非球面相位恢复检测技术研究
|
摘要
非球面光学零件在光学系统中的广泛应用,对现代光学加工和检测技术提出了挑战。因为光学制造的精度和效率很大程度上依赖于检测技术,所以高精度在位检测对于非球面尤其是大型非球面镜制造有着非常重要的意义。利用相位恢复技术测量镜面面形,结构简单,抗振动,测量量程较大,可以获得较高精度的定量检测结果,是实现非球面在位检测最有希望的方案之一。本论文从相位恢复原理出发,围绕非球面检测的特点及要求,充分利用计算机处理技术,对非球面在位测量问题进行了理论和实验研究。论文的研究工作包括以下几个部分:
1、从相位恢复原理出发,研究了相位恢复面形检测中的一般性问题。在分析相位恢复检测中多解来源的基础上,提出先用两个离焦平面初步恢复相位以及人为构造不可分解支持域来保证检测结果的唯一性。基于二维抽样定理和空间带宽积不变性原理确定衍射光场的计算量,并分析相位恢复检测范围的限制因素。根据光线传播的几何模型,提出波前曲率对离焦光强分布的主导作用,总结光强图位置的选择原则。
2、为扩展可测镜面f数范围提出了欠采样相位恢复算法。算法结合亚像素光场思想与非线性交替优化策略,利用远焦点光强图重构高分辨率的近焦点光强图,交替优化近焦点光强图和镜面光场相位,最终使之收敛到正确解。实验研究了欠采样算法的可行性及误差。
3、针对初加工阶段波前像差较大的实际情况,设计了大动态范围测量算法,并用仿真和实验验证了算法的有效性。大动态范围算法融合了参数算法和数据点算法,先用参数算法循环恢复面形的低频轮廓,再将此轮廓作为已知相位,用数据点GS算法循环恢复高频面形信息,从而实现由粗到细的面形恢复。
4、研究了相位恢复非球面直接检测方法。在继承非球面直接检测基本原理的基础上,明确了被测波前像差与面形误差的关系。为了处理大型数据,采用光场拼接计算方法实现非球面衍射光场计算。利用多幅同一位置不同曝光时间的光强图融合消除非球面光强图饱和区域的影响,并分析了光强误差。通过对焦散区的研究,明确划分了焦散区内光强图的有效区域。基于上述研究形成了较为完善的非球面检测算法。此外还提出将点光源和检验点分别置于被测镜面的近轴共轭点上,通过寻求适当的近轴共轭点位置减少测量过程中的系统像差。以双曲面和抛物面为例,用相位恢复在位检测各镜面的面形误差,并分别与干涉仪子孔径拼接和自准直测量结果对比,对相位恢复非球面直接检测的有效性进行了实验验证。
5、利用无像差点光路构建了相位恢复离轴非球面测量系统。通过建立等效衍射模型,将非轴对称衍射光场的相位恢复问题转化成一般球面波相位恢复问题。探索了离轴镜相位恢复检测的光路调整方法。将测量光路调整归结为点光源相对被测镜三个坐标轴方向的平动,并利用线性误差模型分离调整误差。用离轴椭球镜进行测量实验,与干涉仪补偿器测量结果对比表明所提方法能有效实现离轴非球面的面形检测。
Modern technology meets serious challenge in the manufacture and measurement of aspheric optics which are being used widely in optical systems. Because the accuracy and efficiency of manufacture much depends on the optical measurement technology, in-situ test with high accuracy is very useful to aspheric optics manufacture,especially to those with large aperture. Since it has advantages of simplicity, vibration insensitivity, broad testing range and capability of quantitative calculation, phase retrieval is promising to realize in-situ test of aspheric optics. This thesis is dedicated to applying phase retrieval to problems in aspheric optical metrology. Beginning with the phase retrieval theory, it presents theoretical and experimental study on the in-situ test problems for aspheres, combined with the characteristics of aspheres and computer technology. The major research efforts include the following points.
1. Some common problems in wave-front metrology are investigated from the view of classical phase retrieval. In view of the existence of ambiguity solutions in phase retrieval, some steps are taken to ensure the uniqueness of the testing result. Those include iterative computations back and forth between two defocus positions and constructing an irreducibility support to enhance restriction on solutions. The number of sampling points is defined theoretically using two-dimensional sampling theorem and space-bandwidth product invariability, and the limits of measurement are analyzed. According to the geometric optics model of wave-front curvature and intensity distributions, some principles about how to select the defocus positions are presented.
2. Under-sampled phase retrieval algorithm is presented to expand the f-number of measurement range. This approach arrives at correct solution by virtue of sub-pixel ideal and nonlinear alternating optimization technique. Super solution intensities close to the focus are reconstructed from intensities away from the focus by sub-pixel phase retrieval algorithm. Then super solution intensities and phases are alternating optimized. An experiment is presented to investigate the validity of this method.
3. A high dynamic range algorithm is described and demonstrated, which retrieves the figure errors beyond one wavelength after the rough polish process. Parameter algorithm and point-by-point algorithm are combined in this algorithm to reconstruct the figure error from outline to details. The low frequency part of the figure error is obtained by parameter algorithm firstly, and treated as a known wave-front phase in the followed point-by-point GS algorithm. And the latter is used to retrieve the high frequency part of the figure error.
4. The phase retrieval method that tests aspheric mirror without auxiliary optics has been developed and demonstrated experimentally. Based on the primary principle of aspheric testing without auxiliary optics, the relationship between tested wave-front aberrations and figure errors is identified. In order to process large-scale data, a stitching method is proposed to calculate the light field produced by aspheres. Due to significant departure from the spherical surface, the intensities are usually saturated which will lead to phase retrieval failure. In order to overcome the effect from saturation, multi-pictures of the same scene with various exposure times are fused and the error in this process is analyzed. Based on the understanding of the caustic region produced by aspheric surfaces, the valid areas of intensities are defined. An aspheric phase retrieval algorithm is then presented. In addition, the light point and test point are proposed to be placed at paraxial conjugate positions properly selected to reduce system aberrations in the test. Phase retrieval tests are performed with a hyperboloid mirror and a paraboloid mirror at in-situ status. The retrieval results are then compared with the stitching and auto-collimating interference tests respectively, which verified the validity of the phase retrieval test.
5. The phase retrieval testing system for off-axis aspheres based on Hindle test has been designed. The problem of phase retrieval for non-axial symmetry wave-front is translated into general spherical wave-front retrieval based on equivalent diffraction model. Adjustment in the test is reduced to moving light point along the direction of coordinate axes of tested mirror, and the displacement errors are separated using linear model about misalignment gradients for each degree of freedom. An experiment about off-axis ellipsoid testing is conducted. The phase retrieval test result is compared with measurements by interferometer and compensator. The agreement demonstrates this approach is feasible and realistic for off-axis ellipsoid test.
