基于焦面图像信息的波前探测技术研究
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摘要
随着对大口径成像望远镜的需求日益紧迫，望远镜的口径增大和非球面光学元件的增加都给光学加工和检测带来很大的挑战。如何在加工过程中在位及时检测出高阶面形误差进行修正，如何在光学系统装调过程中在线检测像差变化，以便及时调整主镜支撑方案和光学系统装调方案；如何在光学系统使用过程中动态检测出系统波像差，以进行故障诊断和图像清晰化。基于焦面图像信息的波前解算系统也称为焦平面波前探测器（WS, Wavefront Sensing），有着光瞳面WS一些不可替代的优势，它通过采集多帧给定离焦像差的短曝光图像，解算得到光学系统的波前相位信息，并可以利用Zernike多项式拟合得到各单项像差。常见的相位解算技术主要有相位恢复法（PR, Phase Retrieval）和相位差异法（PD, Phase Diversity）。焦平面WS可用于光学系统的在位检测，即不用改变光学系统，直接测量出整个系统的传递函数和波前畸变，在轨定量检测，拼接镜的共焦共像检测等领域。
本文在分析国内外研究进展的基础上，进行了大量的计算机仿真实验和实际光路实验工作，对PR和PD技术的原理、性能改进和实际应用进行了深入的探讨和分析，并对其在光学检测方面进行了大量的验证，具体开展的工作如下：
1、通过理论分析和仿真，分析了PR的各种算法、建立和完善了PR数学模型。重点研究了PR技术中的Gerchberg-Saxton算法和梯度搜索算法，推导了当任意多帧输入图像及它们的离焦量作为输入时，梯度搜索算法的目标函数分别关于广义光瞳、波前以及泽尼克系数的偏导数。揭示了GS算法与梯度搜索算法之间的关系。针对单幅和多幅图像作为输入时分别用GS算法和梯度搜索算法设计了仿真实验，实验结果显示：对于单幅图像作为输入时，梯度搜索算法明显优于GS算法，对于多帧不同离焦量的图像作为输入时，GS算法和梯度搜索算法都能很好的解算出波前，但梯度搜索算法的收敛速度明显优于GS算法。
2、对PD法的目标函数进行了改造，解决了自适应光学系统非共光路像差检测中的离焦量测不准问题，并利用多通道约束波前的解集和像差检测与变形镜调整互相迭代最终收敛的办法。使得改进后的方法理论上对波前求解精度更高。
3、搭建了PRWS和ZYGO干涉仪对不同波前畸变进行比较测量的实验平台。采用液晶空间光调制器产生的单项差来验证PRWS对各种像差的检测能力，把PR测量结果与高精度的ZYGO干涉仪测量结果进行比较分析，结果表明在面形误差分布及误差的峰谷值（PV）和方均根值（RMS）上，两者具有一致性，对于波前RMS的测量精度达到3/1000波长左右，这说明PR测量方法的可行性和准确性。
4、为了验证PRWS和PDWS波前检测的能力，分别利用PRWS和PDWS检测球面镜面形的实验平台。将PRWS测量结果和PDWS测量结果分别与ZYGO干涉仪测量结果进行比较，实验结果表明在面形误差分布及误差的峰谷值(PV)和方均根值(RMS)上，两者具有极大的相似性，验证了PRWS测量方法和PDWS测量方法的准确性，所以利用PRWS技术和PDWS技术能有效地检测出球面镜的面形误差。
Along with the increasingly urgent demand for large diameter imagingtelescope, increasing the caliber of the telescope and the increase of the asphericoptical element has posed great challenges to the optical processing and testing.How to timely detect the high-order surface shape error correction, how in theprocess of the optical system with adjustable on-line detection aberration changes, inorder to adjust the primary mirror supporting plan, and the optical system withadjustable how dynamic detecting system in the process of optical system usingwave aberration to carry out fault diagnosis and the image clearer. The system ofwavefront solutions based on the focal plane image information, also known as thefocal plane detector, has some irreplaceable advantages comparing to a pupil surfacewave detector, by gathering multi-frames from a given focal aberration of shortexposure images and obtain phase information wavefront of the optical system bycalculating the wavefront, and can use Zernike polynomial fitting of each individualaberrations. The realizations of phase solver technology mainly include PhaseRetrieval (PR) and Phase Diversity (PD). Focal plane wave detector can be used inthe optical system in-line detection, namely directly measure of the transfer functionof the system of a whole system and wavefront aberration without changing theoptical system; On-orbit quantitative detection; Mosaic mirror image of confocal detection field, etc.
Based on the analysis of domestic and foreign research progress, we have donea large number of simulation and the actual optical experimental work, in this paper,and have carried on the deep discussion and analysis of the principle of the PR andPD technology, performance and practical application, and on the a large number ofverification in optical detection, specific work is as follows:
1. Through theoretical analysis and simulation, this paper analyzes the variousalgorithms of PR, establish and perfect the PR mathematical model. Phase retrievaltechnique is mainly studied the Gerchberg-Saxton algorithm and gradient searchalgorithm, when any amount of input images and their defocus amount as input, thispaper educes the objective function of the gradient search algorithm respectively ongeneralized pupil, wavefront and Nick coefficient of partial derivative, and revealsthe relationship between the GS algorithm with gradient search algorithm. For singleand multiple images are used as input, designs simulation experiment with GSalgorithm and gradient search algorithm, the experimental results show that for asingle image as input, the gradient search algorithm is superior to GS algorithm, formulti-frame different defocus amount of images as input, GS algorithms andgradient search algorithm can be a good solution calculated wavefront, but thegradient search algorithm convergence speed significantly better than the GSalgorithm.
2. The objective function of the phase difference algorithm was modified tosolve the adaptive optics system of non-common path aberration detection ofinaccurate defocus and use the multi-channel constrained wavefront solution set andthe aberration detection with deformable mirror adjustment each iterationconvergence ultimately. The betterment method has higher accuracy in solving thewavefront theoretically.
3. Build an experimental based on the PRWS method comparing with ZYGOinterferometer. This paper utilizes liquid crystal space light modulator (LC-SLM) toproduce single aberration and random aberration, and validates the ability of PRWS measurement for any aberrations. Experimental results demonstrate that agreementis obtained among the errors distribution, PV value and RMS value of ZYGOinterferometer. The measurement precision of wavefront is3/1000wavelength RMS.Therefore, the feasibility and accuracy of the proposed method can be confirmed.
4. In order to verify the performance of phase retrieval wavefront sensingdemonstration system and the phase difference wavefront detector demonstrationsystem by using its own light source to complete the wavefront detection taskindependently. This paper sets up two detection mirror surface shape of experimentplatforms with the method of PRWS and PDWS, and compares both PRWSmeasurement results and PDWS measurement results with ZYGO interferometermeasurement results, experimental results demonstrate that good agreement isobtained among the errors distribution, PV value and RMS value of ZYGOinterferometer, so as to realize the estimation of large mirror aberration, whichvalidates the accuracy of PRWS and PDWS. PRWS technology and PDWStechnology can effectively estimate the aberration of spherical mirror.
