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As a key component of the adaptive optics (AO) system,wavefront corrector plays a crucial role in determining the performance of the AO system.At present,the typical wavefront correctors,including solid deformable mirrors and liquid crystal spatial light modulators,have the common drawbacks of high cost of per actuator channel,and the relatively low stroke deflection (normally less than 50 m) due to the limitation of material and manufacturing technology.In the face of the growing demand for deformable mirrors with large stroke,low power dissipation and low cost,the magnetic fluid based deformable mirror (MFDM) is proposed in this paper.The magnetic fluid has the characteristic of the fluidity of liquid and can be magnetized by an external magnetic field.Therefore,the surface deflection of the MFDM can be controlled by the surrounding magnetic field generated by an array of electromagnetic coils located underneath the magnetic fluid layer.Compared with the conventional deformable mirrors,the MFDM has the advantages of a continuous and smooth mirror surface,large shape deformation,low manufacture cost,and easy extension.The surface dynamics model of MFDM with a circular geometry has been studied previously in the literature.In the present paper, considering the possible applications in the wavefront control of rectangular laser beams,we study the MFDM with a rectangular array of actuators. Firstly,based on the governing equations of the magnetic fluid,derived from the principles of conservation of fluid mass and magnetic field,the dynamics model of surface deflection of the rectangular MFDM is analyzed in Cartesian coordinates under the boundary condition of magnetic field and the kinematic conditions of magnetic fluid.The analytical solutions of the surface movement of the mirror subject to the applied currents in the electromagnetic coils are obtained by properly separating the variables with truncated model numbers.Secondly,based on the derived analytical model, the optimal design procedure for the structure and parameters of the MFDM to obtain the required performance,i.e. the largest stroke and inter-actuator stroke of the mirror,as well as the coupling coefficient of the influence function, is presented.The resulting surface response performance of the designed MFDM is validated by the co-simulation in MATLAB,COMSOL Multiphysics and Tracepro software.Finally,a prototype of square MFDM consisting of the square array of miniature electromagnetic coils,a Maxwell coil and the magnetic fluid filled in a rectangular container is fabricated for experimental evaluation.The experimental results of the surface response of the mirror subject to two adjacent active coils are first presented to validate the stroke performance and linear characteristics of the MFDM. A parabolic surface shape is then further produced in the AO setup system with the MFDM subject to the array of coils driven by the currents calculated from the analytical model.The experimental results verify the accuracy of the established dynamics model and show that the proposed MFDM can be used to effectively control the wavefront of laser beam.
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Keywords:
- magnetic fluid /
- deformable mirror /
- multiphysics coupling /
- dynamics modeling
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[10] Nguyen N T, Beyzavi A, Ng K M, Huang X Y 2007 Microfluid Nanofluid 3 571
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[20] Wu Z Z, Kong X H, Zhang Z, Wu J Q, Wang T, Liu M 2017 Micromachines 8 72
[21] Bayanna A R, Louis R E, Chatterjee A, Mathew S K, Venkatakrishnan P 2015 Appl. Opt. 54 1727
[22] Bastaits R, Alaluf D, Horodinca M, Romanescu I, Burda I, Martic G, Rodrigues G, Preumont A 2014 Appl. Opt. 53 6635
[23] Du R Q, Zhang X J 2011 Opto-Electron. Eng. 38 30
[24] Calero V, Garca-Martnez P, Albero J 2013 Opt. Lett. 38 4663
