基于数字莫尔条纹的非球面检测技术研究
|
摘要
光学系统中应用非球面光学元件可以矫正像差,改善像质,提高系统的光学性能,减小系统外形尺寸和重量,因此近些年来在光学仪器的设计和制造中,非球面光学元件以其优越的光学性能正越来越多的被应用于精密的光学仪器中,然而非球面镜形状种类繁多,尺寸和精度要求各有不同,其检测的方法远比球面镜复杂和困难,尤其是大型高精度的非球面光学元件,面形检测难度更大。
本文针对非球面检测问题,提出了子区域拼接数字莫尔条纹检测非球面的新方法,该方法是一种将数字光栅技术、数字移相技术、莫尔技术、载频图像处理技术、相位展开及拼接技术相结合实现对非球面检测的新方法,本文对此种检测方法的原理进行了比较详细和深入的分析。
1、子区域移相数字莫尔条纹相位测量原理
简要介绍了利用子区域移相数字莫尔进行光学相位测量的原理,包括子区域数字莫尔条纹的获得及其数学模型、相移的实现、子区域划分的目的及该种检测方法应注意的关键问题。
2、数字莫尔条纹的滤波处理
从空域和频域两个角度对数字莫尔条纹的滤波方法进行了研究,通过对大量模拟载频干涉图的处理,得出了空域和频域滤波器截止频率的判断方法,分析了不同滤波方法的特点及其性能,得出了比较适合本文的滤波参数。
3、相位展开
介绍了几种常见的相位展开技术,在数字莫尔条纹滤波处理的基础上,利用分区相位的展开方法及残余点判读理论实现了相位展开的处理。
4、展开相位拼接及多项式拟合借鉴子孔径相位拼接方法,利用误差均化技术将得到子区域展开相位分布通过最小二乘拟合方法统一到相同参考基准下,最后结合Gram-schmidt算法利用zernike多项式拟合相同参考下的大量离散数据点,即可得到非球面相位分布。
5、检测实例
对一口径为130mm的非球面镜进行了实际的检测,有效口径内rms为0.0321?。
实践证明子区域拼接数字莫尔条纹技术不需要补偿器可以实现非球面检测,避免了补偿器引进的误差和装调的难度;通过分区采集干涉图,解决了CCD相机截止频率的限制;利用数字移相技术,避免压电陶瓷移相中非线性误差对测量的影响;可以作为中等精度要求的一种检测手段
Optical system application aspherical can correct differ, improve image quality,improve optical performance, reduce the dimensions and weight, so in recent yearsoptical instrument design and manufacturing, and established various aspheric opticsfabrication with its superior optical properties are increasingly applied in precisionoptical instruments, however aspheric mirrors variety, size and accuracy requirementis different, its testing methods than spherical complex and difficult, especially largeprecisionasphericsurfaceopticalelement,faceshapemeasuringmoredifficult.
This paper aim at aspherical testing problem, puts forward a new method ofaspherical testing base on sub_region splicing digital moirépatterns, this methodcontains digital grating technology, digital phase shifting technique ,moire technique,image processing technology, unwrapping and stitching technique .this paper hascarriedondetailedandthethoroughanalysistothiskindoftesting.
1.phasemeasurementprincipleofsub_regionphaseshiftingdigitalmoirépatterns
Introduced phase measurement principle of sub_region phase shifting digitalmoirépatterns,including sub_region digital moirépatterns acquisition and themathematical model, the phase_shifting,sub_region division goal,the key question ofthistesting.
2.Digitalmoirépatternsfilterprocessing
This paper conducted the research from the space domain filter method and thefrequency domain filter method to the digital moirépatterns,through massive simulationcarrierfrequencyinterferenceprocessing,has obtainedjudgmentmethodofthe space domain and the frequency range cut-off frequency of filter,has analyzed thedifferent filter method characteristic and performance,has obtained the quite suitablethisarticlefilterparameter.
3.unwrapping
Introduced several common unwrapping technology,through digital moirépatterns filtering processing,on the basis of the phase launched by partition methodandresidualpointcentrifugedtheoryrealizeunwrappingprocessing.