本文在分析国内外研究进展的基础上，进行了大量的计算机仿真实验和实际光路实验工作，对PR和PD技术的原理、性能改进和实际应用进行了深入的探讨和分析，并对其在光学检测方面进行了大量的验证，具体开展的工作如下：
1、通过理论分析和仿真，分析了PR的各种算法、建立和完善了PR数学模型。重点研究了PR技术中的Gerchberg-Saxton算法和梯度搜索算法，推导了当任意多帧输入图像及它们的离焦量作为输入时，梯度搜索算法的目标函数分别关于广义光瞳、波前以及泽尼克系数的偏导数。揭示了GS算法与梯度搜索算法之间的关系。针对单幅和多幅图像作为输入时分别用GS算法和梯度搜索算法设计了仿真实验，实验结果显示：对于单幅图像作为输入时，梯度搜索算法明显优于GS算法，对于多帧不同离焦量的图像作为输入时，GS算法和梯度搜索算法都能很好的解算出波前，但梯度搜索算法的收敛速度明显优于GS算法。
2、对PD法的目标函数进行了改造，解决了自适应光学系统非共光路像差检测中的离焦量测不准问题，并利用多通道约束波前的解集和像差检测与变形镜调整互相迭代最终收敛的办法。使得改进后的方法理论上对波前求解精度更高。
3、搭建了PRWS和ZYGO干涉仪对不同波前畸变进行比较测量的实验平台。采用液晶空间光调制器产生的单项差来验证PRWS对各种像差的检测能力，把PR测量结果与高精度的ZYGO干涉仪测量结果进行比较分析，结果表明在面形误差分布及误差的峰谷值（PV）和方均根值（RMS）上，两者具有一致性，对于波前RMS的测量精度达到3/1000波长左右，这说明PR测量方法的可行性和准确性。
4、为了验证PRWS和PDWS波前检测的能力，分别利用PRWS和PDWS检测球面镜面形的实验平台。将PRWS测量结果和PDWS测量结果分别与ZYGO干涉仪测量结果进行比较，实验结果表明在面形误差分布及误差的峰谷值(PV)和方均根值(RMS)上，两者具有极大的相似性，验证了PRWS测量方法和PDWS测量方法的准确性，所以利用PRWS技术和PDWS技术能有效地检测出球面镜的面形误差。
Along with the increasingly urgent demand for large diameter imagingtelescope, increasing the caliber of the telescope and the increase of the asphericoptical element has posed great challenges to the optical processing and testing.How to timely detect the high-order surface shape error correction, how in theprocess of the optical system with adjustable on-line detection aberration changes, inorder to adjust the primary mirror supporting plan, and the optical system withadjustable how dynamic detecting system in the process of optical system usingwave aberration to carry out fault diagnosis and the image clearer. The system ofwavefront solutions based on the focal plane image information, also known as thefocal plane detector, has some irreplaceable advantages comparing to a pupil surfacewave detector, by gathering multi-frames from a given focal aberration of shortexposure images and obtain phase information wavefront of the optical system bycalculating the wavefront, and can use Zernike polynomial fitting of each individualaberrations. The realizations of phase solver technology mainly include PhaseRetrieval (PR) and Phase Diversity (PD). Focal plane wave detector can be used inthe optical system in-line detection, namely directly measure of the transfer functionof the system of a whole system and wavefront aberration without changing theoptical system; On-orbit quantitative detection; Mosaic mirror image of confocal detection field, etc.
Based on the analysis of domestic and foreign research progress, we have donea large number of simulation and the actual optical experimental work, in this paper,and have carried on the deep discussion and analysis of the principle of the PR andPD technology, performance and practical application, and on the a large number ofverification in optical detection, specific work is as follows:
1. Through theoretical analysis and simulation, this paper analyzes the variousalgorithms of PR, establish and perfect the PR mathematical model. Phase retrievaltechnique is mainly studied the Gerchberg-Saxton algorithm and gradient searchalgorithm, when any amount of input images and their defocus amount as input, thispaper educes the objective function of the gradient search algorithm respectively ongeneralized pupil, wavefront and Nick coefficient of partial derivative, and revealsthe relationship between the GS algorithm with gradient search algorithm. For singleand multiple images are used as input, designs simulation experiment with GSalgorithm and gradient search algorithm, the experimental results show that for asingle image as input, the gradient search algorithm is superior to GS algorithm, formulti-frame different defocus amount of images as input, GS algorithms andgradient search algorithm can be a good solution calculated wavefront, but thegradient search algorithm convergence speed significantly better than the GSalgorithm.
2. The objective function of the phase difference algorithm was modified tosolve the adaptive optics system of non-common path aberration detection ofinaccurate defocus and use the multi-channel constrained wavefront solution set andthe aberration detection with deformable mirror adjustment each iterationconvergence ultimately. The betterment method has higher accuracy in solving thewavefront theoretically.
3. Build an experimental based on the PRWS method comparing with ZYGOinterferometer. This paper utilizes liquid crystal space light modulator (LC-SLM) toproduce single aberration and random aberration, and validates the ability of PRWS measurement for any aberrations. Experimental results demonstrate that agreementis obtained among the errors distribution, PV value and RMS value of ZYGOinterferometer. The measurement precision of wavefront is3/1000wavelength RMS.Therefore, the feasibility and accuracy of the proposed method can be confirmed.
4. In order to verify the performance of phase retrieval wavefront sensingdemonstration system and the phase difference wavefront detector demonstrationsystem by using its own light source to complete the wavefront detection taskindependently. This paper sets up two detection mirror surface shape of experimentplatforms with the method of PRWS and PDWS, and compares both PRWSmeasurement results and PDWS measurement results with ZYGO interferometermeasurement results, experimental results demonstrate that good agreement isobtained among the errors distribution, PV value and RMS value of ZYGOinterferometer, so as to realize the estimation of large mirror aberration, whichvalidates the accuracy of PRWS and PDWS. PRWS technology and PDWStechnology can effectively estimate the aberration of spherical mirror.
引文
[1] BRADY GREGORY R, FIENUP J R. Improved optical metrology using phaseretrieval[C].Optical Fabrication&Testing. Rochester, NY,2004,101-3
[2]杨慧珍，龚成龙.一种基于光瞳面相位差的波前传感器相位恢复[J].光学学报，2011，31(11):1112002
[3] Osten W. Some answers to new challenges in optical metrology[C].Proc. SPIE,2008,7155715503-1~715503-16
[4] L FDAHL M G, SCHARMER G B. Wave-front sensing and image restorationfrom focused and defocused solar images [J]. Astron.Astrophys.1994,107:243-264
[5] Redding D, Basinger S, Lowman A, Shi F, et al. Wavefront Sensing and Controlfor a Next Generation Space Telescope[C].Proc. SPIE，1998，3356:758~772
