MEMS微变形镜的系统级建模研究
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摘要
微型自适应光学系统在天文观测、激光武器和现代医学高分辨率成像等领域有着重要的应用前景,基于MEMS技术的微变形镜是微型自适应光学系统的核心器件,涉及光相位调制、机电耦合等诸多方面的研究。如何建立MEMS微变形镜准确有效的光相位调制和机电耦合的系统级模型,从而快速得到其可靠的仿真结果,以减少设计成本,缩短开发周期,便成为微型自适应光学系统设计的一个重要问题。
本文以微型自适应光学系统的关键部件微变形镜为研究对象,研究了微变形镜系统级建模的方法,建立了微变形镜的系统级模型,并实现了微变形镜阵列的仿真。论文的主要研究内容包括:
研究了微变形镜的机电行为建模方法并建立了机电组件模型。基于多端口组件网络方法,采用能量法建立了机电功能组件弹性梁、平板质量块的力学行为模型,应用机电能量转换原理建立了平板式可变电容器的机电耦合行为模型。使用硬件描述语言MAST编码实现了多端口组件模型并将仿真结果与有限元分析结果进行了精确性比较,仿真结果表明模型具有较高的精度,能够实现快速仿真。
研究了微变形镜的光学行为建模方法并建立了光学组件模型。确定了光信号的描述方法,采用几何矩阵光学和高斯光束的理论建立了光学元件平面反射镜和薄透镜的光学模型,用硬件描述语言MAST编码实现了多端口组件模型并进行了光学仿真。研究了微变形镜阵列光学性能的评价指标斯特列尔比和适配误差,建立了阵列光学性能评价的多端口组件模型,并分析了阵列参数对阵列光学性能的影响。
建立了微变形镜系统级模型并实现了系统仿真。建立了微变形镜机电行为系统级模型,进行了频域仿真分析、时域仿真分析和直流瞬态分析,得到了微变形镜的谐振频率、响应时间和吸合电压等重要性能指标,表明所设计的微变形镜满足自适应光学系统的要求。首次建立了微变形镜阵列的光相位调制系统级模型。进行了阵列光相位调制仿真分析,得到了对畸变波前调制后的输出波前,并分析了相对误差。仿真结果表明使用本文所述方法,可以实现微变形镜阵列的系统快速建模与仿真分析,有利于微变形镜阵列的设计与优化。
Micro deformable mirror fabricated by MEMS technologies is one of the core components of the micro-mechanical adaptive optics system which is widely implemented in many fields such as telescope systems, laser beam weapons, medical high-resolution imaging systems and laser communication systems. In order to reduce the cost and shorten the design cycle, accurate and efficient system level modeling of micro deformable mirror involving optical phase modulation and mechanical and electrostatic coupling would invariably be needed.In the thesis, system level modeling methodology is presented for rapid modeling and simulation of micro deformable mirror. Based on the method, the system level model of the micro deformable mirror is established and simulated. The main contents of this thesis are as following:Firstly, The modeling methodology of mechanical and electrostatic behavior of the micro deformable mirror is presented and the models are established accordingly. Based on Multi-Port-Element Network(MuPEN) method, the mechanical model of the spring beam and the rigid plate mass is established according to law of energy conservation, while the mechanical and electrostatic coupling model of electrostatic gap is established based on mechanical and electrostatic energy transition principle. Meanwhile, all models are coded in analog hardware description language (MAST). Furthermore, the accuracy of models is verified by comparison with finite element analysis(FEA) and the results prove that the models have near FEA accuracy.Secondly, The modeling methodology of optical behavior of the micro deformable mirror is investigated and the models are established as a result. The description of optical signal is presented and the behavior model of the optical functional components such as planar reflection mirror and thin lens are established using matrix optics and Gaussian beam theory. The models are coded in analog hardware description language(MAST) and are simulated in MuPEN. In addition, the evaluation parameters of the optical quality for the micro deformable mirror arrays
including the Strehl ratio and fitting error are analyzed. Then, MuPEN models for optical quality evaluation are established and simulation is implemented to analyze the effect of the parameters of mirror arrays on optical quality.Finally, system-level model of micro deformable mirror is established and both mechanical and electrostatic coupling simulation and optical phase modulation simulation are implemented in MuPEN. The resonance frequency, the response time and the pull-in voltage of the micro deformable mirror are ascertained through different simulations and the simulation results show that the micro deformable mirror we designed can satisfy the requirements of adaptive optics system. Moreover, the optical phase modulation behavior model of micro deformable mirror arrays is established for the first time. Then the simulation is implemented and the wavefront after phase modulation is reconstructed together with the analysis of relative error. Simulation results indicate that rapid modeling and simulation of micro deformable mirror can be accomplished in this way which will benefit the design and optimization of micro deformable mirror arrays.
