通用数字化高精度非球面干涉检测技术与系统研究
|
摘要
由于非球面比球面可以提供更大的自由度,所以在光学系统中使用非球面可以缩小系统整体外形尺寸,减轻系统重量,改善像质等,从而提高系统的整体性能。然而,由于非球面形状及光学特性各异,非球面检测系统历来都是个难题。
非球面的检测方法很多,主要有零位干涉检测法、非零位干涉检测法、轮廓法等。零位干涉检测法中的零位补偿透镜法及计算全息法等都是“一对一”型检测,虽然精度较高但无法实现通用化检测,且检测周期长,造价高；仅针对二次曲面的无像差点法需要至少一块口径大于被测非球面的辅助镜,虽具有一定通用性但辅助镜也极大地限制了其的应用。轮廓法的检测效率较低,并且接触式轮廓仪很容易将被测表面划伤。目前的非零位检测法,如长波长法、双波长法、剪切法等虽然一定程度上可以实现通用化检测,但由于非零位检测具有较大的回程误差,而大多都没有进行非零位误差校正,故精度较低。
本论文主要研究可用于非球面通用、数字化的非零位干涉体系、波前补偿、面形重构、测量数据及图像处理技术等。该研究对非球面检测技术,特别是非球面的非零位通用、数字化检测技术具有重要的意义。主要研究内容有：
论述了非球面检测,特别是通用化、数字化检测技术在光学测试及仪器等领域的重要意义。对国内外各种非球面加工及检测技术做了系统分析,提出了研究可用于非球面通用化、数字化检测技术的必要性。
针对非零位检测中返回波前往往具有较大畸变的特点,提出了利用部分零位透镜对一定范围内非球面进行部分补偿。详细论述了部分零位镜的设计过程,分析了部分零位镜的特性,并进而建立一整套可实现非球面通用化检测的部分零位镜体系。
研究了非球面非零位干涉检测中的回程误差问题。详细分析并推导了回程误差的表现形式及其对检测结果的影响。提出了初步校正非球面非零位检测中的回程误差的方法,并进行了实验验证。
建立了能对被测非球面状态进行全面描述的状态矩阵,提出了基于最小二乘算法的非球面面形逆向迭代优化重构技术。并通过大量仿真计算,研究了该重构技术在面形检测方面的能力。
提出了可用于非球面通用、数字化检测的光路布局及处理流程。对整个检测系统进行了系统建模,并通过大量计算机仿真实验,分析了应用逆向迭代优化及部分零位镜补偿进行数字化非球面非零位检测的误差问题,为实际检测系统的建模精度控制提供了有力指导。
建立了基于Twymann-Green干涉体系的实验装置,对实际口径为159mm,顶点球半径为818.952mm的抛物面进行了检测,精度RMS值优于1/30波长,达到了预期的效果,并对整个处理过程进行了误差分析。
对本文所做工作进行了总结,并分析了目前研究中存在的不足之处,对下一步的研究方向及方法提出了建议。
Aspherics can provide more degrees of freedom for aberration control. Use of aspherics helps to reduce the system size and weight while improving image quality. But due to their varieties of shapes and optical characteristics, aspheric testing has always been a great challenge for optical researchers.
There are a good deal of aspheric testing methods, null interferometric test, nonnull interferometric test, profilometer, etc, for instance. Null compensator method and computer generated holograms method, which belong to null test, require one unique null optics for one asphere. They can both obtain high accuracy measurement, but the challenge in design, fabrication and certification of the null optics greatly limit their application. Aberration free methods, which employ auxiliary reflecting mirror, can perform general test for conics. However, the auxiliary mirror usually should have larger aperture than the test aspheric, and its surface figure limits the overall test accuracy. The profilometer is time consuming and also has the danger of damage the surface of the test aspheric. Nonnull tests, which employ long wavelength, multi-wavelength, shearing methods, etc, can also perform general test. But the retace error with nonnull configuration can greatly reduce the test accuracy.
This dissertation mainly research on a general & digitizing nonnull interferometric aspheric testing system, include wavefront compensation, figure reconstruction, experimental data and image processing, etc. This research is of great contribution for aspheric testing, especially the general & digitizing aspheric testing method. The content of this dissertation include:
After review of the various applications and the current fabrication methods of the aspherics, there is also a review over the current aspheric testing methods. And these reviews reflects the necessity of establishing a general & digitizing aspheric testing system.
A type of novel partial null lens(PNL) is proposed to compensate for a range of aspherics. The design process of the PNL is discribed in detail and also the characteristics of the PNL are analyzed. The idea of using a series of PNLs to compensate for a larger range of aspherics is proposed and realized.
The retrace error in nonnull interferometric aspheric testing system is analyzed in detail. The performance and its influence to the testing result are also analyzed and the correcting method is present.
A matrix is proposed to represent the status of the aspheric under test. A reverse optimization figure reconstruction(ROR) process is proposed, which is based on system modeling and employs reverse optimization to reconstruct the figure of the aspheric form the wavefront detected on the detector. The performance of the ROR process is analyzed with lots of simulation.
An interferometric system, which employs partial null lens and reverse optimization reconstruction process, is proposed to perform general aspheric testing. The system layout and figure construction process are present. System modeling and error analysis basing on the system model are also carried out. The error analysis provides important information for the modeling accuracy control of real experiment system.
The validation experiment of the general & digitizing interferometric aspheric testing system has been established and the testing experiment for real paraboloid of 159mm aperture and 818.952mm vertex radius has been carried out with an accuracy of 1/30wave RMS. This dissertation is of great value for the accuracy enhancement of nonnull general aspheric testing.
非球面的检测方法很多,主要有零位干涉检测法、非零位干涉检测法、轮廓法等。零位干涉检测法中的零位补偿透镜法及计算全息法等都是“一对一”型检测,虽然精度较高但无法实现通用化检测,且检测周期长,造价高；仅针对二次曲面的无像差点法需要至少一块口径大于被测非球面的辅助镜,虽具有一定通用性但辅助镜也极大地限制了其的应用。轮廓法的检测效率较低,并且接触式轮廓仪很容易将被测表面划伤。目前的非零位检测法,如长波长法、双波长法、剪切法等虽然一定程度上可以实现通用化检测,但由于非零位检测具有较大的回程误差,而大多都没有进行非零位误差校正,故精度较低。
本论文主要研究可用于非球面通用、数字化的非零位干涉体系、波前补偿、面形重构、测量数据及图像处理技术等。该研究对非球面检测技术,特别是非球面的非零位通用、数字化检测技术具有重要的意义。主要研究内容有：
论述了非球面检测,特别是通用化、数字化检测技术在光学测试及仪器等领域的重要意义。对国内外各种非球面加工及检测技术做了系统分析,提出了研究可用于非球面通用化、数字化检测技术的必要性。
针对非零位检测中返回波前往往具有较大畸变的特点,提出了利用部分零位透镜对一定范围内非球面进行部分补偿。详细论述了部分零位镜的设计过程,分析了部分零位镜的特性,并进而建立一整套可实现非球面通用化检测的部分零位镜体系。
研究了非球面非零位干涉检测中的回程误差问题。详细分析并推导了回程误差的表现形式及其对检测结果的影响。提出了初步校正非球面非零位检测中的回程误差的方法,并进行了实验验证。
建立了能对被测非球面状态进行全面描述的状态矩阵,提出了基于最小二乘算法的非球面面形逆向迭代优化重构技术。并通过大量仿真计算,研究了该重构技术在面形检测方面的能力。
提出了可用于非球面通用、数字化检测的光路布局及处理流程。对整个检测系统进行了系统建模,并通过大量计算机仿真实验,分析了应用逆向迭代优化及部分零位镜补偿进行数字化非球面非零位检测的误差问题,为实际检测系统的建模精度控制提供了有力指导。
建立了基于Twymann-Green干涉体系的实验装置,对实际口径为159mm,顶点球半径为818.952mm的抛物面进行了检测,精度RMS值优于1/30波长,达到了预期的效果,并对整个处理过程进行了误差分析。
对本文所做工作进行了总结,并分析了目前研究中存在的不足之处,对下一步的研究方向及方法提出了建议。
Aspherics can provide more degrees of freedom for aberration control. Use of aspherics helps to reduce the system size and weight while improving image quality. But due to their varieties of shapes and optical characteristics, aspheric testing has always been a great challenge for optical researchers.