[6] Acton D S, Atcheson P D, Cermak M, Kingsbury L K, Shi F, Redding DC.JamesWebbSpaceTelescopeWavefrontSensingandControlAlgorithms[C]Proc.SPIE，2004，5487:887~896
[7] Smith J S, Dean B H, Haghani S. Distributed Computing architecture forImage-based Wavefront Sensing and2D FFTs[C].Proc. SPIE，2006，6274:21-l~21-10
[8] Dean B H，Smith J S，Budinoff J G，Feinberg L.Wavefront Sensing and ControlArchitecture for SPOT (Spherical Primary Optical Telescope)[C].Proc. SPIE，2006，6265:4F-l~4F-10
[9] Millerd J E, Wyant J C. Simultaneous phase-shifting Fizeau interferometer
[P].US Patent,2005,20050046864
[10]Leslie Deck. Vibration-resistant phase-shifting interferometry [J]. Applied Optics,1996,35(34)6655-6662
[11]Burge J H, Wyant J C. Applications of computer-generated holograms forinterferometric measurement of large aspheric optics[C].Proc.SPIE,1995,2576258-269
[12]Reichelt S, Pruss C, Tiziani H J. Absolute interferometric test of aspheres by useof twin computer-generated holograms [J]. Applied Optics,2003,42(22)4468-4479
[13]Sommargren G E, Phillion D W, Campbell E W. Sub-nanometer interferometryfor aspheric mirror fabrication[C].The9th International Conference on ProductionEngineering, Osaka, Japam,1999
[14]Reichelt S, Tiziani H J. Twin-CGHs for absolute calibration in wavefront testinginterferometry [J]. Optics Communications,2003,22023-32
[15]FIENUP J R, MARRON J C, SCHULZ T J,et al. Hubble space telescopecharacterized by using phase-retrieval algorithms[J]. ApplOpt.,1993,32(10)1747-1767
[16]BRADY GREGORY R, FIENUP J R. Phase retrieval as an optical metrologytool[C] Optical Fabrication&Testing. Topical Meeting of the Optical Society ofAmerica, SPIE Technical Digest,2005, TD03139-141
[17]张均，董军等，张艳，等.数字刀口检测技术.光电工程[J]．2005，32(5)：65-68
[18]饶学军，凌宁，王成，等．哈特曼夏克传感器在非球面加工中的应用[J]．光学学报，2002，22(4)
[19]Li Hua-gui, JiangWen-han. Atmospheric turbulence parameter measurementusing Hartmann-Shack wavefront sensor [A]. P roc of ESO [C],1993,48:21～28
[20]Lane R G, TallonM. Wavefront reconstruction using a Shack-Hartmann sensor [J].Applied Optics,1992,31(32):6902～6908
[21]Chao Gen-rui, Yu Xin. Accuracy analysis of a Hartmann-Shack wavefront sensoroperated with a faint object [J]. Optical Engineering,1994,(33):2331～2335
[22]JiangWen-han, Xian Hao, Shen Feng. Detecting error of Shack-Hartmannwavefront sensor [A]. SPIE [C],1997,3126:534～544
[23]Hermann J. Crosscoupling and aliasing in model wavefront estimation [J]. J. Opt.Soc. Am. A,1981,71(8):989～992
[24]Takato N, IyeM, Yamaguchi I. Wavefront reconstruction errors ofShack-Hartmann sensors [J]. Publ A stron Soc Pacific,1994,106:182～188
[25] Patrick Naulleau.Kenneth A.Goldberg.SangH.Lee. The EUV phase-shiftingpoint diffractioninterferometer,2000
[26]Patrick Naulleau.Kenneth Goldberg.Sang Lee Characterization of the accuracy ofEUV phase-shiftingpoint diffraction interferometry,1998
[27]刘晓军，高咏生．横向剪切干涉测量中准确的相位恢复算法[J]．光学精密工程，2004，l2(5)：47-479
[28]R K．Tyson．Adaptive optics engineering handbook [M]．New York：MarcelDekker Inc，l999
[29]周仁忠．自适应光学理论[M]．北京：北京理工大学出版社，1996
[30]FIENUP J R. Phase retrieval algorithms: a comparison [J]. Appl Opt,1982,21(15):2758-2769
[31]SHINICHI MATSUOKA, KOICHI YAMAKAWA. Wavefront reconstructionfrom intensity measurements using Fresnel phase retrieval method [J]. Jpn. J. Appl,Phys,1999,38:1183-1185
[32]Catherine Ohara, Scott Basinger, David Cohen, Jessica Faust, et al. PhaseRetrieval Camera Testing of the Ball AMSD Mirror[R].Mirror Technology Days，Huntsville, AL,2006
[33]曾发，谭峭峰，魏晓峰，等．一种可对复杂光场进行相位恢复的算法[J].中国激光，2006，33(3):339-342
[34]曾发，谭峭峰，魏晓峰，等.强激光畸变波前的高精度重构[J].强激光与粒子束，2007，19(1)：27-30
[35]黄利新，姚新，蔡冬梅，等.一种快速高精度的相位恢复迭代法[J].中国激光，2010，37(5)：1218-1221
[36]马鑫雪，王建立，王斌.相位恢复技术算法的探究.激光与红外，2012，42(2)217-221
[37]Lowman Andrew E, Redding David C, et al. Phase Retrieval Camera for TestingNGST Optics[C], Proc. SPIE,2003,4850:329~335
[38]DEAN BRUCE H, ARONSTEIN DAVID L, SMITH J SCOTT, et al. Phaseretrieval algorithm for JWST flight and tested telescope[C]//Proc. of SPIE,2006,6265:1-17
[39]G. Hislop, G. C. James, A. Hellicar. Phase retrieval of scattered fields[J].IEEETrans. Antennas Propag,2007,55:2332-2341
[40]B.H.Dean, D.L.Aronstein, et al. Phase Retrieval Algorithm for JWST Flight andTestbed Telescope. Proc.SPIC Vol.6265,626511,2011
[41]P. A. Sabelhaus, D. Campbell, M. Clampin, J. Decker, M. Greenhouse, A. Johns,M. Menzel, R. Smith, and P. Sullivan,"An overview of the James Webb SpaceTelescope (JWST) project," Proc. SPIE, Vol.5899,2005
[42]Chang M P, Ersoy O K, Dong B, et al. lterative optimization of diffractive phaseelementssimultaneouslyimplementingseveralopticalfunctions[J].Applied Optics，1995，34(17):3069~3076
[43]Crocker J H, Ford H C, Hartig G F, Jedrzejewski R I. Optical performance oftheCorrectiveOpticsSpaceTelescopeAxialReplacement(COSTAR)[C].Proc. SPIE1994,2198:1170~1180
[44]T. B. Parsonage,“JWST beryllium telescope: material and substrate fabrication,”Proc. SPIE5494,39,2004
[45]J. W. Contreras and P. A. Lightsey,“Optical design and analysis of the JamesWebb Space Telescope: optical telescopeelement,” Proc. SPIE, Vol.5524,30,2004
[46]L. A. Ryder and T. Jamieson,"Lens design for the Near Infrared Camera for theJames Webb Space Telescope," Proc.SPIE, Vol.5904,590409,2005
[47]C. B. Atkinson, S. C. Texter, L. D. Feinberg, and R. A. M. Keski-Kuha,“Status ofthe JWST optical telescope element,”Proc. SPIE, these proceedings,2006
[48]Endelman L L, Enterprises E, Jose S. Hubble Space Telescope: now and then[C].Proc.SPIE,1997,2869:44~57
[49]Krist J E, Burrows C J. Phase Retrieval Analysis of Pre and Post-repairHubbleSpace Telescope images[J].Applied Optics，1995，34:4951~4964
[50]Lyon R, Miller P E, Crusczak A. Hubble Space Telescope Phase Retrieval:AParameterEstimation[C]. Proc. SPIE,1991,1567:317
[51]Roddier C, Roddier F. Combined Approach to the Hubble Space Telescopewavefront distortion analysis[J].Applied optics,1993,32(10):2992~3008
[52]Fienup JR.Iterativemethodappliedtoimagereconstructionandtocomputer-generatedholograms[J].Optical Engineering,1980,19(3):297~305
