摘要
随着光学天文望远镜的口径越来越大，自适应光学系统波前传感器与波前校正器的单元数也越来越多，对波前复原和波前控制技术的要求越来越高。同时，新型自适应光学系统，如变形次镜自适应光学系统的出现及发展，也使得传统的波前复原方法面临了一些新的困难。为此，我们对自适应光学系统的波前复原与波前控制优化技术进行了一系列深入的研究，并取得了一系列的创新成果。
第一，基于Hadamard测量方法的平均效应和直接斜率波前复原法响应矩阵为稀疏矩阵的特点，提出了自适应光学系统响应矩阵的多通道Hadamard测量方法。理论分析和实验结果表明，该方法的测量精度高于纯Hadamard方法与纯多通道方法。
第二，基于正弦调制测量方法对湍流引入噪声的抑制能力和直接斜率波前复原法响应矩阵为稀疏矩阵的特点，提出了自适应光学系统响应矩阵的多通道正弦调制测量方法。理论分析和实验结果表明，该方法能够有效地抑制大气湍流扰动引入的测量误差，同时大幅度减小响应矩阵测量所需的时间。
第三，考虑波前传感器与波前校正器的对准误差，提出了适用于基于哈特曼-夏克波前传感器的自适应光学系统响应矩阵的直接计算方法。实验结果表明，该方法只需测量几个特征驱动器的斜率响应，提高了响应矩阵的测量效率。
第四，考虑实际自适应光学系统存在的时间延迟，修正了自适应光学系统闭环残余误差与闭环带宽的关系式，提出了自适应光学控制系统的修正有效带宽。仿真结果表明，根据修正有效带宽可以准确估计自适应光学系统的闭环残余方差。
第五，基于所提出的自适应光学系统的修正有效带宽，推导了倾斜校正回路的理论最优闭环带宽。不同大气湍流和测量噪声下的数值模拟结果表明，最优闭环带宽的理论结果与仿真结果一致。
最后，基于自适应控制器的自适应特性与积分控制器的稳定性，提出了一种LMS滤波器与积分控制器的联合工作模式：LMSI-2。仿真结果表明，LMSI-2型控制器在有效减小闭环残余误差的同时，还能避免自适应滤波器权值收敛阶段引入的振荡现象。
自适应光学系统波前复原及波前控制优化技术对于充分发挥自适应光学系统各组成部分的性能，提高波前校正能力具有重要意义。通过本文的研究，为自适应光学系统响应矩阵的测量提供了优化方法；为波前控制方法的优化设计提供了重要参考。
With the development of large-diameter optical astronomical telescopes, thenumbers of actuators and subapertures in adaptive optics (AO) systems keepgrowing, requiring the advance of wavefront reconstruction and wavefront control.Meanwhile, the appearance and development of new types of AO systems, forexample, the deformable secondary mirror AO systems, bring new challenges to thetraditional wavefront reconstruction methods. In this paper, regarding to the newrequirements of AO systems, a series of optimized wavefront reconstruction andwavefront control technologies are proposed.
Firstly, based on the averaging effect of the Hadamard calibration and the sparsecharacteristics of the zonal interaction matrix, a novel multichannel-Hadamardcalibration of the interaction matrix of the AO system is proposed. Theory analysisand experiments show that the measurement precision of themultichannel-Hadamard method is higher than the Hadamard only method and themultichannel only method.
Secondly, based on the turbulence induced noise rejection capability of themodulation method and the sparse characteristics of the zonal interaction matrix, anovel multichannel-modulation calibration of the interaction matrix of the AOsystem is presented. Theory analysis and experimental results show that themultichannel-modulation calibration method can effectively reject the atmosphereinduced noise as well as greatly reduce the calibration time.
Thirdly, considering the misalignment between the wavefront sensor andwavefront corrector, a direct compute of the interaction matrix of the AO systemwith a Hartmann-Shack wavefront sensor is proposed. Experimental results showthat the interaction matrix measurement efficiency is greatly improved because thismethod can only need to measure the slope response of several selected actuators.
Fourthly, considering the time delay in real AO systems, the relationshipbetween the closed-loop residual variances and the closed-loop-3dB bandwidths aremodified, and thus the modified effective bandwidths of the AO systems arepresented. Numerical simulation demonstrates that the modified effectivebandwidths can be used to estimate the closed-loop residual variance moreeffectively.
