湍流大气中双层共轭系统激光成像研究
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摘要
大气成像是诸如宇航卫星,航空测绘和成像雷达等工作于湍流大气环境中的光学系统必然遇到的问题,光学系统的角分辨率一般是由其入瞳衍射极限所限制(λ/D),然而,大气成像系统的角分辨率主要由通常小于光学系统入瞳的大气相干长度r_0决定(λ/r_0)。一般情况下,大孔径望远镜系统的长曝光像的角分辨率仅相当于一个0.1m孔径的望远镜的角分辨率。为了弥补这种的缺陷,人们采用自适应光学技术(AO),它能实时感知由大气扰动、环境温度起伏等因素造成的波面畸变,并通过调整光学系统而实现实时畸变的补偿,使现代大型望远镜系统轴上分辨率达到近衍射极限。然而,光束在湍流大气传播中存在的“波前位错”现象阻碍了自适应光学系统对畸变波波前位相的精确重建,加上大气非等晕的影响,使一般自适应光学系统只能在一个很小的视场内进行高清晰度成像,在典型情况下只有微弧度量级。特别是当观察目标稍微偏离光轴时,分辨率便明显下降,这就大大限制了AO系统推广应用。
为了能在大范围获得更清晰的像,本文采用一种新的校正方法一双层共轭自适应光学(DCAO),它是多层共轭自适应光学(MCAO)的简单系统,属于自适应光学范畴。MCAO的基本思想是将大气湍流分成若干层,在每层的共轭位置上设置1块变形镜(DM)以校正该层大气引起的波形畸变。
对大气成像系统的各光学传递函数(理想、湍流、传统AO和DCAO)进行分析并成像仿真,得出DCAO系统的成像比传统AO清晰很多,分辨力几乎接近衍射极限水平,是传统AO的好几倍。通过对校正性能指标(等晕角、相干长度、闪烁指数和斯特列尔比)的数值分析,同样得到,DCAO系统在大气湍流校正方面优势非常明显。
DCAO技术是目前自适应光学技术发展的趋势,也是国际光学校正研究热点之一,而将来必定向MCAO方向(三层、四层…)发展。
An atmospheric imaging is unavoidable for the optical systems,such as satellite remote sensing,navigation mapping and radar imaging,working under the environment of atmospheric turbulence.Commonly,the angular resolution of the optical system is decided by the diffraction limitation of the pupil(λ/D).However,the angular resolution of the atmospheric imaging systems is mostly limited by the coherence length (λ/r_0) which is ordinarily smaller than the pupil aperture.As a rule,the angular resolution of the long-time exposal imaging of the big-aperture systems is only equal to which of a 0.1m aperture telescope.To resolve the problem,an adaptive optics system (AOI) is adopted.The AO technology can be subtle to the wavefront aberrance caused by atmospheric distortion,the fluctuation of the environment temperature etc.and allows to perform a real-time correction through adjusting the optical system,which makes the large telescope equipped with AO offer high resolution to the diffraction limitation.
It is great,however,that a wavefront dislocation influences more accurate reconstruction of the aberrant wavefront with AO,when a beam is propagating in atmospheric turbulence.The same time,there is atmospheric anisoplanatic effects.The very small field of view(FOV),ordinarily it is about several arcseconds,characterized by the isoplanatic angle remains a serious limitation,if keeping high resolution imaging with AO.And when the observed target slightly deviates the light axis,the resolution begins to degrade rapidly.Those will deteriorate the AO performance severely,limit application extension of AO systems consumedly.
To attain more large FOV of high resolution imaging,a new correcting way, named dual-conjugate adaptive optics(DCAO),is adopted,which is a simple system of multi-conjugate adaptive optics(MCAO) belonging to the category of AO.The base theory of the MCAO system is that the atmospheric turbulence is divided into lots of layers,and a deformable mirror(DM) is displayed the conjugate height of every layer so that the wavefront aberrance caused by that turbulent layer is corrected.