1、从相位恢复原理出发,研究了相位恢复面形检测中的一般性问题。在分析相位恢复检测中多解来源的基础上,提出先用两个离焦平面初步恢复相位以及人为构造不可分解支持域来保证检测结果的唯一性。基于二维抽样定理和空间带宽积不变性原理确定衍射光场的计算量,并分析相位恢复检测范围的限制因素。根据光线传播的几何模型,提出波前曲率对离焦光强分布的主导作用,总结光强图位置的选择原则。
2、为扩展可测镜面f数范围提出了欠采样相位恢复算法。算法结合亚像素光场思想与非线性交替优化策略,利用远焦点光强图重构高分辨率的近焦点光强图,交替优化近焦点光强图和镜面光场相位,最终使之收敛到正确解。实验研究了欠采样算法的可行性及误差。
3、针对初加工阶段波前像差较大的实际情况,设计了大动态范围测量算法,并用仿真和实验验证了算法的有效性。大动态范围算法融合了参数算法和数据点算法,先用参数算法循环恢复面形的低频轮廓,再将此轮廓作为已知相位,用数据点GS算法循环恢复高频面形信息,从而实现由粗到细的面形恢复。
4、研究了相位恢复非球面直接检测方法。在继承非球面直接检测基本原理的基础上,明确了被测波前像差与面形误差的关系。为了处理大型数据,采用光场拼接计算方法实现非球面衍射光场计算。利用多幅同一位置不同曝光时间的光强图融合消除非球面光强图饱和区域的影响,并分析了光强误差。通过对焦散区的研究,明确划分了焦散区内光强图的有效区域。基于上述研究形成了较为完善的非球面检测算法。此外还提出将点光源和检验点分别置于被测镜面的近轴共轭点上,通过寻求适当的近轴共轭点位置减少测量过程中的系统像差。以双曲面和抛物面为例,用相位恢复在位检测各镜面的面形误差,并分别与干涉仪子孔径拼接和自准直测量结果对比,对相位恢复非球面直接检测的有效性进行了实验验证。
5、利用无像差点光路构建了相位恢复离轴非球面测量系统。通过建立等效衍射模型,将非轴对称衍射光场的相位恢复问题转化成一般球面波相位恢复问题。探索了离轴镜相位恢复检测的光路调整方法。将测量光路调整归结为点光源相对被测镜三个坐标轴方向的平动,并利用线性误差模型分离调整误差。用离轴椭球镜进行测量实验,与干涉仪补偿器测量结果对比表明所提方法能有效实现离轴非球面的面形检测。
Modern technology meets serious challenge in the manufacture and measurement of aspheric optics which are being used widely in optical systems. Because the accuracy and efficiency of manufacture much depends on the optical measurement technology, in-situ test with high accuracy is very useful to aspheric optics manufacture,especially to those with large aperture. Since it has advantages of simplicity, vibration insensitivity, broad testing range and capability of quantitative calculation, phase retrieval is promising to realize in-situ test of aspheric optics. This thesis is dedicated to applying phase retrieval to problems in aspheric optical metrology. Beginning with the phase retrieval theory, it presents theoretical and experimental study on the in-situ test problems for aspheres, combined with the characteristics of aspheres and computer technology. The major research efforts include the following points.
1. Some common problems in wave-front metrology are investigated from the view of classical phase retrieval. In view of the existence of ambiguity solutions in phase retrieval, some steps are taken to ensure the uniqueness of the testing result. Those include iterative computations back and forth between two defocus positions and constructing an irreducibility support to enhance restriction on solutions. The number of sampling points is defined theoretically using two-dimensional sampling theorem and space-bandwidth product invariability, and the limits of measurement are analyzed. According to the geometric optics model of wave-front curvature and intensity distributions, some principles about how to select the defocus positions are presented.
2. Under-sampled phase retrieval algorithm is presented to expand the f-number of measurement range. This approach arrives at correct solution by virtue of sub-pixel ideal and nonlinear alternating optimization technique. Super solution intensities close to the focus are reconstructed from intensities away from the focus by sub-pixel phase retrieval algorithm. Then super solution intensities and phases are alternating optimized. An experiment is presented to investigate the validity of this method.
3. A high dynamic range algorithm is described and demonstrated, which retrieves the figure errors beyond one wavelength after the rough polish process. Parameter algorithm and point-by-point algorithm are combined in this algorithm to reconstruct the figure error from outline to details. The low frequency part of the figure error is obtained by parameter algorithm firstly, and treated as a known wave-front phase in the followed point-by-point GS algorithm. And the latter is used to retrieve the high frequency part of the figure error.
4. The phase retrieval method that tests aspheric mirror without auxiliary optics has been developed and demonstrated experimentally. Based on the primary principle of aspheric testing without auxiliary optics, the relationship between tested wave-front aberrations and figure errors is identified. In order to process large-scale data, a stitching method is proposed to calculate the light field produced by aspheres. Due to significant departure from the spherical surface, the intensities are usually saturated which will lead to phase retrieval failure. In order to overcome the effect from saturation, multi-pictures of the same scene with various exposure times are fused and the error in this process is analyzed. Based on the understanding of the caustic region produced by aspheric surfaces, the valid areas of intensities are defined. An aspheric phase retrieval algorithm is then presented. In addition, the light point and test point are proposed to be placed at paraxial conjugate positions properly selected to reduce system aberrations in the test. Phase retrieval tests are performed with a hyperboloid mirror and a paraboloid mirror at in-situ status. The retrieval results are then compared with the stitching and auto-collimating interference tests respectively, which verified the validity of the phase retrieval test.
5. The phase retrieval testing system for off-axis aspheres based on Hindle test has been designed. The problem of phase retrieval for non-axial symmetry wave-front is translated into general spherical wave-front retrieval based on equivalent diffraction model. Adjustment in the test is reduced to moving light point along the direction of coordinate axes of tested mirror, and the displacement errors are separated using linear model about misalignment gradients for each degree of freedom. An experiment about off-axis ellipsoid testing is conducted. The phase retrieval test result is compared with measurements by interferometer and compensator. The agreement demonstrates this approach is feasible and realistic for off-axis ellipsoid test.
引文
[1]普利亚耶夫著,杨力译.光学非球面检验[M].北京:科学出版社, 1982.
[2] Endelman L L, Enterprises E, Jose S. Hubble Space Telescope: now and then[C]. Proc. SPIE,1997,2869:44~57.
[3] Dooley J A, Lawson P R. Technology plan for the terrestrial planet finder coronagraph[R]. JPL Publication,2005:33~35.
[4] Torben Andersen, Arne Ardeberg, Jaques Beckers, et al. The Euro50 extremely large telescope[C].Proc.SPIE,2003,4840:214~225.
[5] Vick Charles P. KH-12 Improved Crystal[Z].2007,http://www. globalsecurity.org /space/systems/kh-12.htm.
[6]郝云彩.空间详查相机光学系统研究[D].上海:中国科学院上海药物研究所,2000.
[7]陈晓丽,李博,王永辉等.空间可展开主镜技术途径研究[J].航天返回与遥感, 2008(1):19~24.
[8]杨力.先进光学制造技术[M].北京:科学出版社,2001.
[9]陆永贵,杨建东.光学非球面先进制造关键技术的探讨[J].长春理工大学学报,2006,29(2):31~33.
[10]周旭升.大中型非球面计算机控制研抛工艺方法研究[D].长沙:国防科技大学,2007.
[11] L Yang, D X Wang. Study on distortion control technology of the active stressed lap polishing deeper aspherical mirror[C]. SPIE, 2005, Vol. 6024:1V-1~1V-8.
[12]焦长君.光学镜面离子束加工材料去除机理与基本工艺研究[D].长沙:国防科技学技术大学,2008.
[13]彭小强.确定性磁流变抛光的关键技术研究[D].长沙:国防科技学技术大学, 2004.
[14] D.马拉卡拉主编.光学车间检验[M].北京:机械工业出版社,1983.
[15]潘君骅.谈谈光学检测的指导思想[J].光学与光电技术,2004,2(6):1~3.
[16]张国雄.三坐标测量机[M].天津:天津大学出版社,1999.
[17] Song J F, Vorburger Theodore V. Stylus profiling at high resolution and low force [J].Applied Optics,1991,30(1):42~50.
[18] Mike Conroy, Joe Armstrong. A comparison of surface metrology techniques[C]. Proc.SPIE,2006,6188:1~7.
[19]周翔,赵宏.基于Mexican hat小波变换的三维轮廓术[J].光学学报,2008,28:1~6.
[20] John E Greivenkamp,Daniel G Smith,Robert O Gappinger,et al.Asphericmetrology with a Shack-Hartmann wavefront sensor[C].Proc.SPIE,2001,4419: 1~4.
[21] Ben C Platt, Roland Shack. History and Principles of Shack-Hartmann Wavefront Sensing [J]. Journal of Refractive Surgery, 2001,17: S573~S577.
[22] Craig Kiikkaa, Daniel R Nealb, John Kincade, et al.The JWST Infrared Scanning Shack Hartman System: A new in-process way to measure large mirrors during optical fabrication at Tinsley. Proc.SPIE,2006,6265:3D.
[23] Lars A Selberg. Interferometer accuracy and precision[C]. Proc.SPIE,1990,1400: 24~32.
[24] P Hariharan. Optical interferometry [J]. Rep. Prog. Phys,1990,54:339~390.
[25] Leslie L Deck. Fourier-transform phase-shifting interferometry [J]. Applied Optics, 2003, 42(13):2354~2365.
[26]潘君骅.光学非球面的设计、加工和检测[M].北京:科学出版社,1994.
[27] Paul L Ruben. Refractive null correctors for aspheric surfaces [J]. Applied Optics, 1976, 15(12):3080~3083.
[28] Abe Offner.A Null Corrector for Paraboloidal Mirrors [J]. Applied Optics,1963,2 (2):153~156.
