高精度点衍射球面干涉检测技术及系统研究
|
摘要
光学球面元件由于易加工、成本低等优点,在现代精密光学系统中得到了广泛的应用。随着微电子、航天航空等高科技前沿领域对于光学球面面形精度的不断提高,同时也对球面检测精度提出了很高的要求。虽然Twyman-Green型、Fizeau型球面干涉检测系统以及绝对检测法等传统球面干涉检测技术仍是目前应用最广的检测手段,但其精度都受到了参考标准镜面形精度的限制,因而难以满足高精度球面检测的需要。而作为一种新型的高精度球面检测手段,点衍射干涉检测技术可实现亚纳米量级的检测精度,并具有很好的精度再现性。目前,该技术是目前国内外再高精度面形检测领域的一个重要研究热点,尤其是国内在该技术领域的研究尚不成熟,仍有许多关键技术和问题亟待深入研究解决。
本论文主要研究的是可用于高精度球面检测的针孔式点衍射干涉检测技术和系统、点衍射波前精确仿真模型、系统精度影响因素及其高精度校正技术、数据测量和图像处理技术等。该研究对于实现高精度球面、尤其是大数值孔径球面的检测技术有着重要意义。主要研究内容包括：
论述了高精度球面检测技术在现代光学测试及系统仪器中的重要应用意义。综合国内外球面检测技术研究进展情况,提出了可用于球面高精度检测的点衍射干涉检测技术及系统的必要性。
构建了基于有限时域差分算法的针孔点衍射波前精确仿真模型,并对影响针孔点衍射波前质量的针孔厚度、尺寸、数值孔径范围以及针孔入射波前像差等主要相关因素进行了分析。利用仿真结果,可为点衍射干涉检测系统的相关器件参数设计提供可靠的数值依据。
针对高精度球面检测问题,提出了一套完备的针孔式点衍射球面干涉检测技术及系统方案。并结合实际应用要求,详细论述了检测系统中的关键技术和元器件的设计要求及其依据。
分析了PZT移相器在微位移过程中的端面旋转以及非线性问题,并在分析模型基础上,提出了一种基于干涉条纹分析技术的PZT移相器在线检测技术,根据采集的干涉条纹状态实时分析PZT移相器的端面旋转状态和微位移量,进而实现多步移相干涉检测中相移量的精确控制。
研究了高精度球面、尤其是大数值孔径球面检测中的待测球面调整误差问题,详细分析并精确推导了球面调整误差的表现形式以及波面检测结果的影响。提出了基于波前差分的高精度球面调整误差校正方法,并进行了数值仿真和实验验证。
分析了高精度点衍射球面干涉检测系统中的主要误差因素,并对其进行了理论建模、实验及仿真分析,提出了相应的高精度校正方法及处理技术。研究了高精度点衍射球面干涉检测系统所能实现的理论检测精度,其RMS值达到了近0.0010λ。该分析不但有利于点衍射球面干涉检测系统的高精度实现,还可为其进一步提高、改进提供可行的方案。
设计建立了一套高精度点衍射球面干涉检测原理性实验系统,将高反射率和低反射率球面的实际面形检测结果与Zygo干涉仪进行比较,实现精度PV值优于0.0100λ、RMS值优于0.0020λ,并且重复性精度PV值和RMS值分别优于0.0050λ和0.0010λ,达到了预期实验结果,进而对所提出的检测技术及系统进行了原理性实验论证。
总结了本论文所开展的工作,对下一步工作和研究方向进行展望并提出相关建议。
Optics with spherical surfaces has the advantages of ease to fabricate and low cost, and it is widely applied in modern precise optical systems. The development of the high-tech frontier fields such as microelectronics, aeronautics and asreonautics, has placed ultra-high requirement on the precision of optical surfaces, and so does the measurement tools. Since the achievable precision of traditional interferometers for testing spherical surfaces, such as the Twyman-Green-type and Fizeau-type interferometers and absolute measurement technology, is limited by the aberration of standard optics that produces spherical reference wavefront, they cannot meet the needs of high-precision spherical surface testing. As a novel precise measurement tool, the point diffraction interferometer (PDI) enables the measurement precision in the order of subnanometer, and has good precision reproducibility. It is a significant research focus on the high-precision optical surface testing filed. However, the domestic research on the PDI is at the starting stage, and there are still many key technical issues to further study and problems to solve.
This dissertation mainly research on the pinhole-type point diffraction interferometric system for the high-precision testing of spherical surfaces, including precise modeling analysis of pinhole diffracted wavefront, accurate calibration of testing system error factors, experimental data measurement and image processing, etc. The research carried out in the dissertation is of great significance for the high-precision testing of spherical surfaces, especially the high-numerical-aperture spherical surfaces. The major content of this dissertation include:
The great contribution of high-precision spherical surface testing technology to the modern optical testing system is discussed. After a review over the current spherical surface testing methods, the necessity of the research on the point diffraction interferometric testing system is put forward.
A simulation model based on Finite-Difference Time-Domain method is proposed to precisely analyze the pinhole diffracted wavefront. The related factors to the sphericity of diffracted wavefront, such as the pinhole thickness, diameter, numerical-aperture range and the incident wavefront error, is analyzed in detail. And the simulation results provides theoretical basis for the related devices design in the point diffraction interferometric testing system.
A pinhole point diffraction interferometric testing system and the design scheme are proposed for high-precision spherical surfaces testing. Combined with the practical application, the design of key technologies and devices, as well as the corresponding basis is described in detail.
The end rotation of the PZT phase shifter in interferometric testing system, as well as its nonlinearity. is analyzed. A technique based on the fringe analysis is proposed for the in-situ testing of PZT phase shifter. According to the changes of the acquired interferograms, the end rotation and displacement of PZT phase shifter are tested in real time, by which the precise control of phase shift in the multiple-step phase-shifting interferometry can be realized.
The issue of misalignment aberrations in high-precision spherical surface, especially high-numerical-aperture spherical surface testing is studied, and a rigorous model is presented to analyze the introduced high-order aberrations by misalignment. A novel calibration technique based on the wavefront difference is proposed to calibrate the misalignment aberrations, both the computer simulation and experiments are carried out demonstrate the feasibility of the proposed method.
The main error factors of the proposed high-precision point diffraction interferometric system for spherical surface testing, as well as the theoretical model, are analyzed in detail, and the corresponding precise calibration methods are proposed. The achievable theoretical precision of the proposed system is analyzed. The study not only helps to realize the high precision of the testing system, but also provides a feasible way for its further improvement.
An experimental, point diffraction interferometric system for high-precision spherical surface testing has been established. The testing experiments for the spherical surfaces, respectively with high and low reflectivities, have been carried out. Compared with the testing results of Zygo interferometer, the accuracies better than0.0100λ PV and0.0020λ RMS are realized. Besides, the repeatability precision of the experimental system is measured, with RMS value better than0.0010λ and PV0.0050λ achieved. The feasibility of the proposed testing system has been demonstrated with the experimental testing results, and some suggestions on the further study are given at the end. This dissertation is of great value for the realization and performance improvement of the high-precision point diffraction interferometric testing system.