本文以微型自适应光学系统的关键部件微变形镜为研究对象,研究了微变形镜系统级建模的方法,建立了微变形镜的系统级模型,并实现了微变形镜阵列的仿真。论文的主要研究内容包括:
研究了微变形镜的机电行为建模方法并建立了机电组件模型。基于多端口组件网络方法,采用能量法建立了机电功能组件弹性梁、平板质量块的力学行为模型,应用机电能量转换原理建立了平板式可变电容器的机电耦合行为模型。使用硬件描述语言MAST编码实现了多端口组件模型并将仿真结果与有限元分析结果进行了精确性比较,仿真结果表明模型具有较高的精度,能够实现快速仿真。
研究了微变形镜的光学行为建模方法并建立了光学组件模型。确定了光信号的描述方法,采用几何矩阵光学和高斯光束的理论建立了光学元件平面反射镜和薄透镜的光学模型,用硬件描述语言MAST编码实现了多端口组件模型并进行了光学仿真。研究了微变形镜阵列光学性能的评价指标斯特列尔比和适配误差,建立了阵列光学性能评价的多端口组件模型,并分析了阵列参数对阵列光学性能的影响。
建立了微变形镜系统级模型并实现了系统仿真。建立了微变形镜机电行为系统级模型,进行了频域仿真分析、时域仿真分析和直流瞬态分析,得到了微变形镜的谐振频率、响应时间和吸合电压等重要性能指标,表明所设计的微变形镜满足自适应光学系统的要求。首次建立了微变形镜阵列的光相位调制系统级模型。进行了阵列光相位调制仿真分析,得到了对畸变波前调制后的输出波前,并分析了相对误差。仿真结果表明使用本文所述方法,可以实现微变形镜阵列的系统快速建模与仿真分析,有利于微变形镜阵列的设计与优化。
Micro deformable mirror fabricated by MEMS technologies is one of the core components of the micro-mechanical adaptive optics system which is widely implemented in many fields such as telescope systems, laser beam weapons, medical high-resolution imaging systems and laser communication systems. In order to reduce the cost and shorten the design cycle, accurate and efficient system level modeling of micro deformable mirror involving optical phase modulation and mechanical and electrostatic coupling would invariably be needed.In the thesis, system level modeling methodology is presented for rapid modeling and simulation of micro deformable mirror. Based on the method, the system level model of the micro deformable mirror is established and simulated. The main contents of this thesis are as following:Firstly, The modeling methodology of mechanical and electrostatic behavior of the micro deformable mirror is presented and the models are established accordingly. Based on Multi-Port-Element Network(MuPEN) method, the mechanical model of the spring beam and the rigid plate mass is established according to law of energy conservation, while the mechanical and electrostatic coupling model of electrostatic gap is established based on mechanical and electrostatic energy transition principle. Meanwhile, all models are coded in analog hardware description language (MAST). Furthermore, the accuracy of models is verified by comparison with finite element analysis(FEA) and the results prove that the models have near FEA accuracy.Secondly, The modeling methodology of optical behavior of the micro deformable mirror is investigated and the models are established as a result. The description of optical signal is presented and the behavior model of the optical functional components such as planar reflection mirror and thin lens are established using matrix optics and Gaussian beam theory. The models are coded in analog hardware description language(MAST) and are simulated in MuPEN. In addition, the evaluation parameters of the optical quality for the micro deformable mirror arrays
including the Strehl ratio and fitting error are analyzed. Then, MuPEN models for optical quality evaluation are established and simulation is implemented to analyze the effect of the parameters of mirror arrays on optical quality.Finally, system-level model of micro deformable mirror is established and both mechanical and electrostatic coupling simulation and optical phase modulation simulation are implemented in MuPEN. The resonance frequency, the response time and the pull-in voltage of the micro deformable mirror are ascertained through different simulations and the simulation results show that the micro deformable mirror we designed can satisfy the requirements of adaptive optics system. Moreover, the optical phase modulation behavior model of micro deformable mirror arrays is established for the first time. Then the simulation is implemented and the wavefront after phase modulation is reconstructed together with the analysis of relative error. Simulation results indicate that rapid modeling and simulation of micro deformable mirror can be accomplished in this way which will benefit the design and optimization of micro deformable mirror arrays.
