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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
[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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[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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