There are a good deal of aspheric testing methods, null interferometric test, nonnull interferometric test, profilometer, etc, for instance. Null compensator method and computer generated holograms method, which belong to null test, require one unique null optics for one asphere. They can both obtain high accuracy measurement, but the challenge in design, fabrication and certification of the null optics greatly limit their application. Aberration free methods, which employ auxiliary reflecting mirror, can perform general test for conics. However, the auxiliary mirror usually should have larger aperture than the test aspheric, and its surface figure limits the overall test accuracy. The profilometer is time consuming and also has the danger of damage the surface of the test aspheric. Nonnull tests, which employ long wavelength, multi-wavelength, shearing methods, etc, can also perform general test. But the retace error with nonnull configuration can greatly reduce the test accuracy.
This dissertation mainly research on a general & digitizing nonnull interferometric aspheric testing system, include wavefront compensation, figure reconstruction, experimental data and image processing, etc. This research is of great contribution for aspheric testing, especially the general & digitizing aspheric testing method. The content of this dissertation include:
After review of the various applications and the current fabrication methods of the aspherics, there is also a review over the current aspheric testing methods. And these reviews reflects the necessity of establishing a general & digitizing aspheric testing system.
A type of novel partial null lens(PNL) is proposed to compensate for a range of aspherics. The design process of the PNL is discribed in detail and also the characteristics of the PNL are analyzed. The idea of using a series of PNLs to compensate for a larger range of aspherics is proposed and realized.
The retrace error in nonnull interferometric aspheric testing system is analyzed in detail. The performance and its influence to the testing result are also analyzed and the correcting method is present.
A matrix is proposed to represent the status of the aspheric under test. A reverse optimization figure reconstruction(ROR) process is proposed, which is based on system modeling and employs reverse optimization to reconstruct the figure of the aspheric form the wavefront detected on the detector. The performance of the ROR process is analyzed with lots of simulation.
An interferometric system, which employs partial null lens and reverse optimization reconstruction process, is proposed to perform general aspheric testing. The system layout and figure construction process are present. System modeling and error analysis basing on the system model are also carried out. The error analysis provides important information for the modeling accuracy control of real experiment system.
The validation experiment of the general & digitizing interferometric aspheric testing system has been established and the testing experiment for real paraboloid of 159mm aperture and 818.952mm vertex radius has been carried out with an accuracy of 1/30wave RMS. This dissertation is of great value for the accuracy enhancement of nonnull general aspheric testing.
引文
1. 程灏波.”光学非球面反射镜轻量化制造技术,”光学与光电技术,2004,2(04).26-28.
2. 潘君骅,光学非球面的设计、加工与检测(苏州大学出版社,苏州,2004).
3.LOH公司, http://www.loh-optic.com.
4. C. C. A. Chen, C. M. Chen, and J. R. Chen, "Toolpath generation for diamond shaping of aspheric lens array," J Mater Process Tech,2007,192(1),194-199.
5. S. John, "Single Point Diamond Turning:Progress in Precision," in International Optical Design, Technical Digest (CD) (Optical Society of America,2006), ThB1.
6. M. Warren, "Diamond-Turned Optics Manufacturing and Precision Mechanical Metrology," Opt. Photon. News,2008.19(3).18-21.
7. S. C. West. H. M. Martin. R. H. Nagel, R. S. Young. W. B. Davison. T. J. Trebisky. S. T. DeRigne, and B. B. Hille, "Practical design and performance of the stressed-lap polishing tool," Appl. Opt.,1994,33(34).8094-8100.
8. H. M. Martin, "STRESSED-LAP POLISHING OF LARGE, FAST ASPHERES." Opt. Photon. News,1991,2(12).18-18.
9. H. M. Martin. "Aspheric polishing with a stressed lap." Opt. Photon. News. 1990.1(6),22-24.
10. 孙天祥.杨力.吴永前,万勇建,范斌,”应力抛光技术实验装置的研究,”光电工程.2009,36(10).146-150.
11. 孙天祥.杨力.吴永前.万勇建.范斌,”应力抛光技术加工抛物面的实验研究.”光电工程,2009,36(12),123-126.
12. 万勇建.袁家虎.范斌,杨力.”光学加工中边缘问题的数控处理方法,”红外与激光工程.2007.36(01).92-96.
13. 范斌,万勇建.杨力,曾志革.邓建明,李晓今,”大型非球面主镜能动磨盘加工模型.”光电工程.2005.32(12),59-62.
14. S. Axel. H. Thomas. Z. Michael, and S. Gerhard, "Ion beam figuring and ion beam polishing production tools-processing technology included-for customized solutions." in Optical Fabrication and Testing. OSA Technical Digest (Optical Society of America,2000),OWA6.
15. "Ion beam polishing公司”,http://www.n-t-g.de.
16. C. Miao, S. N. Shafrir. J. C. Lambropoulos. J. Mici. and S. D. Jacobs. "Shear stress in magnetorheological finishing for glasses." Appl. Opt.,2009.48(13). 2585-2594.
17. J. E. DeGroote, A. E. Marino, J. P. Wilson, A. L. Bishop, J. C. Lambropoulos, and S. D. Jacobs, "Removal rate model for magnetorheological finishing of glass," Appl. Opt.,2007,46(32),7927-7941.
18. D. Jessica, D. J. Stephen, and M. S. John, "Experiments on magnetorheological finishing of optical polymers," in Optical Fabrication and Testing, OSA Trends in Optics and Photonics Series (Optical Society of America,2002), OMB 1.
19. J. Stephen and B. S. Aric, "Magnetorheological finishing:new fluids for new materials," in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America,2000),OWB1.
20. Y. Dai, C. Song, X. Peng, and F. Shi, "Calibration and prediction of removal function in magnetorheological finishing," Appl. Opt.,2010,49(3),298-306.
21. 王小鹏,朱日宏,”定量检验光学元件面形的数字刀口仪技术研究,”应用光学,2009,30(01),69-72.
22. D. Malacara, Optical Shop Testing, Third ed. (John Wiley & Sons, Inc., New Jersey,2007).
23. 程子清,耿安兵,杨长城,”轮廓仪检测的系统误差分析,”光学与光电技术,2005,3(02),41-44.
24. 倪颖,余景池,郭培基,丁泽钊,”小型非球面轮廓测量仪的原理及应用,”光学精密工程,2003,11(06),612-616.
25. 李直,赵洋,李达成,肖体乔,夏绍建,”衍射型长程大型非球面轮廓测量仪,”光学学报,2002,22(10),1224-1228.
26. I. A. Palusinski, "Advancements in null corrector design and certification," Ph.D. (The University of Arizona, United States, Arizona,2003).
27. 伍凡,“非球面零检验的Dall补偿器设计,”应用光学,1993,41(02),1-4.