Through the simulation of atmospheric imaging with optical transfer function (OTF) of optical systems(ideal,turbulence,classical AO and DCAO),the results show the imaging of DCAO system is more legible than classical AO,whose resolution is up to the diffraction limitation.And with the analysis of the performance parameters such as isoplanatic angle,coherence length,scintillation index and strehl ratio,a conclusion is that the DCAO system has a great advantage in atmospheric turbulence correction
The DCAO,presently,is a trend of AO technology,which is one of hot spots of optical correction.And in the future,there is a stream to multi-conjugate AO(3,4 layers, and so on).
为了能在大范围获得更清晰的像,本文采用一种新的校正方法一双层共轭自适应光学(DCAO),它是多层共轭自适应光学(MCAO)的简单系统,属于自适应光学范畴。MCAO的基本思想是将大气湍流分成若干层,在每层的共轭位置上设置1块变形镜(DM)以校正该层大气引起的波形畸变。
对大气成像系统的各光学传递函数(理想、湍流、传统AO和DCAO)进行分析并成像仿真,得出DCAO系统的成像比传统AO清晰很多,分辨力几乎接近衍射极限水平,是传统AO的好几倍。通过对校正性能指标(等晕角、相干长度、闪烁指数和斯特列尔比)的数值分析,同样得到,DCAO系统在大气湍流校正方面优势非常明显。
DCAO技术是目前自适应光学技术发展的趋势,也是国际光学校正研究热点之一,而将来必定向MCAO方向(三层、四层…)发展。
An atmospheric imaging is unavoidable for the optical systems,such as satellite remote sensing,navigation mapping and radar imaging,working under the environment of atmospheric turbulence.Commonly,the angular resolution of the optical system is decided by the diffraction limitation of the pupil(λ/D).However,the angular resolution of the atmospheric imaging systems is mostly limited by the coherence length (λ/r_0) which is ordinarily smaller than the pupil aperture.As a rule,the angular resolution of the long-time exposal imaging of the big-aperture systems is only equal to which of a 0.1m aperture telescope.To resolve the problem,an adaptive optics system (AOI) is adopted.The AO technology can be subtle to the wavefront aberrance caused by atmospheric distortion,the fluctuation of the environment temperature etc.and allows to perform a real-time correction through adjusting the optical system,which makes the large telescope equipped with AO offer high resolution to the diffraction limitation.
It is great,however,that a wavefront dislocation influences more accurate reconstruction of the aberrant wavefront with AO,when a beam is propagating in atmospheric turbulence.The same time,there is atmospheric anisoplanatic effects.The very small field of view(FOV),ordinarily it is about several arcseconds,characterized by the isoplanatic angle remains a serious limitation,if keeping high resolution imaging with AO.And when the observed target slightly deviates the light axis,the resolution begins to degrade rapidly.Those will deteriorate the AO performance severely,limit application extension of AO systems consumedly.
To attain more large FOV of high resolution imaging,a new correcting way, named dual-conjugate adaptive optics(DCAO),is adopted,which is a simple system of multi-conjugate adaptive optics(MCAO) belonging to the category of AO.The base theory of the MCAO system is that the atmospheric turbulence is divided into lots of layers,and a deformable mirror(DM) is displayed the conjugate height of every layer so that the wavefront aberrance caused by that turbulent layer is corrected.
Through the simulation of atmospheric imaging with optical transfer function (OTF) of optical systems(ideal,turbulence,classical AO and DCAO),the results show the imaging of DCAO system is more legible than classical AO,whose resolution is up to the diffraction limitation.And with the analysis of the performance parameters such as isoplanatic angle,coherence length,scintillation index and strehl ratio,a conclusion is that the DCAO system has a great advantage in atmospheric turbulence correction
The DCAO,presently,is a trend of AO technology,which is one of hot spots of optical correction.And in the future,there is a stream to multi-conjugate AO(3,4 layers, and so on).
引文
[1]Zhang Yinxin,Tao Chunkan.Wavefront dislocations of Gaussian beams nesting optical vortices in a turbulence atmosphere.CHINESE OPTICS LETTERS,2004,2(10):559-6-561
[2]张逸新,朱拓,徐振源.光波波前位错与相位间歇性-Ⅰ结构理论.激光技术,2002,20(2):97-101
[3]Fried D L.anisoplanatism in adaptive optics.J.Opt.Soc.Am.1982,72:52-58
[4]Fried D L Aperture averaging of scintillation,J.Opt.Soc.Am.,1967,57:169-175
[5]Mauroschat.A.Reliability analysis of a multiple-laser-diode beacon for inter-satellite links.SPIE,1991,417:513-524
[6]Kiasaleh K.Turbo-coded optical PPM communication systems.Lightwave Technology,1998,16:18-26
[7]Wilson K E.Results of the compensated Earth-Moon-Earth retro-reflector laser link(CEMERLL)experiment.TDA Progress Report,1997,42,131:1-13
[8]Beckes J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007:1056-1065.