[29]伍凡.非球面零检验的镜式补偿器设计[J].应用光学,1994,15 (4):10~13.
[30]伍凡.非球面零检验的Offner补偿器设计[J].应用光学,1993,14 (3):8~12.
[31] Charles E Synborski, Mary J Hanes. 10. 6 micron wavelength interferometry and the measurement of infrared transmitting materials index of refraction homogeneity[C]. Proc.SPIE, 1980, 255:32~39.
[32] B Dichler, P Koidl. Scanning CO2 laser interferometer for the inspection of inf rared transmit ting plane parallel plate[C]. Proc.SPIE,1988,966:177~182.
[33]陈进榜,陈磊,王青等.大孔径移相式CO2激光干涉仪[J].中国激光,1998,25(1): 31~36.
[34] Hariharan P, D Sen.Double-passed two-beam interferometers[J]. J. Opt. Soc. Am. A,1960,50(4):357~360.
[35] Thomas D A,Wyant J C. High efficiency grating lateral shear interferometer [J].Optical Engineering,1976,15(5):477.
[36] Chen Shanyong, Li Shengyi, Dai Yifan. Iterative algorithm for subaperture stitching interferometry for general surfaces[J]. J. Opt. Soc. Am. A,2005,22(9): 1929~1936.
[37] Brady G R, Fienup J R. Phase retrieval as an optical metrology tool [EB/OL]. http://www.optics.rochester.edu/workgroups/fienup.html.
[38]吴宇列,胡晓军,戴一帆等.基于相位恢复技术的大型光学镜面面形在位检测技术研究[J].机械工程学报,2009,45(2):157~163.
[39] Osten W. Some answers to new challenges in optical metrology[C]. Proc.SPIE,2008,7155:715503-1~715503-16.
[40] Burgea J H, Davisona B W, Martina H M, Zhaob C. Development of surface metrology for the Giant Magellan Telescope primary mirror [J]. Proc.SPIE, 2008, 7018,14-1~14-12.
[41] Glen C C, James H Burge,Lee R D. Vibration stabilitzation of a phase shifting interfereometer for large optics[C]. Proc. SPIE,3134:438~446.
[42] Millerd J E, Wyant J C. Simultaneous phase-shifting Fizeau interferometer [P].US Patent: 20050046864, 2005.
[43] Leslie Deck. Vibration-resistant phase-shifting interferometry [J]. Applied Optics, 1996,35(34):6655~6662.
[44] Wyant J C. Dynamic interferometry[J].Optics & Photonics News,2003,4:38~41.
[45]虞祖良,金国藩.计算机制全息图[M].北京:清华大学出版社,1984:18~22.
[46] Poleshchuk1 A G, Nasyrovl R K, Asfour J M .Combined computer-generated hologram for testing steep aspheric surfaces[J].Optics Express,2009,17(7):5420~ 5425.
[47]常军,李凤友,翁志成.用计算全息法检测大口径凸非球面的研究[J].光学学报,2003,23(10):1266~1268.
[48]谢意,陈强,伍凡.用双计算全息检测凹非球面[J].光学学报,2008,28:1313~1317.
[49]刘亮.基于离轴型CGH的非球面检测技术研究[D].南京:南京理工大学,2009.
[50] Burge J H, Wyant J C. Applications of computer-generated holograms for interferometric measurement of large aspheric optics [C].Proc.SPIE,1995,2576: 258~269.
[51] Beyerlein M, Lindlein N, Schwider J. Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics [J]. Applied Optics, 2002, 41:2440~2447.
[52] Schwider J, Lindlein N, Mantel K, Harder I. On the calibration of diffractive nulls for transmission tests of aspheric components [J]. Optics Communications, 2007, 279:262~272.
[53] Reichelt S, Pruss C, Tiziani H J.Absolute interferometric test of aspheres by use of twin computer-generated holograms[J]. Applied Optics,2003,42(22):4468~ 4479.
[54] Reichelt S, Tiziani H J. Twin-CGHs for absolute calibration in wavefront testing interferometry [J]. Optics Communications,2003,220:23~32.
[55] Sommargren G E,Phillion D W,Campbell E W.Sub-nanometer interferometry for aspheric mirror fabrication[C].The 9th International Conference on Production Engineering, Osaka, Japan,1999.
[56] Greivenkamp J E. Sub-Nyquist Interferometry[J].Applied Optics,1987,26(24): 5245~ 5258.
[57] Greivenkamp J E. Design of a non-null interferometer for aspheric wave fronts [J].Applied Optics, 2004, 43(27):5143~5151.
[58] Gappinger R O,Greivenkamp J E.Iterative reverse optimization procedure for calibration of aspheric wavefront measurements on a non-null interferometer[J]. Applied Optics, 2004, 43:5152~5161.
[59] Gappinger R O,Greivenkamp J E.Non-null interferometer for measurement of aspheric transmitted wavefronts[C]. Proc. SPIE,2003,5180:301~312.
[60] Piotr Szwaykowski, Raymond Castonguay. Measurements of aspheric surfaces [EB/OL].http://www.engsynthesis.com.
[61] Garbusi E, Pruss C, Osten W. Interferometer for precise and flexible asphere testing [J]. Optics Letters,2008,33(24):2973~2975.
[62] Murphy P, Forbes G, Fleig J, Dumas P, Tricard M. Stitching Interferometry: A Flexible Solution for Surface Metrology [J]. Optics & Photonics News,2003,14: 38~43.
[63] Fleig J, Dumas P, Murphy P E, Forbes G W, An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces[C].Proc. SPIE, 2003,5188:296~307.
[64] Murphy P, Fleig J, Forbes G.Subaperture stitching interferometry for testing mild aspheres[C]. Proc. SPIE,2006,6293:0J.
[65] Tricard M, Kulawiec A, Bauer M, et al. Subaperture stitching interferometry of high-departure aspheres by incorporating a variable configurable null optics[J]. CIRP Annals Manufacturing Technology,2010,59(1):547~550.
[66]刘惠兰.一种利用部分补偿透镜实现非球面面形的干涉测量方法[P].中国专利:200410068823.4,2004.
[67] Gerchberg R W,Saxton W O. Phase determination from image and diffraction plane pictures in the electron microscope[J].Optik,1971,34(3):275~284.
[68] Gerchberg R W,Saxton W O. A practical algorithm for the determination of phase from image and diffraction phase pictures[J]. Optik,1972,35(2):237~246.
[69] Wilkins S W, Gureyev T E, Gao D, et al. Phase-contrast imaging using polychro- -matic hard X-rays[J]. Nature,1996,384:335~338.
[70] Pogany A, Gao D, Wilkins S W. Contrast and resolution in imaging with a microfocus X-ray source[J]. Review Science Insitrument,1997,68(7):2774~ 2782.
[71] Paxman R G, Fienup J R. Misalignment sensing and images reconstruction using phase diversity [J]. J.Opt.Soc.Am.A,1988,5(6):914~923.
[72] Millane R P.Phase retrieval in crystallography and optics[J]. J.Opt.Soc.Am.A, 1990,7:394~411.
[73] Gonsalves R A, Chidlaw R.Wavefront sensing by phase retrieval[C], Proc.SPIE,1979,207:32~39.
[74] Gonsalves R A. Phase retrieval and diversity in adaptive optics[J].Optical Engineering,1982,21:829~832.
[75] Chang M P, Ersoy O K, Dong B, et al .Iterative optimization of diffractive Phase elements simultaneously implementing several optical functions[J]. Applied Optics,1995,34(17):3069~3076.
[76] Fienup J R. Iterative method applied to image reconstruction and to computer- generated holograms [J].Optical Engineering,1980,19(3):297~305.
[77] Fienup J R, Marron J C, Schulz T J, Seldin J H. Hubble Space telescope characterized by using phase-retrieval algorithms[J]. Applied Optics,1993,32(10): 1747~1767.
[78] Roddier C, Roddier F. Combined Approach to the Hubble Space Telescope Wavefront Distortion Analysis[J]. Applied Optics,1993,32(10):2992~3008.
[79] Lyon R,Miller P E,Grusczak A. Hubble Space Telescope Phase Retrieval: A Parameter Estimation[C].Proc.SPIE,1991,1567:317.
[80] Krist J E, Burrows C J. Phase Retrieval Analysis of pre and post-repair Hubble Space Telescope images [J]. Applied Optics,1995,34:4951~4964.