28. A. Offner, "A Null Corrector for Paraboloidal Mirrors," Appl. Opt.,1963,2(2), 153-155.
29. S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, and H. M. Martin, "Optical Metrology for 2 Large Highly Aspheric Telescope Mirrors," Appl Optics,1992,31(34),7191-7197.
30. C. E. DeVoe, "Limitations on aspheric surface testing with simple null correctors," M.S. (The University of Arizona, United States, Arizona,1989).
31. 伍凡,”非球面零检验的Offner补偿器设计,”应用光学,1993,14(03).8-12.
32. I. A. Palusinski and J. M. Sasian, "Sag and phase descriptions for null corrector certifiers," Optical Engineering,2004,43(3).697-701.
33. 薛栋林.郑立功,王淑平,张学军,”离轴二次非球面补偿检验计算机辅助调整技术研究,”光学精密工程,2006,03).
34. 尤锐,王一凡,王文革,薛育,”非球面补偿器的结构设计与装调分析,”长春理工大学学报(自然科学版),2008,31(04),71-83.
35. 陈强,袁家虎,伍凡,高平起,吴高峰,”Φ1.2m F/1.5抛物面主镜补偿器,”光学精密工程,2008,16(08),1384-1388.
36. 伍凡,陈强,“F/1.3抛物面零检验补偿器设计,”光电工程,2004,31(01),12-15.
37. 伍凡,”非球面干涉仪零检验的补偿器设计,”应用光学,1997,18(02),10-13.
38. 伍凡,”非球面零检验的镜式补偿器设计(续一),”应用光学,1995,16(04).10-13.
39. E. J. Danielewicz and D. Selman, "Computer-Generated Holograms Test Aspheric Optics," Laser Focus World,1990,26(4),143-145.
40. F. Y. Pan, "Measurement of aspherical surfaces using a test plate and computer generated holograms," Ph.D. (The Univ. of Arizona, U.S., Arizona,2002).
41. F. Y. Pan and J. Burge, "Efficient testing of segmented aspherical mirrors by use of reference plate and computer-generated holograms. Ⅰ. Theory and system optimization," Appl Optics,2004,43(28),5303-5312.
42. F. Y. Pan, J. Burge, D. Anderson, and A. Poleshchuk, "Efficient testing of segmented aspherical mirrors by use of a reference plate and computer-generated holograms. Ⅱ. Case study, error analysis, and experimental validation," Appl Optics,2004,43(28),5313-5322.
43. P. Zhou and J. H. Burge, "Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors," Opt. Express.2007,15(23). 15410-15417.
44. P. Zhou and J. H. Burge, "Fabrication error analysis and experimental demonstration for computer-generated holograms," Appl. Opt.,2007,46(5), 657-663.
45. J. H. Burge, "Advanced techniques for measuring primary mirrors for astronomical telescopes," Ph.D. (The University of Arizona, United States--Arizona,1993).
46. 刘华.卢振武, 李凤有.”大口径非球面计算全息图检测系统.”红外与激光工程.2006.35(02).177-182.
47. 刘华,卢振武.李凤有, 张红鑫,”计算全息图检测大口径凹非球面系统的研究,”红外与激光工程.2007,36(03).312-315.
48. 刘华.卢振武.李凤有.孙强.翁志成.”用于非球面检测的球面计算全息 图特性分析,”光电工程,2004,31(07),38-41.
49. 刘华,李凤有,卢振武,“利用曲面计算全息图进行非球面检测,”光学精密工程,2004,06).
50. 谢意,陈强,伍凡,邱传凯,侯溪,张晶,”凹非球面检测的双计算全息图设计及制作,”光电工程,2008,35(06),59-62.
51. 谢意,陈强,伍凡,侯溪,张晶,吴高峰,”用双计算全息图检测凹非球面,”光学学报,2008,28(07),1313-1317.
52. 程灏波,”零补偿干涉检测实现及误差量规律,”哈尔滨工业大学学报,2006,38(08),1247-1250.
53. 康果果,谢敬辉,刘祎,”用于非球面检测的计算全息设计及其精度分析,”光学技术,2007,33(05),654-657.
54. 康果果,谢敬辉,张浩,莫晓丽,杨晖,刘祎,”非球面检测中衍射光学补偿器的校准定位研究,”光子学报,2009,38(06),1473-1476.
55. 程灏波,冯之敬,”波像差法构建非球面干涉检测的误差分离模型,”清华大学学报(自然科学版),2006,46(02),187-190.
56. Z. S. Gao, M. M. Kong, R. H. Zhu, and L. Chen, "Problems on design of computer-generated holograms for testing aspheric surfaces:principle and calculation," Chin Opt Lett,2007,5(4),241-244.
57. 马骏,高志山,朱日宏,何勇,陈磊,李建欣,潘裕斌,W.H.Wong,黄立辉,谢常青,朱效立,马杰,"Problems on fabrication of computer-generated holograms for testing aspheric surfaces," Chin Opt Lett,2009,7(01),71-73.
58. 马杰,朱效立,谢常青,叶甜春,赵珉,刘明,陈宝钦,朱日宏,高志山,马骏,”用于非球面测试的位相型计算全息图制作,”微细加工技术,2008,06),7-11.
59. J. Schwider, N. Lindlein, K. Mantel, and I. Harder, "On the calibration of diffractive nulls for transmission tests of aspheric components," Opt Commun, 2007,279(2),262-272.
60. B. Dorband and H. J. Tiziani, "Testing aspheric surfaces with computer-generated holograms:analysis of adjustment and shape errors," Appl. Opt.,1985,24(16),2604-2611.
61. C. R. Munnerlyn and M. Latta, "Rough Surface Interferometry Using a CO2 Laser Source," Appl. Opt.,1968,7(9),1858-1859.
62. K. Verma and B. Han, "Far-Infrared Fizeau Interferometry," Appl. Opt.,2001, 40(28),4981-4987.
63. A. F. Fercher, H. Z. Hu. and U. Vry, "Rough surface interferometry with a two-wavelength heterodyne speckle interferometer," Appl. Opt.,1985,24(14), 2181-2188.
64. P. Lam, J. D. Gaskill, and J. C. Wyant, "Two-wavelength holographic interferometer." Appl. Opt.,1984,23(18),3079-3081.
65. D. Liu. Y. Yang. L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl Optics,2007. 46(34),8305-8314.
66. D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer," Opt Commun,2007,275(1),173-178.
67. D. Liu, Y. Y. Yang. Y. B. Shen, J. M. Weng, and Y. M. Zhuo, "System optimization of radial shearing interferometer for aspheric testing-art. no. 68340U," Optical Design and Testing Ⅲ, Pts 1 and 2,2008, 6834(U8340-U83408700.
68. T. Kohno, D. Matsumoto. T. Yazawa, and Y Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Optical Engineering,2000,39(10),2696-2699.
69. 刘东.杨甬英.夏佐堂,陈阳杰,张小民.陈波,秦兴武,”近红外瞬态脉冲波前高精度干涉检测技术.”光学学报,2006,26(09).1372-1376.
70. O. Kwon. "Infrared lateral shearing interferometers," Appl. Opt.,1980,19(8). 1225-1227.
71. P. Hariharan. "Lateral and radial shearing interferometers:a comparison," Appl. Opt.,1988.27(17).3594-3596.
72. J. B. Song, Y. W. Lee, I. W. Lee, and Y.-H. Lee, "Simple Phase-Shifting Method in a Wedge-Plate Lateral-Shearing Interferometer," Appl. Opt.,2004, 43(20).3989-3992.