[9]周仁忠,阎吉祥.自适应光学理论.北京:北京理工大学出版社,1996,205-217
[10]Hubin N,louan M,Viard L E.New challenges for adaptive optics:the OWL 100m telescope.SPIE,2000,4007:510-517
[11]Fouche J B,Conan J M.Michau V,et al.Correction of scintillation effects by multiconjugate adaptive optics.SPIE,2000,4167:198-206
[12]Rigaut F J,Ellerbroek B L,Flicker R.Principles limitations and performance of multi-conjugate adaptive optics.SP1E,2000,4007(Ⅱ):1022-1031
[13]Johnston D C,Welsh B M.Estimating contributions of turbulent layers to total wavefront phase aberration.SPIE,1992,1688:510-521
[14]Andersena T,Ardeberga A,Beckers J.Euro50.SPIE,2004,5382:169-182
[15]Goncharov A,Mette O-P,Andersen T.Adaptive optics for the Euro50:design and performance.SPIE,2003,4840:36-45
[16]Andersena T,Ardeberga A,Beckers J.The Euro50 Extremely Large Telescope.SPIE,2003,4840:214-225
[17]Ardeberga A,Andersena T,Beckers J.Adaptive optics for the Euro50:design and performance.SPIE,2003,4840:36-46
[18]Ragazzoni R.AO for 100m class telescope new challenges require new solutions.SPIE,2000,4007(Ⅱ):1100-1107
[19]Brusa G,Riccardi A.Esposito S,et al.Study for a multiconjugate AO system for 8 m class telescopes.SPIE,2000,4034:190-200
[20]Hubin N,louan M Le,Viard E.New challenges for adaptive optics:the OWL 100m telescope.SPIE,2000,4007:510-517
[21]Beckes J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007:1056-1065
[22]Tokovin A,Louarn M L.Isoplantism in a multiconjugate adaptive optics system.J.Opt.Soc.Am.,2000,17(10):1819-1827
[23]Johnston D C,Welsh B M.Estimating contributions of turbulent layers to total wavefront phase aberration.SPIE,1992,1688:510-521
[24]Fouche J B,Conan J M,Michan V,et al.Correction of scintillation effects by multiconjugate adaptive optics.SPIE,2000,4167:198-206
[25]Rigaut F J,Ellerbroek B L,Flicker R.limitations and performance of multi- conjugate adaptive optics.SPIE,2000,4007(Ⅱ):1022-1031
[26]Hart M,Milton N.Design and expected performance of the 6.5 m MMT MCAO system.SPIE,2003,4839:578-587
[27]Ellerbroek B.MCAO for Gemini-south.SPIE,2003,4839:55-65
[28]Yan J X,Zhou R.Z.Calculation of the isoplanatic path for multiconjugate adaptive optics.Opt.Eng.,1993,32(12):3161-3163
[29]Yah J X,Zhou R.Z.Problems with multiconjugate correction.Opt.Eng.,1994,33(9):2942-2944
[30]杨昭,李强.大气传输特性对激光雷达探测系统的影响.淮海工学院学报,2005,9:31-36
[31]吴健,杨春平,刘建武.大气中光传输理论.北京:北京邮电大学出版社,2005,142-150
[32]张晓芳,俞信,阎吉祥.大气湍流对光学系统图像分辨力的影响.光学技术,2005,31:263-265
[33]Tatarski V I.Wave propagation in a random medium.New York:McGraw-Hill Book Company,1961:142-165
[34]Hill R J.Modified spectrum of atmospheric temperature fluctuation and its application to optical propagation.J.Opt.Soc.Am.,1978,68:892-905
[35]Andrew L C.Analytical model for the refractive index power spectrum and its application to optical scintillation in the atmosphere.J.Mod.Opt.,1992,39:1849-1856
[36]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,[博士学位论文],成都,中国科学院光电技术研究所,2001
[37]LI Fang,RONG Jian,DING Xue-ke.Staudy on correcting Angle-of-arrival fluctuation of space optical communication.SPIE,2007,6795,67950L:1-5
[38]Fried D L.Optical resolution through a randomly inhomogeneous medium for very long and very short exposures.J.Opt.Soc.Am.1966,56(11):1372-1379