[81] Crocker J H, Ford H C, Hartig G F, Jedrzejewski R I. Optical performance of the Corrective Optics Space Telescope Axial Replacement (COSTAR)[C]. Proc. SPIE,1994,2198:1170~1180.
[82] Hasan H. Pre-COSTAR status of OTA focuses[C]. Instrument Science Report, Baltimore, 1993, 12, OTA-14.
[83] Sabelhaus P A, Campbell D, Clampin M, Decker J, et al.An overview of the James Webb Space Telescope (JWST) project [C].Proc. SPIE, 2005, 5899:0P.
[84] Redding D, Basinger S, Lowman A, Shi F,et al. Wavefront Sensing and Control for a Next Generation Space Telescope[C].Proc. SPIE, 1998,3356:758~772.
[85] Lowman Andrew E, Redding David C, et al. Phase Retrieval Camera for Testing NGST Optics[C], Proc.SPIE, 2003,4850:329~335.
[86] Acton D S, Atcheson P D, Cermak M, Kingsbury L K, Shi F, Redding D C. James Webb Space Telescope Wavefront Sensing and Control Algorithms[C]. Proc. SPIE, 2004,5487:887~896.
[87] Smith J S, Dean B H, Haghani S. Distributed Computing architecture for image-based Wavefront Sensing and 2D FFTs[C]. Proc.SPIE,2006,6274: 21-1~ 21-10.
[88] Dean B H, Smith J S, Budinoff J G, Feinberg L. Wavefront Sensing and Control Architecture for SPOT (Spherical Primary Optical Telescope)[C].Proc.SPIE, 2006,6265:4F-1~4F-10.
[89] Catherine Ohara,Scott Basinger,David Cohen,Jessica Faust, et al. Phase Retrieval Camera Testing of the Ball AMSD Mirror[R].Mirror Technology Days,Huntsville, AL,2006.
[90] Ellerbroek B L, Thelen B J, Lee D J, Carrara D A, et al. Comparison of Shack- Hartmann wavefront sensing and phase-diverse phase retrieval[C].Proc.SPIE, 3126:307~320.
[91] Walther A.The Question of Phase Retrieval in Optics. Opt. Acta,1963,10:41~49.
[92] Misell D L. A method for the solution of the phase problem in electron microscopy [J]. Applied Physics,1973,D6:L6~L9.
[93] Fienup J R. Phase retrieval algorithms: a comparison [J].Applied Optics, 1982, 21(15):2758~2760.
[94] Bruel Laurent. Numerical Phase retrieval from beam intensity measurements in three planes[C]. Proc.SPlE,2003,4932:590~598.
[95] Ivanov V Yu,Sivokon V P,Vorontsov M A. Phase retrieval from a set of intensity measurements:theory and experiment[J]. J.Opt.Soc.Am.A,1992,9(9):515~1524.
[96] Pedrini G,Osten W,Zhang Y.Wave-front reconstruction from a sequence of interferograms recorded at different planes [J].Optics Letters,2005,30:833~835.
[97] Zhang Y,Pedrini G, Osten W, Tiziani H. Whole optical wave field reconstruction from double or multi inline holograms by phase retrieval algorithm [J].Optics Express, 2003,l (11):3234~3241.
[98] Mcalister D F, Beck M, Clarke L, et al. Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms [J]. Optics Letters,1995,20 (10):1181~1183.
[99] M. Gunhan Ertosun, Haluk Ath, Haldun M. Ozaktas et al .Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence [J]. Optics Communications,2005,244:61~70.
[100] Fienup J R. Phase retrieval for undersampled broadband images [J]. J. Opt. Soc. Am. A,1999,16(7):1831~1837.
[101] ShizhuoYin, Mingzhe Lu, Chu lung Chen, et al. Design of a bipolar composite filter by a simulated annealing algorithm[J]. Optics Letters,1995,20(12):1409 ~1411.
[102] Gia-Wei Chem,Lon A Wang. Design of binary long-period fiber grating filters by the inverse scatering method with genetic algorithm optimization[J]. J.Opt.Soc.Am.A, 2002,19(4):772~780.
[103] Guangya Zhou,Yixin Chen, Zong guang Wang, et al. Genetic local search algorithm for optimization design of diffractive optical elements[J]. Applied Optics,1999,38(20):4281~ 4290.
[104] Myung Soo Kim, Clark C .Guest. Simulated annealing algorithm for binary phase only filters in patern classification [J].Applied Optics,1990,28(8):1203~ 1208.
[105] Millane R P, Stroud W J. Reconstructing symmetric images from theirundersampled Fouier intensities [J]. J. Opt. Soc. Am. A,1997,14(3):568~579.
[106] Jefferies Stuart M, Lloyd-Hart Michael, Hege E Keith, Georges James. Sensing wave-front amplitude and phase with phase diversity [J]. Applied Optics,2002, 41(11):2095~2102.
[107] Brady G R, Fienup J R.Nonlinear optimization algorithm for retrieving the full complex pupil function [J]. Optics Express, 2006,14(2):474~486.
[108] Cohen D,Redding D C. NGST high dynamic range unwrapped phase estimation [C]. Proc.SPIE, 2003,4850:336~344.
[109] Dean B H, Aronstein D L, et al, Phase Retrieval Algorithm for JWST Flight and Testbed Telescope[C]. Proc.SPIE, 2006, 6265:11-1~11-17.
[110] Roddier F,Roddier C.Wavefront reconstruction using iterative Fourier transforms [J]. Applied Optics,1991,30(11):1325~1327.
[111] Roddier C, Roddier F.Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes[J]. J. Opt. Soc. Am. A,1993,10(11): 2277~2287.
[112] Yang G Z, Dong B Z, Gu B Y, Zhuang J, Ersoy O K. Gerchbeg-Saxton and Yang-Gu algorithm for phase retrieval in a nonunitary transform system: a comparison [J]. Applied Optics,1994,33:209~218.
[113] Dong Bizhen , Zhang Yan , Gu Benyuan et al. Numerical investigation of phase retrieval in afractional Fourier transform[J]. J. Opt. Soc. Am. A,1997,14(10): 2709~2714.
[114] Cong Wenxiang, Chen Nanxian, Gu Benyuan. Recursive algorithm for phase retrieval in the fractional Fourier transform domain[J]. Applied Optics,1998,37 (29):6906~6910.
[115]曾发,谭峭峰,魏晓峰,向勇等.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.
[116]曾发,谭峭峰,魏晓峰,向勇等.基于多个分数阶次的复杂光场相位恢复算法[J].中国激光,2006,33(12):1621~1625.
[117] Mao Heng, Wang Xiao, Zhao Dazun. Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics[J].Chinese Optics Letters,2007,5(7):397~399.
[118]毛珩,王潇,赵达尊.复杂光瞳波前相位恢复算法与实验验证[J].光学学报,2009,29(3):575~581.
[119]李强,沈忙作.基于相位差方法的天文目标高分辨率成像研究[J].天文学报,2007,48(1):113~120.
[120]李强,沈忙作.利用相位差法测量望远镜像差[J].光学学报,2007,27(9):1554~ 1557.
[121] Talor C A,Thompson B J. Attempt to investigate experimently the intensity distribution near the focus in the error-free diffraction patterns of circular and annular apertures[J]. J. Opt. Soc. Am.A,1958,48:844~850.
[122]蒋筑英,李剑白等.光学系统成像质量评价及检验文集[C].北京中国计量出版社,1988:191~203.
[123] Welford W T. Use of Annular Apertures to Increase Focal Depth [J]. J. Opt. Soc. Am. A ,1960,50(8):749~753.
[124] Brady G R. Application of Phase Retrieval to the Measurement of Optical Surfaces and Wavefronts[D]. New York: University of Rochester,2008.
[125] Brady G R, Manuel Guizar-Sicairos, Fienup J R. Phase retrieval as an optical metrology tool[C]. Proc.SPIE,2005,TD03:139~141.
[126] Brady G R,Fienup J R.Range of phase retrieval in optical metrology [J]. Applied Optics, 2009, 48(3):442~449.
[127] Brady G R, Manuel Guizar-Sicairos, Fienup J R. Optical wavefront measurement using phase retrieval with transverse translation diversity[J]. Optics Express, 2009,17(2):624~ 639.