73. D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," in (SPIE.2007).68340U.
74. 横向剪切干涉仪公司.http://www.zeeko.co.uk/index.php.
75. H. P. Stahl, "Aspheric surface testing techniques," in (SPIE.1991),66-76.
76. X. Hou, F. Wu, L. Yang. S. B. Wu, and 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 Optics,2006.45(15).3442-3455.
77. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard. "Stitching Interferometry:A Flexible Solution for Surface Metrology." Optics & Photonics News,2003.14(38-43.
78. G. Forbes, P. R. Dumas, J. F. Fleig. and P. E. Murphy, "Subaperture stitching interferometer for versatile and accurate surface metrology," in Optical Fabrication and Testing,2002),
79. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G DeVries, and S. O'Donohue, "Subaperture stitching interferometry for testing mild aspheres," in (SPIE, 2006),62930J.
80. 王孝坤,王丽辉,张学军,“子孔径拼接干涉法检测非球面,”光学精密工程,2007,15(02),192-198.
81. 王孝坤,王丽辉,郑立功,薛栋林,邓伟杰,张学军,”子孔径拼接技术在大口径高陡度非球面检测中的应用,”强激光与粒子束,2007,19(07),1144-1148.
82. 王孝坤,张学军,王丽辉,郑立功,”环形子孔径拼接干涉检测非球面的数学模型和仿真研究,”光学精密工程,2006,14(04),527-532.
83. 王孝坤,郑立功,张斌智,闫锋,张忠玉,张学军,“子孔径拼接干涉测量—大口径双曲面(英文),”红外与激光工程,2009,38(01),114-119.
84. 王伟波,谭久彬,”非球面非零位拼接测量的对准误差模型,”光电子.激光,201 0,21(02),240-244.
85. 王月珠,田义,李洪玉,鞠有伦,”环形子孔径拼接干涉检测非球面的建模与实验,”光学学报,2009,29(11),3082-3087.
86. 乔玉晶,王伟波,”一种提高子孔径拼接测量精度的误差修正方法,”四川大学学报(自然科学版),2007,44(04),845-850.
87. 乔玉晶,谭久彬,王伟波,”子孔径干涉拼接测量非球面的模型分析,”仪器仪表学报,2007,28(10),1880-1885.
88. 乔玉晶,谭久彬,王伟波,”非球面拼接测量中偏置误差修正模型,”光电子.激光,2008,19(11),1497-1451.
89. 杜玉军,任海霞,刘中本,”光学非球面元件非球面度计算方法,”应用光学,2002,23(05),42-45.
90. 陆永贵,杨建东,”光学非球面度的探讨,”长春理工大学学报,2005,28(04),16-18.
91. 肖光辉,郭伟远,李新南,”离轴扇形镜面非球面度的计算,”天文研究与技术,2004,1(04),289-299.
92. 程灏波,张学军,郑立功,张峰,常军,张忠玉,程仕东,”大偏离量非球面加工系统的精度标定,”光学技术,2003,29(01),125-127.
93. 程灏波,王英伟,冯之敬,”大偏离量非球面最接近球面的确定方法,”清华大学学报(自然科学版),2004,44(08),1040-1046.
94. 普利亚耶夫,光学非球面检测(1982).
95. 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,1993.03).
96. Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer," in Optical Design and Testing Ⅲ, (SPIE,2007),68340T-68349.
97. 刘东,杨甬英.田超,卓永模,“用于非球面通用化检测的部分零位透镜,”红外与激光工程,2009,35(5),322-325.
98. D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, "Non-null interferometric aspheric testing with partial null lens and reverse optimization," in Optical Manufacturing and Testing Ⅷ, (SPIE,2009), 74260M-74267.
99. Z. Malacara-Hernandez, D. Malacara-Hernandez, and M. Servin, "Digitization of interferograms of aspheric wavefronts," Optical Engineering,1996,35(7), 2102-2105.
100. J. M. Geary. Introduction to Lens Design (2002).
101. 张以漠,应用光学(机械工业出版社,北京,1988).
102. 杨甬英,刘东,卓永模,“可实现非球面通用化检测的大球差补偿镜及其装置,” 国家发明专利,申请号：200710156621.9(2007).
103. 美国ZYGO公司,www.zygo.com.
104. 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,2004.24(7).
105. H. Q. Liu Huilan, Zhu Qiudong, Sha Dingguo, Zhang Chunxi, "A novel aspheric surface testing method using part-compensating lens." Proc. of SPIE. 2005.5638(324-329.
106. O. Kwon. J. C. Wyant, and C. R. Hayslett, "Rough surface interferometry at 10.6 μm,"Appl Optics,1980,19(11),1862-1869.
107. U. Vry, "Absolute Statistical Error in 2-Wavelength Rough-Surface Interferometry (Rosi)." Optica Acta,1986.33(10),1221-1225.
108. N. Gardner and A. Davies, "Retrace error evaluation on a figure-measuring interferometer," in Optical Manufacturing and Testing Ⅵ, (SPIE,2005), 58690V-58698.
109. S. Han and E. Novak. "Retrace error for the measurement of a long-radius optic." in 18th Congress of the International Commission for Optics, (SPIE, 1999),597-598.
110. J. M. Gean, K. M. Yoo. and G. Si. "Retrace error:a case study," in Interferometry:Surface Characterization and Testing. (SPIE,1992),98-105.
111. D. Liu, Y. Y. Yang, C. Tian, Y. J. Luo, and L. Wang, "Practical methods for retrace error correction in nonnull aspheric testing." Opt Express,2009,17(9). 7025-7035.
112. T.-C. Poom and T. Kim, Engineering Optics with Matlab (World Scientific Publishing Co. Pte. Ltd., Singapore,2006).
113. 刘东,杨甬英,田超,翁俊淼,卓永模,杨李茗,”非球面非零位检测中的回程误差分析与校正,”光学学报,2009,29(03),688-696.
114. J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere," in (SPIE,2007),68342V.
115. D. Liu, Y. Yang, C. Tian, Y. Luo, and L. Wang, "Practical methods for retrace error correction in nonnull aspheric testing," Opt. Express,2009,17(9), 7025-7035.
116. Z. Malacara and D. Malacara, "Design of Lenses to Project the Image of a Pupil in Optical-Testing Interferometers," Appl Optics,1995,34(4),739-742.
117. J. C. Wyant and V. P. Bennett, "Using Computer Generated Holograms to Test Aspheric Wavefronts," Appl Optics,1972,11(12),2833-2839.
118. J. E. Greivenkamp and R. O. Gappinger, "Design of a nonnull interferometer for aspheric wave fronts," Appl Optics,2004,43(27),5143-5151.
119. M. A. Lundgren and W. L. Wolfe, "Alignment of a 3-Mirror Off-Axis Telescope by Reverse Optimization," Optical Engineering,1991,30(3), 307-311.
120. E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization Alignment Algorithm using Zernike Sensitivity," J. Opt. Soc. Korea,2005, 9(2),68-73.
121. I. Powell, "Employment of Reverse Optimization to Relax Manufacturing Tolerances Imposed on System Constructional Parameters Associated with Complex Optical Systems." Appl. Opt.,2000,39(13),2174-2183.
122. C. R. Wolfe and J. K. Lawson. "Measurement and analysis of wavefront structure from large-aperture ICF optics," in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), (SPIE,1995),361-385.
123. 刘耀红,滕霖,李大琪,张萧,”功率谱密度(Psd)在评价超精密光学表面中的应用研究,”航空精密制造技术,2006,42(02),1-3.