Fifthly, based on the modified effective bandwidths, the optimal closed-loopbandwidth of the tilt-correction loop in the AO system is derived. Simulations withdifferent atmospheric turbulences and measurement noises show that the theoreticalvalues of the optimal closed-loop bandwidths agree with the simulated values.
Finally, based on the self-adaption of the adaptive filter and the stability of thePI controller, a “LMSI-2” controller is proposed. Simulations show that the LMSI-2contoller can effectively reduce the closed-loop residual error as well as avoid theoscillation phenomenon during the convergence process of the adaptive filter.
引文
[1]段海峰.自适应光学技术在激光光束像差控制与参数测量中的应用研究[D].成都:中国科学院光电技术研究所博士论文,2003
[2]姜文汉.自适应光学技术[J].自然杂志,2006,28(1):7-13
[3] J. W. Hardy. Adaptive Optics for Astronomical Telescopes[M]. New York: Oxford UniversityPress,1998
[4] I. Newton. Opticks[M]. London: The Royal Society,1704
[5]陈丹.“哈勃”的辉煌十年[J].科技潮,2000,6:156-159
[6] H. W. Babcock. The possibility of compensating astronomical seeing[J]. Publ. Astron. Soc.Pac,1953,65(386):229–236
[7] M. Tarenghi, R. N. Wilson. The ESO NTT (New Technology Telescope): The First ActiveOptics Telescope[C]. Proc. SPIE,1989,1114
[8] B. Macintosh, J. Graham, D. Palmer, et. al. The Gemini Planet Imager[C]. Proc. SPIE,2006,6272:62720L
[9] P. Wizinowich, D. S. Acton, C. Shelton, et. al. First light adaptive optics images from the KeckII Telescope: a new era of high angular resolution imagery[J]. Publ. Astron. Soc. Pac.2000,112:315–319
[10] S. Esposito, A. Tozzi, D. Ferruzzi, et al. First-light adaptive optics system for large binoculartelescope[C]. Proc. SPIE,20134839
[11] B. Macintosh, M. Troy, R. Doyon, et. al. Extreme Adaptive Optics for the Thirty MeterTelescope[C]. Proc. SPIE,2006,6272:62720N
[12] R. Gilmozzi, J. Spyromilio. The42m European ELT: Status[C]. Proc. SPIE,2008,7012701219
[13] R. Fugate, D. Fried, G. Ameer, et. al. Measurement of atmospheric wavefront distortion usingscattered light from a laser guide-star[J]. Nature,1991,353:144–146
[14] J. Beckers. Increasing the Size of the Isoplanatic patch with Multiconjugate AdaptiveOptics[C]. Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed.,Vol.2of ESOConference and Workshop Proceedings(European Southern Observatory, Garching, Germany,1988), pp.693–703.
[15] F. Wildi, G. Brusa, A. Riccardi, et al. Towards first light of the6.5m MMT adaptive opticssystem with deformable secondary mirror[J]. Astronomical Telescopes and Instrumentation.International Society for Optics and Photonics,2003:155-163
[16] H. Martin; G. Brusa B. Cuerden. Deformable secondary mirrors for the LBT adaptive opticssystem[C]. Proc. SPIE2006627262720U
[17] C. Rao, A. Zhang, X. Fan. Adaptive optical system based on deformable secondary mirror on1.8-meter telescope[C], Proc. SPIE2012844784473H
[18]李超宏,鲜浩,姜文汉等.用于白天自适应光学的波前探测方法分析[J].物理学报,2007,56:4289
[19]蒋志凌.哈特曼波前传感器特性和应用研究[D].武汉：中国科学院武汉物理与数学研究所博士学位论文,2005
[20]张昂.不同子孔径像素数时的夏克-哈特曼波前传感器探测性能究[D].成都:中国科学院光电技术研究所博士学位论文,2006
[21]李华强.夏克-哈特曼波前传感器的若干问题分析[D].成都：中国科学院光电技术研究所博士学位论文,2008
[22] J. Hardy, J. Lefebvre, C. Koliopoulos. Real-time atmospheric compensation[J]. J. Opt. Soc.Am. A,1977,67(3):360-369