[128] Brady G R, Fienup J R. Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology[C]. Proc.SPIE,6617:0I-1~0I-8.
[129]胡晓军.大型光学镜面相位恢复在位检测技术研究[D].长沙:国防科学技术大学,2008.
[130] Sheng Yi Li, Xiao Jun Hu, Yulie Wu. Resolution enhancement phase retrieval with sub-pixel method[J].Applied Optics, 2009,47(32):6079~6087.
[131] Goodman J W. Introduction to Fourier optics [M]. 3rd ed. Roberts and Company Publishers, 2005:50~55.
[132]邹谋炎.反卷积和信号复原[M].北京:国防工业出版社,2001.
[133] Barakat R, Newsam G. Necessary conditions for a unique solution to two- dimension phase recovery [J]. Math.Phys.,1984,25:3190~3193.
[134] Bruck Y M, Sodin L G. On the ambiquity of the image reconstruction problem [J]. Optis Communications,1979,30:304~308.
[135] Fiddy M A, Brames B J, Dainty J C.Enforcing irreducibility for phase retrieval in two dimensions [J]. Optics Letters,1983,8:96~98.
[136] Brames B J. Unique phase retrieval with explicit support information [J]. Optics Letters,1986,11:61~63.
[137] Seldin J H, Fienup J R. Numerical investigation of the uniqueness of phase retrieval [J]. J. Opt. Soc. Am. A,1990,7(3):412~427.
[138] Fienup J R, Wackerman C C. Phase-retrieval stagnation problems and solutions [J]. J. Opt. Soc. Am. A,1986,3(11):1897~1907.
[139] Lee D J,Roggemann N C, Welsh B M. Cramer-Rao analysis of phase-diversewave-front sensing[J], J. Opt. Soc. Am. A,1999,16:1005~1015.
[140] Cederquist J N, Robinson S R,et al.Cramer-Rao lower bound on wavefront sensor error[J].Optical Engineering,1986,25:586~592.
[141] Cederquist J N, Wackerman C C. Phase-retrieval error: a lower bound [J]. J. Opt. Soc. Am. A,1987,4:1788~1792.
[142] Dean B H, Charles W. Bowers. Diversity selection for phase diverse phase retrieval [J]. J. Opt. Soc. Am. A, 2003,20(8):1490~1504.
[143] Green J J, Dean B H, Ohara C M, Redding D C, et al. Target selection and imaging requirements for JWST fine phasing[C].Proc.SPIE,2004,5487:944 ~953.
[144]索尼推出全新1420万像素1/2.3英寸CCD[Z].http:\\www.xinhuanet.com.
[145]徐文东,干福熹.测量大数值孔径光学系统小光斑的方法[J].中国激光, 2003,30(2):171~174.
[146] Sziklas Edward A, Siegman A E. Diffraction Calculations Using Fast Fourier Transform Methods [J]. Proceedings Letters,1974,3:410~412.
[147]吴冬良.确定性光学加工条件下制造误差的特性研究[D].长沙:国防科学技术大学,2009.
[148] Ghiglia D C, Pritt M D.Two-dimensional phase unwrapping theory, algorithms and software[M]. New York: Wiley-Interscience, 1998.
[149] Karout S A, Gdeisat M A, Burton D R, Lalor M J. Residue Vector, An Approach To Branch-Cut Placement In Phase Unwrapping: Theoretical Study[J]. Applied Optics, 2007, 46(21):4712~4727.
[150]吕海宝.激光光电检测[M].长沙:国防科技大学出版社, 2000.
[151]王庆有.CCD应用技术[M].天津:天津大学出版社, 2000.
[152] F-145B/F-145C,AVT Dolphin Manual [Z].Germany: Allied Vision Technologies GmbH, 2003.
[153] Debevec P E,Malik J. Recovering high dynamic range radiance maps from photographs[C].SIG-GRAPH 97 Conference Proceedings, New York: ACM, 1997:369~378.
[154] Gonzalez-Moreno G, Quiroga J A, Alonso J, et a1.Laser beam profiling with extended image range techniques[J].Optical Engineering,2005,44(2):02360.
[155]周建康,沈为民,唐敏学.CCD测量动态范围的扩展技术[J].光电工程, 2006,33(10):96~110.
[156] Thurman S T, Fienup J R. Phase retrieval with signal bias [J]. J. Opt. Soc. Am. A, 2009,26(4):1008~1014.
[157]马科斯.波恩,埃米尔.沃尔夫著,杨葭荪等译.光学原理(上册)[M].北京:电子工业出版社,2005.
[158] Wyant J C, Creath K.Apllied optics and optical engineering Vol.XI:Basicwavefront aberration theory for optical metrology[M]. New York:Academic press, 1992.
[159] ICX285AL: Diagonal 11 mm (Type 2/3) Progressive Scan CCD Image Sensor with Square Pixel for B/W Cameras [Z]. Sony Corporation.
[160] Cook L G. Three-mirror anastigmat used off-axis in aperture and field [C]. Proc.SPIE,1979,183:207~211.
[161]李俊昌.激光的衍射和热作用[M].北京:科学出版社,2002.
[162] Pedro Arguijo and Marija Strojnik Scholl. Exact ray-trace beam for an off-axis paraboloid surface [J]. Applied Optics,2003,42(16):3284~3289.
[163] Dresel T, Lindlein N, Schwider J.Empirical strategy for detection and removal of misalignment aberrations in interferometry [J]. Optik,2001,112:304~308.
[164]郑立功.离轴非球面CCOS加工过程关键技术研究[D].长春:中国科学院研究生院长春光学精密机械与物理研究所,2003.
[165] Burke Jan, Wang Kai, Bramble Adam. Null test of an off-axis parabolic mirror.I. Configuration with spherical reference wave and flat return surface [J]. Optics Express, 2009,17(5):3196~3210.
[166] Lawson J. K., Auerbach J. M., English R. E. et al. NIF optical specifcations - the importance of the RMS gradient[R].LLNL Report UCRL-JC-130032,1998:7~12.
[167]周仁忠.自适应光学[M].北京:国防工业出版社,1996.
[168] Alan V Oppenheim等著,刘树棠译.信号与系统[M].西安:西安交通大学出版社,2002.
[169]柯略帕洛娃,浦连耶夫著,徐德衍,路敦武译.光学系统的研究与检验[M].北京:机械工业出版社,1983.
[170]刘文耀等.光电图像处理[M].北京:电子工业出版社,2002.
[171] Almoro P, Pedrini G, Osten W. Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field[J]. Applied Optics, 2006,45:8596~8605.
[2] Endelman L L, Enterprises E, Jose S. Hubble Space Telescope: now and then[C]. Proc. SPIE,1997,2869:44~57.
[3] Dooley J A, Lawson P R. Technology plan for the terrestrial planet finder coronagraph[R]. JPL Publication,2005:33~35.
[4] Torben Andersen, Arne Ardeberg, Jaques Beckers, et al. The Euro50 extremely large telescope[C].Proc.SPIE,2003,4840:214~225.
[5] Vick Charles P. KH-12 Improved Crystal[Z].2007,http://www. globalsecurity.org /space/systems/kh-12.htm.
[6]郝云彩.空间详查相机光学系统研究[D].上海:中国科学院上海药物研究所,2000.
[7]陈晓丽,李博,王永辉等.空间可展开主镜技术途径研究[J].航天返回与遥感, 2008(1):19~24.
[8]杨力.先进光学制造技术[M].北京:科学出版社,2001.
[9]陆永贵,杨建东.光学非球面先进制造关键技术的探讨[J].长春理工大学学报,2006,29(2):31~33.
[10]周旭升.大中型非球面计算机控制研抛工艺方法研究[D].长沙:国防科技大学,2007.
[11] L Yang, D X Wang. Study on distortion control technology of the active stressed lap polishing deeper aspherical mirror[C]. SPIE, 2005, Vol. 6024:1V-1~1V-8.
[12]焦长君.光学镜面离子束加工材料去除机理与基本工艺研究[D].长沙:国防科技学技术大学,2008.
[13]彭小强.确定性磁流变抛光的关键技术研究[D].长沙:国防科技学技术大学, 2004.
[14] D.马拉卡拉主编.光学车间检验[M].北京:机械工业出版社,1983.
[15]潘君骅.谈谈光学检测的指导思想[J].光学与光电技术,2004,2(6):1~3.
