学报 28 91]
[14] Hasan M, Hossain N, Naylor P 2005 IEEE Proceedings-Proceedings of the Vision, Image and Signal Processing 152 520
[15] Zheng W X 2006 IEEE Trans. Circ. Syst. II: Express Briefs 53 1471
[16] Hu G S 2003 Digital Signal Processing: Theory, Algorithms and Implementation (Beijing: Tsinghua University Press Ltd.) p533 (in Chinese) [胡广书 2003数字信号处理: 理论, 算法与实现 (北京: 清华大学出版社有限公司) 第533页]
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