[23] F. Roddier. Curvature sensing: a Diffraction Theory. NOAO R&D Note,1987,No.87
[24] F. Roddier. Curvature sensing and compensation: a new concept in adaptive optics[J]. Appl.Opt.1988,27(7):1223-1225
[25] R. Ragazzoni. Pupil plane wavefront sensing with an oscillating prism[J]. Journal of ModernOptics.1996,43(2),289-293
[26] R. Ragazzoni, J. Farinato. Sensitivity of a pyramidic Wave Front sensor in closed loopAdaptive Optics[J]. A&A,1999,350: L23-L26
[27]凌宁.自适应光学波前校正器[J].光学技术,1998，3(3):12-16
[28]凌宁，陈东红，官春林等.两维高速压电倾斜反射镜[J].光电工程,1995,22(1):51-60
[29]姜文汉.能动光学与自适应光学（综述）[J].光学工程,1979,1:1-19
[30]苏定强.主动光学—新一代大望远镜的关键技术[J].天文学进展,1999,17(1):1-14
[31] A. N. Kolmogorov. The local structure of Turbulence in Incompressible Viscous Fluid forVery large Reynold’s Numbers [J]. Dokl Akad Naud SSSR,1941,30:301-305
[32] V. L. Tatarski. Wave Propagation in a Turbulent Medium [M]. New York：Dover Publication,1961
[33] D. L. Fried. Statistics of a geometric representation of wavefront distortion[J]. J. Opt. Soc.Am. A.,1965,55(11):1427-1435
[34] D. P. Greenwood. C. A. Primmerman, Adaptive optics research at Lincoln Laboratory[J]. TheLincoln Laboratory Journal,1992,5(1):3-24
[35] J. T. Salmon. Real time wavefront correction system using a zonal deformable mirror andaHartmann sensor[C]. Proc. SPIE,1991,1542:2-17
[36] D. L. Fried. Least squares fitting a wavefront distortion estimate to an array ofphase-difference measurements[J]. J. Opt. Soc. Am. A.,1977,67(3):370-375
[37] R. H. Hudgin. Waverfront reconstruction for compensated imaging[J]. J. Opt. Soc. Am. A.,1977,67(3):375-378
[38] J. Herrmann. Least squares wavefront errors of minimum norm[J]. J. Opt. Soc. Am. A.,1980,70(1):28-35
[39] T. R. O’Meara. The multidither principle in adaptive optics[J]. J. Opt. Soc. Am. A.,1977,67(3):306-315
[40] P. Kern, P. Lena, P, Gigan. Come-On: An Adaptive Optics Prototype Dedicated TO InfraredAstronomy[C]. Proc. SPIE,1989,1130,17
[41] E. Genetron, J. Cuby, F. Rigaut, et al. Come-On-Plus project: an upgrade of the Come-Onadaptive optics prototype system[C]. Proc. SPIE1991,1542:297-307
[42]姜文汉.光电技术研究所的自适应光学技术[J].光电工程,1995,22(1):1-13
[43]饶长辉,姜文汉.2.16m望远镜红外自适应光学系统的误差和性能分析[J].天体物理学报，1996,16(4):428-437
[44]饶长辉,姜文汉.云南天文台1.2米望远镜61单元自适应光学系统[J].量子电子学报，2006,23(3)：295-302
[45] C. Rao, K. Wei, X. Zhang. First observations on the127-element adaptive optical system for1.8m telescope[C]. Proc. SPIE,765476541H
[46] L. Zhu, N. Gu, S. Chen, et.al. Real Time Controller for37-Element Low-order SolarAdaptive Optics System at1m New Vacuum Solar Telescope[C]. Proc. SPIE2012841584150V
[47] O. Guyon. Limits of adaptive optics for high-contrast imaging[J]. The Astrophysical Journal,2005,629(1):592-622
[48] M. Kasper. Adaptive Optics for High-Contrast Imaging[C]. Proc. SPIE,2012,8447,844711
[49] A. Bouchez, R. Dekany, J. Angione. The PALM-3000high-order adaptive optics system forPalomar Observatory[C]. Proc. SPIE,2008,7015,70150Z
[50] J. Roberts, R. Dekany, R. Burruss. Results from the PALM-3000high-order adaptive opticssystem[C]. Proc. SPIE,2012,8447,84470Y