4.phasesplicingandpolynomialfitting
Reference subaperture phase stitching method, using the error homogenizationtechnology,we unifysub_region phase into the same reference datum byleast-squaresfitting method.finally base on the Gram_schmidt algorithm and utilizes zernikepolynomial fitting the same under reference of discrete points, can get asphericalphasedistribution.
5.Testingexamples
The asphere whose diameter is 130mm has carried on the actual examination, thefaceshapeprecisionachieved rms ? 0.0321?intheeffectiveaperture.
Practice proves sub-region splicing digital moirépatterns technology does notneed compensator can realize aspherical testing, to avoid the compensatorintroduction of error and the difficulty of assembly and adjustment, Through thepartition acquisition interference patterns, solve the CCD camera cut-off frequencylimit,Usingdigitalphaseshiftingtechnology,avoidpiezoelectricceramicmovephasenonlinearerrorofmeasurementinfluence.
本文针对非球面检测问题,提出了子区域拼接数字莫尔条纹检测非球面的新方法,该方法是一种将数字光栅技术、数字移相技术、莫尔技术、载频图像处理技术、相位展开及拼接技术相结合实现对非球面检测的新方法,本文对此种检测方法的原理进行了比较详细和深入的分析。
1、子区域移相数字莫尔条纹相位测量原理
简要介绍了利用子区域移相数字莫尔进行光学相位测量的原理,包括子区域数字莫尔条纹的获得及其数学模型、相移的实现、子区域划分的目的及该种检测方法应注意的关键问题。
2、数字莫尔条纹的滤波处理
从空域和频域两个角度对数字莫尔条纹的滤波方法进行了研究,通过对大量模拟载频干涉图的处理,得出了空域和频域滤波器截止频率的判断方法,分析了不同滤波方法的特点及其性能,得出了比较适合本文的滤波参数。
3、相位展开
介绍了几种常见的相位展开技术,在数字莫尔条纹滤波处理的基础上,利用分区相位的展开方法及残余点判读理论实现了相位展开的处理。
4、展开相位拼接及多项式拟合借鉴子孔径相位拼接方法,利用误差均化技术将得到子区域展开相位分布通过最小二乘拟合方法统一到相同参考基准下,最后结合Gram-schmidt算法利用zernike多项式拟合相同参考下的大量离散数据点,即可得到非球面相位分布。
5、检测实例
对一口径为130mm的非球面镜进行了实际的检测,有效口径内rms为0.0321?。
实践证明子区域拼接数字莫尔条纹技术不需要补偿器可以实现非球面检测,避免了补偿器引进的误差和装调的难度;通过分区采集干涉图,解决了CCD相机截止频率的限制;利用数字移相技术,避免压电陶瓷移相中非线性误差对测量的影响;可以作为中等精度要求的一种检测手段
Optical system application aspherical can correct differ, improve image quality,improve optical performance, reduce the dimensions and weight, so in recent yearsoptical instrument design and manufacturing, and established various aspheric opticsfabrication with its superior optical properties are increasingly applied in precisionoptical instruments, however aspheric mirrors variety, size and accuracy requirementis different, its testing methods than spherical complex and difficult, especially largeprecisionasphericsurfaceopticalelement,faceshapemeasuringmoredifficult.
This paper aim at aspherical testing problem, puts forward a new method ofaspherical testing base on sub_region splicing digital moirépatterns, this methodcontains digital grating technology, digital phase shifting technique ,moire technique,image processing technology, unwrapping and stitching technique .this paper hascarriedondetailedandthethoroughanalysistothiskindoftesting.
1.phasemeasurementprincipleofsub_regionphaseshiftingdigitalmoirépatterns
Introduced phase measurement principle of sub_region phase shifting digitalmoirépatterns,including sub_region digital moirépatterns acquisition and themathematical model, the phase_shifting,sub_region division goal,the key question ofthistesting.
2.Digitalmoirépatternsfilterprocessing
This paper conducted the research from the space domain filter method and thefrequency domain filter method to the digital moirépatterns,through massive simulationcarrierfrequencyinterferenceprocessing,has obtainedjudgmentmethodofthe space domain and the frequency range cut-off frequency of filter,has analyzed thedifferent filter method characteristic and performance,has obtained the quite suitablethisarticlefilterparameter.
3.unwrapping
Introduced several common unwrapping technology,through digital moirépatterns filtering processing,on the basis of the phase launched by partition methodandresidualpointcentrifugedtheoryrealizeunwrappingprocessing.