124. 于瀛洁,”关于光学元件波面测量中的功率谱密度,”计量学报,2003,24(2),103-107.
125. 刘红婕,景峰,左言磊,胡东霞,粟敬钦,彭志涛,周维,李强,张昆,”激光波前功率谱密度与焦斑旁瓣的关系,”中国激光,2006,33(04),504-508.
126. 柴立群,许乔,邓燕,石崎凯,”强激光系统波前功率谱密度的数值计算研究,”光学技术,2005,31(04),577-579.
127. 许乔,顾元元,柴林,李伟,“大口径光学元件波前功率谱密度检测,”光学 学报.2001,33(03),20-23.
128. 徐芳,魏全忠,伍凡,”用功率谱密度函数评价光学面形中频误差特性,”光电工程,1999,26(S1),139-143.
129. 沈卫星,徐德衍,”强激光光学元件表面功率谱密度函数估计,”强激光与粒子束,2000,12(04),392-396.
130. 刘东,杨甬英,田超,卓永模,”用于校正非球面非零位检测中的原理误差的方法,”(2008).
131. 郑立功,常军,张学军,程灏波,张峰,”大数值孔径、高次非球面透镜的加工与检验,”光学技术,2003,29(05),584-586.
132. 付联效,吴永刚,郝沛明,王鹏,”透镜补偿检验的研究与分析,”光子学报,2007,36(11),2057-2061.
133. D. Liu, Y. Y. Yang, J. M. Weng. X. M. Zhang. B. Chen, and X. W. Qin. "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer." Opt Commun,2007.275(1). 173-178.
134. D. Liu, Y. Y. Yang, L. Wang, and Y. M. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl Optics. 2007.46(34).8305-8314.
135. Z. Malacara and D. Malacara, "Design of lenses to project the image of a pupil in optical testing interferometers," Appl. Opt.,1995,34(4),739-742.
136. J. Sullivan, Optical Science Center, University of Arizona, Tucson. AZ, USA (personal communication.2009).
137. B. M. Robinson and P. J. Reardon, "Distortion compensation in interferometric testing of mirrors," Appl. Opt.,2009,48(3).560-565.
138. J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces." in Optical Manufacturing and Testing Ⅶ, (SPIE.2007). 66710W-66718.
139. S. Djidel, J. K. Gansel. H. I. Campbell, and A. H. Greenaway, "High-speed, 3-dimensional, telecentric imaging." Opt. Express,2006,14(18),8269-8277.
140. W. C. Folz and B. G. Ledley, "Telecentric optical system for observing daytime chemical releases at high altitudes." Appl. Opt.,1981.20(6).951-954.
141. 董卫斌.张敏,达争尚,陈良益,董晓娜,何俊华.”强激光装置中玻璃疵病在线检测的光学系统设计.”光子学报.2009.38(03).685-688.
142. 叶军君.兰劲.郭隐彪.”非球面检测误差分析和误差补偿策略研究.”中国机械工程.2007.18(23).2793-2797.
143. 美国ZEMAX公司. www.zemax.com.
144. ZEMAX CORP., "ZEMAX users' manual," 2005.
145. PI公司,http://www.pi-china.cn/.
146. 杨甬英,卓永模,杨明建,”用于超光滑表面无损检测的光学轮廓仪,”光电工程,1999,26(06),12-16.
147. 杨甬英,徐敏,卓永模,”实时扫描非接触测量表面微观轮廓仪,”浙江大学学报(工学版),1999,33(03),317-322.
148. M. Servin, J. L. Marroquin, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," Journal of the Optical Society of America a-Optics Image Science and Vision,2001, 18(3),689-695.
149. M. Servin, J. L. Marroquin, and F. J. Cuevas, "Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique," Appl. Opt.,1997,36(19),4540-4548.
150. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," Journal of the Optical Society of America a-Optics Image Science and Vision,2001,18(8),1862-1870.
151. K. G. Larkin, "Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform," Journal of the Optical Society of America a-Optics Image Science and Vision,2001, 18(8),1871-1881.
152. M. Servin, J. L. Marroquin, and J. A. Quiroga, "Regularized quadrature and phase tracking from a single closed-fringe interferogram," J. Opt. Soc. Am. A, 2004,21(3),411-419.
153. J. C. Estrada, M. Servin, and J. L. Marroquin, "Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes," Opt. Express, 2007,15(5),2288-2298.
154. T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," Journal of the Optical Society of America a-Optics Image Science and Vision,1986,3(6),847-855.
155. P. Kuttner, "Modulation Transfer Functions of Ground-Glass Screens," Appl. Opt.,1972,11(9),2024-2027.
156. 黄浩,郭隐彪.王振忠,谢仁宁,”轴对称非球面加工误差分离及补偿技术.”机械工程学报,2005,41(12),177-181.
157. 贾立德,郑子文,李圣怡,戴一帆,”光学非球面坐标测量中位姿误差的分离与优化.”光学精密工程,2007,15(08),1229-1234.
2. 潘君骅,光学非球面的设计、加工与检测(苏州大学出版社,苏州,2004).
3.LOH公司, http://www.loh-optic.com.
4. C. C. A. Chen, C. M. Chen, and J. R. Chen, "Toolpath generation for diamond shaping of aspheric lens array," J Mater Process Tech,2007,192(1),194-199.
5. S. John, "Single Point Diamond Turning:Progress in Precision," in International Optical Design, Technical Digest (CD) (Optical Society of America,2006), ThB1.
6. M. Warren, "Diamond-Turned Optics Manufacturing and Precision Mechanical Metrology," Opt. Photon. News,2008.19(3).18-21.
7. S. C. West. H. M. Martin. R. H. Nagel, R. S. Young. W. B. Davison. T. J. Trebisky. S. T. DeRigne, and B. B. Hille, "Practical design and performance of the stressed-lap polishing tool," Appl. Opt.,1994,33(34).8094-8100.
8. H. M. Martin, "STRESSED-LAP POLISHING OF LARGE, FAST ASPHERES." Opt. Photon. News,1991,2(12).18-18.
9. H. M. Martin. "Aspheric polishing with a stressed lap." Opt. Photon. News. 1990.1(6),22-24.
10. 孙天祥.杨力.吴永前,万勇建,范斌,”应力抛光技术实验装置的研究,”光电工程.2009,36(10).146-150.
11. 孙天祥.杨力.吴永前.万勇建.范斌,”应力抛光技术加工抛物面的实验研究.”光电工程,2009,36(12),123-126.
12. 万勇建.袁家虎.范斌,杨力.”光学加工中边缘问题的数控处理方法,”红外与激光工程.2007.36(01).92-96.
13. 范斌,万勇建.杨力,曾志革.邓建明,李晓今,”大型非球面主镜能动磨盘加工模型.”光电工程.2005.32(12),59-62.
14. S. Axel. H. Thomas. Z. Michael, and S. Gerhard, "Ion beam figuring and ion beam polishing production tools-processing technology included-for customized solutions." in Optical Fabrication and Testing. OSA Technical Digest (Optical Society of America,2000),OWA6.
15. "Ion beam polishing公司”,http://www.n-t-g.de.
16. C. Miao, S. N. Shafrir. J. C. Lambropoulos. J. Mici. and S. D. Jacobs. "Shear stress in magnetorheological finishing for glasses." Appl. Opt.,2009.48(13). 2585-2594.
17. J. E. DeGroote, A. E. Marino, J. P. Wilson, A. L. Bishop, J. C. Lambropoulos, and S. D. Jacobs, "Removal rate model for magnetorheological finishing of glass," Appl. Opt.,2007,46(32),7927-7941.