[53]C.Roddier, F.Roddier. Combined approach to Hubble Space Telescope wave-frontdistortion analysis. Appl.Opt.32,2992-3008,1993
[54]吴宇列，胡晓军，等.基于相位恢复技术的大型光学镜面面型在位检测技术.机械工程学报稿件，2007，9
[55]马鑫雪，王建立，王斌，汪宗洋.相位恢复波前传感器测量精度的定量分析.光学学报.2013，33(10)：1028001
[56]ROGGEMANN M C, WELSH B M. Imaging Through Turbulence [M].Washington: CRC Press,1996
[57]吴元昊，王斌，赵金宇，名明，董磊，杨轻云，王明浩，王国强.利用相位差异技术恢复宽带白光图像.光学精密工程，2010，18(8):1849-1854
[58]Paxman R G, Fienup J R. Misalignment sensing and images reconstructionusingPhase diversity [J]. J. Opt. Soc. Am. A,1988,5(6):914~923
[59]Paxman R G, Schulz T J, Fienup J R. Joint estimation of object and aberrations byusing phase diversity [J]. Opt.Soc.Am,1992, A9:1072-1085
[60]THELEN B J, PAXMAN R G, CARRARA D A, et al. Maximum a posterioriestimation of fixed aberrations, dynamic aberrations, and the object fromPhase-diverse Speckle data[J]. J.Opt.Soc.Am.1999, A16:1759-1768
[61]VOGEl C R.Computational Methods for Inverse Problems [M]. Philadelphia:SIAM Press,2002
[62]VOGEL C R, CHAN T, PLEMMONS R. Fast algorithms for PhaseDiversity-Based Blind Deconvolution[C]. Adaptive Optical System Technologies,Kona, Hawaii, USA. SPIE,1998,3353:994-1005
[63]L FDAHL M G, BERGER T E, SHINE R S, et al. Preparation of a dualwavelength sequence of high-resolution solar photospheric images using PhaseDiversity [J]. The Astrophysical Journal.1998,495:965-972
[64]SELDIN J H, Paxman R G, Phase-diverse speckle reconstruction of solardata[C].Image Reconstruction and Restoration, Proc. SPIE,1994,2302:268-280
[65]BLANC A, FUSCO T, HARTUNG M, et al. Calibration of NAOS and CONICAstatic aberrations Application of the phase diversity technique[J]. Astron.Astrophys.2003,399:373-383
[66]BLANC A, MUGNIER L M, IDIER J. Marginal estimation of aberrations andimage restoration by use of phase diversity [J]. Opt.Soc.Am.2003,20(6):1035-1046
[67]易红伟，李英才，马臻，李旭阳.空间光学成像系统波像差的相位差异估计方法.光子学报，2009，38(6):2676-2681
[68]李斐，饶长辉.利用Cramer-Rao理论研究相位差法的最佳离焦量.强激光与粒子束.2011，23(6):1492-1496
[69]李斐，饶长辉.相位差法波前传感系统自身误差的分析及消除方法.强激光与粒子束.2011，23(3):599-605
[70]王斌，汪宗洋，王建立，赵金宇，吴元昊，张世学，董磊，文明.双相机相位差异散斑成像技术.光学精密工程，2011，19(6):1384-1390
[71]王建立，汪宗洋，王斌，等.相位差异散斑法图像复原技术.光学精密工程，2011，19(5):1165-1170
[72]赵金宇，陈占芳，王斌，汪宗洋，张楠，王建立，吴元昊，张世学.相位差异法目标函数并行化改造.光学精密工程，2012，20(2):431-438
[73]汪宗洋，王建立，王斌，吴元昊.基于相位差异的图像复原方法.光电工程，2010，37(12):25-29
[74]赵金宇，吴元昊，贾建禄，等.基于实时波前信息的图像复原技术[J].光学精密工程，2012
[75]Wu Yuanhao, Wang Bin, Wang Zongyang, Cao Jingtai, Zhang Xuguang. Phaseerror estimation with broadband white light by Phase Diversity, SPIE,7544,Proceedings of SPIE–The International Society for Optical Engineering, Hangzhou,China
[76]汪宗洋，王斌，吴元昊，孟浩然，刘欣悦，林旭东.利用相位差异技术校准非共光路静态像差.光学学报，2012，32(7):0701007
[77]王斌，汪宗洋，吴元昊，马鑫雪，等.利用多通道相位差异波前探测法检测自适应光学系统非共光路像差[J].光学精密工程，2013，21(7):1683-1692
[78]B. H. Dean and C. Bowers,“Diversity Selection for Phase-Diverse-PhaseRetrieval,” J. Opt. Soc. Am. A201490-1504,2003
[79]B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, andR. G. Paxman,“Comparison of Shack–Hartmann wavefrontsensing and phase-diverse phaseretrieval,” in Adaptive Opticsand Applications, R. K. Tyson and R. Q. Fugate, eds.,Proc.SPIE3126,307–320~1997
[80]B. H. Dean,‘‘Crame′r–Rao analysis for phase-diversephase-retrieval: diversityfunctions and broadband phase-retrieval,’’ presented at the Wavefront Sensing&ControlsConference, sponsored by Kamuela Optical Associates, KohalaCoast, Hawaii,November13–16,2000
[81]Heng Mao, Xiao Wang, and Dazun Zhao,“Application of phase-diverse phaseretrieval to wavefrontsensing in non-connected complicated pupil optics”, ChineseOpt. Lett.5,397-399,2007
[82]T. Zielinski, and J. R. Fienup,"Compensation for DynamicOptomechanicalVibrations in a Phase-Diverse Phase Retrieval Algorithm," inFrontiers in Optics(Optical Society of America),2008, p. FMF5
[83]B. J. Daniel, M. R. Bolcar, J. R. Schott, and J. R. Fienup,"Phase retrievalinsparse aperture systems with phase diversity: a trade space study," in SensorsandSystems for Space Applications II, Proc. SPIE, R. T. Howard, and P.Motaghedi,eds.,6958,2008, pp.69580K-69512
[84]Measure Piston Misalignment on the Segmented Primary Mirror of the Keck IITelescope[J], Part of the SPIE Conference on Space Telescopes and Instruments V.Kona, Hawaii March,3356:1190-1201,1998
[85]M. G. Lofdahl, R. L. Kendrick, A. Harwit, et.al. A Phase Diversity Experiment toMeasure Piston Misalignment on the Segmented Primary Mirror of the Keck IITelescope[C]. Part of the SPIE Conference on Space Telescopes and Instruments V.Kona, Hawaii March,1998,3356:1190-1201
[86]F. Zernike,“Diffraction theory of knife-edge test and its improved form, thephase contrast method,” Mon. Not. R.Astron. Soc.94,377–384,1934
[87]V. N. Mahajan,“Zernike annular polynomials and optical aberrations of systemswithannular pupils,” Appl. Opt.33,8125–8127,1994
[88]Ragazzoni, Testing the pyramid wavefront sensor on the sky, Proceedings of SPIE,4000,423-430,2000
[89]Esposito S, Pinna E, Co-phasing of segmented mirrors usingpyramidsensor,Proe．SPIE5169,2003
[90]J.B. Costa et al.,“PYRAMIR: a near-infrared wave front sensor for the calar altoadaptive optics system,”SPIE4839, pp.280–287,2003
[91]S. Ligori et al.,“Performance of pyramid detector system,”SPIE5490, pp.1278–218,2004
[92]Jess A Johnson, Pyramid Wavefront Sensing:Theory and component technologydevelopment at LAO, Proc. of SPIE Vol.6272,62724R,2006
[93]M. Feldt et al.,“PYRAMIR: first on sky results from an infrared pyramidwavefront sensor,” Proc. SPIE6272,2006
[94]A. Tozzi,The Double Pyramid wavefront sensor for LBT, Proc. of SPIE Vol.7015,701558,2008
[95]D. Peter, PYRAMIR: Construction and Implementation of the World’s firstinfrared pyramid sensor, Proc. of SPIE Vol.7015,701558,2008
[96]陈欣扬，朱能鸿.基于四棱锥传感器的波前检测仿真设计，《天文学进展》，2006，4:362-372
[97]陈欣扬.四棱锥传感器在天文光学综合孔径望远镜中的波前检测仿真研究，电子测量与仪器学报，2006增刊
[98]朱能鸿等.利用四棱锥传感器检测光学拼接镜的法向光程差，传感技术学报，2009，3
[99]V. N. Mahajan,“Zernike circle polynomials and optical aberrations of systemswith circular pupils,” Appl. Opt.33,8121–8124,1994
[100] A. B. Bhatia and E. Wolf,“On the circle polynomials of Zernike and relatedorthogonal sets,” Proc. CambridgePhilos. Soc.50,40–48,1954