引文
[1]. Robert K. Tyson, Principles of Adaptive Optics (2nd edition), California, Academic Press, 1998.
[2]. Francois Roddier, Adaptive Optics in Astronomy, British, Cambridge University Press, 1999.
[3]. John Hardy, Adaptive Optics for Astronomical Telescopes, London, Oxford Press, 1998.
[4]. Rodney L.Clark,Adaptive Optics aims for earthly applications, photonics spectra, 1997,4:100-106
[5]. ,Gunar Lorenza, Arthur Morrisb, Issam Lakkisc ,A top-down design flow for MOEMS
[6]. Thomas E. Plowman, Robert A. Stoll, David Winick, and Arthur S. Morris III, A Study of Optomechanical Variations and Control in a MOEMS Switch Model
[7]. John Comtois, Adrian Michalicek, et al. Surface-micromachined polysilicon MOEMS for adaptive optics, Sensors and Actuators, 1999, 78.
[8]. M. Adrian Michalicek, Natalie Clarkl, John H. Comtois, and Heather K. Schriner,Design and simulation of advanced surface micromachined micromirror devices for telescope adaptive optics applications,Air Force Research Laboratory
[9]. Shaun Roger Hick,Demonstrating optica aberration correction with a MEMS micro_mirror device, M.S. thesis,Air Force Institute of Technology, 1996
[10]. Perter C. Roberts, modeling and simulation of optical characteristics of microelectromechanical mirror arrays, M.S. thesis, Air Force Institute of Technology, 1996
[11]. William D. Cowan, Foundry Mircofabrication of Adaptive Optics. Ph.D. thesis, Air Force Institute of Technology, 1998.
[12]. Harris J. Hall. Control and Characterization of Line-addressable micromirror arrays. M.S. thesis, Air Force Institute of Technology, 2001.
[13]. N. Clark, P. Furth. Design and performance evaluation of a silicon eye using micro-mirrors, The 43rd Midwest Symposium on Circuits and Systems, Lansing, MI, August 2000.
[14]. Claire Max, Wavefront Correction Deformable Mirrors Lecture 7. UC Santa Cruz, 2002.
[15]. Peter Krulevitch, Paul Bierden, MOEMS spatial light modulator development at the Center for Adaptive Optics, Proc. SPIE 2002, Vol.4825.
[16]. Adisorn Tuantranont, Victor M. Bright, Segmented Silicon-Micromachined Microelectromechanical Deformable Mirrors for Adaptive Optics, IEEE JOURNAL. 2002, 8.
[17]. W. Zhang, and Y. C. Lee, "Bulk-Etched Surface Micromachined and Flip-Chip Integrated Micromirror Array for Infrared Applications", University of Colorado, CO, USA
[18]. M.C. Roggemann, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, and J. H. Comtois, "Use ofmicro-electromechanical deformable mirrors to control aberration in optical systems", Opt. Eng., Vol. 36, No. 5, pp.1326-1338, May 1997
[19]. William D. Cowan, Max K. Lee, Byron M. Welsh, Surface Micromachined Segmented Mirrors for Adaptive Optics, IEEE Journal of Selected Topics in Quantum electronics, Vol 5, No 1, January/February 1999.
[20].姜文汉,光电技术研究所的自适应光学技术,光电工程.1995,22
[21].姜春晖,自适应光学系统对活体人眼视网膜的初步观察,成都:中国科学院光电技术研究所博士论文.2002.
[22]. Ling Ning, et al. Small tabletop adaptive optical systems for human retinal imaging. Proc. SPIE 2002, Vol.4825.
[23].张志伟,马俊,俞信,微小型自适应光学系统及其在星载光学遥感器上的应用,红外与激光工程,第29卷第1期,2000年2月
[24].陈珂等,微机械薄膜变形镜光学影响函数矩阵的测试与研究,北京理工大学,高技术通讯,2000.09
[25].蒋军彪等,微镜单元的设计与加工工艺研究,航空精密制造技术,2001年2月,第37卷第1期,P11
[26].乔大勇,基于MEMS技术的自适应光学微变形镜的设计与分析,硕士 学位论文,西北工业大学
[27]. D. Ramaswamy, N. Aluru, and J. White, "Fast coupled-domain, mixedregime electromechanicat simulation," in Proc. Int. Conf. Solid-State Sensors and Actuators (Transducers'99), Sendal, Japan, June 1999, pp. 314-317.