[16]张国雄.三坐标测量机[M].天津:天津大学出版社,1999.
[17] Song J F, Vorburger Theodore V. Stylus profiling at high resolution and low force [J].Applied Optics,1991,30(1):42~50.
[18] Mike Conroy, Joe Armstrong. A comparison of surface metrology techniques[C]. Proc.SPIE,2006,6188:1~7.
[19]周翔,赵宏.基于Mexican hat小波变换的三维轮廓术[J].光学学报,2008,28:1~6.
[20] John E Greivenkamp,Daniel G Smith,Robert O Gappinger,et al.Asphericmetrology with a Shack-Hartmann wavefront sensor[C].Proc.SPIE,2001,4419: 1~4.
[21] Ben C Platt, Roland Shack. History and Principles of Shack-Hartmann Wavefront Sensing [J]. Journal of Refractive Surgery, 2001,17: S573~S577.
[22] Craig Kiikkaa, Daniel R Nealb, John Kincade, et al.The JWST Infrared Scanning Shack Hartman System: A new in-process way to measure large mirrors during optical fabrication at Tinsley. Proc.SPIE,2006,6265:3D.
[23] Lars A Selberg. Interferometer accuracy and precision[C]. Proc.SPIE,1990,1400: 24~32.
[24] P Hariharan. Optical interferometry [J]. Rep. Prog. Phys,1990,54:339~390.
[25] Leslie L Deck. Fourier-transform phase-shifting interferometry [J]. Applied Optics, 2003, 42(13):2354~2365.
[26]潘君骅.光学非球面的设计、加工和检测[M].北京:科学出版社,1994.
[27] Paul L Ruben. Refractive null correctors for aspheric surfaces [J]. Applied Optics, 1976, 15(12):3080~3083.
[28] Abe Offner.A Null Corrector for Paraboloidal Mirrors [J]. Applied Optics,1963,2 (2):153~156.
[29]伍凡.非球面零检验的镜式补偿器设计[J].应用光学,1994,15 (4):10~13.
[30]伍凡.非球面零检验的Offner补偿器设计[J].应用光学,1993,14 (3):8~12.
[31] Charles E Synborski, Mary J Hanes. 10. 6 micron wavelength interferometry and the measurement of infrared transmitting materials index of refraction homogeneity[C]. Proc.SPIE, 1980, 255:32~39.
[32] B Dichler, P Koidl. Scanning CO2 laser interferometer for the inspection of inf rared transmit ting plane parallel plate[C]. Proc.SPIE,1988,966:177~182.
[33]陈进榜,陈磊,王青等.大孔径移相式CO2激光干涉仪[J].中国激光,1998,25(1): 31~36.
[34] Hariharan P, D Sen.Double-passed two-beam interferometers[J]. J. Opt. Soc. Am. A,1960,50(4):357~360.
[35] Thomas D A,Wyant J C. High efficiency grating lateral shear interferometer [J].Optical Engineering,1976,15(5):477.
[36] Chen Shanyong, Li Shengyi, Dai Yifan. Iterative algorithm for subaperture stitching interferometry for general surfaces[J]. J. Opt. Soc. Am. A,2005,22(9): 1929~1936.
[37] Brady G R, Fienup J R. Phase retrieval as an optical metrology tool [EB/OL]. http://www.optics.rochester.edu/workgroups/fienup.html.
[38]吴宇列,胡晓军,戴一帆等.基于相位恢复技术的大型光学镜面面形在位检测技术研究[J].机械工程学报,2009,45(2):157~163.
[39] Osten W. Some answers to new challenges in optical metrology[C]. Proc.SPIE,2008,7155:715503-1~715503-16.
[40] Burgea J H, Davisona B W, Martina H M, Zhaob C. Development of surface metrology for the Giant Magellan Telescope primary mirror [J]. Proc.SPIE, 2008, 7018,14-1~14-12.
[41] Glen C C, James H Burge,Lee R D. Vibration stabilitzation of a phase shifting interfereometer for large optics[C]. Proc. SPIE,3134:438~446.
[42] Millerd J E, Wyant J C. Simultaneous phase-shifting Fizeau interferometer [P].US Patent: 20050046864, 2005.
[43] Leslie Deck. Vibration-resistant phase-shifting interferometry [J]. Applied Optics, 1996,35(34):6655~6662.
[44] Wyant J C. Dynamic interferometry[J].Optics & Photonics News,2003,4:38~41.
[45]虞祖良,金国藩.计算机制全息图[M].北京:清华大学出版社,1984:18~22.
[46] Poleshchuk1 A G, Nasyrovl R K, Asfour J M .Combined computer-generated hologram for testing steep aspheric surfaces[J].Optics Express,2009,17(7):5420~ 5425.
[47]常军,李凤友,翁志成.用计算全息法检测大口径凸非球面的研究[J].光学学报,2003,23(10):1266~1268.
[48]谢意,陈强,伍凡.用双计算全息检测凹非球面[J].光学学报,2008,28:1313~1317.
[49]刘亮.基于离轴型CGH的非球面检测技术研究[D].南京:南京理工大学,2009.
[50] Burge J H, Wyant J C. Applications of computer-generated holograms for interferometric measurement of large aspheric optics [C].Proc.SPIE,1995,2576: 258~269.
[51] Beyerlein M, Lindlein N, Schwider J. Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics [J]. Applied Optics, 2002, 41:2440~2447.
[52] Schwider J, Lindlein N, Mantel K, Harder I. On the calibration of diffractive nulls for transmission tests of aspheric components [J]. Optics Communications, 2007, 279:262~272.
[53] Reichelt S, Pruss C, Tiziani H J.Absolute interferometric test of aspheres by use of twin computer-generated holograms[J]. Applied Optics,2003,42(22):4468~ 4479.
[54] Reichelt S, Tiziani H J. Twin-CGHs for absolute calibration in wavefront testing interferometry [J]. Optics Communications,2003,220:23~32.
[55] Sommargren G E,Phillion D W,Campbell E W.Sub-nanometer interferometry for aspheric mirror fabrication[C].The 9th International Conference on Production Engineering, Osaka, Japan,1999.
[56] Greivenkamp J E. Sub-Nyquist Interferometry[J].Applied Optics,1987,26(24): 5245~ 5258.
[57] Greivenkamp J E. Design of a non-null interferometer for aspheric wave fronts [J].Applied Optics, 2004, 43(27):5143~5151.
[58] Gappinger R O,Greivenkamp J E.Iterative reverse optimization procedure for calibration of aspheric wavefront measurements on a non-null interferometer[J]. Applied Optics, 2004, 43:5152~5161.
[59] Gappinger R O,Greivenkamp J E.Non-null interferometer for measurement of aspheric transmitted wavefronts[C]. Proc. SPIE,2003,5180:301~312.
[60] Piotr Szwaykowski, Raymond Castonguay. Measurements of aspheric surfaces [EB/OL].http://www.engsynthesis.com.
[61] Garbusi E, Pruss C, Osten W. Interferometer for precise and flexible asphere testing [J]. Optics Letters,2008,33(24):2973~2975.
[62] Murphy P, Forbes G, Fleig J, Dumas P, Tricard M. Stitching Interferometry: A Flexible Solution for Surface Metrology [J]. Optics & Photonics News,2003,14: 38~43.
[63] Fleig J, Dumas P, Murphy P E, Forbes G W, An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces[C].Proc. SPIE, 2003,5188:296~307.
[64] Murphy P, Fleig J, Forbes G.Subaperture stitching interferometry for testing mild aspheres[C]. Proc. SPIE,2006,6293:0J.
[65] Tricard M, Kulawiec A, Bauer M, et al. Subaperture stitching interferometry of high-departure aspheres by incorporating a variable configurable null optics[J]. CIRP Annals Manufacturing Technology,2010,59(1):547~550.
[66]刘惠兰.一种利用部分补偿透镜实现非球面面形的干涉测量方法[P].中国专利:200410068823.4,2004.
[67] Gerchberg R W,Saxton W O. Phase determination from image and diffraction plane pictures in the electron microscope[J].Optik,1971,34(3):275~284.
[68] Gerchberg R W,Saxton W O. A practical algorithm for the determination of phase from image and diffraction phase pictures[J]. Optik,1972,35(2):237~246.
[69] Wilkins S W, Gureyev T E, Gao D, et al. Phase-contrast imaging using polychro- -matic hard X-rays[J]. Nature,1996,384:335~338.