[101] M. A. A. Neil, M. J. Booth, and T. Wilson,‘‘Closed-loop aberrationcorrectionusing a modal Zernike wave-front sensor,’’Opt. Lett.25,1083–1085,2000
[102] J. Y. Wand and D. E. Silva,“Wavefront interpretation with Zernikepolynomials,” Appl. Opt.19,1510–1518,1980
[103] R. J. Noll,“Zernike polynomials and atmospheric turbulence,” J. Opt. Soc.Am.66,207–211,1976
[104] V. N. Mahajan,“Zernike-Gauss polynomials for optical systems withGaussian pupils,” Appl. Opt.34,8057–8059,1995
[105] A. J. E. M. Janssen,“Extended Nijboer-Zernike approach for thecomputationof optical point-spread functions,” J. Opt. Soc. Am. A19,849–857,2002
[106] J. J. M. Braat, P. Dirksen, A. J. E. M. Janssen, and A. S. van de Nes,“Extended Nijboer-Zernike representation of the vector field in the focalregion of anaberrated high-aperture optical system,” J. Opt. Soc. Am. A20,2281–2292,2003
[107] P. Dirksen, J. J. M. Braat, A. J. E. M. Janssen, and C. Juffermans,“Aberrationretrieval using the extended Nijboer-Zernike approach,” J.Microlith.,Microfabr., Microsyst.2,61,2003
[108] A. J. E. M. Janssen, J. J. M. Braat, and P. Dirksen,“On the computationofthe Nijboer-Zernike aberration integrals at arbitrary defocus,” J. Mod. Opt.51,687–703,2004
[109] C. van der Avoort, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“Aberration retrieval from the intensity point-spread function in the focalregionusing the extended Nijboer-Zernike approach,” J. Mod. Opt.52,1695–1728,2005
[110] J. J. M. Braat, P. Dirksen, A. J. E. M. Janssen, S. van Haver, and A. S. vandeNes,“Extended Nijboer-Zernike approach to aberration and birefringenceretrieval ina high-numerical-aperture optical system,” J. Opt. Soc. Am. A22,2635–2650,2005
[111] P. Dirksen, J. J. Braat, A. J. Janssen, and A. Leeuwestein,“Aberrationretrieval for high-NA optical systems using the extendedNijboer-Zerniketheory,” Proc. SPIE5754,262–273,2005
[112] S. van Haver, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“High-NAaberration retrieval with the extended Nijboer-Zernike vector diffractiontheory,” J.Europ. Opt. Soc. Rap. Public.1,06004,2006
[113] P. Dirksen, J. J. M. Braat, and A. J. Janssen,“Estimating resist parametersinoptical lithography using the extended Nijboer-Zernike theory,” J.Microlith.,Microfabr., Microsyst.5,1–11,2006
[114] S. van Haver, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“High-NAaberration retrieval with the extended Nijboer-Zernike vector diffractiontheory-Erratum,” J. Europ. Opt. Soc. Rap. Public.2,07011e,2007
[115] J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen,“Energyandmomentum flux in a high-numerical-aperture beam using theextendedNijboer-Zernike diffraction formalism,” J. Europ. Opt. Soc. Rap. Public.2,2007
[116] S. van Haver, O. T. A. Janssen, J. J. M. Braat, A. J. E. M. Janssen, H.P.Urbach, and S. F. Pereira,“General imaging of advanced3D mask objectsbased onthe fully-vectorial extended Nijboer-Zernike (ENZ) theory,” Proc.SPIE6924,69240U,2008
[117] S. van Haver, J. J.M. Braat, A. J. E. M. Janssen, O.T. A. Janssen, and S.F.Pereira,“Vectorial aerial-image computations of three-dimensional objectsbased onthe Extended Nijboer-Zernike theory,” J. Opt. Soc. Am. A26,1221–1234,2009
[118] J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and S. F. Pereira,“Imageformation in a multilayer using the Extended Nijboer-Zernike theory,”J.Europ. Opt. Soc. Rap. Public.4,09048,2009
[119] F. Roddier,"Curvature Sensing and Compensation: a New Concept inAdaptive Optics," Appl. Opt.i,1223-1225,1988
[120] F. Roddier, C. Roddier, and N. Roddier,"Curvature sensing: a newwavefrontsensing method," in Statistical Optics, Proc. SPW976,203—209,1988
[121]《数学手册》编写组著议者.《数学手册》[M].北京：高等教育出版社，2010，197-199
[122]毛用才著《.随机过程》[M].北京:西安电子科技大学出版社，1998，1-202
[123] J.W.Goodman著.统计光学[M].北京：科学出版社，1992，1-414
[124] J.W.Goodman著.傅里叶光学导论[M].北京：电子工业出版社，2006，1-150
[125] Gerchberg R W, Saxton W O. Phase determination from image anddiffractionplane pictures in the electron microscope [J]. Optik,1971,34(3):275~284
[126] Gerchberg R W, Saxton W O. A practical algorithm for the determinationofphase from image and diffraction phase pictures [J]. Optik,1972,35(2):237~246
[127] Gonsalves R A, Chidlaw R. Wavefront sensing by phase retrieval[C]. Proc.SPIE,1979,207:32~39
[128] Wilkins S W,Gureyev T E,Gao D,et al. Phase-contrast imaging usingpolychro-Matic hard X-rays[J].Nature,1996,384:335~338
[129] Pogany A,Gao D,Wilkins S W. Contrast and resolution in imaging with amicrofocus X-ray source[J].Review Science Insitrument,1997,68(7):2774~2782
[130] YU Bin, PENG Xiang, TIAN Jindong, et al. Phase retrieval for in-line hardx-ray phase-contrast imaging with the Yang-Gu algorithm[C]//Proc. ofSPIE,2006,6026:60260Z.1-60260Z.6
[131] Millane R P. Phase retrieval in crystallography and optics [J].J. Opt. Soc. Am.A,1990,7:394~411
[132]于斌，彭翔，田劲东，等．硬x射线同轴相衬成像的相位恢复[J].物理学报，2005，54(5):2034-2037
[133] GonsalvesRA.Phaseretrievalanddiversityinadaptiveoptics[J].OpticalEngineering,1982,21:829~832
[134] J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R.Robinson, and D.Kryskowski,"Wave-front phaseestimationfrom Fourier intensity measurements," J.Opt. Soc. Am. A6,1020-1026,1989
[135] BYRD R H, LU P, Nocedal J, et al. A Limited Memory Algorithm for BoundConstrained Optimization[R]. Report NAM-08,EECS Department, NorthwesternUniversity,1994
[136] R. H. Byrd, P. Lu, and J. Nocedal,“A limited-memory algorithm forbound-constrained optimization,” SIAM Journal on Scientific and StatisticalComputing,1995,16(5), pp.1190–1208
[137] Richard A. Carreras, Sergio R. Restaino, et al. Phase diversity experimentalresults: deconvolution of v Scorpii. Optics Communications,130,1996,13-19
[138] RODDIER N. Atmospheric wavefirst simulation using Zernike polynomials[J]. Optical Engineering,1995,29(10):1174-1180
[139]李敏，李新阳，姜文汉.线性相位反演传感器与哈特曼传感器的实验研究对比[J]．光学学报，2008，28(4)：619-625
[140]李圣怡，胡晓军，吴宇列.大镜面在位检测中的相位恢复技术研究[J].光
子学报，2009，38(2)：365-370
[2]杨慧珍，龚成龙.一种基于光瞳面相位差的波前传感器相位恢复[J].光学学报，2011，31(11):1112002
[3] Osten W. Some answers to new challenges in optical metrology[C].Proc. SPIE,2008,7155715503-1~715503-16