4.phasesplicingandpolynomialfitting
Reference subaperture phase stitching method, using the error homogenizationtechnology,we unifysub_region phase into the same reference datum byleast-squaresfitting method.finally base on the Gram_schmidt algorithm and utilizes zernikepolynomial fitting the same under reference of discrete points, can get asphericalphasedistribution.
5.Testingexamples
The asphere whose diameter is 130mm has carried on the actual examination, thefaceshapeprecisionachieved rms ? 0.0321?intheeffectiveaperture.
Practice proves sub-region splicing digital moirépatterns technology does notneed compensator can realize aspherical testing, to avoid the compensatorintroduction of error and the difficulty of assembly and adjustment, Through thepartition acquisition interference patterns, solve the CCD camera cut-off frequencylimit,Usingdigitalphaseshiftingtechnology,avoidpiezoelectricceramicmovephasenonlinearerrorofmeasurementinfluence.
引文
[1].唐健冠,伍凡,吴时彬.大口径非球面精磨表面形状检测技术研究.光学技术,2001(11):1-6.
[2].H.J.Tiziani,S.Reichelt,C.Prub.etal.TestingofAsphericSurfaces.SPIE.2001,4440:109-11.
[3].李国.新型非球面超精密加工装置数控系统的研究:[哈尔滨工业大学硕士论文].哈尔滨:哈尔滨工业大学.2006.
[4].李圣怡,戴一帆.超精密加工技术的发展及对策.中国机械工程,2000,11(8):7-10.
[5].P.R.Hannah,R.D.Day,D.Hateh.Computercontrolledprecisionopticalpolishing on the diamond turning machine.ASPE 8th Annual Meeting,Seattle,Washington.1993(11).
[6].N.Bueseher,T.ADow,A.Sohn,etal,Live AxisTurning.httP://www.asPe.net/Publieations/Annual_2005/PAPERS/IPRMOT.
[7].P.A.MeKeown,W.J.Wills-Moren,R.F.J.Read,etal.ThedesignandDevelopmentofalargeultra-PrecisionCNCdiamondturningmachine.MaterialsAndManufacturingProcesses,1986,1(l):133-157.
[8].罗松保,张建明,非球面曲面的超精密加工与测量技术的研究.制造技术与机床,2003,(9):55-62.
[9].韩成顺,张龙江,董申,等.大型光学非球面零件超精密切削新方法.哈尔滨工业大学学报,2007,39(7):1062-1064.
[10].H.Yin,T.Kun,Y.J.Zhu,etal.Fabricationofmicroglasslensmouldbyusing.ultra-Precisionmicro-grindingProeess.ProceedingofSPIE,2009,7282:6-11.
[11].左巍,辛科,赵广木.高陡度非球面光学元件加工技术研究.现代制造工程,2009,(7):l-5.
[12].王贵林,李圣怡,戴一帆.光学非球面复合加工机床的设计与精度分析.中国机械工程,2004,15(02):99-102.
[13].闫锋,范镝,张斌智,等.一种SIC非回转对称非球面的加工与检测.光电工程,2009,36(3):135-139.
[14].宁博.Gram-Schmidt正交基的行列式表示法.高等数学研究,2007,10(1),113.
[15].孙卓明,江莹.Schmidt正交化过程的改进.上饶师范学院学报。2003,15(6),15-18.
[16].唐建国.LU分解与广义Schmidt正交化方法,大学数学.2005,21(4),95-99.
[17].鄢静舟,雷凡.用Zernike多项式进行波面拟合的几种算法[J].光学精密工程,1999,7(5):119-128.
[18].单宝忠,王淑岩,牛憨笨等. Zernike多项式拟合方法及应用[J].光学精密工程2002,10(3):318-323.
[19].惠梅,牛憨笨.运用泽尼克多项式进行物面波前数据拟合.光子学报,1999,28(12):1113-1116.
[20].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.
[21].李新南,张明意,大口径光学平面的子孔径拼接检验研究.光学技术.2006.7:514-517.
[22].张蓉竹,杨春林,石奇凯,等.子孔径拼接干涉检验及其精度分析.光学学报,2003.23(10):1241-1244.