本论文主要研究的是可用于高精度球面检测的针孔式点衍射干涉检测技术和系统、点衍射波前精确仿真模型、系统精度影响因素及其高精度校正技术、数据测量和图像处理技术等。该研究对于实现高精度球面、尤其是大数值孔径球面的检测技术有着重要意义。主要研究内容包括：
论述了高精度球面检测技术在现代光学测试及系统仪器中的重要应用意义。综合国内外球面检测技术研究进展情况,提出了可用于球面高精度检测的点衍射干涉检测技术及系统的必要性。
构建了基于有限时域差分算法的针孔点衍射波前精确仿真模型,并对影响针孔点衍射波前质量的针孔厚度、尺寸、数值孔径范围以及针孔入射波前像差等主要相关因素进行了分析。利用仿真结果,可为点衍射干涉检测系统的相关器件参数设计提供可靠的数值依据。
针对高精度球面检测问题,提出了一套完备的针孔式点衍射球面干涉检测技术及系统方案。并结合实际应用要求,详细论述了检测系统中的关键技术和元器件的设计要求及其依据。
分析了PZT移相器在微位移过程中的端面旋转以及非线性问题,并在分析模型基础上,提出了一种基于干涉条纹分析技术的PZT移相器在线检测技术,根据采集的干涉条纹状态实时分析PZT移相器的端面旋转状态和微位移量,进而实现多步移相干涉检测中相移量的精确控制。
研究了高精度球面、尤其是大数值孔径球面检测中的待测球面调整误差问题,详细分析并精确推导了球面调整误差的表现形式以及波面检测结果的影响。提出了基于波前差分的高精度球面调整误差校正方法,并进行了数值仿真和实验验证。
分析了高精度点衍射球面干涉检测系统中的主要误差因素,并对其进行了理论建模、实验及仿真分析,提出了相应的高精度校正方法及处理技术。研究了高精度点衍射球面干涉检测系统所能实现的理论检测精度,其RMS值达到了近0.0010λ。该分析不但有利于点衍射球面干涉检测系统的高精度实现,还可为其进一步提高、改进提供可行的方案。
设计建立了一套高精度点衍射球面干涉检测原理性实验系统,将高反射率和低反射率球面的实际面形检测结果与Zygo干涉仪进行比较,实现精度PV值优于0.0100λ、RMS值优于0.0020λ,并且重复性精度PV值和RMS值分别优于0.0050λ和0.0010λ,达到了预期实验结果,进而对所提出的检测技术及系统进行了原理性实验论证。
总结了本论文所开展的工作,对下一步工作和研究方向进行展望并提出相关建议。
Optics with spherical surfaces has the advantages of ease to fabricate and low cost, and it is widely applied in modern precise optical systems. The development of the high-tech frontier fields such as microelectronics, aeronautics and asreonautics, has placed ultra-high requirement on the precision of optical surfaces, and so does the measurement tools. Since the achievable precision of traditional interferometers for testing spherical surfaces, such as the Twyman-Green-type and Fizeau-type interferometers and absolute measurement technology, is limited by the aberration of standard optics that produces spherical reference wavefront, they cannot meet the needs of high-precision spherical surface testing. As a novel precise measurement tool, the point diffraction interferometer (PDI) enables the measurement precision in the order of subnanometer, and has good precision reproducibility. It is a significant research focus on the high-precision optical surface testing filed. However, the domestic research on the PDI is at the starting stage, and there are still many key technical issues to further study and problems to solve.
This dissertation mainly research on the pinhole-type point diffraction interferometric system for the high-precision testing of spherical surfaces, including precise modeling analysis of pinhole diffracted wavefront, accurate calibration of testing system error factors, experimental data measurement and image processing, etc. The research carried out in the dissertation is of great significance for the high-precision testing of spherical surfaces, especially the high-numerical-aperture spherical surfaces. The major content of this dissertation include:
The great contribution of high-precision spherical surface testing technology to the modern optical testing system is discussed. After a review over the current spherical surface testing methods, the necessity of the research on the point diffraction interferometric testing system is put forward.
A simulation model based on Finite-Difference Time-Domain method is proposed to precisely analyze the pinhole diffracted wavefront. The related factors to the sphericity of diffracted wavefront, such as the pinhole thickness, diameter, numerical-aperture range and the incident wavefront error, is analyzed in detail. And the simulation results provides theoretical basis for the related devices design in the point diffraction interferometric testing system.
A pinhole point diffraction interferometric testing system and the design scheme are proposed for high-precision spherical surfaces testing. Combined with the practical application, the design of key technologies and devices, as well as the corresponding basis is described in detail.
The end rotation of the PZT phase shifter in interferometric testing system, as well as its nonlinearity. is analyzed. A technique based on the fringe analysis is proposed for the in-situ testing of PZT phase shifter. According to the changes of the acquired interferograms, the end rotation and displacement of PZT phase shifter are tested in real time, by which the precise control of phase shift in the multiple-step phase-shifting interferometry can be realized.
The issue of misalignment aberrations in high-precision spherical surface, especially high-numerical-aperture spherical surface testing is studied, and a rigorous model is presented to analyze the introduced high-order aberrations by misalignment. A novel calibration technique based on the wavefront difference is proposed to calibrate the misalignment aberrations, both the computer simulation and experiments are carried out demonstrate the feasibility of the proposed method.
The main error factors of the proposed high-precision point diffraction interferometric system for spherical surface testing, as well as the theoretical model, are analyzed in detail, and the corresponding precise calibration methods are proposed. The achievable theoretical precision of the proposed system is analyzed. The study not only helps to realize the high precision of the testing system, but also provides a feasible way for its further improvement.
An experimental, point diffraction interferometric system for high-precision spherical surface testing has been established. The testing experiments for the spherical surfaces, respectively with high and low reflectivities, have been carried out. Compared with the testing results of Zygo interferometer, the accuracies better than0.0100λ PV and0.0020λ RMS are realized. Besides, the repeatability precision of the experimental system is measured, with RMS value better than0.0010λ and PV0.0050λ achieved. The feasibility of the proposed testing system has been demonstrated with the experimental testing results, and some suggestions on the further study are given at the end. This dissertation is of great value for the realization and performance improvement of the high-precision point diffraction interferometric testing system.
引文
1. D. M. Williamson, "Lithographic Lenses," (Nikon Research Corporation of america,2006).
2. T. Matsuyama, Y. Ohmura, D. M. Williamson, "The lithographic lens:its history and evolution," in Optical Microlithography XIX, Pts 1-3, (SPIE. 2006),615403.
3. C. C. A. Chen, C. M. Chen, J. R. Chen, "Toolpath generation for diamond shaping of aspheric lens array," J Mater Process Tech,2007,192(194-199.
4. M. Warren, "Diamond-Turned Optics Manufacturing and Precision Mechanical Metrology," Optics & Photonics News,2008,19(3):18-21.
5. 德国NTGL公司网址http://www.n-t-g.de/
6. 美国QED Technologies公司网址http://q edmef.com/.
7. 饶学军,凌宁.王成,姜文汉,”哈特曼-夏克传感器在非球面加工中的应用,”光学学报,2002,22(4)：491-494.
8. I. Ghozeil, "Use of screen rotation in testing large mirrors," in Instrumentation in astronomy Ⅱ, (SPIE,1974),
9. 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(1)：69-72.
10. 李直,赵洋,李达成,”衍射型长程大型非球面轮廓测量仪,”光学学报,2002,22(10)：1224-1228.
11. 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(2)：41-44.
12. J. E. Griffith, D. A. Grigg, "Dimensional Metrology with Scanning Probe Microscopes," J Appl Phys,1993,74(9):R83-R109.
13. N. I. Chkhalo, D. G. Raskin, N. N. Salashchenko, "Capabilities of microinterferometer with digital recording of images for study micro objects with sub nanometer resolution," in Micro- and Nanoelectronics 2007, (SPIE. 2008),702512.
14. 日本Olympus公司网址http://cn.olvmpus.com/opto mechatronics/index.aspx.
15. 美国ZYGO公司网址www.zygo.com.
