非球面非零位环形子孔径拼接干涉检测技术与系统研究
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摘要
随着光学工程学科的不断发展,非球面光学元件越来越多地应用到国民经济的各个方面。然而,在设计、加工、检测和装调等各个环节之中,非球面面形的高精度检测已经成为制约其应用的最主要因素。本文研究了可用于深度非球面和非球面波前高精度检测的非零位环形子孔径拼接干涉(非零位ASSI)检测技术和系统。
     提出了利用非球面波前拼接检测非球面的ASSI技术。其基本原理是在Twyman Green干涉系统中,利用补偿系统(PCS)出射的非球面波前部分补偿被测非球面,通过轴向移动非球面,实现不同环带的拼接检测。为了进行系统仿真,提出了基于光学设计软件或自编光线追迹的系统仿真方法。系统中,被测非球面环形子孔径的边界和重叠区可以利用像面波前斜率的方法确定。实验采集的多帧移相干涉图,可以利用经典的移相算法进行位相解调,并自动确定有效孔径;采集的单帧闭环条纹干涉图,可以利用提出的路径无关相位跟踪(PIRPT)或多项式相位拟合(PPF)算法进行位相解调。解调位相可以利用Zernike多项式进行正交波前分解。
     研究了非零位ASSI系统原理误差(即回程误差)校正和子孔径拼接问题。提出了系统的传递函数模型,揭示了系统回程误差校正的实质,即逆问题求解。提出了多孔径逆向优化(ROR)和理论参考波前(TRW)两种回程误差校正算法。前者的基本思想是非线性优化,后者的基本思想则是波前的加减。对于校正回程误差后的各独立子孔径数据,可以利用拼接算法重构被测非球面的完整面形。误差分析表明,多孔径ROR和TRW算法理论误差的峰谷(PV)值分别优于λ/1000和λ/20,拼接算法误差的PV值优于λ/1000。
     研究了非零位ASSI系统中的关键性误差。分析了除上述回程误差和软件误差外的四种硬件误差,分别是PCS的1)模型误差和2)对准误差;非球面的3)定位误差和4)对准误差。1)提出了PCS模型误差的校准指标,即折射率误差小于e-5、厚度误差小于5μm)曲率半径相对误差小于0.005%;2)提出了基于辅助平板和辅助球面的PCS对准方法,可以将其倾斜和偏心误差分别控制在±10"和±6μm内;3)提出了基于组合消球差镜或像面波前离焦量的非球面定位方法,可以将其定位误差控制在±6μm内;4)提出了基于像面波前倾斜和慧差的非球面对准方法,可以将其倾斜和偏心误差分别控制在±2"和±5μm内。
     实验验证了非零位ASSI技术的正确性和系统的检测精度。利用非零位ASSI系统对3块抛物非球面(其中2块与顶点球最大偏离56.5μm,另1块最大偏离9.0μn)进行了子孔径拼接和无拼接检测实验。其检测结果与无像差点法和Zygo公司Verifire干涉仪检测结果一致,PV值偏差小于λ/10,均方根(RMS)值偏差小于λ/50。这证明ASSI系统具有较高的检测精度、较强的检测能力和较大的动态检测范围。
     本文以理论和实验并重,重点研究了非零位ASSI系统中的理论基础和主要误差问题,并进行了实验验证。考虑到日益增长的非球面应用范围,非零位ASSI检测系统潜存着巨大的经济效益,将有力推动我国乃至世界非球面面形检测技术的发展。
Although the design, fabrication and assembly techniques of aspheres have made considerable developments, general and accurate measurement of aspheres is difficult and continues to be a challenge. I combined the two concepts of non-null testing and subaperture stitching and developed non-null annular subaperture stitching interferometry (non-null ASSI), which has much larger dynamic range and can be used to measure steep aspheres or aspheric wavefronts.