18. D. Jessica, D. J. Stephen, and M. S. John, "Experiments on magnetorheological finishing of optical polymers," in Optical Fabrication and Testing, OSA Trends in Optics and Photonics Series (Optical Society of America,2002), OMB 1.
19. J. Stephen and B. S. Aric, "Magnetorheological finishing:new fluids for new materials," in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America,2000),OWB1.
20. Y. Dai, C. Song, X. Peng, and F. Shi, "Calibration and prediction of removal function in magnetorheological finishing," Appl. Opt.,2010,49(3),298-306.
21. 王小鹏,朱日宏,”定量检验光学元件面形的数字刀口仪技术研究,”应用光学,2009,30(01),69-72.
22. D. Malacara, Optical Shop Testing, Third ed. (John Wiley & Sons, Inc., New Jersey,2007).
23. 程子清,耿安兵,杨长城,”轮廓仪检测的系统误差分析,”光学与光电技术,2005,3(02),41-44.
24. 倪颖,余景池,郭培基,丁泽钊,”小型非球面轮廓测量仪的原理及应用,”光学精密工程,2003,11(06),612-616.
25. 李直,赵洋,李达成,肖体乔,夏绍建,”衍射型长程大型非球面轮廓测量仪,”光学学报,2002,22(10),1224-1228.
26. I. A. Palusinski, "Advancements in null corrector design and certification," Ph.D. (The University of Arizona, United States, Arizona,2003).
27. 伍凡,“非球面零检验的Dall补偿器设计,”应用光学,1993,41(02),1-4.
28. A. Offner, "A Null Corrector for Paraboloidal Mirrors," Appl. Opt.,1963,2(2), 153-155.
29. S. C. West, J. H. Burge, R. S. Young, D. S. Anderson, C. Murgiuc, D. A. Ketelsen, and H. M. Martin, "Optical Metrology for 2 Large Highly Aspheric Telescope Mirrors," Appl Optics,1992,31(34),7191-7197.
30. C. E. DeVoe, "Limitations on aspheric surface testing with simple null correctors," M.S. (The University of Arizona, United States, Arizona,1989).
31. 伍凡,”非球面零检验的Offner补偿器设计,”应用光学,1993,14(03).8-12.
32. I. A. Palusinski and J. M. Sasian, "Sag and phase descriptions for null corrector certifiers," Optical Engineering,2004,43(3).697-701.
33. 薛栋林.郑立功,王淑平,张学军,”离轴二次非球面补偿检验计算机辅助调整技术研究,”光学精密工程,2006,03).
34. 尤锐,王一凡,王文革,薛育,”非球面补偿器的结构设计与装调分析,”长春理工大学学报(自然科学版),2008,31(04),71-83.
35. 陈强,袁家虎,伍凡,高平起,吴高峰,”Φ1.2m F/1.5抛物面主镜补偿器,”光学精密工程,2008,16(08),1384-1388.
36. 伍凡,陈强,“F/1.3抛物面零检验补偿器设计,”光电工程,2004,31(01),12-15.
37. 伍凡,”非球面干涉仪零检验的补偿器设计,”应用光学,1997,18(02),10-13.
38. 伍凡,”非球面零检验的镜式补偿器设计(续一),”应用光学,1995,16(04).10-13.
39. E. J. Danielewicz and D. Selman, "Computer-Generated Holograms Test Aspheric Optics," Laser Focus World,1990,26(4),143-145.
40. F. Y. Pan, "Measurement of aspherical surfaces using a test plate and computer generated holograms," Ph.D. (The Univ. of Arizona, U.S., Arizona,2002).
41. F. Y. Pan and J. Burge, "Efficient testing of segmented aspherical mirrors by use of reference plate and computer-generated holograms. Ⅰ. Theory and system optimization," Appl Optics,2004,43(28),5303-5312.
42. F. Y. Pan, J. Burge, D. Anderson, and A. Poleshchuk, "Efficient testing of segmented aspherical mirrors by use of a reference plate and computer-generated holograms. Ⅱ. Case study, error analysis, and experimental validation," Appl Optics,2004,43(28),5313-5322.
43. P. Zhou and J. H. Burge, "Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors," Opt. Express.2007,15(23). 15410-15417.
44. P. Zhou and J. H. Burge, "Fabrication error analysis and experimental demonstration for computer-generated holograms," Appl. Opt.,2007,46(5), 657-663.
45. J. H. Burge, "Advanced techniques for measuring primary mirrors for astronomical telescopes," Ph.D. (The University of Arizona, United States--Arizona,1993).
46. 刘华.卢振武, 李凤有.”大口径非球面计算全息图检测系统.”红外与激光工程.2006.35(02).177-182.
47. 刘华,卢振武.李凤有, 张红鑫,”计算全息图检测大口径凹非球面系统的研究,”红外与激光工程.2007,36(03).312-315.
48. 刘华.卢振武.李凤有.孙强.翁志成.”用于非球面检测的球面计算全息 图特性分析,”光电工程,2004,31(07),38-41.
49. 刘华,李凤有,卢振武,“利用曲面计算全息图进行非球面检测,”光学精密工程,2004,06).
50. 谢意,陈强,伍凡,邱传凯,侯溪,张晶,”凹非球面检测的双计算全息图设计及制作,”光电工程,2008,35(06),59-62.
51. 谢意,陈强,伍凡,侯溪,张晶,吴高峰,”用双计算全息图检测凹非球面,”光学学报,2008,28(07),1313-1317.
52. 程灏波,”零补偿干涉检测实现及误差量规律,”哈尔滨工业大学学报,2006,38(08),1247-1250.
53. 康果果,谢敬辉,刘祎,”用于非球面检测的计算全息设计及其精度分析,”光学技术,2007,33(05),654-657.
54. 康果果,谢敬辉,张浩,莫晓丽,杨晖,刘祎,”非球面检测中衍射光学补偿器的校准定位研究,”光子学报,2009,38(06),1473-1476.
55. 程灏波,冯之敬,”波像差法构建非球面干涉检测的误差分离模型,”清华大学学报(自然科学版),2006,46(02),187-190.
56. Z. S. Gao, M. M. Kong, R. H. Zhu, and L. Chen, "Problems on design of computer-generated holograms for testing aspheric surfaces:principle and calculation," Chin Opt Lett,2007,5(4),241-244.
57. 马骏,高志山,朱日宏,何勇,陈磊,李建欣,潘裕斌,W.H.Wong,黄立辉,谢常青,朱效立,马杰,"Problems on fabrication of computer-generated holograms for testing aspheric surfaces," Chin Opt Lett,2009,7(01),71-73.
58. 马杰,朱效立,谢常青,叶甜春,赵珉,刘明,陈宝钦,朱日宏,高志山,马骏,”用于非球面测试的位相型计算全息图制作,”微细加工技术,2008,06),7-11.
59. J. Schwider, N. Lindlein, K. Mantel, and I. Harder, "On the calibration of diffractive nulls for transmission tests of aspheric components," Opt Commun, 2007,279(2),262-272.
60. B. Dorband and H. J. Tiziani, "Testing aspheric surfaces with computer-generated holograms:analysis of adjustment and shape errors," Appl. Opt.,1985,24(16),2604-2611.
61. C. R. Munnerlyn and M. Latta, "Rough Surface Interferometry Using a CO2 Laser Source," Appl. Opt.,1968,7(9),1858-1859.
62. K. Verma and B. Han, "Far-Infrared Fizeau Interferometry," Appl. Opt.,2001, 40(28),4981-4987.
63. A. F. Fercher, H. Z. Hu. and U. Vry, "Rough surface interferometry with a two-wavelength heterodyne speckle interferometer," Appl. Opt.,1985,24(14), 2181-2188.