16. K. Creath, J. C. Wyant, "Testing Spherical Surfaces-a Fast, Quasi-Absolute Technique," Appl Optics,1992,31(22):4350-4354.
17. J. Pfund, N. Lindlein, J. Schwider, R. Burow, T. Blumel, K. E. Elssner. "Absolute sphericity measurement:a comparative study of the use of interferometry and a Shack-Hartmann sensor," Opt Lett,1998,23(10): 742-744.
18. D. S. Wang, K. W. Wang, Y. B. Shen, J. H. Peng, "Error Analysis of Spherical Ultra-Precision Measurement," in 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies:Optical Test and Measurement Technology and Equipment, (SPIE,2010),757600.
19. 彭建华,沈亦兵,汪凯巍,刘勇,“两位置球面面形检测方法研究,”光子学报,2011,40(9)：1361-1365.
20. R. N. Smartt, W. H. Steel, "Theory and Application of Point-Diffraction Interferometers," Japanese Journal of Applied Physics,1975,14(351-356.
21. G. E. Sommargren, "Phase Shifting Diffraction Interferometry for Measuring Extreme Ultraviolet Optics," OSA Trends in Optics and Photonics,1996, V4(108-112.
22. G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty. F. J. Snell, D. R. Dillon, L. S. Bradsher, " 100-picometer interferometry for EUVL," in Emerging Lithographic Technologies Ⅵ, (SPIE,2002),316-328.
23. H. Kihm, S.-W. Kim, "Fiber optic diffraction interferometer for testing spherical mirrors," in Interferometry Ⅺ:Techniques and Analysis, (SPIE, 2002),394-400.
24. H. Kihm, S. W. Kim, "Oblique fiber optic diffraction interferometer for testing spherical mirrors," Optical Engineering,2005,44(12):125601.
25. T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, "Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers," Optical Review,2007,14(6):401-405.
26. T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, T. Kataoka, "Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers," Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2010,616(2-3):233-236.
27. K. Otaki, F. Bonneau. Y. Ichihara. "Absolute measurement of spherical surface by point diffraction interferometer." in Optical Engineering for Sensing and Nanotechnology, (SPIE,1999).602-605.
28. K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, S. Okazaki. "Development of the point diffraction interferometer for extreme ultraviolet lithography:Design, fabrication, and evaluation," Journal of Vacuum Science & Technology B,2002.20(6):2449-2458.
29. K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama. S. Okazaki, "Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror," Journal of Vacuum Science & Technology B,2002,20(1):295-300.
30. K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, T. Gemma, "Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL," in SPIE,2003),182-190.
31. E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowell, J. Bokor, D. Attwood, "At-wavelength interferometry for extreme ultraviolet lithography," Journal of Vacuum Science & Technology B, 1997,15(6):2455-2461.
32. P. P. Naulleau, K. A. Goldberg, S. H. Lee, C. Chang. D. Attwood, J. Bokor, "Extreme-ultraviolet phase-shifting point-diffraction interferometer:a wave-front metrology tool with subangstrom reference-wave accuracy," Appl Optics,1999,38(35):7252-7263.
33. M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada. K. Otaki, K. Murakami. J. Saito. M. Niibe, M. Takeda, "Recent progress of EUV wavefront metrology in EUVA," in Advances in Mirror Technology for X-Ray, Euv Lithography, Laser, and Other Applications II, (SPIE,2004).27-36.
34. M. A. Johnson, D. W. Phillion, G. E. Sommargren, T. A. Decker. J. S. Taylor. Y. Gomei, O. Kakuchi, S. Takeuchi, "Construction and testing of wavefront reference sources for interferometry of ultra-precise imaging systems," in Optical Manufacturing and Testing Ⅵ, (SPIE,2005).58690P.
35. 刘国淦,张学军,王权陡,张忠玉,郭培基,张峰,齐涤菲,”光纤点衍射干涉仪的技术研究,”光学精密工程,2001.9(2)：4.
36. 曹晓君,张学军,李艳红,”光纤点衍射干涉仪调整方法与条纹分析,”光机电信息,2003,3)：3.
37. L. F. Chen, L. Nie, T. G. Zhou, D. G. Sha, "The comparison of two kinds of fiber phase shifting point-diffraction interferometer," in 27th International Congress on High-Spheed Photography and Photonics, (SPIE,2007).627974.
38. S. Wu, T. G. Zhou, D. G. Sha, J. M. Lin, L. F. Chen, "Key techniques in an absolute measurement method of spherical lens," in Optical Design and Testing II, (SPIE,2007),683435.
39. S. Wu, T. G. Zhou, J. M. Lin, L. F. Chen, L. Nie, D. G. Sha. "Fiber point diffraction interferometer in measurement of spherical lens," in International Symposium on Photoelectronic Detection and Imaging 2007:Optoelectronic System Design, Manufacturing, and Testing, (SPIE.2008),662415.
40. L. F. Chen, Y. Q. Ren, J. Li, "Flat surface measurements on fiber point diffraction interferometer," Optical Engineering,2010,49(5):050503.
41. 邢廷文,何国良,舒亮,“193nm移相点衍射干涉仪的测量误差分析,”光电工程,2009,36(2)：67-72.
42. 邓小玖,李怀龙,刘彩霞,胡继刚,王飞,”矢量衍射理论的比较研究及标量近似的有效性,”量子电子学报,2007,24(5)：543-547.
43. K. L. Duan, B. D. Lu, "A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations," Optik,2004,115(5):218-222.
44. 陈琛,杨甬英,王道档,卓永模,”基于时域有限差分方法的点衍射波前误差分析,”中国激光,2011,38(9)：0908003.
45. Y. Kane, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," Antennas and Propagation, IEEE Transactions on Antennas and Propagation,1966,14(3):302-307.
46. 葛德彪,闫玉波,电磁波时域有限差分方法,西安：西安电子科技大学出版社,2002,pp.15-18.
47. A. Taflove, S. C.Haguess, Computational Electrodynamics:The Finite-Diffraction Time-Domain Method,2nd ed., London:Artech House, 2000.
48. Y. Jiang, H. Y. Gao, S. P. Yu, H. Xiao, X. P. Liu, W. Teng, "The Influence of Different Grid Length to the FDTD Calculation," Ieee Intl Conf Ind I,2008: 618-621.
49. Y. Sekine, A. Suzuki, M. Hasegawa, C. Ouchi, S. Hara, T. Hasegawa, Y. Kuramoto, S. Kato, "Wave-front errors of reference spherical waves in high-numerical aperture point diffraction interferometers," Journal of Vacuum Science & Technology B,2004,22(1):104-108.
50. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics,1994,114(2): 185-200.
51. J. A. Kong, Electromagnetic, New York:John Wiley & Sons,1986. pp. 380-382.
52. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Polarization point-diffraction interferometer for high-precision testing of spherical surface," in 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies:Optical Test and Measurement Technology? and Equipment, (SPIE,2010),76560F.
53. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Point Diffraction Interferometer with Adjustable Fringe Contrast for Testing Spherical Surfaces," Appl Optics,2011, 50(16):2342-2348.
54. 美国MellesGriot公司网址：www.mellesgriot.com.
55. 陈军,光学电磁理论,北京：科学出版社,2005,pp.94-116.
56. A. Paturzo, S. Grilli, P. Ferraro, "Point-diffraction interferometer by electro-optic effect in lithium niobate crystals," in Optical Measurement Systems for Industrial Inspection V, Pts 1 and 2, (SPIE,2007),66160F.
57. 杨国光等,群光学与系统,杭州：浙江大学出版社,2008,pp.218-294.