[23].李国培,于瀛洁,陈明仪.误差均化的拼接技术.光学精密工程,2001.9(6):561-564.
[24].杨力.先进光学制造技术[M].北京:科学出版社,2001.
[25].潘君骅.光学非球面的设计、加工与检测[M].江苏:苏州大学出版社,2004.
[26].杨志文.光学测量[M].北京:北京理工大学出版社,1995.
[27].普里亚耶夫.光学非球面检验[M].北京:科学出版社,1982.
[28].庞永杰.计算全息法检测凹非球面研究[D]: [硕士论文].昆明:昆明理工大学,2008.
[29].王美成,廖广兰,史铁林.小型非球面光学元件测量技术研究[J].计测技术,2007,27(4):1-4.
[30]伍凡.大口径透镜凸面零检验的补偿器设计.应用光学.1996,17(5):511-515.
[31] Jeng-dang Kuang.The Testing of a General Rotationally Symmetrical Aspherical Surface byUsingaNullLensinaZygoInterferometerMeaurment.1994,(13):85-90.
[32]伍凡,陈强.F/1.3抛物面零检验补偿器设计.光电工程.2004,31(1):12-15.
[33] B PHildebrand,K AHaines.Interferometric measurement using the wavefront reconstructiontechniques[J].Appl.Opt.1966.5(1):172-173.
[34]吴震.光学干涉测量技术[M].北京:中国计量出版社,1995.
[35] M.Mauro,P.Luca,M.Alessandro.Testing aspheric surfaces using mulitiple annularinterferograms[J].Opt.Eng.,1993,32(5):1073-1079.
[36] Y.J.Fan,K.G.Struik,P.C.Mulders et al..Stitching interferometry for the measurement ofasphericsurfacesannalsoftheCIRP[C].1997,46(1):459-462.
[37] S.Aric,I.K.Will,T.Marc.Magnet orheological finishing and sub-aperture stitchinginterferometryoflargeandlightweightoptics[C].SPIE,2004,5494:81-90.
[38] T.Marc,D.Paul,F.Greg.Sub-aperture approaches for aspheric polishing andmetrology[C].SPIE,2005,5638:284-299.
[39]王孝坤,张学军,王丽辉等.环形子孔径拼接干涉检测非球面的数学模型和仿真研究[J].光学精密工程,2006,14(4):527-532.
[40] SUZUKI M.KANAYA M,Application of Moire topography measurement methods inindustry.Opt&Lasereng,1988,8(3):171-188.
[41].Jun-ichi Kato, Ichirou Yamaguchi, Toru Nakamura, et al. Video-rate fringe analyzer based onphase-shiftingelectronicmoirépatterns.[J].Appl.Opt.,1997,36:8403-8412.
[42].程仕东,张学军等.基于相移电子莫尔条纹的深度非球面检测[J].光学精密工程,2003,11(3):250-256.
[43].DeAngelisM.DeNicolaS.FerraroP.Analysisofmoiréfringesformeasuringthefocallengthoflenses[J].OpticsandLasersinEngi-neering,1998,30:279—286.
[44]郝群,丁凌,栗孟娟,朱秋东.用于数字莫尔干涉术的莫尔滤波合成法[J].光学技术,2006,32(1):81-84.
[45]杨国光.近代光学测试技术,第一版.浙江:浙江大学出版社,1997年.
[46]谢建平,明海,徐继泽,吴云霞。一种新的莫尔条纹法[J],中国科技技术大学学报,1990,2(1):99-103.
[47]施宇清.用莫尔测偏法在线快速测非球面表面形貌。振动、测试与诊断,2002,22(1):16-19.
[48]马平,周绍林,胡松,徐文祥.莫尔条纹分析及其在光刻对准中的应用,光电工程,2010,37(7):103-106.
[49]吴玲玲,吴国俊,仓玉萍,陈良益.基于Talbot-Moiré法测量透镜焦距的莫尔条纹的图像处理.光子学报,2010,39(9):1723-1726.
[50]曹向群,黄维实.莫尔技术的现状和展望(综述).光电工程.1990(3):48-56.
[51]满玉春,张学军.子区域拼接数字莫尔条纹非球面检测的理论分析[J].光学精密工程,2008,16(3):420-425.