64. P. Lam, J. D. Gaskill, and J. C. Wyant, "Two-wavelength holographic interferometer." Appl. Opt.,1984,23(18),3079-3081.
65. D. Liu. Y. Yang. L. Wang, and Y. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl Optics,2007. 46(34),8305-8314.
66. D. Liu, Y. Yang, J. Weng, X. Zhang, B. Chen, and X. Qin, "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer," Opt Commun,2007,275(1),173-178.
67. D. Liu, Y. Y. Yang. Y. B. Shen, J. M. Weng, and Y. M. Zhuo, "System optimization of radial shearing interferometer for aspheric testing-art. no. 68340U," Optical Design and Testing Ⅲ, Pts 1 and 2,2008, 6834(U8340-U83408700.
68. T. Kohno, D. Matsumoto. T. Yazawa, and Y Uda, "Radial shearing interferometer for in-process measurement of diamond turning," Optical Engineering,2000,39(10),2696-2699.
69. 刘东.杨甬英.夏佐堂,陈阳杰,张小民.陈波,秦兴武,”近红外瞬态脉冲波前高精度干涉检测技术.”光学学报,2006,26(09).1372-1376.
70. O. Kwon. "Infrared lateral shearing interferometers," Appl. Opt.,1980,19(8). 1225-1227.
71. P. Hariharan. "Lateral and radial shearing interferometers:a comparison," Appl. Opt.,1988.27(17).3594-3596.
72. J. B. Song, Y. W. Lee, I. W. Lee, and Y.-H. Lee, "Simple Phase-Shifting Method in a Wedge-Plate Lateral-Shearing Interferometer," Appl. Opt.,2004, 43(20).3989-3992.
73. D. Liu, Y. Yang, Y. Shen, J. Weng, and Y. Zhuo, "System optimization of radial shearing interferometer for aspheric testing," in (SPIE.2007).68340U.
74. 横向剪切干涉仪公司.http://www.zeeko.co.uk/index.php.
75. H. P. Stahl, "Aspheric surface testing techniques," in (SPIE.1991),66-76.
76. X. Hou, F. Wu, L. Yang. S. B. Wu, and 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 Optics,2006.45(15).3442-3455.
77. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard. "Stitching Interferometry:A Flexible Solution for Surface Metrology." Optics & Photonics News,2003.14(38-43.
78. G. Forbes, P. R. Dumas, J. F. Fleig. and P. E. Murphy, "Subaperture stitching interferometer for versatile and accurate surface metrology," in Optical Fabrication and Testing,2002),
79. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G DeVries, and S. O'Donohue, "Subaperture stitching interferometry for testing mild aspheres," in (SPIE, 2006),62930J.
80. 王孝坤,王丽辉,张学军,“子孔径拼接干涉法检测非球面,”光学精密工程,2007,15(02),192-198.
81. 王孝坤,王丽辉,郑立功,薛栋林,邓伟杰,张学军,”子孔径拼接技术在大口径高陡度非球面检测中的应用,”强激光与粒子束,2007,19(07),1144-1148.
82. 王孝坤,张学军,王丽辉,郑立功,”环形子孔径拼接干涉检测非球面的数学模型和仿真研究,”光学精密工程,2006,14(04),527-532.
83. 王孝坤,郑立功,张斌智,闫锋,张忠玉,张学军,“子孔径拼接干涉测量—大口径双曲面(英文),”红外与激光工程,2009,38(01),114-119.
84. 王伟波,谭久彬,”非球面非零位拼接测量的对准误差模型,”光电子.激光,201 0,21(02),240-244.
85. 王月珠,田义,李洪玉,鞠有伦,”环形子孔径拼接干涉检测非球面的建模与实验,”光学学报,2009,29(11),3082-3087.
86. 乔玉晶,王伟波,”一种提高子孔径拼接测量精度的误差修正方法,”四川大学学报(自然科学版),2007,44(04),845-850.
87. 乔玉晶,谭久彬,王伟波,”子孔径干涉拼接测量非球面的模型分析,”仪器仪表学报,2007,28(10),1880-1885.
88. 乔玉晶,谭久彬,王伟波,”非球面拼接测量中偏置误差修正模型,”光电子.激光,2008,19(11),1497-1451.
89. 杜玉军,任海霞,刘中本,”光学非球面元件非球面度计算方法,”应用光学,2002,23(05),42-45.
90. 陆永贵,杨建东,”光学非球面度的探讨,”长春理工大学学报,2005,28(04),16-18.
91. 肖光辉,郭伟远,李新南,”离轴扇形镜面非球面度的计算,”天文研究与技术,2004,1(04),289-299.
92. 程灏波,张学军,郑立功,张峰,常军,张忠玉,程仕东,”大偏离量非球面加工系统的精度标定,”光学技术,2003,29(01),125-127.
93. 程灏波,王英伟,冯之敬,”大偏离量非球面最接近球面的确定方法,”清华大学学报(自然科学版),2004,44(08),1040-1046.
94. 普利亚耶夫,光学非球面检测(1982).
95. 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,1993.03).
96. Y. Yang, D. Liu, Y. Shen, J. Weng, and Y. Zhuo, "Study on testing larger asphericity in non-null interferometer," in Optical Design and Testing Ⅲ, (SPIE,2007),68340T-68349.
97. 刘东,杨甬英.田超,卓永模,“用于非球面通用化检测的部分零位透镜,”红外与激光工程,2009,35(5),322-325.
98. D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, "Non-null interferometric aspheric testing with partial null lens and reverse optimization," in Optical Manufacturing and Testing Ⅷ, (SPIE,2009), 74260M-74267.
99. Z. Malacara-Hernandez, D. Malacara-Hernandez, and M. Servin, "Digitization of interferograms of aspheric wavefronts," Optical Engineering,1996,35(7), 2102-2105.
100. J. M. Geary. Introduction to Lens Design (2002).
101. 张以漠,应用光学(机械工业出版社,北京,1988).
102. 杨甬英,刘东,卓永模,“可实现非球面通用化检测的大球差补偿镜及其装置,” 国家发明专利,申请号：200710156621.9(2007).
103. 美国ZYGO公司,www.zygo.com.
104. 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,2004.24(7).
105. H. Q. Liu Huilan, Zhu Qiudong, Sha Dingguo, Zhang Chunxi, "A novel aspheric surface testing method using part-compensating lens." Proc. of SPIE. 2005.5638(324-329.
106. O. Kwon. J. C. Wyant, and C. R. Hayslett, "Rough surface interferometry at 10.6 μm,"Appl Optics,1980,19(11),1862-1869.
107. U. Vry, "Absolute Statistical Error in 2-Wavelength Rough-Surface Interferometry (Rosi)." Optica Acta,1986.33(10),1221-1225.
108. N. Gardner and A. Davies, "Retrace error evaluation on a figure-measuring interferometer," in Optical Manufacturing and Testing Ⅵ, (SPIE,2005), 58690V-58698.
109. S. Han and E. Novak. "Retrace error for the measurement of a long-radius optic." in 18th Congress of the International Commission for Optics, (SPIE, 1999),597-598.
110. J. M. Gean, K. M. Yoo. and G. Si. "Retrace error:a case study," in Interferometry:Surface Characterization and Testing. (SPIE,1992),98-105.
111. D. Liu, Y. Y. Yang, C. Tian, Y. J. Luo, and L. Wang, "Practical methods for retrace error correction in nonnull aspheric testing." Opt Express,2009,17(9). 7025-7035.