58. 郑颖君,精密计量与测试技术,杭州：中国计量学院,2000,pp.131-138.
59. 周剑平,”基于MATLAB的圆度评定方法,”计量与测试技术,2005,32(2)：5-7.
60. 王利娟,刘立人,栾竹,孙建锋,周煜,”相移雅满横向剪切干涉仪,”中国激光,2009,36(5)：127-131.
61. 孔梅梅,高志山,陈磊,徐春生,”基于偏振移相的环路径向剪切干涉,”光学学报,2010,30(1)：1156-1159.
62. K. Patorski, L. Salbut, "Simple polarization phase-stepping scatterplate interferometry," Optical Engineering,2004,43(2):393-397.
63. R. M. Neal, J. C. Wyant, "Polarization phase-shifting point-diffraction interferometer," Appl Optics,2006,45(15):3463-3476.
64. P. F. Forman, "The Zygo interferometer system," in Interferometry, (SPIE, 1979),41-48.
65. D. Malacara, Optical Shop Testing, Third ed., New Jersey:John Wiley & Sons, Inc.,2007, pp.24-25.
66. 马强,刘伟奇,李香波,康玉思,魏忠伦,冯睿,柳华,”点衍射干涉仪中小孔衍射波面误差分析,”光学学报,2008,28(12)：4.
67. 卢增雄,金春水,张立超,王丽萍,”极紫外三维小孔矢量衍射波面质量分析,”光学学报,2010,30(10)：2849-2854.
68. 郁道银,谈恒英,工程光学,北京：机械工业出版社,1999,pp.198-201.
69. 王道档,杨甬英,陈琛,卓永模.”点衍射球面检测中的斜反射波前像差校正,”光学学报,2011,31(6)：0612003.
70. 陈菽莹,汪歆,韩振兴,都智刚,王晓扬,李新碗,陈建平,”干涉型光纤Michelson微弱磁场传感器降噪方法研究,”光电子·激光,2008,19(7)：888-890.
71. J. Rohlin, "An Interferometer for Precision Angle Measurements," Appl Optics, 1963,2(7):762-763.
72. D. Malacara, O. Harris, "Interferometric Measurement of Angles," Appl Optics,1970,9(7):1630-1633.
73. P. Shi, E. Stijns, "New Optical Method for Measuring Small-Angle Rotations," Appl Optics,1988,27(20):4342-4344.
74. A. E. Ennos, M. S. Virdee, "High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation," Precision Engineering. 1982,4(1):5-8.
75. J. Yuan, X. W. Long, "CCD-area-based autocollimator for precision small-angle measurement," Rev. Sci. Instrum.,2003,74(3):1362-1365.
76. J. Yuan, X. W. Long, K. Y. Yang, "Temperature-controlled autocollimator with ultrahigh angular measuring precision," Rev. Sci. Instrum.,2005,76(12): 125106.
77. P. S. Huang, S. Kiyono, O. Kamada, "Angle Measurement Based on the Internal-Reflection Effect-a New Method," Appl Optics,1992,31(28): 6047-6055.
78. P. S. Huang, J. Ni, "Angle Measurement Based on the Internal-Reflection Effect and the Use of Right-Angle Prisms," Appl Optics,1995,34(22): 4976-4981.
79. P. S. Huang, J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl Optics,1996,35(13):2239-2241.
80. S. F. Wang, M. H. Chiu, C. W. Lai, R. S. Chang, "High-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry," Appl Optics,2006,45(26):6702-6707.
81. S. Prakash, S. Singh, S. Rana, "Automated small tilt-angle measurement using Lau interferometry," Appl Optics,2005,44(28):5905-5909.
82. X. L. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, "Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns," Appl Optics,1996.35(28):5657-5666.
83. X. L. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, "High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns," Appl Optics,1997,36(25):6190-6195.
84. P. S. Chung, F. J. Wen, "Use of the circular Dammann grating in angle measurement," Appl Optics,2008,47(28):5197-5200.
85. 武旭华,陈磊,颜加军,“移相器微位移旋转误差的分析及测试,”光子学报,2006,35(6)：919-923.
86. R. Nerino, "Capacitive sensor arrays in dimensional analysis of surfaces," IEEE Trans. Instrum. Meas.,1995,44(4):875-880.
87. M. S. Damnjanovic, L. D. Zivanov, L. F. Nagy. S. M. Djuric, B. N. Biberdzic, "A Novel Approach to Extending the Linearity Range of Displacement Inductive Sensor," Ieee T Magn,2008,44(11):4123-4126.
88. 王道档,杨甬英,刘东,田超,骆永洁,卓永模,”压电移相器的空间旋转误差建模与实验分析,”光电子·激光,2009,20(5)：571-575.
89. E. Gelmini, U. Minoni, F. Docchio, "Tunable, Double-Wavelength Heterodyne-Detection Interferometer for Absolute-Distance Measurements." Opt Lett,1994,19(3):213-215.
90. 张书练,韩艳梅,”用激光频差调谐曲线进行纳米位移测量的初步研究,”仪器仪表学报,1995,16(1)：393-397.
91. T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, "A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser," Meas Sci Technol,2001,12(2): 157-162.
92. S. Topcu, L. Chassagne, D. Haddad, Y. Alayli, P. Juncar, "Heterodyne interferometric technique for displacement control at the nanometric scale," Rev Sci Instrum,2003,74(11):4876-4880.
93. J. Chen, R. Zhu, L. Liu, D. Chen, M. Chen, "Two-dimensional Fourier transform algorithm analyzing the interferogram and the fringe shift," in Laser Interferometry Ⅳ:Computer-Aided Inter-ferometry, (SPIE,1992),616-625.
94. 朱日宏,王青,陈磊,陈进榜,”压电晶体位移特性曲线干涉自动测量方法,”光子学报,1998,27(2)：180-184.
95. M. Wang, T. Sato, G. M. Lai, S. Shinohara, "Self-mixing interferometry for distance and displacement measurement by Fourier transform method," in Laser Diodes and Leds in Industrial, Measurement, Imaging, and Sensors Applications Ii; Testing, Packaging and Reliability of Semiconductor Lasers V (SPIE,2000),193-200.
96. 袁纵横,周晓军,刘永智,周元庆,”采用频谱分析技术的高分辨率微位移测量方法,”仪器仪表学报,2000,21(1)：101-104.
97. D. D. Wang. Y. Y. Yang, D. Liu, Y. M. Zhuo, "High-precision technique for in-situ testing of the PZT scanner based on fringe analysis," Opt Commun, 2010,283(16):3115-3121.
98. 王道档,杨甬英,陈琛,刘东,卓永模,”模板匹配算法在高精度压电微位移测量中的应用,”纳米技术与精密工程,2010,8(4)：374-379.
99. 王道档,杨甬英,骆永洁,刘东,卓永模,”基于模板匹配算法的压电微位移原位测量技术-”仪器仪表学报,2010-31(3)：530-535.
100. 丘江,刘波,杨静,”基于图像差距分割的快速目标匹配识别算法,”光子学报,2001,30(11)：1343-1347.
101. D. Liu, Y. Y. Yang, L. Wang, Y M. Zhuo, C. H. Lu. L. M. Yang, R. J. Li. "Microscopic scattering imaging measurement and digital evaluation system of defects for fine optical surface," Opt Commun,2007,278(2):240-246.
102. 德国PI公司网址:http://www.physikinstrumente.com/.
103. M. P. Rimmer, D. G. Fox, C. M. King, "Computer Program for Analysis of Interferometric Test Data," Appl Optics,1972,11(12):2790-2796.