[52]蔡伟建,李津蓉.利用莫尔偏转法测量轴对称相位物体.传感技术学报,2007,20(2):442-445.
[53] CHENG Shi-dong, ZHANG Xue-jun, ZHANG Zhong-yu, ZHANG Feng. Deep aspherictesting based on phase-shift electronic Moirépatterns.Optics and PrecisionEngineering.2003,11(3):251-254.
[54]王学礼.基于莫尔理论的大面积快速高精度3D测量技术研究.[博士学位论文],西安:西安交通大学,2000.
[55]郝煌栋,赵洋,李达成.光学投影式三维轮廓测量技术综述.光学技术.1998(5):57-60.
[56]李田泽,李会贞.基于莫尔干涉技术相位物体测试系统及其分析.山东工程学报.1999(2):35-43.
[57]Seung-WooKim(MEMBERSpIE),Geno-SooHan.Aeelerated phase-measuring algorithmof least squares for Phase shifting interferometry.Optical Engineering.November1997(36):3101-3106.
[58]P.Hariharan,B.eoreb,T.Eiju.Digitalphase-shiftinginterferometry:asimpleerror-compensatingphaseealculation.AppiedOpties.July1987:504-2505.
[59]李霖,赵宏.一种基于相移技术的物体表面三维轮廓测量方法.仪器仪表学报.2003(3):41-43.
[60]马少鹏,金观昌,代树红.应用时域相位解包方法的三维形貌测量系统.光学技术.28(5).2002.
[61]S.Chan , A.Asundi , Phase-shifting digital system for profile measurement.SPIE.Vo12354:444-452.
[62]HaiXiaShang,HuiMinXie,FuLongDai.APPlieationofphaseshiftingTeehniqueforSEMseanningmoiremethodinmemes.SPIE.50(58),2003:417-422.
[63]Zhang,Yonglin.Automatie36003-Dobjeetusingshearinginterferometer&virtualgrating.SPIE.vo12899:162-168.
[64]B.Bhushan,J.C Wyant,and C.LKoliopoulos.Measurement of surface topogranhpy of magnetictapesbyMiraunterferometryAppl.Opt.1985(24):1489-1497.
[65] J.E Greiveenkamp,J.Hbruning .Phase Shifting Interferometry.Optical Shoptesting,1992:201-595.
[66]D.Malacara.Interferogramanalysisforopticaltesting.MareelDekker ,newYork 1998.
[67]朱日宏,陈进榜,王青,等。移相干涉术的一种新算法:重叠平均法。光学学报,199414(2):1288-1293.
[68]李田泽,李会贞.基于莫尔干涉技术相位物体测试系统及其分析.山东工程学报.1999(2):35-43.
[69]李霖,赵宏.一种基于相移技术的物体表面三维轮廓测量方法.仪器仪表学报.2003(3):41-43.
[70]P.Hariharan,BeOreb,T.Eiju.Digitalphase-shiftinginterferometry:asimpleError-compensatingPhaseealculation.APPied OPties.July1987:504-505.
[71]钱克矛,续伯钦,伍小平.光学干涉计量中的位相测量方法,实验力学.2001(3)
[72]孙仲康.离散傅立叶变换及其应用.第一版.北京:人民邮电出版社,1982年
[73]王世一.数字信号处理.第一版.北京:北京理工大学出版社,1997年.
[74]罗军辉,冯平等,matlab在图像处理中的应用.北京:机械工业出版社,2005。
[75]林爱英,谷小青,郑宝周.用频率采样法设计FIR滤波器。现代电子技术,2010,17:85-88.
[76]]J.M.Huntley,Noise-immunephaseunwrappingalgorithm,Appl.Opt.1989,28:3268-3270.
[78].J.A.Quiroga,A.Gonzalez-Cano,andE.Bernabeu,Stablemarriagesa1gorithmforPreproeessingphasemapswithdiseontinuitysourees,Appl.Opt.1995,34:5029-5038.
[79]. Zhijun wang and Shusun li.Phase unwrapping through aBranch-cut-based cut-bridging andwindow-patehingmethod.Appl.Opt.1999,38(5):805-814.
[80].D.J.Bone,fourierfringeanalysis:thetwo-dimensionalphaseunwrappingproblem,Appl.Opt,1991,30(25):3627-3632.