112. T.-C. Poom and T. Kim, Engineering Optics with Matlab (World Scientific Publishing Co. Pte. Ltd., Singapore,2006).
113. 刘东,杨甬英,田超,翁俊淼,卓永模,杨李茗,”非球面非零位检测中的回程误差分析与校正,”光学学报,2009,29(03),688-696.
114. J. Weng, Y. Yang, D. Liu, Y. Shen, and Y. Zhuo, "The wavefront aberration analysis and testing accuracy evaluation for the large aberration aspheric system based on the best fit sphere," in (SPIE,2007),68342V.
115. D. Liu, Y. Yang, C. Tian, Y. Luo, and L. Wang, "Practical methods for retrace error correction in nonnull aspheric testing," Opt. Express,2009,17(9), 7025-7035.
116. Z. Malacara and D. Malacara, "Design of Lenses to Project the Image of a Pupil in Optical-Testing Interferometers," Appl Optics,1995,34(4),739-742.
117. J. C. Wyant and V. P. Bennett, "Using Computer Generated Holograms to Test Aspheric Wavefronts," Appl Optics,1972,11(12),2833-2839.
118. J. E. Greivenkamp and R. O. Gappinger, "Design of a nonnull interferometer for aspheric wave fronts," Appl Optics,2004,43(27),5143-5151.
119. M. A. Lundgren and W. L. Wolfe, "Alignment of a 3-Mirror Off-Axis Telescope by Reverse Optimization," Optical Engineering,1991,30(3), 307-311.
120. E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization Alignment Algorithm using Zernike Sensitivity," J. Opt. Soc. Korea,2005, 9(2),68-73.
121. I. Powell, "Employment of Reverse Optimization to Relax Manufacturing Tolerances Imposed on System Constructional Parameters Associated with Complex Optical Systems." Appl. Opt.,2000,39(13),2174-2183.
122. C. R. Wolfe and J. K. Lawson. "Measurement and analysis of wavefront structure from large-aperture ICF optics," in Solid State Lasers for Application to Inertial Confinement Fusion (ICF), (SPIE,1995),361-385.
123. 刘耀红,滕霖,李大琪,张萧,”功率谱密度(Psd)在评价超精密光学表面中的应用研究,”航空精密制造技术,2006,42(02),1-3.
124. 于瀛洁,”关于光学元件波面测量中的功率谱密度,”计量学报,2003,24(2),103-107.
125. 刘红婕,景峰,左言磊,胡东霞,粟敬钦,彭志涛,周维,李强,张昆,”激光波前功率谱密度与焦斑旁瓣的关系,”中国激光,2006,33(04),504-508.
126. 柴立群,许乔,邓燕,石崎凯,”强激光系统波前功率谱密度的数值计算研究,”光学技术,2005,31(04),577-579.
127. 许乔,顾元元,柴林,李伟,“大口径光学元件波前功率谱密度检测,”光学 学报.2001,33(03),20-23.
128. 徐芳,魏全忠,伍凡,”用功率谱密度函数评价光学面形中频误差特性,”光电工程,1999,26(S1),139-143.
129. 沈卫星,徐德衍,”强激光光学元件表面功率谱密度函数估计,”强激光与粒子束,2000,12(04),392-396.
130. 刘东,杨甬英,田超,卓永模,”用于校正非球面非零位检测中的原理误差的方法,”(2008).
131. 郑立功,常军,张学军,程灏波,张峰,”大数值孔径、高次非球面透镜的加工与检验,”光学技术,2003,29(05),584-586.
132. 付联效,吴永刚,郝沛明,王鹏,”透镜补偿检验的研究与分析,”光子学报,2007,36(11),2057-2061.
133. D. Liu, Y. Y. Yang, J. M. Weng. X. M. Zhang. B. Chen, and X. W. Qin. "Measurement of transient near-infrared laser pulse wavefront with high precision by radial shearing interferometer." Opt Commun,2007.275(1). 173-178.
134. D. Liu, Y. Y. Yang, L. Wang, and Y. M. Zhuo, "Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer," Appl Optics. 2007.46(34).8305-8314.
135. Z. Malacara and D. Malacara, "Design of lenses to project the image of a pupil in optical testing interferometers," Appl. Opt.,1995,34(4),739-742.
136. J. Sullivan, Optical Science Center, University of Arizona, Tucson. AZ, USA (personal communication.2009).
137. B. M. Robinson and P. J. Reardon, "Distortion compensation in interferometric testing of mirrors," Appl. Opt.,2009,48(3).560-565.
138. J. J. Sullivan and J. E. Greivenkamp, "Design of partial nulls for testing of fast aspheric surfaces." in Optical Manufacturing and Testing Ⅶ, (SPIE.2007). 66710W-66718.
139. S. Djidel, J. K. Gansel. H. I. Campbell, and A. H. Greenaway, "High-speed, 3-dimensional, telecentric imaging." Opt. Express,2006,14(18),8269-8277.
140. W. C. Folz and B. G. Ledley, "Telecentric optical system for observing daytime chemical releases at high altitudes." Appl. Opt.,1981.20(6).951-954.
141. 董卫斌.张敏,达争尚,陈良益,董晓娜,何俊华.”强激光装置中玻璃疵病在线检测的光学系统设计.”光子学报.2009.38(03).685-688.
142. 叶军君.兰劲.郭隐彪.”非球面检测误差分析和误差补偿策略研究.”中国机械工程.2007.18(23).2793-2797.
143. 美国ZEMAX公司. www.zemax.com.
144. ZEMAX CORP., "ZEMAX users' manual," 2005.
145. PI公司,http://www.pi-china.cn/.
146. 杨甬英,卓永模,杨明建,”用于超光滑表面无损检测的光学轮廓仪,”光电工程,1999,26(06),12-16.
147. 杨甬英,徐敏,卓永模,”实时扫描非接触测量表面微观轮廓仪,”浙江大学学报(工学版),1999,33(03),317-322.
148. M. Servin, J. L. Marroquin, and F. J. Cuevas, "Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms," Journal of the Optical Society of America a-Optics Image Science and Vision,2001, 18(3),689-695.
149. M. Servin, J. L. Marroquin, and F. J. Cuevas, "Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique," Appl. Opt.,1997,36(19),4540-4548.
150. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," Journal of the Optical Society of America a-Optics Image Science and Vision,2001,18(8),1862-1870.
151. K. G. Larkin, "Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform," Journal of the Optical Society of America a-Optics Image Science and Vision,2001, 18(8),1871-1881.
152. M. Servin, J. L. Marroquin, and J. A. Quiroga, "Regularized quadrature and phase tracking from a single closed-fringe interferogram," J. Opt. Soc. Am. A, 2004,21(3),411-419.
153. J. C. Estrada, M. Servin, and J. L. Marroquin, "Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes," Opt. Express, 2007,15(5),2288-2298.
154. T. Kreis, "Digital Holographic Interference-Phase Measurement Using the Fourier-Transform Method," Journal of the Optical Society of America a-Optics Image Science and Vision,1986,3(6),847-855.
155. P. Kuttner, "Modulation Transfer Functions of Ground-Glass Screens," Appl. Opt.,1972,11(9),2024-2027.
156. 黄浩,郭隐彪.王振忠,谢仁宁,”轴对称非球面加工误差分离及补偿技术.”机械工程学报,2005,41(12),177-181.
157. 贾立德,郑子文,李圣怡,戴一帆,”光学非球面坐标测量中位姿误差的分离与优化.”光学精密工程,2007,15(08),1229-1234.