[4] L FDAHL M G, SCHARMER G B. Wave-front sensing and image restorationfrom focused and defocused solar images [J]. Astron.Astrophys.1994,107:243-264
[5] Redding D, Basinger S, Lowman A, Shi F, et al. Wavefront Sensing and Controlfor a Next Generation Space Telescope[C].Proc. SPIE，1998，3356:758~772
[6] Acton D S, Atcheson P D, Cermak M, Kingsbury L K, Shi F, Redding DC.JamesWebbSpaceTelescopeWavefrontSensingandControlAlgorithms[C]Proc.SPIE，2004，5487:887~896
[7] Smith J S, Dean B H, Haghani S. Distributed Computing architecture forImage-based Wavefront Sensing and2D FFTs[C].Proc. SPIE，2006，6274:21-l~21-10
[8] Dean B H，Smith J S，Budinoff J G，Feinberg L.Wavefront Sensing and ControlArchitecture for SPOT (Spherical Primary Optical Telescope)[C].Proc. SPIE，2006，6265:4F-l~4F-10
[9] Millerd J E, Wyant J C. Simultaneous phase-shifting Fizeau interferometer
[P].US Patent,2005,20050046864
[10]Leslie Deck. Vibration-resistant phase-shifting interferometry [J]. Applied Optics,1996,35(34)6655-6662
[11]Burge J H, Wyant J C. Applications of computer-generated holograms forinterferometric measurement of large aspheric optics[C].Proc.SPIE,1995,2576258-269
[12]Reichelt S, Pruss C, Tiziani H J. Absolute interferometric test of aspheres by useof twin computer-generated holograms [J]. Applied Optics,2003,42(22)4468-4479
[13]Sommargren G E, Phillion D W, Campbell E W. Sub-nanometer interferometryfor aspheric mirror fabrication[C].The9th International Conference on ProductionEngineering, Osaka, Japam,1999
[14]Reichelt S, Tiziani H J. Twin-CGHs for absolute calibration in wavefront testinginterferometry [J]. Optics Communications,2003,22023-32
[15]FIENUP J R, MARRON J C, SCHULZ T J,et al. Hubble space telescopecharacterized by using phase-retrieval algorithms[J]. ApplOpt.,1993,32(10)1747-1767
[16]BRADY GREGORY R, FIENUP J R. Phase retrieval as an optical metrologytool[C] Optical Fabrication&Testing. Topical Meeting of the Optical Society ofAmerica, SPIE Technical Digest,2005, TD03139-141
[17]张均，董军等，张艳，等.数字刀口检测技术.光电工程[J]．2005，32(5)：65-68
[18]饶学军，凌宁，王成，等．哈特曼夏克传感器在非球面加工中的应用[J]．光学学报，2002，22(4)
[19]Li Hua-gui, JiangWen-han. Atmospheric turbulence parameter measurementusing Hartmann-Shack wavefront sensor [A]. P roc of ESO [C],1993,48:21～28
[20]Lane R G, TallonM. Wavefront reconstruction using a Shack-Hartmann sensor [J].Applied Optics,1992,31(32):6902～6908
[21]Chao Gen-rui, Yu Xin. Accuracy analysis of a Hartmann-Shack wavefront sensoroperated with a faint object [J]. Optical Engineering,1994,(33):2331～2335
[22]JiangWen-han, Xian Hao, Shen Feng. Detecting error of Shack-Hartmannwavefront sensor [A]. SPIE [C],1997,3126:534～544
[23]Hermann J. Crosscoupling and aliasing in model wavefront estimation [J]. J. Opt.Soc. Am. A,1981,71(8):989～992
[24]Takato N, IyeM, Yamaguchi I. Wavefront reconstruction errors ofShack-Hartmann sensors [J]. Publ A stron Soc Pacific,1994,106:182～188
[25] Patrick Naulleau.Kenneth A.Goldberg.SangH.Lee. The EUV phase-shiftingpoint diffractioninterferometer,2000
[26]Patrick Naulleau.Kenneth Goldberg.Sang Lee Characterization of the accuracy ofEUV phase-shiftingpoint diffraction interferometry,1998
[27]刘晓军，高咏生．横向剪切干涉测量中准确的相位恢复算法[J]．光学精密工程，2004，l2(5)：47-479
[28]R K．Tyson．Adaptive optics engineering handbook [M]．New York：MarcelDekker Inc，l999
[29]周仁忠．自适应光学理论[M]．北京：北京理工大学出版社，1996
[30]FIENUP J R. Phase retrieval algorithms: a comparison [J]. Appl Opt,1982,21(15):2758-2769
[31]SHINICHI MATSUOKA, KOICHI YAMAKAWA. Wavefront reconstructionfrom intensity measurements using Fresnel phase retrieval method [J]. Jpn. J. Appl,Phys,1999,38:1183-1185
[32]Catherine Ohara, Scott Basinger, David Cohen, Jessica Faust, et al. PhaseRetrieval Camera Testing of the Ball AMSD Mirror[R].Mirror Technology Days，Huntsville, AL,2006
[33]曾发，谭峭峰，魏晓峰，等．一种可对复杂光场进行相位恢复的算法[J].中国激光，2006，33(3):339-342
[34]曾发，谭峭峰，魏晓峰，等.强激光畸变波前的高精度重构[J].强激光与粒子束，2007，19(1)：27-30
[35]黄利新，姚新，蔡冬梅，等.一种快速高精度的相位恢复迭代法[J].中国激光，2010，37(5)：1218-1221
[36]马鑫雪，王建立，王斌.相位恢复技术算法的探究.激光与红外，2012，42(2)217-221
[37]Lowman Andrew E, Redding David C, et al. Phase Retrieval Camera for TestingNGST Optics[C], Proc. SPIE,2003,4850:329~335
[38]DEAN BRUCE H, ARONSTEIN DAVID L, SMITH J SCOTT, et al. Phaseretrieval algorithm for JWST flight and tested telescope[C]//Proc. of SPIE,2006,6265:1-17
[39]G. Hislop, G. C. James, A. Hellicar. Phase retrieval of scattered fields[J].IEEETrans. Antennas Propag,2007,55:2332-2341
[40]B.H.Dean, D.L.Aronstein, et al. Phase Retrieval Algorithm for JWST Flight andTestbed Telescope. Proc.SPIC Vol.6265,626511,2011
[41]P. A. Sabelhaus, D. Campbell, M. Clampin, J. Decker, M. Greenhouse, A. Johns,M. Menzel, R. Smith, and P. Sullivan,"An overview of the James Webb SpaceTelescope (JWST) project," Proc. SPIE, Vol.5899,2005
[42]Chang M P, Ersoy O K, Dong B, et al. lterative optimization of diffractive phaseelementssimultaneouslyimplementingseveralopticalfunctions[J].Applied Optics，1995，34(17):3069~3076
[43]Crocker J H, Ford H C, Hartig G F, Jedrzejewski R I. Optical performance oftheCorrectiveOpticsSpaceTelescopeAxialReplacement(COSTAR)[C].Proc. SPIE1994,2198:1170~1180
[44]T. B. Parsonage,“JWST beryllium telescope: material and substrate fabrication,”Proc. SPIE5494,39,2004
[45]J. W. Contreras and P. A. Lightsey,“Optical design and analysis of the JamesWebb Space Telescope: optical telescopeelement,” Proc. SPIE, Vol.5524,30,2004
[46]L. A. Ryder and T. Jamieson,"Lens design for the Near Infrared Camera for theJames Webb Space Telescope," Proc.SPIE, Vol.5904,590409,2005
[47]C. B. Atkinson, S. C. Texter, L. D. Feinberg, and R. A. M. Keski-Kuha,“Status ofthe JWST optical telescope element,”Proc. SPIE, these proceedings,2006
[48]Endelman L L, Enterprises E, Jose S. Hubble Space Telescope: now and then[C].Proc.SPIE,1997,2869:44~57
[49]Krist J E, Burrows C J. Phase Retrieval Analysis of Pre and Post-repairHubbleSpace Telescope images[J].Applied Optics，1995，34:4951~4964
[50]Lyon R, Miller P E, Crusczak A. Hubble Space Telescope Phase Retrieval:AParameterEstimation[C]. Proc. SPIE,1991,1567:317
[51]Roddier C, Roddier F. Combined Approach to the Hubble Space Telescopewavefront distortion analysis[J].Applied optics,1993,32(10):2992~3008