     The concept and principle of the non-null ASSI are proposed. Based on the Twyman-Green interferometer, aspheric wavefront emerging from the diverging lens (PCS) partially compensates for aberrations of normals of the asphere under test. Annular subaperture with different radii can be measured by translating the asphere along the optical axis. Simulation methods of the system based on optical design software or home-made raytracing codes are proposed. The boundaries and overlapping areas of subapertures of the asphere are determined by the slope of the wavefront on the detector. For multi-frame phase-shifted interferograms acquired, the well-known four step formula is used to demodulated the phase while for single-frame interferograms with closed fringes, the proposed path-independent regularized phase-tracking (PIRPT) or polynomial-based phase-fitting (PPF) techniques is employed. The extracted phase is decomposed by Zernike polynomials for further analysis.
     The calibration of retrace error of the non-null ASSI is extensively investigated. A transfer function model is proposed and the calibration procedure is understood as to find its inverse solution. Two practical algorithms are proposed, i.e., synthetically reverse optimization reconstruction (ROR) and theoretical reference wavefront (TRW). The former attempts to find the solution by nonlinear optimization while the latter by wavefronts subtraction. Residual wavefront errors after calibration by both methods are typically smaller than λ/1000(peak to valley, PV) and λ/20, respectively. The subaperture stitching process is introduced to reconstruct full-aperture figure shape of the asphere from subaperture data with retrace error removal. Numerical experiments show its accuracy is better than λ/1000.
     The errors of the non-null ASSI are systematically analyzed. Besides the retrace error and software errors mentioned above, four hardware errors are analyzed with emphasis, i.e.,1)model errors and2)alignment errors of the PCS,3)position error and4) alignment errors of the asphere. For1),(relative) errors of refractive indices, thicknesses and curvatures are required to be no greater than e-5,5um and0.005%, respectively. For2), adjustment methods based on auxiliary parallel plate and sphere are proposed, which can respectively minimize tilt and decenter errors of the PCS within10" and6μm. For3), two methods based on aplanatic lens or defocus of the wavefront are proposed, which can both control the error within10μm. For4), adjustment method based on tilt and coma of the wavefront is proposed and can reduce tilt and decenter errors to2" and5um.
     Finally, the correctness and measurement precision of the non-null ASSI are experimentally demonstrated. Three paraboloids (two with departure from the vertex sphere56.5um and one9.0um) were measured by the non-null ASSI with and without subaperture stitching. The results agree well with those by the stigmatic null test and Zygo Verifire interferometer. The PV and root mean square (RMS) values of the deviations of all the results are smaller than λ/10and λ/50, respectively. The results show the non-null ASSI has good measurement precision, strong measurement ability and great dynamic range.
     In summary, the paper investigated the non-null ASSI from both theory and experiment. Since aspheres are increasingly being used nowadays, the non-null ASSI has potential huge economic benefits and will greatly promote the progress of aspheric testing.
引文
1.H. P. Stahl, "Aspheric surface testing techniques," in OSA Trends in Optics and Photonics (Optical Society of America, 1999), T2.
    2.D. Malacara, Optical Shop Testing, 3 ed. (John Wiley & Sons, 2007).
    3. 张淑娜,”光学薄膜相位特性测试的研究,”硕士学位论文(浙江大学,2011).
    4."Aspherical Lenses",retrieved 03/15, 2013, http://www.nikon.com/about/technology/rd/core/optics/aspherical_lenses_e/index.htm.
    5.C. C. A. Chen, J. C. Tang, L. M. Teng, "Effects of Mold Design of Aspheric Projector Lens for Head Up Display," in Polymer Optics Design, Fabrication, and Materials, D. H. Krevor and W. S. Beich, eds. (2010).
    6.C.-M. Tsai, Y.-C. Fang, "Improvement of Petzval field curvature in projector lens optimization design," in 2012 International Symposium on Photonics and Optoelectronics, SOPO 2012, May 21, 2012-May 23, 2012, 2012 Symposium on Photonics and Optoelectronics, SOPO 2012 (IEEE Computer Society, 2012), IEEE Photonics Society; IEEE Wuhan Section; Optics and Photonics Society of Singapore; Wuhan University; Beijing Jiaotong University.
    7.A. Eckardt, B. Braunecker, R. Sandau, "Performance of the imaging system in the LH Systems—ADS40 Airborne Digital Sensor," International Archives of Photogrammetry and Remote Sensing 33(2000).