104. 李贤辉,吴清文,杨洪波,“光学工程分析中的镜面面形处理新方法,”光学技术,2003,29(6)：752-756.
105. J. C. Wyant, K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic Press, San Diego, CA,1992), pp.9-15.
106. S. Han, E. Novak, "Retrace error for the measurement of a long-radius optic,' in 18th Congress of the International Commission for Optics:Optics for the Next Millennium, Technical Digest, (SPIE,1999),597-598.
107. S. Han, J. A. Lamb, A. Olszak, E. Novak, "Design of an interferometer for the measurement of long radius optics," in Machine Vision Applications in Industrial Inspection Viii, (SPIE,2000),377-384.
108. V. N. Mahajan, "Zernike polynomials and wavefront fitting," in Optical Shop Testing, third ed., D. Malacara, ed. (Wiley, New York,2007), pp.498-546.
109. J. Y. Wang, D. E. Silva, "Wave-Front Interpretation with Zernike Polynomials," Appl Optics,1980,19(9):1510-1518.
110. D. Malacara. M. Servin. Z. Malacara, "Interferogram Analysis For Optical Testing," Second ed. (CRC Press, Florida,2005).
111. B. Dorband, H. J. Tiziani, "Testing Aspheric Surfaces with Computer-Generated Holograms:Analysis of Adjustment and Shape Errors," Appl Optics,1985,24(16):2604-2611.
112. H. J. Tiziani, "Optical Methods for Precision Measurements," Optical and Quantum Electronics,1989,21(4):253-282.
113. C. S. Huang, "Propagation Errors in Precision Fizeau Interferometry." Appl Optics,1993,32(34):7016-7021.
114. A. E. Lowman, J. E. Greivenkamp, "Interferometer errors due to the presence of fringes," Appl Optics,1996,35(34):6826-6828.
115. M. R. Descour. M. R. Willer, D. S. Clarke, C. E. Volin, "Misalignment modes in high-performance optical systems," Optical Engineering,2000,39(7): 1737-1747.
116. P. E. Murphy, T. G. Brown, D. T. Moore, "Measurement and calibration of interferometric imaging aberrations," Appl Optics,2000,39(34):6421-6429.
117. 张斌,韩昌元,”离轴非球面三反射镜光学系统中计算机优化方法的研究,'光学学报,2001,21(1)：54-58.
118. S. Reichelt, C. Pruss, H. J. Tiziani, "Absolute interferometric test of aspheres by use of twin computer-generated holograms," Appl Optics,2003,42(22): 4468-4479.
119. 罗淼,朱永田,”计算机辅助装调方法在离轴卡塞格林系统中的应用,”光学技术,2008,34(4)：514-517.
120. 王孝坤,王丽辉,张学军,”干涉法事实测量浅度非球面技术,”光学精密工程,2008,16(2)：184-189.
121. P. Zhou, J. H. Burge, "Limits for interferometer calibration using the random ball test," in Optical Manufacturing and Testing VIII, (SPIE,2009),74260U.
122. 巩盾,田铁印,王红,”利用Zernike系数对离轴三反射系统进行计算机辅助装调,”光学精密工程,2010,18(8)：1754-1759.
123. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Misalignment Aberrations Calibration in Testing of High-Numerical-Aperture Spherical Surfaces," Appl Optics, 2011,50(14):2024-2031.
124. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Calibration of Geometrical Systematic Error in High-Precision Spherical Surface Measurement," Opt Commun,2011, 284(16):3878-3885.
125. G. Wang, X.-P. Ling, "Accuracy of fringe pattern analysis," Proc. SPIE,1989, 1163(251-257.
126. 孙学真,苏显渝,荆海龙,”抽样点对基于Zernike多项式曲面拟合精度的影响,”光学仪器,2008,30(4)：6-10.
127. K. Creath, "Error sources in phase-measuring interferometry (Invited Paper)." in Intl Symp on Optical Fabrication, Testing, and Surface Evaluation, (SPIE. 1992).428-435.
128. P. J. d. Groot,"Vibration in phase-shifting interferometry," J. Opt. Soc. Am. A, 1995,12(2):354-365.
129. L. L. Deck, "Suppressing phase errors from vibration in phase-shifting interferometry," Appl. Opt..2009,48(20):3948-3960.
130. 费业泰,误差原理与数据处理,Fifth ed.,北京：机械工业出版社,2004,pp.1-8.
131. P. Hariharan, B. F. Oreb, T. Eiju, "Digital Phase-Shifting Interferometry-a Simple Error-Compensating Phase Calculation Algorithm," Appl Optics,1987, 26(13):2504-2506.
132. C. P. Brophy, "Effect of Intensity Error Correlation on the Computed Phase of Phase-Shifting Interferometry." J Opt Soc Am A,1990,7(4):537-541.
133. B. Gutmann, H. Weber, "Phase-shifter calibration and error detection in phase-shifting applications:a new method," Appl Optics,1998,37(32): 7624-7631.
134. 钱克矛,伍小平,”相移技术中五步等步长Stoilov算法的性能分析，”光学技术,2001,27(1)：13-16.
135. J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik,2003,114(2):63-68.
136. Z. Malacara, D. Malacara, "Design of Lenses to Project the Image of a Pupil in Optical-Testing Interferometers," Appl Optics,1995,34(4):739-742.
137. 卓永模,包正康,相干测试系统与技术,杭州：浙江大学光电系,pp.13-46.
138. 刘东,”通用数字化非球面高精度干涉检测技术与系统研究,”Ph.D.(浙江大学,杭州,2010).
139. 苗二龙,张健,谷勇强,康玉思,刘伟奇,”用于光刻投影物镜检测的高精度菲佐干涉仪误差分析,”中国激光,2010,37(8)：2029-2034.
140. 赵光宙,舒勤,君号分析与处理,北京：机械工业出版社,2001.pp.218-231.
141. B. Edlen, "The Refractive Index of Air " Metrologia,1966,2(2):71-80.
142. K. P. Birch, M. J. Downs, "Correction to the Updated Edlen Equation for the Refractive Index of Air " Metrologia,1994,31(4):315-316.
143. 魏豪明,邢廷文,李云,刘志祥,”632.8nm高精度移相菲佐干涉仪测量误差分析,”激光与光电子学进展,2010,47(4)：041202.
144. 日本西格玛光机株式会网址http://www.sigxna-koki.com.
145. 费业泰,误差理论与数据处理,Fifth ed.,北京：机械工业出版社,2004,pp.43-53.
2. T. Matsuyama, Y. Ohmura, D. M. Williamson, "The lithographic lens:its history and evolution," in Optical Microlithography XIX, Pts 1-3, (SPIE. 2006),615403.
3. C. C. A. Chen, C. M. Chen, J. R. Chen, "Toolpath generation for diamond shaping of aspheric lens array," J Mater Process Tech,2007,192(194-199.
4. M. Warren, "Diamond-Turned Optics Manufacturing and Precision Mechanical Metrology," Optics & Photonics News,2008,19(3):18-21.
5. 德国NTGL公司网址http://www.n-t-g.de/
6. 美国QED Technologies公司网址http://q edmef.com/.
7. 饶学军,凌宁.王成,姜文汉,”哈特曼-夏克传感器在非球面加工中的应用,”光学学报,2002,22(4)：491-494.
8. I. Ghozeil, "Use of screen rotation in testing large mirrors," in Instrumentation in astronomy Ⅱ, (SPIE,1974),
9. 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(1)：69-72.
10. 李直,赵洋,李达成,”衍射型长程大型非球面轮廓测量仪,”光学学报,2002,22(10)：1224-1228.