[52]Fienup JR.Iterativemethodappliedtoimagereconstructionandtocomputer-generatedholograms[J].Optical Engineering,1980,19(3):297~305
[53]C.Roddier, F.Roddier. Combined approach to Hubble Space Telescope wave-frontdistortion analysis. Appl.Opt.32,2992-3008,1993
[54]吴宇列，胡晓军，等.基于相位恢复技术的大型光学镜面面型在位检测技术.机械工程学报稿件，2007，9
[55]马鑫雪，王建立，王斌，汪宗洋.相位恢复波前传感器测量精度的定量分析.光学学报.2013，33(10)：1028001
[56]ROGGEMANN M C, WELSH B M. Imaging Through Turbulence [M].Washington: CRC Press,1996
[57]吴元昊，王斌，赵金宇，名明，董磊，杨轻云，王明浩，王国强.利用相位差异技术恢复宽带白光图像.光学精密工程，2010，18(8):1849-1854
[58]Paxman R G, Fienup J R. Misalignment sensing and images reconstructionusingPhase diversity [J]. J. Opt. Soc. Am. A,1988,5(6):914~923
[59]Paxman R G, Schulz T J, Fienup J R. Joint estimation of object and aberrations byusing phase diversity [J]. Opt.Soc.Am,1992, A9:1072-1085
[60]THELEN B J, PAXMAN R G, CARRARA D A, et al. Maximum a posterioriestimation of fixed aberrations, dynamic aberrations, and the object fromPhase-diverse Speckle data[J]. J.Opt.Soc.Am.1999, A16:1759-1768
[61]VOGEl C R.Computational Methods for Inverse Problems [M]. Philadelphia:SIAM Press,2002
[62]VOGEL C R, CHAN T, PLEMMONS R. Fast algorithms for PhaseDiversity-Based Blind Deconvolution[C]. Adaptive Optical System Technologies,Kona, Hawaii, USA. SPIE,1998,3353:994-1005
[63]L FDAHL M G, BERGER T E, SHINE R S, et al. Preparation of a dualwavelength sequence of high-resolution solar photospheric images using PhaseDiversity [J]. The Astrophysical Journal.1998,495:965-972
[64]SELDIN J H, Paxman R G, Phase-diverse speckle reconstruction of solardata[C].Image Reconstruction and Restoration, Proc. SPIE,1994,2302:268-280
[65]BLANC A, FUSCO T, HARTUNG M, et al. Calibration of NAOS and CONICAstatic aberrations Application of the phase diversity technique[J]. Astron.Astrophys.2003,399:373-383
[66]BLANC A, MUGNIER L M, IDIER J. Marginal estimation of aberrations andimage restoration by use of phase diversity [J]. Opt.Soc.Am.2003,20(6):1035-1046
[67]易红伟，李英才，马臻，李旭阳.空间光学成像系统波像差的相位差异估计方法.光子学报，2009，38(6):2676-2681
[68]李斐，饶长辉.利用Cramer-Rao理论研究相位差法的最佳离焦量.强激光与粒子束.2011，23(6):1492-1496
[69]李斐，饶长辉.相位差法波前传感系统自身误差的分析及消除方法.强激光与粒子束.2011，23(3):599-605
[70]王斌，汪宗洋，王建立，赵金宇，吴元昊，张世学，董磊，文明.双相机相位差异散斑成像技术.光学精密工程，2011，19(6):1384-1390
[71]王建立，汪宗洋，王斌，等.相位差异散斑法图像复原技术.光学精密工程，2011，19(5):1165-1170
[72]赵金宇，陈占芳，王斌，汪宗洋，张楠，王建立，吴元昊，张世学.相位差异法目标函数并行化改造.光学精密工程，2012，20(2):431-438
[73]汪宗洋，王建立，王斌，吴元昊.基于相位差异的图像复原方法.光电工程，2010，37(12):25-29
[74]赵金宇，吴元昊，贾建禄，等.基于实时波前信息的图像复原技术[J].光学精密工程，2012
[75]Wu Yuanhao, Wang Bin, Wang Zongyang, Cao Jingtai, Zhang Xuguang. Phaseerror estimation with broadband white light by Phase Diversity, SPIE,7544,Proceedings of SPIE–The International Society for Optical Engineering, Hangzhou,China
[76]汪宗洋，王斌，吴元昊，孟浩然，刘欣悦，林旭东.利用相位差异技术校准非共光路静态像差.光学学报，2012，32(7):0701007
[77]王斌，汪宗洋，吴元昊，马鑫雪，等.利用多通道相位差异波前探测法检测自适应光学系统非共光路像差[J].光学精密工程，2013，21(7):1683-1692
[78]B. H. Dean and C. Bowers,“Diversity Selection for Phase-Diverse-PhaseRetrieval,” J. Opt. Soc. Am. A201490-1504,2003
[79]B. L. Ellerbroek, B. J. Thelen, D. J. Lee, D. A. Carrara, andR. G. Paxman,“Comparison of Shack–Hartmann wavefrontsensing and phase-diverse phaseretrieval,” in Adaptive Opticsand Applications, R. K. Tyson and R. Q. Fugate, eds.,Proc.SPIE3126,307–320~1997
[80]B. H. Dean,‘‘Crame′r–Rao analysis for phase-diversephase-retrieval: diversityfunctions and broadband phase-retrieval,’’ presented at the Wavefront Sensing&ControlsConference, sponsored by Kamuela Optical Associates, KohalaCoast, Hawaii,November13–16,2000
[81]Heng Mao, Xiao Wang, and Dazun Zhao,“Application of phase-diverse phaseretrieval to wavefrontsensing in non-connected complicated pupil optics”, ChineseOpt. Lett.5,397-399,2007
[82]T. Zielinski, and J. R. Fienup,"Compensation for DynamicOptomechanicalVibrations in a Phase-Diverse Phase Retrieval Algorithm," inFrontiers in Optics(Optical Society of America),2008, p. FMF5
[83]B. J. Daniel, M. R. Bolcar, J. R. Schott, and J. R. Fienup,"Phase retrievalinsparse aperture systems with phase diversity: a trade space study," in SensorsandSystems for Space Applications II, Proc. SPIE, R. T. Howard, and P.Motaghedi,eds.,6958,2008, pp.69580K-69512
[84]Measure Piston Misalignment on the Segmented Primary Mirror of the Keck IITelescope[J], Part of the SPIE Conference on Space Telescopes and Instruments V.Kona, Hawaii March,3356:1190-1201,1998
[85]M. G. Lofdahl, R. L. Kendrick, A. Harwit, et.al. A Phase Diversity Experiment toMeasure Piston Misalignment on the Segmented Primary Mirror of the Keck IITelescope[C]. Part of the SPIE Conference on Space Telescopes and Instruments V.Kona, Hawaii March,1998,3356:1190-1201
[86]F. Zernike,“Diffraction theory of knife-edge test and its improved form, thephase contrast method,” Mon. Not. R.Astron. Soc.94,377–384,1934
[87]V. N. Mahajan,“Zernike annular polynomials and optical aberrations of systemswithannular pupils,” Appl. Opt.33,8125–8127,1994
[88]Ragazzoni, Testing the pyramid wavefront sensor on the sky, Proceedings of SPIE,4000,423-430,2000
[89]Esposito S, Pinna E, Co-phasing of segmented mirrors usingpyramidsensor,Proe．SPIE5169,2003
[90]J.B. Costa et al.,“PYRAMIR: a near-infrared wave front sensor for the calar altoadaptive optics system,”SPIE4839, pp.280–287,2003
[91]S. Ligori et al.,“Performance of pyramid detector system,”SPIE5490, pp.1278–218,2004
[92]Jess A Johnson, Pyramid Wavefront Sensing:Theory and component technologydevelopment at LAO, Proc. of SPIE Vol.6272,62724R,2006
[93]M. Feldt et al.,“PYRAMIR: first on sky results from an infrared pyramidwavefront sensor,” Proc. SPIE6272,2006
[94]A. Tozzi,The Double Pyramid wavefront sensor for LBT, Proc. of SPIE Vol.7015,701558,2008
[95]D. Peter, PYRAMIR: Construction and Implementation of the World’s firstinfrared pyramid sensor, Proc. of SPIE Vol.7015,701558,2008
[96]陈欣扬，朱能鸿.基于四棱锥传感器的波前检测仿真设计，《天文学进展》，2006，4:362-372
[97]陈欣扬.四棱锥传感器在天文光学综合孔径望远镜中的波前检测仿真研究，电子测量与仪器学报，2006增刊
[98]朱能鸿等.利用四棱锥传感器检测光学拼接镜的法向光程差，传感技术学报，2009，3
[99]V. N. Mahajan,“Zernike circle polynomials and optical aberrations of systemswith circular pupils,” Appl. Opt.33,8121–8124,1994