[70] Pogany A, Gao D, Wilkins S W. Contrast and resolution in imaging with a microfocus X-ray source[J]. Review Science Insitrument,1997,68(7):2774~ 2782.
[71] Paxman R G, Fienup J R. Misalignment sensing and images reconstruction using phase diversity [J]. J.Opt.Soc.Am.A,1988,5(6):914~923.
[72] Millane R P.Phase retrieval in crystallography and optics[J]. J.Opt.Soc.Am.A, 1990,7:394~411.
[73] Gonsalves R A, Chidlaw R.Wavefront sensing by phase retrieval[C], Proc.SPIE,1979,207:32~39.
[74] Gonsalves R A. Phase retrieval and diversity in adaptive optics[J].Optical Engineering,1982,21:829~832.
[75] Chang M P, Ersoy O K, Dong B, et al .Iterative optimization of diffractive Phase elements simultaneously implementing several optical functions[J]. Applied Optics,1995,34(17):3069~3076.
[76] Fienup J R. Iterative method applied to image reconstruction and to computer- generated holograms [J].Optical Engineering,1980,19(3):297~305.
[77] Fienup J R, Marron J C, Schulz T J, Seldin J H. Hubble Space telescope characterized by using phase-retrieval algorithms[J]. Applied Optics,1993,32(10): 1747~1767.
[78] Roddier C, Roddier F. Combined Approach to the Hubble Space Telescope Wavefront Distortion Analysis[J]. Applied Optics,1993,32(10):2992~3008.
[79] Lyon R,Miller P E,Grusczak A. Hubble Space Telescope Phase Retrieval: A Parameter Estimation[C].Proc.SPIE,1991,1567:317.
[80] Krist J E, Burrows C J. Phase Retrieval Analysis of pre and post-repair Hubble Space Telescope images [J]. Applied Optics,1995,34:4951~4964.
[81] Crocker J H, Ford H C, Hartig G F, Jedrzejewski R I. Optical performance of the Corrective Optics Space Telescope Axial Replacement (COSTAR)[C]. Proc. SPIE,1994,2198:1170~1180.
[82] Hasan H. Pre-COSTAR status of OTA focuses[C]. Instrument Science Report, Baltimore, 1993, 12, OTA-14.
[83] Sabelhaus P A, Campbell D, Clampin M, Decker J, et al.An overview of the James Webb Space Telescope (JWST) project [C].Proc. SPIE, 2005, 5899:0P.
[84] Redding D, Basinger S, Lowman A, Shi F,et al. Wavefront Sensing and Control for a Next Generation Space Telescope[C].Proc. SPIE, 1998,3356:758~772.
[85] Lowman Andrew E, Redding David C, et al. Phase Retrieval Camera for Testing NGST Optics[C], Proc.SPIE, 2003,4850:329~335.
[86] Acton D S, Atcheson P D, Cermak M, Kingsbury L K, Shi F, Redding D C. James Webb Space Telescope Wavefront Sensing and Control Algorithms[C]. Proc. SPIE, 2004,5487:887~896.
[87] Smith J S, Dean B H, Haghani S. Distributed Computing architecture for image-based Wavefront Sensing and 2D FFTs[C]. Proc.SPIE,2006,6274: 21-1~ 21-10.
[88] Dean B H, Smith J S, Budinoff J G, Feinberg L. Wavefront Sensing and Control Architecture for SPOT (Spherical Primary Optical Telescope)[C].Proc.SPIE, 2006,6265:4F-1~4F-10.
[89] Catherine Ohara,Scott Basinger,David Cohen,Jessica Faust, et al. Phase Retrieval Camera Testing of the Ball AMSD Mirror[R].Mirror Technology Days,Huntsville, AL,2006.
[90] Ellerbroek B L, Thelen B J, Lee D J, Carrara D A, et al. Comparison of Shack- Hartmann wavefront sensing and phase-diverse phase retrieval[C].Proc.SPIE, 3126:307~320.
[91] Walther A.The Question of Phase Retrieval in Optics. Opt. Acta,1963,10:41~49.
[92] Misell D L. A method for the solution of the phase problem in electron microscopy [J]. Applied Physics,1973,D6:L6~L9.
[93] Fienup J R. Phase retrieval algorithms: a comparison [J].Applied Optics, 1982, 21(15):2758~2760.
[94] Bruel Laurent. Numerical Phase retrieval from beam intensity measurements in three planes[C]. Proc.SPlE,2003,4932:590~598.
[95] Ivanov V Yu,Sivokon V P,Vorontsov M A. Phase retrieval from a set of intensity measurements:theory and experiment[J]. J.Opt.Soc.Am.A,1992,9(9):515~1524.
[96] Pedrini G,Osten W,Zhang Y.Wave-front reconstruction from a sequence of interferograms recorded at different planes [J].Optics Letters,2005,30:833~835.
[97] Zhang Y,Pedrini G, Osten W, Tiziani H. Whole optical wave field reconstruction from double or multi inline holograms by phase retrieval algorithm [J].Optics Express, 2003,l (11):3234~3241.
[98] Mcalister D F, Beck M, Clarke L, et al. Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms [J]. Optics Letters,1995,20 (10):1181~1183.
[99] M. Gunhan Ertosun, Haluk Ath, Haldun M. Ozaktas et al .Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence [J]. Optics Communications,2005,244:61~70.
[100] Fienup J R. Phase retrieval for undersampled broadband images [J]. J. Opt. Soc. Am. A,1999,16(7):1831~1837.
[101] ShizhuoYin, Mingzhe Lu, Chu lung Chen, et al. Design of a bipolar composite filter by a simulated annealing algorithm[J]. Optics Letters,1995,20(12):1409 ~1411.
[102] Gia-Wei Chem,Lon A Wang. Design of binary long-period fiber grating filters by the inverse scatering method with genetic algorithm optimization[J]. J.Opt.Soc.Am.A, 2002,19(4):772~780.
[103] Guangya Zhou,Yixin Chen, Zong guang Wang, et al. Genetic local search algorithm for optimization design of diffractive optical elements[J]. Applied Optics,1999,38(20):4281~ 4290.
[104] Myung Soo Kim, Clark C .Guest. Simulated annealing algorithm for binary phase only filters in patern classification [J].Applied Optics,1990,28(8):1203~ 1208.
[105] Millane R P, Stroud W J. Reconstructing symmetric images from theirundersampled Fouier intensities [J]. J. Opt. Soc. Am. A,1997,14(3):568~579.
[106] Jefferies Stuart M, Lloyd-Hart Michael, Hege E Keith, Georges James. Sensing wave-front amplitude and phase with phase diversity [J]. Applied Optics,2002, 41(11):2095~2102.
[107] Brady G R, Fienup J R.Nonlinear optimization algorithm for retrieving the full complex pupil function [J]. Optics Express, 2006,14(2):474~486.
[108] Cohen D,Redding D C. NGST high dynamic range unwrapped phase estimation [C]. Proc.SPIE, 2003,4850:336~344.
[109] Dean B H, Aronstein D L, et al, Phase Retrieval Algorithm for JWST Flight and Testbed Telescope[C]. Proc.SPIE, 2006, 6265:11-1~11-17.
[110] Roddier F,Roddier C.Wavefront reconstruction using iterative Fourier transforms [J]. Applied Optics,1991,30(11):1325~1327.
[111] Roddier C, Roddier F.Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes[J]. J. Opt. Soc. Am. A,1993,10(11): 2277~2287.
[112] Yang G Z, Dong B Z, Gu B Y, Zhuang J, Ersoy O K. Gerchbeg-Saxton and Yang-Gu algorithm for phase retrieval in a nonunitary transform system: a comparison [J]. Applied Optics,1994,33:209~218.
[113] Dong Bizhen , Zhang Yan , Gu Benyuan et al. Numerical investigation of phase retrieval in afractional Fourier transform[J]. J. Opt. Soc. Am. A,1997,14(10): 2709~2714.
[114] Cong Wenxiang, Chen Nanxian, Gu Benyuan. Recursive algorithm for phase retrieval in the fractional Fourier transform domain[J]. Applied Optics,1998,37 (29):6906~6910.
[115]曾发,谭峭峰,魏晓峰,向勇等.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.