[51] B. Macintosh, J. Graham, D. Palmer, et. al. The Gemini Planet Imager: from science todesign construction[C]. Proc. SPIE,2008,7015,701518
[52] S. Thomas, L. Poyneer, R. de Rose, et. al. Integration and test of the Gemini Planet Imager[C].Proc. SPIE,2011,8149,814903
[53] http://www.gemini.edu/node/12113
[54] T. Fusco, G. Rousset, J.-F. Sauvage. High-order adaptive optics requirements for directdetection of extrasolar planets: Application to the SPHERE instrument[J]. Opt. Express,2006,14(17):7515-7534
[55] T. Fusco, J.-F. Sauvage, C. Petit, et. al. INTEGRATION OF SAXO, THE VLT-SPHEREEXTREME AO: FINAL PERFORMANCE[C]. Third AO4ELT Conference Florence, Italy. May2013
[56] C. Rao, K. Wei, A. Zhang, et. al. The Laboratory Results of a595-unit Adaptive OpticalSystem[C]. Third AO4ELT Conference Florence, Italy. May2013
[57] J. Beckers. A proposal to the National Science Foundation, in the NOAO8M TelescopeDescription Vol. II, by the Association for University Research in Astronomy,1989
[58]樊新龙.1.8m望远镜变形次镜优化设计及测试技术研究[D].成都:中国科学院光电技术研究所博士论文,2012
[59] L. M. Close and D. W. McCarthy. High-resolution imaging with a tip/tilt Cassegrainsecondary [J]. Publ. Astron. Soc. Pac.,1994,106(695):77–86
[60] E. Pitz, R. R. Rohloff, and H. Marth. UKIRT5-axis tip/tilt secondary electro-mechanical andoptical design [C]. Proc. ESO, Garching, Germany1993.
[61] http://femto.ru/
[62] D. Bruns, T. Barrett, D. Sandier, et. al. Force-actuated adaptive secondary mirrorprototype[C]. ESO Conference proceedings No.54Topical meeting on adaptive optics, Garching,Germany, October1995:251-256
[63] F. Wildi, G. Brusa, M. Lloyd-Hart et. al. First light of the6.5-m MMT adaptive opticssystem[C]. Proc. SPIE,2003,5169:17-25;
[64] D. Gallieni, E. Anaclerio, et. al. LBT adaptive secondary units final design andconstruction[C]. Proc. SPIE,2003,4839:765-771
[65] S. Esposito, A. Riccardi, L. Fini, et. al. First light AO (FLAO) system for LBT: finalintegration, acceptance test in Europe, and preliminary on-sky commissioning results[C]. Proc.SPIE,2010,7736,773609
[66] S. Esposito, D. Mesa, A. Skemer, et. al. LBT observations of the HR8799planetary systemFirst detection of HR8799e in H band[J]. A&A,2013,549-555
[67]樊新龙,官春林,饶长辉.1.8m望远镜变形次镜波前拟合能力分析[J].光学学报,2011,31(8),0822002
[68] C. Boyer, V. Michau, and G. Rousset. Adaptive Optics: Interaction matrix measurements andreal time control algorithms for the COME-ON project[C]. Proc. SPIE,1990,1237,406-421
[69] W. Jiang and H. Li. Hartmann-Shack wavefront sensing and wavefront control algorithm[C].Proc. SPIE,1990,1271:82-93
[70] M. Kasper, E. Fedrigo, D. P. Looze, et. al. Fast calibration of high-order adaptive opticssystems[J]. J. Opt. Soc. Am. A,2004,21(6):1004-1008
[71] S. Meimon, T. Fusco and C. Petit. An optimized calibration strategy for high order adaptiveoptics systems: the Slope-Oriented Hadmard Actuation[C].1st AO4ELT conference,2010, paper07009
[72] F. Wildi and G. Brusa. Determining the interaction matrix using starlight[C]. Proc. SPIE,2004,5490:164-173
[73] S. Esposito, R. Tubbs, A. Puglisi, et. al. High SNR measurement of interaction matrix on-skyand in lab[C]. Proc. SPIE,2006,6272,62721C.