[100] A. B. Bhatia and E. Wolf,“On the circle polynomials of Zernike and relatedorthogonal sets,” Proc. CambridgePhilos. Soc.50,40–48,1954
[101] M. A. A. Neil, M. J. Booth, and T. Wilson,‘‘Closed-loop aberrationcorrectionusing a modal Zernike wave-front sensor,’’Opt. Lett.25,1083–1085,2000
[102] J. Y. Wand and D. E. Silva,“Wavefront interpretation with Zernikepolynomials,” Appl. Opt.19,1510–1518,1980
[103] R. J. Noll,“Zernike polynomials and atmospheric turbulence,” J. Opt. Soc.Am.66,207–211,1976
[104] V. N. Mahajan,“Zernike-Gauss polynomials for optical systems withGaussian pupils,” Appl. Opt.34,8057–8059,1995
[105] A. J. E. M. Janssen,“Extended Nijboer-Zernike approach for thecomputationof optical point-spread functions,” J. Opt. Soc. Am. A19,849–857,2002
[106] J. J. M. Braat, P. Dirksen, A. J. E. M. Janssen, and A. S. van de Nes,“Extended Nijboer-Zernike representation of the vector field in the focalregion of anaberrated high-aperture optical system,” J. Opt. Soc. Am. A20,2281–2292,2003
[107] P. Dirksen, J. J. M. Braat, A. J. E. M. Janssen, and C. Juffermans,“Aberrationretrieval using the extended Nijboer-Zernike approach,” J.Microlith.,Microfabr., Microsyst.2,61,2003
[108] A. J. E. M. Janssen, J. J. M. Braat, and P. Dirksen,“On the computationofthe Nijboer-Zernike aberration integrals at arbitrary defocus,” J. Mod. Opt.51,687–703,2004
[109] C. van der Avoort, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“Aberration retrieval from the intensity point-spread function in the focalregionusing the extended Nijboer-Zernike approach,” J. Mod. Opt.52,1695–1728,2005
[110] J. J. M. Braat, P. Dirksen, A. J. E. M. Janssen, S. van Haver, and A. S. vandeNes,“Extended Nijboer-Zernike approach to aberration and birefringenceretrieval ina high-numerical-aperture optical system,” J. Opt. Soc. Am. A22,2635–2650,2005
[111] P. Dirksen, J. J. Braat, A. J. Janssen, and A. Leeuwestein,“Aberrationretrieval for high-NA optical systems using the extendedNijboer-Zerniketheory,” Proc. SPIE5754,262–273,2005
[112] S. van Haver, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“High-NAaberration retrieval with the extended Nijboer-Zernike vector diffractiontheory,” J.Europ. Opt. Soc. Rap. Public.1,06004,2006
[113] P. Dirksen, J. J. M. Braat, and A. J. Janssen,“Estimating resist parametersinoptical lithography using the extended Nijboer-Zernike theory,” J.Microlith.,Microfabr., Microsyst.5,1–11,2006
[114] S. van Haver, J. J. M. Braat, P. Dirksen, and A. J. E. M. Janssen,“High-NAaberration retrieval with the extended Nijboer-Zernike vector diffractiontheory-Erratum,” J. Europ. Opt. Soc. Rap. Public.2,07011e,2007
[115] J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and P. Dirksen,“Energyandmomentum flux in a high-numerical-aperture beam using theextendedNijboer-Zernike diffraction formalism,” J. Europ. Opt. Soc. Rap. Public.2,2007
[116] S. van Haver, O. T. A. Janssen, J. J. M. Braat, A. J. E. M. Janssen, H.P.Urbach, and S. F. Pereira,“General imaging of advanced3D mask objectsbased onthe fully-vectorial extended Nijboer-Zernike (ENZ) theory,” Proc.SPIE6924,69240U,2008
[117] S. van Haver, J. J.M. Braat, A. J. E. M. Janssen, O.T. A. Janssen, and S.F.Pereira,“Vectorial aerial-image computations of three-dimensional objectsbased onthe Extended Nijboer-Zernike theory,” J. Opt. Soc. Am. A26,1221–1234,2009
[118] J. J. M. Braat, S. van Haver, A. J. E. M. Janssen, and S. F. Pereira,“Imageformation in a multilayer using the Extended Nijboer-Zernike theory,”J.Europ. Opt. Soc. Rap. Public.4,09048,2009
[119] F. Roddier,"Curvature Sensing and Compensation: a New Concept inAdaptive Optics," Appl. Opt.i,1223-1225,1988
[120] F. Roddier, C. Roddier, and N. Roddier,"Curvature sensing: a newwavefrontsensing method," in Statistical Optics, Proc. SPW976,203—209,1988
[121]《数学手册》编写组著议者.《数学手册》[M].北京：高等教育出版社，2010，197-199
[122]毛用才著《.随机过程》[M].北京:西安电子科技大学出版社，1998，1-202
[123] J.W.Goodman著.统计光学[M].北京：科学出版社，1992，1-414
[124] J.W.Goodman著.傅里叶光学导论[M].北京：电子工业出版社，2006，1-150
[125] Gerchberg R W, Saxton W O. Phase determination from image anddiffractionplane pictures in the electron microscope [J]. Optik,1971,34(3):275~284
[126] Gerchberg R W, Saxton W O. A practical algorithm for the determinationofphase from image and diffraction phase pictures [J]. Optik,1972,35(2):237~246
[127] Gonsalves R A, Chidlaw R. Wavefront sensing by phase retrieval[C]. Proc.SPIE,1979,207:32~39
[128] Wilkins S W,Gureyev T E,Gao D,et al. Phase-contrast imaging usingpolychro-Matic hard X-rays[J].Nature,1996,384:335~338
[129] Pogany A,Gao D,Wilkins S W. Contrast and resolution in imaging with amicrofocus X-ray source[J].Review Science Insitrument,1997,68(7):2774~2782
[130] YU Bin, PENG Xiang, TIAN Jindong, et al. Phase retrieval for in-line hardx-ray phase-contrast imaging with the Yang-Gu algorithm[C]//Proc. ofSPIE,2006,6026:60260Z.1-60260Z.6
[131] Millane R P. Phase retrieval in crystallography and optics [J].J. Opt. Soc. Am.A,1990,7:394~411
[132]于斌，彭翔，田劲东，等．硬x射线同轴相衬成像的相位恢复[J].物理学报，2005，54(5):2034-2037
[133] GonsalvesRA.Phaseretrievalanddiversityinadaptiveoptics[J].OpticalEngineering,1982,21:829~832
[134] J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R.Robinson, and D.Kryskowski,"Wave-front phaseestimationfrom Fourier intensity measurements," J.Opt. Soc. Am. A6,1020-1026,1989
[135] BYRD R H, LU P, Nocedal J, et al. A Limited Memory Algorithm for BoundConstrained Optimization[R]. Report NAM-08,EECS Department, NorthwesternUniversity,1994
[136] R. H. Byrd, P. Lu, and J. Nocedal,“A limited-memory algorithm forbound-constrained optimization,” SIAM Journal on Scientific and StatisticalComputing,1995,16(5), pp.1190–1208
[137] Richard A. Carreras, Sergio R. Restaino, et al. Phase diversity experimentalresults: deconvolution of v Scorpii. Optics Communications,130,1996,13-19
[138] RODDIER N. Atmospheric wavefirst simulation using Zernike polynomials[J]. Optical Engineering,1995,29(10):1174-1180
[139]李敏，李新阳，姜文汉.线性相位反演传感器与哈特曼传感器的实验研究对比[J]．光学学报，2008，28(4)：619-625
[140]李圣怡，胡晓军，吴宇列.大镜面在位检测中的相位恢复技术研究[J].光
子学报，2009，38(2)：365-370