[116]曾发,谭峭峰,魏晓峰,向勇等.基于多个分数阶次的复杂光场相位恢复算法[J].中国激光,2006,33(12):1621~1625.
[117] Mao Heng, Wang Xiao, Zhao Dazun. Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics[J].Chinese Optics Letters,2007,5(7):397~399.
[118]毛珩,王潇,赵达尊.复杂光瞳波前相位恢复算法与实验验证[J].光学学报,2009,29(3):575~581.
[119]李强,沈忙作.基于相位差方法的天文目标高分辨率成像研究[J].天文学报,2007,48(1):113~120.
[120]李强,沈忙作.利用相位差法测量望远镜像差[J].光学学报,2007,27(9):1554~ 1557.
[121] Talor C A,Thompson B J. Attempt to investigate experimently the intensity distribution near the focus in the error-free diffraction patterns of circular and annular apertures[J]. J. Opt. Soc. Am.A,1958,48:844~850.
[122]蒋筑英,李剑白等.光学系统成像质量评价及检验文集[C].北京中国计量出版社,1988:191~203.
[123] Welford W T. Use of Annular Apertures to Increase Focal Depth [J]. J. Opt. Soc. Am. A ,1960,50(8):749~753.
[124] Brady G R. Application of Phase Retrieval to the Measurement of Optical Surfaces and Wavefronts[D]. New York: University of Rochester,2008.
[125] Brady G R, Manuel Guizar-Sicairos, Fienup J R. Phase retrieval as an optical metrology tool[C]. Proc.SPIE,2005,TD03:139~141.
[126] Brady G R,Fienup J R.Range of phase retrieval in optical metrology [J]. Applied Optics, 2009, 48(3):442~449.
[127] Brady G R, Manuel Guizar-Sicairos, Fienup J R. Optical wavefront measurement using phase retrieval with transverse translation diversity[J]. Optics Express, 2009,17(2):624~ 639.
[128] Brady G R, Fienup J R. Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology[C]. Proc.SPIE,6617:0I-1~0I-8.
[129]胡晓军.大型光学镜面相位恢复在位检测技术研究[D].长沙:国防科学技术大学,2008.
[130] Sheng Yi Li, Xiao Jun Hu, Yulie Wu. Resolution enhancement phase retrieval with sub-pixel method[J].Applied Optics, 2009,47(32):6079~6087.
[131] Goodman J W. Introduction to Fourier optics [M]. 3rd ed. Roberts and Company Publishers, 2005:50~55.
[132]邹谋炎.反卷积和信号复原[M].北京:国防工业出版社,2001.
[133] Barakat R, Newsam G. Necessary conditions for a unique solution to two- dimension phase recovery [J]. Math.Phys.,1984,25:3190~3193.
[134] Bruck Y M, Sodin L G. On the ambiquity of the image reconstruction problem [J]. Optis Communications,1979,30:304~308.
[135] Fiddy M A, Brames B J, Dainty J C.Enforcing irreducibility for phase retrieval in two dimensions [J]. Optics Letters,1983,8:96~98.
[136] Brames B J. Unique phase retrieval with explicit support information [J]. Optics Letters,1986,11:61~63.
[137] Seldin J H, Fienup J R. Numerical investigation of the uniqueness of phase retrieval [J]. J. Opt. Soc. Am. A,1990,7(3):412~427.
[138] Fienup J R, Wackerman C C. Phase-retrieval stagnation problems and solutions [J]. J. Opt. Soc. Am. A,1986,3(11):1897~1907.
[139] Lee D J,Roggemann N C, Welsh B M. Cramer-Rao analysis of phase-diversewave-front sensing[J], J. Opt. Soc. Am. A,1999,16:1005~1015.
[140] Cederquist J N, Robinson S R,et al.Cramer-Rao lower bound on wavefront sensor error[J].Optical Engineering,1986,25:586~592.
[141] Cederquist J N, Wackerman C C. Phase-retrieval error: a lower bound [J]. J. Opt. Soc. Am. A,1987,4:1788~1792.
[142] Dean B H, Charles W. Bowers. Diversity selection for phase diverse phase retrieval [J]. J. Opt. Soc. Am. A, 2003,20(8):1490~1504.
[143] Green J J, Dean B H, Ohara C M, Redding D C, et al. Target selection and imaging requirements for JWST fine phasing[C].Proc.SPIE,2004,5487:944 ~953.
[144]索尼推出全新1420万像素1/2.3英寸CCD[Z].http:\\www.xinhuanet.com.
[145]徐文东,干福熹.测量大数值孔径光学系统小光斑的方法[J].中国激光, 2003,30(2):171~174.
[146] Sziklas Edward A, Siegman A E. Diffraction Calculations Using Fast Fourier Transform Methods [J]. Proceedings Letters,1974,3:410~412.
[147]吴冬良.确定性光学加工条件下制造误差的特性研究[D].长沙:国防科学技术大学,2009.
[148] Ghiglia D C, Pritt M D.Two-dimensional phase unwrapping theory, algorithms and software[M]. New York: Wiley-Interscience, 1998.
[149] Karout S A, Gdeisat M A, Burton D R, Lalor M J. Residue Vector, An Approach To Branch-Cut Placement In Phase Unwrapping: Theoretical Study[J]. Applied Optics, 2007, 46(21):4712~4727.
[150]吕海宝.激光光电检测[M].长沙:国防科技大学出版社, 2000.
[151]王庆有.CCD应用技术[M].天津:天津大学出版社, 2000.
[152] F-145B/F-145C,AVT Dolphin Manual [Z].Germany: Allied Vision Technologies GmbH, 2003.
[153] Debevec P E,Malik J. Recovering high dynamic range radiance maps from photographs[C].SIG-GRAPH 97 Conference Proceedings, New York: ACM, 1997:369~378.
[154] Gonzalez-Moreno G, Quiroga J A, Alonso J, et a1.Laser beam profiling with extended image range techniques[J].Optical Engineering,2005,44(2):02360.
[155]周建康,沈为民,唐敏学.CCD测量动态范围的扩展技术[J].光电工程, 2006,33(10):96~110.
[156] Thurman S T, Fienup J R. Phase retrieval with signal bias [J]. J. Opt. Soc. Am. A, 2009,26(4):1008~1014.
[157]马科斯.波恩,埃米尔.沃尔夫著,杨葭荪等译.光学原理(上册)[M].北京:电子工业出版社,2005.
[158] Wyant J C, Creath K.Apllied optics and optical engineering Vol.XI:Basicwavefront aberration theory for optical metrology[M]. New York:Academic press, 1992.
[159] ICX285AL: Diagonal 11 mm (Type 2/3) Progressive Scan CCD Image Sensor with Square Pixel for B/W Cameras [Z]. Sony Corporation.
[160] Cook L G. Three-mirror anastigmat used off-axis in aperture and field [C]. Proc.SPIE,1979,183:207~211.
[161]李俊昌.激光的衍射和热作用[M].北京:科学出版社,2002.
[162] Pedro Arguijo and Marija Strojnik Scholl. Exact ray-trace beam for an off-axis paraboloid surface [J]. Applied Optics,2003,42(16):3284~3289.
[163] Dresel T, Lindlein N, Schwider J.Empirical strategy for detection and removal of misalignment aberrations in interferometry [J]. Optik,2001,112:304~308.
[164]郑立功.离轴非球面CCOS加工过程关键技术研究[D].长春:中国科学院研究生院长春光学精密机械与物理研究所,2003.
[165] Burke Jan, Wang Kai, Bramble Adam. Null test of an off-axis parabolic mirror.I. Configuration with spherical reference wave and flat return surface [J]. Optics Express, 2009,17(5):3196~3210.
[166] Lawson J. K., Auerbach J. M., English R. E. et al. NIF optical specifcations - the importance of the RMS gradient[R].LLNL Report UCRL-JC-130032,1998:7~12.
[167]周仁忠.自适应光学[M].北京:国防工业出版社,1996.
[168] Alan V Oppenheim等著,刘树棠译.信号与系统[M].西安:西安交通大学出版社,2002.
[169]柯略帕洛娃,浦连耶夫著,徐德衍,路敦武译.光学系统的研究与检验[M].北京:机械工业出版社,1983.
[170]刘文耀等.光电图像处理[M].北京:电子工业出版社,2002.
[171] Almoro P, Pedrini G, Osten W. Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field[J]. Applied Optics, 2006,45:8596~8605.