[74] S. Oberti, H. Bonnet, E. Fedrigo, et. al. Calibration of a curvature sensor/bimorph mirror AOsystem: interaction matrix measurement on MACAO systems[C]. Proc. SPIE,2004,5490:139-150
[75] C. Kulcsar, H. Raynaud, C. Petit et. al. Optimal control, observers and integrators in adaptiveoptics[J]. Opt. Express,2006,14(17):7464-7476
[76]李新阳.自适应光学系统模式复原算法和控制算法的优化研究[D].成都：中国科学院光电技术研究所博士学位论文,2000
[77] R. Paschall, D. Anderson. Linear quadratic Gaussian control of a deformable mirror adaptiveoptics system with time-delayed measurements[J]. Appl. Opt.,199332(31):6347-6358
[78] B. Roux, J.-M. Conan, C. Kulcsar, et. al. Optimal control law for classical and multiconjugateadaptive optics[J]. J. Opt. Soc. Am. A,2004,21(7):1261-1276
[79] C. Kulcsar, H.-F. Raynaud, C. Petit, et.al. Can LQG Adaptive Optics control cope withactuator saturation?[J]. Appl. Opt.,2007PMA1
[80] P. Piatrou, M. C. Roggemann. Performance study of Kalman filter controller formulticonjugate adaptive optics[J]. Appl. Opt.,2007,46(9):1446-1455
[81] C. Petit, J-M. Conan, C. Kulcsar, et. al. First laboratory validation of vibration filtering withLQG control law for Adaptive Optics[J]. Opt. Express,2008,16(1):87-97
[82] C. Petit, J-M. Conan, C. Kulcsar, et. al. Linear quadratic Gaussian control for adaptive opticsand multiconjugate adaptive optics: experimental and numerical analysis[J]. J. Opt. Soc. Am. A,2009,26(6):1307-1325
[83] D. P. Looze. Linear-quadratic-Gaussian control for adaptive optics systems using a hybridmodel[J]. J. Opt. Soc. Am. A,2009,26(1):1-9
[84] S.-B. Jiang and J. S. Gibson. An unwindowed multichannel lattice filter with orthogonalchannels[J]. IEEE Trans. Signal Process,1995,43(12),2831–2842
[85] J. Gibson, C.-C.Chang, and B. Ellerbroek. Adaptive optics: wavefront correction by use ofadaptive filtering and control[J]. Appl. Opt.,2000,39(16),2525–2538
[86] C.-C. Chang and J. Gibson. Parallel control loops based on spatial subband processing foradaptive optics[C]. American Control Conference,2000, pp.2113–2117
[87] J. Gibson, C.-C. Chang, and B. Ellerbroek. Adaptive optics: wavefront reconstruction byadaptive filtering and control[C]. Proceedings of38th IEEE Conference on Decision and Control,1999, pp.761–766
[88] J. Gibson, C.-C. Chang, and Neil Chen. Adaptive optics with a new modal decomposition ofactuator and sensor spaces[C]. American Control Conference,2001, pp.4619–4625
[89] Y.-T. Liu and J. Gibson. AO with adaptive filtering and control[C]. American ControlConference,2004, pp.3176–3179
[90] T. Rhoadarmer, L. Klein, J. Gibson, et. al. Adaptive control and filtering for closed-loopadaptive optical wave front reconstruction[C]. Proc.SPIE,2006,6306,63060E
[91] J. Gibson and Y.-T. Liu. Adaptive control in adaptive optics for directed energy system[J].Opt. Eng.,2007,46,046601:1–13
[92] P. Orzechowski, J. Gibson, and T.-C. Tsao. Optimal suppression of laser beam jitter byhigh-order RLS adaptive control[J]. IEEE Trans. Control Syst. Technol.,2008,16(2):255–267
[93] N. Pérez-Arancibia, J. Gibson, and T.-C. Tsao. Frequency-weighted minimum-varianceadaptive control of laser beam jitter[J]. IEEE/ASME Trans. Mechatron.,2009,14(3):337–348
[94] S. Monirabbasi and S. Gibson. Adaptive control in an adaptive optics experiment[J]. J. Opt.Soc. Am. A,2010,27(11):A84-A96
[95] M. Jorgenson and G. Aitken. Neural net work prediction of turbulence induced wavefrontdegredations with applications to adaptive optics[C]. Adaptive and Learning Systems, F.A.Sadjadi, ed., Proc. SPIE,1992,1706:113–121
[96] D. Montera, B. Welsh, C. Roggemann. Prediction of wave-front sensor slope measurementswith artificial neural net works[J]. Appl. Opt.199736(3):675-681
[97] G. I. Taylor. The Spectrum of Turbulence[J]. Proceedings of Royal Society of London, SeriesA-Mathematical and Physical Sciences,1938,164(919):476–490
[98]饶长辉.非Kolmogorov湍流情况下低阶校正自适应光学系统的性能研究[D].成都：中国科学院光电技术研究所博士学位论文,2001.