    8.N. Zhao, J. Chang, Z. Sun, Y. Wang, "Summarize of conformal optics," in International Symposium on Photoelectronic Detection and Imaging 2007-' Optoelectronic System Design, Manufacturing, and Testing, L. Zhou, ed. (2008), pp. N6241-N6241.
    9.W. Ulrich, H.-J. r. Rostalski, R. Hudyma, "Development of dioptric projection lenses for deep ultraviolet lithography at Carl Zeiss," Journal of Micro/Nanolithography, MEMS, and MOEMS 3, 87-96 (2004).
    10.W. Ulrich, H.-J. Rostalski, R. Hudyma, "The development of dioptric projection lenses for DUV lithography," in International Optical Design Conference 2002, June 3, 2002- June 5, 2002, Proceedings of SPIE - The International Society for Optical Engineering (SPIE, 2002), 158-169.
    11.J. M. Hill, P. Salinari, "The Large Binocular Telescope Project," in Advanced Technology Optical/Ir Telescopes Vi, L. M. Stepp, ed. (1998), pp. 23-33.
    12.X.-Q. Cui, Y.-H. Zhao, Y.-Q. Chu, e. al, "The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)," Research in Astronomy and Astrophysics 12, 1197 (2012).
    13.L. Feinberg, M. Wilson, "Hubble Space Telescope COSTAR asphere verification with a modified computer generated hologram interferometer," Appl. Opt. 32, 1786-1788 (1993).
    14.W. Kordonski, S. Gorodkin, "Material removal in magnetorheological finishing of optics," Appl. Opt. 50, 1984-1994 (2011).
    15. D. Golini, P. Dumas, W. Kordonski, S. Hogan, S. Jacobs, Aspe, Precision optics fabrication using magnetorheological finishing, Proceedings of the Thirteenth Annual Meeting of the American Society for Precision Engineering (1998), pp.597-597.
    16. 肖冰,”大口径光学元件表面疵病自动化检测系统关键问题讨论与研究,”硕士学位论文(浙江大学,2010).
    17. 肖冰,杨甬英,高鑫,刘东,王道档,卓永模,”适于大口径精密光学表面疵病图像的拼接算法,”浙江大学学报(工学版)v.45;No.250,375-381(2011).
    18. 杨甬英,陆春华,梁蛟,刘东,杨李茗,李瑞洁,”光学元件表面缺陷的显微散射暗场成像及数字化评价系统,”光学学报No.303,1031-1038(2007).
    19. 徐建程,”高分辨率波前干涉检测技术研究,”硕士学位论文(中国工程物理研究院,2006).
    20. 徐建程,”相位干涉测量的信息理论分析,”博士学位论文(中国工程物理研究院,2009).
    21. 许乔,”光学元件高精度波前检测分析,”in第六届全国激光科学技术青年学术交流会,2001),4.
    22. "Taylor Hobson", retrieved 03/15,2013, http://www.taylorhobson.com.
    23. "3D Optical Surface Profilers " (Zygo), retrieved 03/15,2013, http://www.zygo.com/?/met/profilers/.
    24. P. J. Scott, "Recent developments in the measurement of aspheric surfaces by contact stylus instrumentation," in Optical Design and Testing, Z. H. Weng, J. M. Sasian, and Y. T. Wang, eds. (2002), pp.199-207.
    25. "Coordinate measuring machines for the measuring room ", retrieved 03/15,2013, http://www.leitz-metrology.com/CMMs---Measuring-Room_538.htm.
    26. C. Tian, Y. Yang, T. Wei, Y. Zhuo, "Nonnull interferometer simulation for aspheric testing based on ray tracing," Appl. Opt.50,3559-3569 (2011).
    27. ISO, "Part 12:Surface form tolerances," in Optics and photonics-Preparation of dra wings for optical elements and systems, (2007).