[25] Yao K, Wang J, Liu X, Liu W 2014 Opt. Express 22 17216
[26] Peng F, Lee Y, Luo Z, Wu S 2015 Opt. Lett. 40 5097
[27] Ghaffaria A, Hashemabadi S H, Bazmib M 2015 Colloid. Surface A 481 186
[28] Shi D, Bi Q, Zhou R 2014 Numer. Heat Tr. A: Appl. 66 144
[29] Akhtar S N, Sharma S, Dayal G, Ramakrishna S A, Ramkumar J 2015 J. Micromech. Microeng. 25 065001
[30] Jiao L, Cai J, Ma H H, Li G X, Shen Z W, Tang Z P 2014 Appl. Surf. Sci. 301 481
[31] Marmo J, Injeyan H, Komine H, McNaught S, Machan J, Sollee J 2009 Proc. SPIE 7195 719507A
[32] Wu Z Z, Iqbal A, Ben Amara F 2013 Modeling and Control of Magnetic Fluid Deformable Mirrors for Adaptive Optics Systems (New York: Springer) pp99-115
[33] Caprari R S 1995 Meas. Sci. Technol. 6 593
[34] Wu J Q, Wu Z Z, Kong X H, Zhang Z, Liu M 2017 Optoelectron. Lett. 13 90
[35] Lu F, He Z W 2012 Comput. Simul. 29 1006 (in Chinese) [卢飞, 何忠武 2012 计算机仿真 29 1006]
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[1] Rosensweig R E 1985 Ferrohydrodynamics (Cambridge: Cambridge University Press) pp1-64
[2] Wang A R, Xu G, Shu C J 2010 Magnetic Fluid and Applications (Chengdu: Southwest Jiaotong University Press) pp1-20 (in Chinese) [王安蓉, 许刚, 舒纯军 2010 磁性液体及其应用 (成都: 西南交通大学出版社) 第120页]
[3] Li D C 2010 Theory and Applications of Magnetic Fluid Seal (Beijing: Science Press) pp38-68 (in Chinese) [李德才 2010 磁性液体密封理论及应用 (北京: 科学出版社) 第3868页]
[4] Papell S S 1965 US Patent 3 215 572
[5] Yuichi M, Hiroshi S, Hayato Y, Hidenori S 2015 Procedia CIRP 33 581
[6] Rajesh C S, Parsania M M 2013 Am. J. Math. Stat. 3 179
[7] Yao J, Chang J J, Li D C, Yang X L 2016 J. Magn. Magn. Mater. 402 28
[8] Mitamura Y, Yano T, Nakamura W, Okamoto E 2013 Bio-Med. Mater. Eng. 23 63
[9] Dave V, Virpura H A, Patel R J 2015 AIP Conf. Proc. 1665 050139
[10] Nguyen N T, Beyzavi A, Ng K M, Huang X Y 2007 Microfluid Nanofluid 3 571
[11] Liu J, Tan S H, Yap Y F, Ng M Y, Nguyen N T 2011 Microfluid Nanofluid 11 177
[12] Brousseau D, Borra E F, Hubert J R, Parent J 2006 Opt. Express 14 11486
[13] Brousseau D, Borra E F, Thibault S 2007 Opt. Express 15 18190
[14] Borra E F, Brousseau D, Cliche M, Parent J 2008 Mon. Not. R. Astron. Soc. 391 1925
[15] Iqbal A, Amara F B 2008 Int. J. Optomechatroni. 2 126
[16] Ritcey A M, Borra E 2010 ChemPhysChem 11 981
[17] Lemmer A J, Griffiths I M, Groff T D, Rousing A W, Kasdin N J 2016 Proc. SPIE 9912 99122K
[18] Dery J P, Brousseau D, Rochette M, Borra E F, Ritcey A M 2016 J. Appl. Polym. Sci. 134 44542
[19] Wu Z Z, Kong X H, Wu J Q, Liu M, Xie S R 2016 Chin. J. Sci. Instrum. 37 1509 (in Chinese) [吴智政, 孔祥会, 吴君秋, 刘梅, 谢少荣 2016 仪器仪表学报 37 1509]
[20] Wu Z Z, Kong X H, Zhang Z, Wu J Q, Wang T, Liu M 2017 Micromachines 8 72
[21] Bayanna A R, Louis R E, Chatterjee A, Mathew S K, Venkatakrishnan P 2015 Appl. Opt. 54 1727
[22] Bastaits R, Alaluf D, Horodinca M, Romanescu I, Burda I, Martic G, Rodrigues G, Preumont A 2014 Appl. Opt. 53 6635
[23] Du R Q, Zhang X J 2011 Opto-Electron. Eng. 38 30
[24] Calero V, Garca-Martnez P, Albero J 2013 Opt. Lett. 38 4663
[25] Yao K, Wang J, Liu X, Liu W 2014 Opt. Express 22 17216
[26] Peng F, Lee Y, Luo Z, Wu S 2015 Opt. Lett. 40 5097
[27] Ghaffaria A, Hashemabadi S H, Bazmib M 2015 Colloid. Surface A 481 186
[28] Shi D, Bi Q, Zhou R 2014 Numer. Heat Tr. A: Appl. 66 144
[29] Akhtar S N, Sharma S, Dayal G, Ramakrishna S A, Ramkumar J 2015 J. Micromech. Microeng. 25 065001
[30] Jiao L, Cai J, Ma H H, Li G X, Shen Z W, Tang Z P 2014 Appl. Surf. Sci. 301 481
[31] Marmo J, Injeyan H, Komine H, McNaught S, Machan J, Sollee J 2009 Proc. SPIE 7195 719507A
[32] Wu Z Z, Iqbal A, Ben Amara F 2013 Modeling and Control of Magnetic Fluid Deformable Mirrors for Adaptive Optics Systems (New York: Springer) pp99-115
[33] Caprari R S 1995 Meas. Sci. Technol. 6 593
[34] Wu J Q, Wu Z Z, Kong X H, Zhang Z, Liu M 2017 Optoelectron. Lett. 13 90
[35] Lu F, He Z W 2012 Comput. Simul. 29 1006 (in Chinese) [卢飞, 何忠武 2012 计算机仿真 29 1006]
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