[28]. Robert M. K, George E K, et al. An Integrated Simulator for Coupled Domain Problems. MEMS. Journal of MicroElectroMechanical Systems. 2001, 10(3): 379～391.
[29]. T. Veijola, H. Kuisma, et. al. Equivalent-circuit model of the squeezed gas film in a silicon accelerometer, Sensors and Actuators, A: Physical. 1995, 48(3): 239-248.
[30]. A.C. Tilmans, Equivalent circuit representation of electromechanical transducers: Ⅰ. Lumped-parameter systems, Journal of Micromechanics and Microengineering. 1996, 6(1): 157-176.
[31]. T. Veijola, Nonlinear Circuit Simulation of MEMS Components: Controlled Current Source Approach. Proceedings of ECCTD'01. Espoo, Finland. 2001,3: 377-380.
[32]. G. Lorenz, A. Morris, I. Lakkis. A Top-Down Design Flow for MOEMS. DT/P 2001.
[33]. Zhou, Ningning. Simulation and synthesis of MicroElectroMechanical systems. University of California, Berkeley. PhD Thesis.2002.
[34]. Fedder, Gary K.; Jing, Qi.Hierarchical circuit-level design methodology for microelectromechanical systems. IEEE Trans Circuits Syst Ⅱ Analog Digital Signal Process. 1999, 46(10): 1309-1315.
[35].霍鹏飞,马炳和,苑伟政.基于组件网络方法的微加速度计建模与仿真.航空学报.2003,24(5):466-470.
[36].马炳和,霍鹏飞,苑伟政.MEMS系统级设计与基于多端口组件网络的建模方法.微纳电子技术.2003(7/8).
[37].霍鹏飞,微机电系统的多端口组件网络方法系统级建模研究,博士学位论文,西北工业大学
[38]. J. Qi. Modeling and Simulation for Design of Suspended MEMS. PhD Thesis. Carnegie Mellon University. 1999.
[39]. J.M. Gere and S.P Timoshenko, Mechanics of Materials, 2nd Ed., Van Nostrand Reinhold Co., New York, 1972.
[40]. S.P Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York, 3rd ed., 1970.
[41]. P. Mario, Structural Dynamics, Theory and Computation, Van Nostrand Reinhold, New York, 1980.
[42]. X. Zhang and W.C. Tang. Viscous Air Damping in Laterally Driven Microresonators. Sensors and Materials. 1995, 7(6): 415-430.
[43]. T. Veijola, M. Turowski. Compact Damping Models for Laterally Moving Microstructures with Gas-Rarefaction Effects. JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, 2001,10(2): 263-273.
[44]. Guangya Zhou, Francis E H Tay and Fook Siong Chau, Macro-modelling of a double-gimballed electrostatic torsional micromirror,J. Micromech. Microeng. 13 (2003) 532-547 PII: S0960-1317(03)54903-8
[45]. Jan E. Vandemeer, Nodal Design of Actuators and Sensors, technical report Carnegie Mellon University, May, 1998
[46]. Saleh, Bahaa E. A.; Teich, Malvin Carl .Fundamentals of phototonics ,New York John Wiley & Sons, Inc. (US), 1991.
[47]. J. Albrecht, R. Seidel, L. Melzer and D. M(?)uller,System-level Optical Models of 3-D Laser Projection Systems using Micromirror Arrays,Chemnitz University of Technology, D-09107 Chemnitz, Germany
[48]. Timothy P. Kurzweg etc..Optical Propagation Methodologies for Optical MEM Systems, Department of Electrical Engineering, University of Pittsburgh
[49]. David Russell Luke. Analysis of Optical Wavefront Reconstruction and Deconvolution in Adaptive optics. Ph.D. thesis, Department of Electrical Engineering, University of Washington, 2001.
[50]. Fang Shi, Douglas MacMartin, Mitchell Troy. Local Wavefront Reconstruction: Simulations, Experiments and Predictions. California Institute of Technology. 2002.
[51]. Fang Shia, Douglas G. MacMartinb, Mitchell Troya. Sparse Matrix Wavefront Reconstruction Simulations and Experiments. Proc. SPIE. 2003, Vol.4839.
[52]. Brian Bauman. Optical Aberrations. The Center for Adaptive Optics. 2004.