[39]Fried D L.Limiting resolution looking down through the atmosphere.J.Opt.Soc.Am.1966,56(11):1380-1385
[40]李新阳,姜文汉,王春红,等.激光实际大气水平传输湍流畸变波前的功率分析:波前相位与格林伍德频率,光学学报,2000,20(8):1035-1042
[41]Wallace B,Bradley C,Richardson H.Dual conjugate adaptive optics testbed:progress report.SPIE,2003,5169:255-231
[42]Kelly T L,Buschei D F.Dualconjugate adaptive optics.SPIE,2001,4353:273-208
[42]Bello D,Verinaud C,Conan J M,et al.Comparison of different 3D wavefront sensing and reconstruction techniques for MCAO.SPIE,2003,4839:554-565
[43]Beckers J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007(Ⅱ):1056-1065
[44]Farinato J,Ragazzoni R.Novel techniques concerning MCAO:trying to overcome fundamental limitations.SPIE,2004,5490:1229-1238
[45]Farinato J,Ragazzoni R The MCAO wavefront sensing of LINC-NIRVANA:status report.SPIE,2006,6272,627229:1-9
[46]Egner S E,Gassler W T,Herbet M.LINC-NIRVANA:The single arm MCAO experiment.SPIE,2004,5490:924-933
[47]Feinleib J.Adaptive Optics Associates.MA,Cambridge,1982
[48]Happer W.Jason report.JSR-82-106,1983.
[49]阎吉祥,俞信.自适应光学人造钠导星对激光能量的要求.北京理工大学学报,1996,16(6):616-620
[50]Hackenberg W,Bouncing D.Fiber Raman laser development for multiconjugate adaptive optics with sodium laser guide stars.SPIE,2001,4494:271-275
[51]Lloyd-Hart M,Gcorges J,Angel R,et al.Dynamically refocused Rayleigh laser beacons for atmospheric tomogramphy.SPIE,2001,4494:259-270
[52]DING Xue-ke,RONG Jian.Study of isoplanatic angle of dual-conjugate AO system in atmospheric turbulence.SPIE,2007,6795,67955Y:1-5
[53]丁学科,荣健.激光雷达中双层共轭AO系统等晕角的理论分析与仿真.18届全国激光会议,2007,D-2-26
[54]Lukin V P,Fortes B V.Estimation of turbulent degradation and required spatial resolution of adaptive system.SPIE,2003,3494:192-203
[55]DING Xue-ke,RONG Jian.Theoretical analysis and simulation of conjugate heights for dual-conjugate AO system in lidar.CHINESE OPTICS LETTERS,2008,6(1):1-4
[56]荣健,丁学科.单双层共轭系统的共轭高度对等晕角的影响.强激光与离子束,2007,19(19):1429-1433
[57]Elena Masciadd,Sebastian Egner.First complete seasonal variation study of the 3D Optical turbulence above San Pedro Martir Observatory.SPIE,2004,5490:818-829
[58]Nicolas R.Atmospheric wavefront simulation using Zerinike polynomials.Opt.Eng.,1990,29:1174-1180
[59]Roddier E The effects of atmospheric turbulence in optical astronomy.Progress in Optics,North-Holland,1981,ⅪⅩ,281-376
[60]Veran J P,Rigaut F,Maitre H.Estimation of the adaptive optics long-exposure point-spread function using control loop data.J.Opt.Soc.Am.(A),1997,14(11):3057-3069
[61]fante R L Optical beam spread in turbulent medium:Effect of the outer scale of turbulence.JOSA,1974,64(5):592-598
[2]张逸新,朱拓,徐振源.光波波前位错与相位间歇性-Ⅰ结构理论.激光技术,2002,20(2):97-101
[3]Fried D L.anisoplanatism in adaptive optics.J.Opt.Soc.Am.1982,72:52-58
[4]Fried D L Aperture averaging of scintillation,J.Opt.Soc.Am.,1967,57:169-175
[5]Mauroschat.A.Reliability analysis of a multiple-laser-diode beacon for inter-satellite links.SPIE,1991,417:513-524
[6]Kiasaleh K.Turbo-coded optical PPM communication systems.Lightwave Technology,1998,16:18-26
[7]Wilson K E.Results of the compensated Earth-Moon-Earth retro-reflector laser link(CEMERLL)experiment.TDA Progress Report,1997,42,131:1-13
[8]Beckes J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007:1056-1065.