    28. E. Abbe, "Lens System," US697959 (1899).
    29. G. W. Forbes, "Shape specification for axially symmetric optical surfaces," Opt. Express 15,5218-5226 (2007).
    30. G. W. Forbes, C. P. Brophy, "Asphere, O Asphere, how shall we describe thee?," in Optical Design and Engineering Iii, Pts 1 and 2, L. Mazuray, R. Wartmann, A. Wood, J. L. Tissot, and J. M. Raynor, eds. (2008).
    31. 陆永贵,杨建东,”光学非球面度的探讨,”长春理工大学学报,16-18(2005).
    32. 高宏,辛企明,李爱民,黄开祥,”非球面干涉测量方法的原理误差分析,”应用光学,61-64(1993).
    33. 辛企明,光学塑料非球面制造技术(国防工业出版社,2005).
    34. B. Braunecker, R. Hentschel, H. J. Tiziani, Advanced Optics Using Aspherical Elements (SPIE,2008).
    35. E. Heynacher, "ASPHERIC OPTICS-HOW THEY ARE MADE AND WHY THEY ARE NEEDED," Physics in Technology 10,124-131 (1979).
    36. 辛企明,近代光学制造技术(国防工业出版社,1997).
    37. 张坤领,林彬,王晓峰,”非球面加工现状,”组合机床与自动化加工技术No.399,1-5+10(2007).
    38. 庞长涛,罗松保,”非球面加工先进技术,”航空精密制造技术,1-5(2001).
    39. D. P. Spector, J. M. Kingsbury, "Fabrication of thermoplastic optical components by injection/compression molding," US4836960 (1987).
    40. 王勤,余景池,胡祖元,”非球面复制成型技术的研究,”光学技术,121-123(2006).
    41. 普里亚耶夫,光学非球面检验(1980).
    42. R. R. Rigby, "NEW DEVELOPMENTS IN OPTICAL FABRICATION TECHNIQUES," Optical Engineering 14,145-148 (1975).
    43. "SCG 600·Grinding of large flats, spheres and aspheres" (Schneider), retrieved 03/15, 2013,http://www.schneider-om.com/products/precision-optics/gvinding/scg-600.html.
    44. T. Cao, J. Zhang, "Computer-controlled polishing of aspheric surfaces," in (SPIE,1992), 60-65.
    45. F. W. Preston, "The Theory and Design of Plate Glass Polishing Machines," J. Glass Tech. 11(1927).
    46. "SLP 301" (Schneider), retrieved 03/15,2013, http://www.schneiderom.com/prod ucts/precision/optics/polishing/slp-301.html.
    47. D. C. Harris, "History of magnetorheological finishing," in Window and Dome Technologies and Materials XII, April 27,2011-April 28,2011, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2011), The Society of Photo-Optical Instrumentation Engineers (SPIE).
    48. W. I. Kordonsky, I. V. Prokhorov, S. R. Gorodkin, G. R. Gorodkin, L. K. Gleb, B. E. Kashevsky, "Magnetorheological polishing devices and methods," 5449313 (1993).
    49. 张峰,余景池,张学军,王权陡,”磁流变抛光技术,”光学精密工程,1-8(1999).
    50. 彭小强,戴一帆,李圣怡,”磁流变抛光的材料去除数学模型,”机械工程学报,67-70(2004).
    51. 孙希威,张飞虎,董申,康桂文,”磁流变抛光去除模型及驻留时间算法研究,”新技术新工艺,73-75(2006).
    52. 张云,冯之敬,赵广木,”磁流变抛光工具及其去除函数,”清华大学学报(自然科学版),190-193(2004).
    53. 王小鹏,朱日宏,王雷,许荣国,”数字刀口仪定量检验非球面光学元件面形,”光学学报v.31;No.346,148-151(2011).
    54. 张金平,”夏克—哈特曼波前传感器检测大口径非球面应用研究,”博士学位论文(中国科学院研究生院(长春光学精密机械与物理研究所),2012).
    55. 雷柏平,伍凡,陈强,”大口径非球面Ronchi光栅测量方法,”光电工程No.209,140-144(2007).
    56. 贾世奎,李成贵,杨辉,张庆荣,“非球而光学元件面形检测方法,”上海计量测试v.36;No.213,2-6(2009).