[53]. Geunyoung Yoon. Aberration Theory. Department of Ophthalmology Center for Visual Science University of Rochester. 2004.
[2]. Francois Roddier, Adaptive Optics in Astronomy, British, Cambridge University Press, 1999.
[3]. John Hardy, Adaptive Optics for Astronomical Telescopes, London, Oxford Press, 1998.
[4]. Rodney L.Clark,Adaptive Optics aims for earthly applications, photonics spectra, 1997,4:100-106
[5]. ,Gunar Lorenza, Arthur Morrisb, Issam Lakkisc ,A top-down design flow for MOEMS
[6]. Thomas E. Plowman, Robert A. Stoll, David Winick, and Arthur S. Morris III, A Study of Optomechanical Variations and Control in a MOEMS Switch Model
[7]. John Comtois, Adrian Michalicek, et al. Surface-micromachined polysilicon MOEMS for adaptive optics, Sensors and Actuators, 1999, 78.
[8]. M. Adrian Michalicek, Natalie Clarkl, John H. Comtois, and Heather K. Schriner,Design and simulation of advanced surface micromachined micromirror devices for telescope adaptive optics applications,Air Force Research Laboratory
[9]. Shaun Roger Hick,Demonstrating optica aberration correction with a MEMS micro_mirror device, M.S. thesis,Air Force Institute of Technology, 1996
[10]. Perter C. Roberts, modeling and simulation of optical characteristics of microelectromechanical mirror arrays, M.S. thesis, Air Force Institute of Technology, 1996
[11]. William D. Cowan, Foundry Mircofabrication of Adaptive Optics. Ph.D. thesis, Air Force Institute of Technology, 1998.
[12]. Harris J. Hall. Control and Characterization of Line-addressable micromirror arrays. M.S. thesis, Air Force Institute of Technology, 2001.
[13]. N. Clark, P. Furth. Design and performance evaluation of a silicon eye using micro-mirrors, The 43rd Midwest Symposium on Circuits and Systems, Lansing, MI, August 2000.
[14]. Claire Max, Wavefront Correction Deformable Mirrors Lecture 7. UC Santa Cruz, 2002.
[15]. Peter Krulevitch, Paul Bierden, MOEMS spatial light modulator development at the Center for Adaptive Optics, Proc. SPIE 2002, Vol.4825.
[16]. Adisorn Tuantranont, Victor M. Bright, Segmented Silicon-Micromachined Microelectromechanical Deformable Mirrors for Adaptive Optics, IEEE JOURNAL. 2002, 8.
[17]. W. Zhang, and Y. C. Lee, "Bulk-Etched Surface Micromachined and Flip-Chip Integrated Micromirror Array for Infrared Applications", University of Colorado, CO, USA
[18]. M.C. Roggemann, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, and J. H. Comtois, "Use ofmicro-electromechanical deformable mirrors to control aberration in optical systems", Opt. Eng., Vol. 36, No. 5, pp.1326-1338, May 1997
[19]. William D. Cowan, Max K. Lee, Byron M. Welsh, Surface Micromachined Segmented Mirrors for Adaptive Optics, IEEE Journal of Selected Topics in Quantum electronics, Vol 5, No 1, January/February 1999.
[20].姜文汉,光电技术研究所的自适应光学技术,光电工程.1995,22
[21].姜春晖,自适应光学系统对活体人眼视网膜的初步观察,成都:中国科学院光电技术研究所博士论文.2002.
[22]. Ling Ning, et al. Small tabletop adaptive optical systems for human retinal imaging. Proc. SPIE 2002, Vol.4825.
[23].张志伟,马俊,俞信,微小型自适应光学系统及其在星载光学遥感器上的应用,红外与激光工程,第29卷第1期,2000年2月
[24].陈珂等,微机械薄膜变形镜光学影响函数矩阵的测试与研究,北京理工大学,高技术通讯,2000.09
[25].蒋军彪等,微镜单元的设计与加工工艺研究,航空精密制造技术,2001年2月,第37卷第1期,P11
[26].乔大勇,基于MEMS技术的自适应光学微变形镜的设计与分析,硕士 学位论文,西北工业大学
[27]. D. Ramaswamy, N. Aluru, and J. White, "Fast coupled-domain, mixedregime electromechanicat simulation," in Proc. Int. Conf. Solid-State Sensors and Actuators (Transducers'99), Sendal, Japan, June 1999, pp. 314-317.