11. 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(2)：41-44.
12. J. E. Griffith, D. A. Grigg, "Dimensional Metrology with Scanning Probe Microscopes," J Appl Phys,1993,74(9):R83-R109.
13. N. I. Chkhalo, D. G. Raskin, N. N. Salashchenko, "Capabilities of microinterferometer with digital recording of images for study micro objects with sub nanometer resolution," in Micro- and Nanoelectronics 2007, (SPIE. 2008),702512.
14. 日本Olympus公司网址http://cn.olvmpus.com/opto mechatronics/index.aspx.
15. 美国ZYGO公司网址www.zygo.com.
16. K. Creath, J. C. Wyant, "Testing Spherical Surfaces-a Fast, Quasi-Absolute Technique," Appl Optics,1992,31(22):4350-4354.
17. J. Pfund, N. Lindlein, J. Schwider, R. Burow, T. Blumel, K. E. Elssner. "Absolute sphericity measurement:a comparative study of the use of interferometry and a Shack-Hartmann sensor," Opt Lett,1998,23(10): 742-744.
18. D. S. Wang, K. W. Wang, Y. B. Shen, J. H. Peng, "Error Analysis of Spherical Ultra-Precision Measurement," in 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies:Optical Test and Measurement Technology and Equipment, (SPIE,2010),757600.
19. 彭建华,沈亦兵,汪凯巍,刘勇,“两位置球面面形检测方法研究,”光子学报,2011,40(9)：1361-1365.
20. R. N. Smartt, W. H. Steel, "Theory and Application of Point-Diffraction Interferometers," Japanese Journal of Applied Physics,1975,14(351-356.
21. G. E. Sommargren, "Phase Shifting Diffraction Interferometry for Measuring Extreme Ultraviolet Optics," OSA Trends in Optics and Photonics,1996, V4(108-112.
22. G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty. F. J. Snell, D. R. Dillon, L. S. Bradsher, " 100-picometer interferometry for EUVL," in Emerging Lithographic Technologies Ⅵ, (SPIE,2002),316-328.
23. H. Kihm, S.-W. Kim, "Fiber optic diffraction interferometer for testing spherical mirrors," in Interferometry Ⅺ:Techniques and Analysis, (SPIE, 2002),394-400.
24. H. Kihm, S. W. Kim, "Oblique fiber optic diffraction interferometer for testing spherical mirrors," Optical Engineering,2005,44(12):125601.
25. T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, "Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers," Optical Review,2007,14(6):401-405.
26. T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, T. Kataoka, "Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers," Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2010,616(2-3):233-236.
27. K. Otaki, F. Bonneau. Y. Ichihara. "Absolute measurement of spherical surface by point diffraction interferometer." in Optical Engineering for Sensing and Nanotechnology, (SPIE,1999).602-605.
28. K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, S. Okazaki. "Development of the point diffraction interferometer for extreme ultraviolet lithography:Design, fabrication, and evaluation," Journal of Vacuum Science & Technology B,2002.20(6):2449-2458.
29. K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama. S. Okazaki, "Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror," Journal of Vacuum Science & Technology B,2002,20(1):295-300.
30. K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, T. Gemma, "Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL," in SPIE,2003),182-190.
31. E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowell, J. Bokor, D. Attwood, "At-wavelength interferometry for extreme ultraviolet lithography," Journal of Vacuum Science & Technology B, 1997,15(6):2455-2461.
32. P. P. Naulleau, K. A. Goldberg, S. H. Lee, C. Chang. D. Attwood, J. Bokor, "Extreme-ultraviolet phase-shifting point-diffraction interferometer:a wave-front metrology tool with subangstrom reference-wave accuracy," Appl Optics,1999,38(35):7252-7263.
33. M. Hasegawa, C. Ouchi, T. Hasegawa, S. Kato, A. Ohkubo, A. Suzuki, K. Sugisaki, M. Okada. K. Otaki, K. Murakami. J. Saito. M. Niibe, M. Takeda, "Recent progress of EUV wavefront metrology in EUVA," in Advances in Mirror Technology for X-Ray, Euv Lithography, Laser, and Other Applications II, (SPIE,2004).27-36.
34. M. A. Johnson, D. W. Phillion, G. E. Sommargren, T. A. Decker. J. S. Taylor. Y. Gomei, O. Kakuchi, S. Takeuchi, "Construction and testing of wavefront reference sources for interferometry of ultra-precise imaging systems," in Optical Manufacturing and Testing Ⅵ, (SPIE,2005).58690P.
35. 刘国淦,张学军,王权陡,张忠玉,郭培基,张峰,齐涤菲,”光纤点衍射干涉仪的技术研究,”光学精密工程,2001.9(2)：4.
36. 曹晓君,张学军,李艳红,”光纤点衍射干涉仪调整方法与条纹分析,”光机电信息,2003,3)：3.
37. L. F. Chen, L. Nie, T. G. Zhou, D. G. Sha, "The comparison of two kinds of fiber phase shifting point-diffraction interferometer," in 27th International Congress on High-Spheed Photography and Photonics, (SPIE,2007).627974.
38. S. Wu, T. G. Zhou, D. G. Sha, J. M. Lin, L. F. Chen, "Key techniques in an absolute measurement method of spherical lens," in Optical Design and Testing II, (SPIE,2007),683435.
39. S. Wu, T. G. Zhou, J. M. Lin, L. F. Chen, L. Nie, D. G. Sha. "Fiber point diffraction interferometer in measurement of spherical lens," in International Symposium on Photoelectronic Detection and Imaging 2007:Optoelectronic System Design, Manufacturing, and Testing, (SPIE.2008),662415.
40. L. F. Chen, Y. Q. Ren, J. Li, "Flat surface measurements on fiber point diffraction interferometer," Optical Engineering,2010,49(5):050503.
41. 邢廷文,何国良,舒亮,“193nm移相点衍射干涉仪的测量误差分析,”光电工程,2009,36(2)：67-72.
42. 邓小玖,李怀龙,刘彩霞,胡继刚,王飞,”矢量衍射理论的比较研究及标量近似的有效性,”量子电子学报,2007,24(5)：543-547.
43. K. L. Duan, B. D. Lu, "A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations," Optik,2004,115(5):218-222.
44. 陈琛,杨甬英,王道档,卓永模,”基于时域有限差分方法的点衍射波前误差分析,”中国激光,2011,38(9)：0908003.
45. Y. Kane, "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," Antennas and Propagation, IEEE Transactions on Antennas and Propagation,1966,14(3):302-307.
46. 葛德彪,闫玉波,电磁波时域有限差分方法,西安：西安电子科技大学出版社,2002,pp.15-18.
47. A. Taflove, S. C.Haguess, Computational Electrodynamics:The Finite-Diffraction Time-Domain Method,2nd ed., London:Artech House, 2000.
48. Y. Jiang, H. Y. Gao, S. P. Yu, H. Xiao, X. P. Liu, W. Teng, "The Influence of Different Grid Length to the FDTD Calculation," Ieee Intl Conf Ind I,2008: 618-621.
49. Y. Sekine, A. Suzuki, M. Hasegawa, C. Ouchi, S. Hara, T. Hasegawa, Y. Kuramoto, S. Kato, "Wave-front errors of reference spherical waves in high-numerical aperture point diffraction interferometers," Journal of Vacuum Science & Technology B,2004,22(1):104-108.
50. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics,1994,114(2): 185-200.
51. J. A. Kong, Electromagnetic, New York:John Wiley & Sons,1986. pp. 380-382.
52. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Polarization point-diffraction interferometer for high-precision testing of spherical surface," in 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies:Optical Test and Measurement Technology? and Equipment, (SPIE,2010),76560F.
53. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Point Diffraction Interferometer with Adjustable Fringe Contrast for Testing Spherical Surfaces," Appl Optics,2011, 50(16):2342-2348.
54. 美国MellesGriot公司网址：www.mellesgriot.com.
55. 陈军,光学电磁理论,北京：科学出版社,2005,pp.94-116.
56. A. Paturzo, S. Grilli, P. Ferraro, "Point-diffraction interferometer by electro-optic effect in lithium niobate crystals," in Optical Measurement Systems for Industrial Inspection V, Pts 1 and 2, (SPIE,2007),66160F.
57. 杨国光等,群光学与系统,杭州：浙江大学出版社,2008,pp.218-294.
58. 郑颖君,精密计量与测试技术,杭州：中国计量学院,2000,pp.131-138.
59. 周剑平,”基于MATLAB的圆度评定方法,”计量与测试技术,2005,32(2)：5-7.
60. 王利娟,刘立人,栾竹,孙建锋,周煜,”相移雅满横向剪切干涉仪,”中国激光,2009,36(5)：127-131.
61. 孔梅梅,高志山,陈磊,徐春生,”基于偏振移相的环路径向剪切干涉,”光学学报,2010,30(1)：1156-1159.
62. K. Patorski, L. Salbut, "Simple polarization phase-stepping scatterplate interferometry," Optical Engineering,2004,43(2):393-397.
63. R. M. Neal, J. C. Wyant, "Polarization phase-shifting point-diffraction interferometer," Appl Optics,2006,45(15):3463-3476.
64. P. F. Forman, "The Zygo interferometer system," in Interferometry, (SPIE, 1979),41-48.
65. D. Malacara, Optical Shop Testing, Third ed., New Jersey:John Wiley & Sons, Inc.,2007, pp.24-25.
66. 马强,刘伟奇,李香波,康玉思,魏忠伦,冯睿,柳华,”点衍射干涉仪中小孔衍射波面误差分析,”光学学报,2008,28(12)：4.
67. 卢增雄,金春水,张立超,王丽萍,”极紫外三维小孔矢量衍射波面质量分析,”光学学报,2010,30(10)：2849-2854.
68. 郁道银,谈恒英,工程光学,北京：机械工业出版社,1999,pp.198-201.
69. 王道档,杨甬英,陈琛,卓永模.”点衍射球面检测中的斜反射波前像差校正,”光学学报,2011,31(6)：0612003.
70. 陈菽莹,汪歆,韩振兴,都智刚,王晓扬,李新碗,陈建平,”干涉型光纤Michelson微弱磁场传感器降噪方法研究,”光电子·激光,2008,19(7)：888-890.
71. J. Rohlin, "An Interferometer for Precision Angle Measurements," Appl Optics, 1963,2(7):762-763.
72. D. Malacara, O. Harris, "Interferometric Measurement of Angles," Appl Optics,1970,9(7):1630-1633.
73. P. Shi, E. Stijns, "New Optical Method for Measuring Small-Angle Rotations," Appl Optics,1988,27(20):4342-4344.
74. A. E. Ennos, M. S. Virdee, "High accuracy profile measurement of quasi-conical mirror surface by laser autocollimation," Precision Engineering. 1982,4(1):5-8.
75. J. Yuan, X. W. Long, "CCD-area-based autocollimator for precision small-angle measurement," Rev. Sci. Instrum.,2003,74(3):1362-1365.
76. J. Yuan, X. W. Long, K. Y. Yang, "Temperature-controlled autocollimator with ultrahigh angular measuring precision," Rev. Sci. Instrum.,2005,76(12): 125106.
77. P. S. Huang, S. Kiyono, O. Kamada, "Angle Measurement Based on the Internal-Reflection Effect-a New Method," Appl Optics,1992,31(28): 6047-6055.
78. P. S. Huang, J. Ni, "Angle Measurement Based on the Internal-Reflection Effect and the Use of Right-Angle Prisms," Appl Optics,1995,34(22): 4976-4981.
79. P. S. Huang, J. Ni, "Angle measurement based on the internal-reflection effect using elongated critical-angle prisms," Appl Optics,1996,35(13):2239-2241.
80. S. F. Wang, M. H. Chiu, C. W. Lai, R. S. Chang, "High-sensitivity small-angle sensor based on surface plasmon resonance technology and heterodyne interferometry," Appl Optics,2006,45(26):6702-6707.
81. S. Prakash, S. Singh, S. Rana, "Automated small tilt-angle measurement using Lau interferometry," Appl Optics,2005,44(28):5905-5909.
82. X. L. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, "Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns," Appl Optics,1996.35(28):5657-5666.
83. X. L. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, "High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns," Appl Optics,1997,36(25):6190-6195.
84. P. S. Chung, F. J. Wen, "Use of the circular Dammann grating in angle measurement," Appl Optics,2008,47(28):5197-5200.
85. 武旭华,陈磊,颜加军,“移相器微位移旋转误差的分析及测试,”光子学报,2006,35(6)：919-923.
86. R. Nerino, "Capacitive sensor arrays in dimensional analysis of surfaces," IEEE Trans. Instrum. Meas.,1995,44(4):875-880.
87. M. S. Damnjanovic, L. D. Zivanov, L. F. Nagy. S. M. Djuric, B. N. Biberdzic, "A Novel Approach to Extending the Linearity Range of Displacement Inductive Sensor," Ieee T Magn,2008,44(11):4123-4126.
88. 王道档,杨甬英,刘东,田超,骆永洁,卓永模,”压电移相器的空间旋转误差建模与实验分析,”光电子·激光,2009,20(5)：571-575.
89. E. Gelmini, U. Minoni, F. Docchio, "Tunable, Double-Wavelength Heterodyne-Detection Interferometer for Absolute-Distance Measurements." Opt Lett,1994,19(3):213-215.
90. 张书练,韩艳梅,”用激光频差调谐曲线进行纳米位移测量的初步研究,”仪器仪表学报,1995,16(1)：393-397.
91. T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, "A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser," Meas Sci Technol,2001,12(2): 157-162.
92. S. Topcu, L. Chassagne, D. Haddad, Y. Alayli, P. Juncar, "Heterodyne interferometric technique for displacement control at the nanometric scale," Rev Sci Instrum,2003,74(11):4876-4880.
93. J. Chen, R. Zhu, L. Liu, D. Chen, M. Chen, "Two-dimensional Fourier transform algorithm analyzing the interferogram and the fringe shift," in Laser Interferometry Ⅳ:Computer-Aided Inter-ferometry, (SPIE,1992),616-625.
94. 朱日宏,王青,陈磊,陈进榜,”压电晶体位移特性曲线干涉自动测量方法,”光子学报,1998,27(2)：180-184.
95. M. Wang, T. Sato, G. M. Lai, S. Shinohara, "Self-mixing interferometry for distance and displacement measurement by Fourier transform method," in Laser Diodes and Leds in Industrial, Measurement, Imaging, and Sensors Applications Ii; Testing, Packaging and Reliability of Semiconductor Lasers V (SPIE,2000),193-200.
96. 袁纵横,周晓军,刘永智,周元庆,”采用频谱分析技术的高分辨率微位移测量方法,”仪器仪表学报,2000,21(1)：101-104.
97. D. D. Wang. Y. Y. Yang, D. Liu, Y. M. Zhuo, "High-precision technique for in-situ testing of the PZT scanner based on fringe analysis," Opt Commun, 2010,283(16):3115-3121.