[9]周仁忠,阎吉祥.自适应光学理论.北京:北京理工大学出版社,1996,205-217
[10]Hubin N,louan M,Viard L E.New challenges for adaptive optics:the OWL 100m telescope.SPIE,2000,4007:510-517
[11]Fouche J B,Conan J M.Michau V,et al.Correction of scintillation effects by multiconjugate adaptive optics.SPIE,2000,4167:198-206
[12]Rigaut F J,Ellerbroek B L,Flicker R.Principles limitations and performance of multi-conjugate adaptive optics.SP1E,2000,4007(Ⅱ):1022-1031
[13]Johnston D C,Welsh B M.Estimating contributions of turbulent layers to total wavefront phase aberration.SPIE,1992,1688:510-521
[14]Andersena T,Ardeberga A,Beckers J.Euro50.SPIE,2004,5382:169-182
[15]Goncharov A,Mette O-P,Andersen T.Adaptive optics for the Euro50:design and performance.SPIE,2003,4840:36-45
[16]Andersena T,Ardeberga A,Beckers J.The Euro50 Extremely Large Telescope.SPIE,2003,4840:214-225
[17]Ardeberga A,Andersena T,Beckers J.Adaptive optics for the Euro50:design and performance.SPIE,2003,4840:36-46
[18]Ragazzoni R.AO for 100m class telescope new challenges require new solutions.SPIE,2000,4007(Ⅱ):1100-1107
[19]Brusa G,Riccardi A.Esposito S,et al.Study for a multiconjugate AO system for 8 m class telescopes.SPIE,2000,4034:190-200
[20]Hubin N,louan M Le,Viard E.New challenges for adaptive optics:the OWL 100m telescope.SPIE,2000,4007:510-517
[21]Beckes J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007:1056-1065
[22]Tokovin A,Louarn M L.Isoplantism in a multiconjugate adaptive optics system.J.Opt.Soc.Am.,2000,17(10):1819-1827
[23]Johnston D C,Welsh B M.Estimating contributions of turbulent layers to total wavefront phase aberration.SPIE,1992,1688:510-521
[24]Fouche J B,Conan J M,Michan V,et al.Correction of scintillation effects by multiconjugate adaptive optics.SPIE,2000,4167:198-206
[25]Rigaut F J,Ellerbroek B L,Flicker R.limitations and performance of multi- conjugate adaptive optics.SPIE,2000,4007(Ⅱ):1022-1031
[26]Hart M,Milton N.Design and expected performance of the 6.5 m MMT MCAO system.SPIE,2003,4839:578-587
[27]Ellerbroek B.MCAO for Gemini-south.SPIE,2003,4839:55-65
[28]Yan J X,Zhou R.Z.Calculation of the isoplanatic path for multiconjugate adaptive optics.Opt.Eng.,1993,32(12):3161-3163
[29]Yah J X,Zhou R.Z.Problems with multiconjugate correction.Opt.Eng.,1994,33(9):2942-2944
[30]杨昭,李强.大气传输特性对激光雷达探测系统的影响.淮海工学院学报,2005,9:31-36
[31]吴健,杨春平,刘建武.大气中光传输理论.北京:北京邮电大学出版社,2005,142-150
[32]张晓芳,俞信,阎吉祥.大气湍流对光学系统图像分辨力的影响.光学技术,2005,31:263-265
[33]Tatarski V I.Wave propagation in a random medium.New York:McGraw-Hill Book Company,1961:142-165
[34]Hill R J.Modified spectrum of atmospheric temperature fluctuation and its application to optical propagation.J.Opt.Soc.Am.,1978,68:892-905
[35]Andrew L C.Analytical model for the refractive index power spectrum and its application to optical scintillation in the atmosphere.J.Mod.Opt.,1992,39:1849-1856
[36]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,[博士学位论文],成都,中国科学院光电技术研究所,2001