    57. 丁凌艳,”非球面相位恢复检测技术研究,”博士学位论文(国防科学技术大学,2011).
    58. 满玉春,”基于数字莫尔条纹的非球面检测技术研究,”博士学位论文(中国科学院研究生院(长 春光学精密机械与物理研究所),2011).
    59. R. Schreiner, J. Schwider, N. Lindlein, K. Mantel, "Absolute testing of the reference surface of a Fizeau interferometer through even/odd decompositions," Appl. Opt.47, 6134-6141 (2008).
    60. 郭培基,”补偿法检测非球面的若干关键技术研究,”博士学位论文(中国科学院长春光学精密机械与物理研究所,2000).
    61. A. Offner, "A Null Corrector for Paraboloidal Mirrors," Appl. Opt.2,153-155 (1963).
    62. H. E. Dall, "A Null Test for Paraboloids," J. Br. Astron. Assoc.57(1947).
    63. A. J. MacGovern, J. C. Wyant, "Computer Generated Holograms for Testing Optical Elements," Appl. Opt.10,619-624 (1971).
    64. B. R. Brown, A. W. Lohmann, "Complex Spatial Filtering with Binary Masks," Appl. Opt. 5,967-969 (1966).
    65. K. S. Urquhart, S. H. Lee, C. C. Guest, M. R. Feldman, H. Farhoosh, "Computer aided design of computer generated holograms for electron beam fabrication," Appl. Opt.28, 3387-3396 (1989).
    66. P. Zhou, J. H. Burge, "Fabrication error analysis and experimental demonstration for computer-generated holograms," Appl. Opt.46,657-663 (2007).
    67. "Diffraction International", retrieved 03/15,2013, http://www.diffraction.com/.
    68. "Jenoptik", retrieved 03/15,2013, http://www.jenoptik.com/en home.
    69. J.-B. Song, H.-S. Yang, H.-G. Rhee, Y.-W. Lee, "Modified alignment CGHs for aspheric surface test," in Optical Manufacturing and Testing Ⅷ, August 4,2009-August 5, 2009, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2009), The International Society for Optical Engineering (SPIE).
    70. "Zygo Corporation", retrieved 03/15,2013, http://www.zygo.com/?/met/interferometers/gpi/.
    71. B. Dorband, H. J. Tiziani, "Testing aspheric surfaces with computer-generated holograms:analysis of adjustment and shape errors," Appl. Opt.24,2604-2611 (1985).
    72. 卢振武,刘华,李凤有,“利用曲面计算全息图进行非球面检测,”光学精密工程,555-559(2004).
    73. 刘华,”利用曲面计算全息图检测非球面,”博士学位论文(中国科学院研究生院(长春光学精密机械与物理研究所),2006).
    74. 刘亮,”基于离轴型CGH的非球面检测技术研究,”硕士学位论文(南京理工大学,2009).
    75. 洪小苗,”双CGH检测凸非球面研究,”硕士学位论文(苏州大学,2012).
    76. 庞永杰,”计算全息法检测凹非球面研究,”硕士学位论文(昆明理工大学,2008).
    77. J. E. Greivenkamp, R. O. Gappinger, "Design of a Nonnull Interferometer for Aspheric Wave Fronts," Appl. Opt.43,5143-5151 (2004).
    78. J. E. Greivenkamp, "Sub-Nyquist interferometry," Appl. Opt.26,5245-5258 (1987).
    79. T. Wu, J. D. Valera, A. J. Moore, "High-speed, sub-Nyquist interferometry," Opt. Express 19,10111-10123 (2011).
    80. O. Kwon, J. C. Wyant, C. R. Hayslett, "Rough surface interferometry at 10.6μm," Appl. Opt.19,1862-1869 (1980).
    81. J. C. Wyant, K. Creath, "Two-wavelength phase-shifting interferometer and method," US4832489 (1980).
    82. B. E. Truax, "PROGRAMMABLE INTERFEROMETRY," in Surface Characterization and Testing., Proceedings of SPIE-The International Society for Optical Engineering (SPIE,1986),10-18.