98. 王道档,杨甬英,陈琛,刘东,卓永模,”模板匹配算法在高精度压电微位移测量中的应用,”纳米技术与精密工程,2010,8(4)：374-379.
99. 王道档,杨甬英,骆永洁,刘东,卓永模,”基于模板匹配算法的压电微位移原位测量技术-”仪器仪表学报,2010-31(3)：530-535.
100. 丘江,刘波,杨静,”基于图像差距分割的快速目标匹配识别算法,”光子学报,2001,30(11)：1343-1347.
101. D. Liu, Y. Y. Yang, L. Wang, Y M. Zhuo, C. H. Lu. L. M. Yang, R. J. Li. "Microscopic scattering imaging measurement and digital evaluation system of defects for fine optical surface," Opt Commun,2007,278(2):240-246.
102. 德国PI公司网址:http://www.physikinstrumente.com/.
103. M. P. Rimmer, D. G. Fox, C. M. King, "Computer Program for Analysis of Interferometric Test Data," Appl Optics,1972,11(12):2790-2796.
104. 李贤辉,吴清文,杨洪波,“光学工程分析中的镜面面形处理新方法,”光学技术,2003,29(6)：752-756.
105. J. C. Wyant, K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic Press, San Diego, CA,1992), pp.9-15.
106. S. Han, E. Novak, "Retrace error for the measurement of a long-radius optic,' in 18th Congress of the International Commission for Optics:Optics for the Next Millennium, Technical Digest, (SPIE,1999),597-598.
107. S. Han, J. A. Lamb, A. Olszak, E. Novak, "Design of an interferometer for the measurement of long radius optics," in Machine Vision Applications in Industrial Inspection Viii, (SPIE,2000),377-384.
108. V. N. Mahajan, "Zernike polynomials and wavefront fitting," in Optical Shop Testing, third ed., D. Malacara, ed. (Wiley, New York,2007), pp.498-546.
109. J. Y. Wang, D. E. Silva, "Wave-Front Interpretation with Zernike Polynomials," Appl Optics,1980,19(9):1510-1518.
110. D. Malacara. M. Servin. Z. Malacara, "Interferogram Analysis For Optical Testing," Second ed. (CRC Press, Florida,2005).
111. B. Dorband, H. J. Tiziani, "Testing Aspheric Surfaces with Computer-Generated Holograms:Analysis of Adjustment and Shape Errors," Appl Optics,1985,24(16):2604-2611.
112. H. J. Tiziani, "Optical Methods for Precision Measurements," Optical and Quantum Electronics,1989,21(4):253-282.
113. C. S. Huang, "Propagation Errors in Precision Fizeau Interferometry." Appl Optics,1993,32(34):7016-7021.
114. A. E. Lowman, J. E. Greivenkamp, "Interferometer errors due to the presence of fringes," Appl Optics,1996,35(34):6826-6828.
115. M. R. Descour. M. R. Willer, D. S. Clarke, C. E. Volin, "Misalignment modes in high-performance optical systems," Optical Engineering,2000,39(7): 1737-1747.
116. P. E. Murphy, T. G. Brown, D. T. Moore, "Measurement and calibration of interferometric imaging aberrations," Appl Optics,2000,39(34):6421-6429.
117. 张斌,韩昌元,”离轴非球面三反射镜光学系统中计算机优化方法的研究,'光学学报,2001,21(1)：54-58.
118. S. Reichelt, C. Pruss, H. J. Tiziani, "Absolute interferometric test of aspheres by use of twin computer-generated holograms," Appl Optics,2003,42(22): 4468-4479.
119. 罗淼,朱永田,”计算机辅助装调方法在离轴卡塞格林系统中的应用,”光学技术,2008,34(4)：514-517.
120. 王孝坤,王丽辉,张学军,”干涉法事实测量浅度非球面技术,”光学精密工程,2008,16(2)：184-189.
121. P. Zhou, J. H. Burge, "Limits for interferometer calibration using the random ball test," in Optical Manufacturing and Testing VIII, (SPIE,2009),74260U.
122. 巩盾,田铁印,王红,”利用Zernike系数对离轴三反射系统进行计算机辅助装调,”光学精密工程,2010,18(8)：1754-1759.
123. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Misalignment Aberrations Calibration in Testing of High-Numerical-Aperture Spherical Surfaces," Appl Optics, 2011,50(14):2024-2031.
124. D. Wang, Y. Yang, C. Chen, Y. Zhuo, "Calibration of Geometrical Systematic Error in High-Precision Spherical Surface Measurement," Opt Commun,2011, 284(16):3878-3885.
125. G. Wang, X.-P. Ling, "Accuracy of fringe pattern analysis," Proc. SPIE,1989, 1163(251-257.
126. 孙学真,苏显渝,荆海龙,”抽样点对基于Zernike多项式曲面拟合精度的影响,”光学仪器,2008,30(4)：6-10.
127. K. Creath, "Error sources in phase-measuring interferometry (Invited Paper)." in Intl Symp on Optical Fabrication, Testing, and Surface Evaluation, (SPIE. 1992).428-435.
128. P. J. d. Groot,"Vibration in phase-shifting interferometry," J. Opt. Soc. Am. A, 1995,12(2):354-365.
129. L. L. Deck, "Suppressing phase errors from vibration in phase-shifting interferometry," Appl. Opt..2009,48(20):3948-3960.
130. 费业泰,误差原理与数据处理,Fifth ed.,北京：机械工业出版社,2004,pp.1-8.
131. P. Hariharan, B. F. Oreb, T. Eiju, "Digital Phase-Shifting Interferometry-a Simple Error-Compensating Phase Calculation Algorithm," Appl Optics,1987, 26(13):2504-2506.
132. C. P. Brophy, "Effect of Intensity Error Correlation on the Computed Phase of Phase-Shifting Interferometry." J Opt Soc Am A,1990,7(4):537-541.
133. B. Gutmann, H. Weber, "Phase-shifter calibration and error detection in phase-shifting applications:a new method," Appl Optics,1998,37(32): 7624-7631.
134. 钱克矛,伍小平,”相移技术中五步等步长Stoilov算法的性能分析，”光学技术,2001,27(1)：13-16.
135. J. Novak, "Five-step phase-shifting algorithms with unknown values of phase shift," Optik,2003,114(2):63-68.
136. Z. Malacara, D. Malacara, "Design of Lenses to Project the Image of a Pupil in Optical-Testing Interferometers," Appl Optics,1995,34(4):739-742.
137. 卓永模,包正康,相干测试系统与技术,杭州：浙江大学光电系,pp.13-46.
138. 刘东,”通用数字化非球面高精度干涉检测技术与系统研究,”Ph.D.(浙江大学,杭州,2010).
139. 苗二龙,张健,谷勇强,康玉思,刘伟奇,”用于光刻投影物镜检测的高精度菲佐干涉仪误差分析,”中国激光,2010,37(8)：2029-2034.
140. 赵光宙,舒勤,君号分析与处理,北京：机械工业出版社,2001.pp.218-231.
141. B. Edlen, "The Refractive Index of Air " Metrologia,1966,2(2):71-80.
142. K. P. Birch, M. J. Downs, "Correction to the Updated Edlen Equation for the Refractive Index of Air " Metrologia,1994,31(4):315-316.
143. 魏豪明,邢廷文,李云,刘志祥,”632.8nm高精度移相菲佐干涉仪测量误差分析,”激光与光电子学进展,2010,47(4)：041202.
144. 日本西格玛光机株式会网址http://www.sigxna-koki.com.
145. 费业泰,误差理论与数据处理,Fifth ed.,北京：机械工业出版社,2004,pp.43-53.