[28]. Robert M. K, George E K, et al. An Integrated Simulator for Coupled Domain Problems. MEMS. Journal of MicroElectroMechanical Systems. 2001, 10(3): 379～391.
[29]. T. Veijola, H. Kuisma, et. al. Equivalent-circuit model of the squeezed gas film in a silicon accelerometer, Sensors and Actuators, A: Physical. 1995, 48(3): 239-248.
[30]. A.C. Tilmans, Equivalent circuit representation of electromechanical transducers: Ⅰ. Lumped-parameter systems, Journal of Micromechanics and Microengineering. 1996, 6(1): 157-176.
[31]. T. Veijola, Nonlinear Circuit Simulation of MEMS Components: Controlled Current Source Approach. Proceedings of ECCTD'01. Espoo, Finland. 2001,3: 377-380.
[32]. G. Lorenz, A. Morris, I. Lakkis. A Top-Down Design Flow for MOEMS. DT/P 2001.
[33]. Zhou, Ningning. Simulation and synthesis of MicroElectroMechanical systems. University of California, Berkeley. PhD Thesis.2002.
[34]. Fedder, Gary K.; Jing, Qi.Hierarchical circuit-level design methodology for microelectromechanical systems. IEEE Trans Circuits Syst Ⅱ Analog Digital Signal Process. 1999, 46(10): 1309-1315.
[35].霍鹏飞,马炳和,苑伟政.基于组件网络方法的微加速度计建模与仿真.航空学报.2003,24(5):466-470.
[36].马炳和,霍鹏飞,苑伟政.MEMS系统级设计与基于多端口组件网络的建模方法.微纳电子技术.2003(7/8).
[37].霍鹏飞,微机电系统的多端口组件网络方法系统级建模研究,博士学位论文,西北工业大学
[38]. J. Qi. Modeling and Simulation for Design of Suspended MEMS. PhD Thesis. Carnegie Mellon University. 1999.
[39]. J.M. Gere and S.P Timoshenko, Mechanics of Materials, 2nd Ed., Van Nostrand Reinhold Co., New York, 1972.
[40]. S.P Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York, 3rd ed., 1970.
[41]. P. Mario, Structural Dynamics, Theory and Computation, Van Nostrand Reinhold, New York, 1980.
[42]. X. Zhang and W.C. Tang. Viscous Air Damping in Laterally Driven Microresonators. Sensors and Materials. 1995, 7(6): 415-430.
[43]. T. Veijola, M. Turowski. Compact Damping Models for Laterally Moving Microstructures with Gas-Rarefaction Effects. JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, 2001,10(2): 263-273.
[44]. Guangya Zhou, Francis E H Tay and Fook Siong Chau, Macro-modelling of a double-gimballed electrostatic torsional micromirror,J. Micromech. Microeng. 13 (2003) 532-547 PII: S0960-1317(03)54903-8
[45]. Jan E. Vandemeer, Nodal Design of Actuators and Sensors, technical report Carnegie Mellon University, May, 1998
[46]. Saleh, Bahaa E. A.; Teich, Malvin Carl .Fundamentals of phototonics ,New York John Wiley & Sons, Inc. (US), 1991.
[47]. J. Albrecht, R. Seidel, L. Melzer and D. M(?)uller,System-level Optical Models of 3-D Laser Projection Systems using Micromirror Arrays,Chemnitz University of Technology, D-09107 Chemnitz, Germany
[48]. Timothy P. Kurzweg etc..Optical Propagation Methodologies for Optical MEM Systems, Department of Electrical Engineering, University of Pittsburgh
[49]. David Russell Luke. Analysis of Optical Wavefront Reconstruction and Deconvolution in Adaptive optics. Ph.D. thesis, Department of Electrical Engineering, University of Washington, 2001.
[50]. Fang Shi, Douglas MacMartin, Mitchell Troy. Local Wavefront Reconstruction: Simulations, Experiments and Predictions. California Institute of Technology. 2002.
[51]. Fang Shia, Douglas G. MacMartinb, Mitchell Troya. Sparse Matrix Wavefront Reconstruction Simulations and Experiments. Proc. SPIE. 2003, Vol.4839.
[52]. Brian Bauman. Optical Aberrations. The Center for Adaptive Optics. 2004.
[53]. Geunyoung Yoon. Aberration Theory. Department of Ophthalmology Center for Visual Science University of Rochester. 2004.