    83. D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, Y. Zhuo, "Non-null interferometric aspheric testing with partial null lens and reverse optimization," in Optical Manufacturing and Testing VIII, August 4,2009-August 5,2009, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2009), The International Society for Optical Engineering (SPIE).
    84. D. Liu, Y. Yang, C. Tian, L. Wang, Y. Zhuo, "Non-null interferometric system for general aspheric test," in 4th International Symposium on Advanced Optical Manufacturing and Testing Technologies:Optical Test and Measurement Technology and Equipment, November 19,2008-November 21,2008, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2009), The Chinese Optical Society (COS); CAS, The Institute of Optics and Electronics (IOE); State Key Laboratory of Optical Technology for Microfabrication; Sichuan Optical Society (SOS).
    85. C. Tian, Y. Yang, Y. Zhuo, "Generalized data reduction approach for aspheric testing in a non-null interferometer," Appl. Opt.51,1598-1604 (2012).
    86. 刘惠兰,郝群,朱秋东,沙定国,“利用部分补偿透镜进行非球面面形测量,”北京理工大学学报,625-628(2004).
    87. 孟晓辰,郝群,朱秋东,胡摇,“基于Zemax的部分补偿透镜的优化设计,”光学学报,222-228(2011).
    88. E. Garbusi, C. Pruss, W. Osten, "Interferometer for precise and flexible asphere testing," Opt. Lett.33,2973-2975 (2008).
    89. Y.-M. Liu, G. N. Lawrence, C. L. Koliopoulos, "Subaperture testing of aspheres with annular zones," Appl. Opt.27,4504-4513 (1988).
    90. M. Melozzi, L. Pezzati, A. Mazzoni, "Testing aspherical surfaces using multiple annular interferograms," in Specification and Measurement of Optical Systems, September 14, 1992-September 16,1992, Proceedings of SPIE-The International Society for Optical Engineering (Publ by Int Soc for Optical Engineering,1992),232-240.
    91. J. Liesener, H. J. Tiziani, "Interferometer with Dynamic Reference," in Optical Fabrication, Testing, and Metrology, September 30,2003-October 3,2003, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2004),264-271.
    92. X. Wang, L. Wang, L. Yin, B. Zhang, D. Fan, X. Zhang, "Measurement of large aspheric surfaces by annular subaperture stitching interferometry," Chin. Opt. Lett.5,645-647 (2007).
    93. M. F. Kuchel, "Interferometric measurement of rotationally symmetric aspheric surfaces," in Optical Measurement Systems for Industrial Inspection Ⅵ, June 15,2009 June 18,2009, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2009), SPIE Europe.
    94. P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, "Stitching Interferometry:A Flexible Solution for Surface Metrology," Opt. Photon. News 14,38-43 (2003).
    95. M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, P. Murphy, "Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null," Cirp Annals-Manufacturing Technology 59, 547-550 (2010).
    96. 朱黎明,”基于子孔径拼接的非球面检测方法研究,”硕士学位论文(哈尔滨工业大学,2009).
    97. 张蓉竹,“ICF系统光学元件高精度波前检测技术研究,”博士(四川大学,2003).
    98. M. Kuechel, "Absolute Measurement of Rotationally Symmetric Aspheric Surfaces," in OSA Technical Digest (CD) (Optical Society of America,2006), OFTuBS.
    99. M. Kuchel, "Scanning interferometer for aspheric surfaces and wavefronts," US 7218403 B2 (2007).
    100. J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes, "An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces," in Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies, August 3,2003-August 5,2003, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2003),296-307.
    101. P. Murphy, G. Devries, J. Fleig, G. Forbes, A. Kulawiec, D. Miladinovic, "Measurement of high-departure aspheric surfaces using subaperture stitching with variable null optics," in Optical Manufacturing and Testing Ⅷ, August 4,2009-August 5,2009, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2009), The International Society for Optical Engineering (SPIE).
    102. A. Kulawiec, P. Murphy, M. DeMarco, "Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VON)," in 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies-Advanced Optical Manufacturing Technologies, April 26,2010-April 29,2010, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2010), The Chinese Optical Society (COS); CAS, The Institute of Optics and Electronics (IOE); The Society of Photo-Optical Instrumentation Engineers (SPIE).