[99] D. P. Greenwood. Bandwidth specification for adaptive optics systems[J]. J. Opt. Soc. Am. A,1977,67(3):390-393
[100] G. A. Tyler. Bandwidth considerations for tracking through turbulence[J]. J. Opt. Soc. Am.A,1994,11(1):358-367
[101] D. Malacara. Optical shop testing[M]. John Wiley&Sons, New York,1978,105
[102] S. Esposito, A. Riccardi, F. Q-Pacheco, et. al. Laboratory characterization and performanceof the high-order adap-tive optics system for the large binocular telescope[J]. Appl. Opt.,2010,49(31): G174–G189
[103] R. H. Hudgin. Optimal wavefront estimation[J]. J. Opt. Soc. Am. A,1977,67:375-378
[104] D. L. Fried. Least-square fitting a wavefront distortion estimate to an array ofphase-difference measurements[J]. J. Opt. Soc. Am. A,1977,67:370-375
[105] W. H. Southewell, Wavefront estimation from wavefront slope measurement[J]. J. Opt. Soc.Am. A,1980,70:998-1006
[106] R. Noll. Zernike polynomials and atmospheric turbulence[J]. J. Opt. Soc. Am. A,1976,66(3):207–211
[107]李斐.相位差波前探测技术及其在图像恢复中的应用研究[D].长沙:国防科学技术大学博士学位论文,2011
[108]张现榆.自适应光学系统和多层共轭自适应光学系统[D].成都:中国科学院光电技术研究所博士学位论文,2011
[109] E. Pinna, F. Quiros-Pacheco, A. Riccardi, et. al. First on-sky calibration of a high orderadaptive optics system[C]. Proc. SPIE,2012,844784472B
[110]李新阳,姜文汉.自适应光学控制系统的有效带宽分析[J].光学学报,1997,17(12)：1697-1702
[111]李新阳,姜文汉.自适应光学系统的控制残余方差分析[J].光学学报,2000,20(10):1328-1334
[112] E. Gendron and P. Lena. Astronomical adaptive optics I. Modal control optimization[J].A&A,1994,291(1):337-347
[113] E. Gendron and P. Lena. Astronomical adaptive optics II. Experimental results of anoptimized modal control[J]. A&A Suppl. Ser.,1995,111:153-167
[114] B. Ellerbroek, C. Van Loan, N. P. Pitsianis. Optimizing closed-loop adaptive-opticsperformance with use of multiple control bandwiths[J]. J. Opt. Soc. Am. A,1994,11(11):2871-2886
[115] C. Dessenne, P.-Y. Madec, and G. Rousset. Optimization of a predictive controllerforclosed-loop adaptive optics[J]. Appl. Opt.,1998,37(21):4623-4633
[116] C. Dessenne, P.-Y. Madec, and G. Rousset. Sky implementation of modal predictive controlin adaptive optics[J]. Opt. Lett.,1999,24(5):339-341
[117]李新阳,姜文汉,王春鸿等.自适应光学系统中的自适应控制算法研究[J].光学学报,2001,21(3):283-289
[118] R. J. Watkins and B. N. Agrawal. Use of least means squares filter in control of opticalbeam jitter[J]. Journal of Guidance, Control, and Dynamics,2007,30(4):1116–1122
[119] M. Beerer, H. Yoon, B. Agrawal. Adaptive Filter Techniques for Optical Beam JitterControl[C]. Proc. SPIE,2009,7338,733802
[120] L. Poyneer, D. Gavel, and J. Brase. Fast wave-front reconstruction in large adaptive opticssystems with use of the Fourier transform[J]. J. Opt. Soc. Am. A,2002,19(10):2100–2111