[37]LI Fang,RONG Jian,DING Xue-ke.Staudy on correcting Angle-of-arrival fluctuation of space optical communication.SPIE,2007,6795,67950L:1-5
[38]Fried D L.Optical resolution through a randomly inhomogeneous medium for very long and very short exposures.J.Opt.Soc.Am.1966,56(11):1372-1379
[39]Fried D L.Limiting resolution looking down through the atmosphere.J.Opt.Soc.Am.1966,56(11):1380-1385
[40]李新阳,姜文汉,王春红,等.激光实际大气水平传输湍流畸变波前的功率分析:波前相位与格林伍德频率,光学学报,2000,20(8):1035-1042
[41]Wallace B,Bradley C,Richardson H.Dual conjugate adaptive optics testbed:progress report.SPIE,2003,5169:255-231
[42]Kelly T L,Buschei D F.Dualconjugate adaptive optics.SPIE,2001,4353:273-208
[42]Bello D,Verinaud C,Conan J M,et al.Comparison of different 3D wavefront sensing and reconstruction techniques for MCAO.SPIE,2003,4839:554-565
[43]Beckers J M.Multi-conjugate adaptive optics:Experiments in atmospheric tomography.SPIE,2000,4007(Ⅱ):1056-1065
[44]Farinato J,Ragazzoni R.Novel techniques concerning MCAO:trying to overcome fundamental limitations.SPIE,2004,5490:1229-1238
[45]Farinato J,Ragazzoni R The MCAO wavefront sensing of LINC-NIRVANA:status report.SPIE,2006,6272,627229:1-9
[46]Egner S E,Gassler W T,Herbet M.LINC-NIRVANA:The single arm MCAO experiment.SPIE,2004,5490:924-933
[47]Feinleib J.Adaptive Optics Associates.MA,Cambridge,1982
[48]Happer W.Jason report.JSR-82-106,1983.
[49]阎吉祥,俞信.自适应光学人造钠导星对激光能量的要求.北京理工大学学报,1996,16(6):616-620
[50]Hackenberg W,Bouncing D.Fiber Raman laser development for multiconjugate adaptive optics with sodium laser guide stars.SPIE,2001,4494:271-275
[51]Lloyd-Hart M,Gcorges J,Angel R,et al.Dynamically refocused Rayleigh laser beacons for atmospheric tomogramphy.SPIE,2001,4494:259-270
[52]DING Xue-ke,RONG Jian.Study of isoplanatic angle of dual-conjugate AO system in atmospheric turbulence.SPIE,2007,6795,67955Y:1-5
[53]丁学科,荣健.激光雷达中双层共轭AO系统等晕角的理论分析与仿真.18届全国激光会议,2007,D-2-26
[54]Lukin V P,Fortes B V.Estimation of turbulent degradation and required spatial resolution of adaptive system.SPIE,2003,3494:192-203
[55]DING Xue-ke,RONG Jian.Theoretical analysis and simulation of conjugate heights for dual-conjugate AO system in lidar.CHINESE OPTICS LETTERS,2008,6(1):1-4
[56]荣健,丁学科.单双层共轭系统的共轭高度对等晕角的影响.强激光与离子束,2007,19(19):1429-1433
[57]Elena Masciadd,Sebastian Egner.First complete seasonal variation study of the 3D Optical turbulence above San Pedro Martir Observatory.SPIE,2004,5490:818-829
[58]Nicolas R.Atmospheric wavefront simulation using Zerinike polynomials.Opt.Eng.,1990,29:1174-1180
[59]Roddier E The effects of atmospheric turbulence in optical astronomy.Progress in Optics,North-Holland,1981,ⅪⅩ,281-376
[60]Veran J P,Rigaut F,Maitre H.Estimation of the adaptive optics long-exposure point-spread function using control loop data.J.Opt.Soc.Am.(A),1997,14(11):3057-3069
[61]fante R L Optical beam spread in turbulent medium:Effect of the outer scale of turbulence.JOSA,1974,64(5):592-598