    103. 韦涛,”非球面环形子孔径拼接检测方法及高精度定位方法研究,”硕士学位论文(浙江大学2013).
    104. X. Hou, F. Wu, L. Yang, S. Wu, Q. Chen, "Full-aperture wavefront reconstruction from annular subaperture interferometric data by use of Zernike annular polynomials and a matrix method for testing large aspheric surfaces," Appl. Opt.45,3442-3455 (2006).
    105. 季波,”子孔径拼接干涉检测非球而光学元件,”硕士学位论文(南京理工大学,2008).
    106. 刘崇,”非球面环形子孔径拼接干涉测试方法研究,”硕士学位论文(南京理工大学,2009).
    107. 刘智颖,“子孔径拼接光学系统的研究,”博士学位论文(长春理工大学,2009).
    108. W. J. Smith, Modern Optical Engineering-The Design of Optical Systems,3rd ed. (McGraw-Hill, New York,2000).
    109. D. Malacara, Z. Malacara, Handbook of Optical Design (Marcel Uekker, Inc., New York, 2004).
    110. D. P. Feder, "Optical Calculations with Automatic Computing Machinery," J. Opt. Soc. Am.41,630-634 (1951).
    111. G. H. Spencer, M. V. R. K. Murty, "General Ray-Tracing Procedure," J. Opt. Soc. Am.52, 672-676 (1962).
    112. 郁道银,谈恒英,工程光学, (机械工业出版社,2000).
    113. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am.66, 207-211 (1976).
    114. 卓永模,包正康,相干计量仪器与技术(浙江大学出版社,1992).
    115. M. Takeda, H. Ina, S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am.72,156-160 (1982).
    116. D. Liu, Y. Yang, L. Wang, Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl. Opt.46,8305-8314 (2007).
    117. 杨甬英,”可用于瞬态激光波前畸变实时检测技术的研究,”博士学位论文(浙江大学,2002).
    118. C. Tian, Y. Yang, D. Liu, Y. Luo, Y. Zhuo, "Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique," Appl. Opt.49,170-179(2010).
    119. M. Servin, J. L. Marroquin, F. J. Cuevas, "Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique," Appl. Opt.36,4540-4548 (1997).
    120. J. A. Quiroga, J. Antonio Gomez-Pedrero, A. Garcia-Botella, "Algorithm for fringe pattern normalization," Optics Communications 197,43-51 (2001).
    121. M. Servin, J. L. Marroquin, F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," J. Opt. Soc. Am. A 18,689-695 (2001).
    122.0. S. Dalmau-Cedeno, M. Rivera, R. Legarda-Saenz, "Fast phase recovery from a single closed-fringe pattern," J. Opt. Soc. Am. A 25,1361-1370 (2008).
    123. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, "Local phase from local orientation by solution of a sequence of linear systems," J. Opt. Soc. Am. A 15,1536-1544 (1998).
    124. F. J. Cuevas, J. H. Sossa-Azuela, M. Servin, "A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm," Optics Communications 203,213-223 (2002).
    125. 刘东,杨甬英,田超,骆永洁,卓永模,“高精度单幅闭合条纹干涉图相位重构技术,”中国激光,531-536(2010).
    126. K. G. Larkin, D. J. Bone, M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc.Am.A18,1862-1870(2001).
    127. K. G. Larkin, "Natural demodulation of two-dimensional fringe patterns.Ⅱ. Stationary phase analysis of the spiral phase quadrature transform," J. Opt. Soc. Am. A 18, 1871-1881 (2001).
    128. M. Servin, J. A. Quiroga, J. L. Marroquin, "General n-dimensional quadrature transform and its application to interferogram demodulation," J. Opt. Soc. Am. A 20,925-934 (2003).
    129. Q. Kemao, S. H. Soon, "Sequential demodulation of a single fringe pattern guided by local frequencies," Optics Letters 32,127-129 (2007).