[121] L. A. Poyneer, M. Troy, B. Macintosh, et. al. Experimental validation of Fourier transformwave-front reconstruction at the Palomar Observatory[J]. Opt. Lett.,2003,28(10):798–800
[122] D. P. Looze. Linear-quadratic-Gaussian control for adaptive optics systems using a hybridmodel[J]. J. Opt. Soc. Am. A,2009,26(1):1-9
[123] C. Correia, H.-F. Raynaud, C. Kulcsar. On the optimal reconstruction and control ofadaptive optics systems with mirror dynamics[J]. J. Opt. Soc. Am. A,2010,27(2):333-349
[124]李新阳，凌宁，陈东红等.自适应光学系统中高速倾斜反射镜的稳定控制[J].强激光与粒子束,1999,11(1):31-36
[125]张小军,凌宁.高速压电倾斜镜动态特性分析[J].强激光与粒子束,2003,15(10):966-968
[126] Y. Ning, W. Jiang, N. Ling, et. al. Response function calculation and sensitivity comparisonanalysis of various bimorph deformable mirrors[J]. Opt. Express,2007,15(19):12030-12038
[127] S. Cornelissen, P. Bierden, S. Menn, et. al. A4096-element micromirror for high constrastastronomical imaging. SPIE Newsroom,2007
[128] X. H. Wang, B. Wang, et al. Performance of evaluation of a liquid crystal on silicon spatiallight modulator[J]. Opt Eng.,2004,43:2769-2774
[129]宁禹,余浩,周虹等.20单元双压电片变形镜对Zernike像差空间拟合能力的实验研究[J].2009,29(7):1756-1760
[130]杜祥琬.实际强激光远场靶面上光束质量的评价因素[J].中国激光,1997,24(4):327-332
[131]鲜浩,姜文汉.波像差与光束质量指标的关系[J].中国激光,1999，26(5)：415-419
[132]胡诗杰,许冰,侯静.H-S波前传感器在测量光束质量因子M2中的应用[J].光电工程,2002,29(2):6-9
[133]郭友明,饶长辉.基于Hadamard矩阵多通道方法的自适应光学系统传递矩阵测量装置及方法[P].中国,发明专利,授权号: CN102494785B,2013
[134] J.-M. Conan, G. Rousset, and P.-Y.Madec. Wave-front temporal spectra in high-resolutionimaging through turbulence[J]. J. Opt. Soc. Am. A,1995,12(7):1559–1570
[135] B. McGlamery. Restoration of Turbulence-Degraded Images[J]. J. Opt. Soc. Am. A,1967,57(3):293-297
[136]杨连臣.大气湍流效应的模拟[D].成都：中国科学院光电技术研究所博士学位论文,2004
[137]郭友明,饶长辉,魏凯等.自适应光学系统传递矩阵的正弦调制同步测量装置及方法[P].中国,发明专利,申请号:201210249478.9,2012
[138]饶学军,凌宁,姜文汉.用数字干涉仪测量变形镜影响函数的实验研究[J].光学学报,1995,15(10):1446-1449
[139]郭友明,饶长辉,鲍华等.一种提高自适应光学系统传递矩阵测量精度的方法[P].中国,发明专利,申请号:201310095509.4,2013
[140]王广雄,何朕.控制系统设计[M].北京:清华大学出版社,2008,65
[141]孙恺,容太平.一种基于DSP的任意功率谱随机信号发生器[J].华中科技大学学报,2002,30(4):55-57
[142]郭友明,马晓燠,饶长辉.自适应光学控制系统对Kolmogorov湍流补偿的修正有效带宽[J].物理学报,2013,62(13),134207
[143]郭友明,马晓燠,饶长辉.自适应光学系统倾斜校正回路的最优闭环带宽[J].物理学报,2014,63(6),069502
[144]颜召军.自适应光学系统预测控制及多层共轭技术研究[D].成都：中国科学院光电技术研究所博士学位论文,2013
[145] J. Doyle, G. Stein. Multivariable Feedback Desgin: Concepts for a Classical/ModernSynthesis[J]. IEEE Trans. Auto. Control,1981,26(1):4-16
[146] Y. Guo, X. Ma and C. Rao. Adaptive filter and linear quadratic Gaussian/loop transferrecovery compensator combination control of a non-linear tip-tilt mirror[C]. SPIE,2012,8415,84150X