    130. K. Li, K. M. Qian, "Fast frequency-guided sequential demodulation of a single fringe pattern," Optics Letters 35,3718-3720 (2010).
    131. H. X. Wang, K. Li, Q. Kemao, "Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching," Optics and Lasers in Engineering 49, 564-569 (2011).
    132. H. X. Wang, K. M. Qian, "Frequency guided methods for demodulation of a single fringe pattern," Optics Express 17,15118-15127 (2009).
    133. L. Kai, Q. Kemao, "A generalized regularized phase tracker for demodulation of a single fringe pattern," Opt. Express 20,12579-12592 (2012).
    134. C. Tian, Y. Yang, T. Wei, T. Ling, Y. Zhuo, "Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm," Opt. Lett.36,2318-2320 (2011).
    135. R. Storn, K. Price, "Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization 11,341-359 (1997).
    136. 鄢静舟,雷凡,周必方,高志强,"用Zernike多项式进行波面拟合的几种算法,”光学精密工程,119-128(1999).
    137. 冯婕,白瑜,邢廷文,"Zernike多项式波而拟合精度研究,"光电技术应用,31-34(2011).
    138. 翁俊淼,“非球面检测的若干基础理论研究,”硕士学位论文(浙江大学,2008).
    139. V. N. Mahajan, "Zernike annular polynomials for imaging systems with annular pupils,' J. Opt. Soc. Am.71,75-85 (1981).
    140. R. O. Gappinger, J. E. Greivenkamp, "Iterative Reverse Optimization Procedure for Calibration of Aspheric Wave-Front Measurements on a Nonnull Interferometer," Appl. Opt.43,5152-5161 (2004).
    141. 刘东,”通用数字化高精度非球面干涉检测技术与系统研究,”博士学位论文(浙江大学,2010).
    142. 李晓彤,岑兆丰,几何光学,像差理论与光学系统. (浙江大学出版社,2003).
    143. 白剑,程上彝,“子孔径检测及拼接的目标函数分析法,”光学仪器,36-39(1997).
    144. 程维明,林有略,陈明仪,“多孔径扫描波面恢复技术的精度评定及影响因素,”光学学报,711-716(1993).
    145. 侯溪,伍凡,杨力,吴时彬,陈强,”环形子孔径拼接算法的精度影响因素分析,”光电工程, 20-24(2005).
    146. 刘勇,”高精度球面绝对测量及参考镜校准技术研究,”硕士学位论文(浙江大学,2013).
    147. 彭建华,”干涉法球面面形绝对检测技术研究,”硕士学位论文(浙江大学,2012).
    148. 骆永洁,”非球面部分补偿干涉检测方法的误差分析及系统优化研究,”硕士学位论文(浙江大学,2011).
    149. 王东升,”高精度球面面形绝对检测方法研究,”硕士学位论文(浙江大学,2011).
    150. "SpectroMaster" (TriOptics), retrieved 04/28,2013, http://www.trioptics.com/spectromaster/description.php.
    151. "Spherometers" (TriOptics), retrieved 04/28,2013, http://www.trioptics.com/spherometers/description.php.
    152. 杨甬英,田超,张磊,韦涛,”非球面非零位干涉检测中部分补偿透镜对准装置与方法,”中国发明专利,201210054455.2(2012).
    153. 杨甬英,刘东,田超,卓永模,”非球面非零检测中非零补偿镜精密干涉定位调整装置及方法,”中国发明专利,200910099785.1(2012).
    154. Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, Y. Zhuo, "Research of precision interference locating method for a partial null compensator at aspheric testing," in Optical Manufacturing and Testing VIII, August 4,2009-August 5,2009, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2009), The International Society for Optical Engineering (SPIE).
    155. W. Tao, L. Dong, T. Chao, Z. Lei, Y. Yang, "New interferometric method to locate aspheric in the partial null aspheric testing system," 84173I-84173I (2012).
    156. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, S. O'Donohue, "Subaperture stitching interferometry for testing mild aspheres," in Interferometry ⅩⅢ:Applications, August 16,2007-August 17,2007, Proceedings of SPIE-The International Society for Optical Engineering (SPIE,2006), SPIE.

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