[81].Suxianyu,ChenWenjing.Reliability-guidedphaseunwrappinga1gorithm:a review,OpticsandLasersinEngineering,2004,42:245-261.
[82].J.Meneses,T.GharbiandP.Humbertphaseunwapping algorithmforImageswith highnoisecontentbasedonalocalhistogram.Appppl.Opt.2005,44(7):1207-1215.
[83].Jin-JungChyou,Shean-JenChen,andYi-KuangChen,two-dimensionalPhase unwrapping with a multiehannel least-mean-squarealgorithm.Appl.Opt.2004 ,43(30):5655-5659.
[84]. Miguel Arevalillo Herraez,Jessus.Botieario,Miehael J.Lalor,And David R.Burton,Agglomerative eclustering-based approach for Two-dimensional Phaseunwrapping.Appl.Opt.2005,44(7):1129-1140.
[85].杨磊,赵拥军,王志刚.最小生成树相位解缠中冗余去除算法.遥感学报.200610(6):779-884.
[86].穆冬朱兆达张焕春.干涉SAR最小二乘二维相位展开法的改进.现代雷达.2001,23(2):23-26.
[87].杨锋涛,吕晓旭,王殿元,江长双.基于二阶差分的加权最小费用流相位展开算法.激光技术.2006,30(6):667-673.
[88].宋芳,苏显渝.InSAR中基于干涉图质量参数的相位展开.激光杂志.2006,27(3):32-34.
[89].刘景峰,李艳秋,刘克.含噪声包裹相位图的加权最小二乘相位展开算法研究.光学技术.2008,34(5):643-646.
[90].宋芳,苏显渝.可靠性排序在InSAR相位展开中的应用.光电子.激光。2005,16(1):9-13.
[91].毛志杰,廖桂生,刘向阳,戴继光。基于最小费用流的InSAR干涉相位展开算法。2008,24(6):491-495.
[92].Richard M.Goldstein,Howare A.Zebker,and Charles L.Werner.Satellie radar interferometry:two-dimensionalphaseumwrapping.radioscience.1988,(23)4:713-720.
[93] R.Cusaek,J.M.Huntley,H.T.Goldrein,Improved noise immune phase Unwrappingalgorithm.Appl.Opt.1995,34(5):781-789.
[94]B.GutmannandH.Weber,Phaseunwrappingwiththebraneh-cutmethod:c1ustering of diseontinuity sources and reverse simulatedannealing , Appl.Opt.1999 ,38:5577-5593.
[95]J.R.Buekland J.M.Huntley,andS.R.E.Turner,UnwrappingnoisyphaseMapsbyUseofaminimum-cost-matehingalgorithm,Appl.Opt.1995,34:5100-5108.
[96]D.J.Bone,Fourier fringe analysis: the two-dimensional Phase unwrapping Problem,AppliedOptics.1991,30:36273632.
[97].Y.Xu and C.Ai,Simple and effective Phase unwrapping technique,Interferometry TechniquesandAnalysis,Proc.SPIE,vol.2003,PP.254-263,1993.
[98].杨锋涛,罗江龙,刘志强,吕晓旭,相位展开的6种算法比较。激光技术2008,32(3):323-326.
[99]. D.C.Ghiglia,L. A.Romero.Robust two-dimensional weighted and unweighted Phaseunwrappingthatusefasttransformsanditerativemethods.J.Opt.Soe.Am.A,1994,11(l):107-117.
[100].S.M.Song,S.Napel,etal,phaseunwrappingofMRphaseimagesusingpassionequation,IEEETtans.OnImageProcessing,1995,l4:.667-676.
[101].M.D.PrittandJ.S.Shipman,Least-squarestwodimensionalphaseunwrappingusingFFTs,IEEETrans.Geosei.RemoteSens.1994,32:706-708.
[102].M.D.Pritt,PhaseunwrappingbymeansofmultigridtechniquesforInterferometricSAR,IEEETrans.Geosei.RemoteSess.1996:34:728-738.
[103].G.Fornaro,G..Franeeschetti,and R.Lanari Interferometrie SAR Phase unwrapping usingGreenformulation,IEEET.rans.Geosei.RemoteSensing,1996,34:720-727.
[104]李绍恩,向茂生,吴一戎.一种新的相位展开算法—最近相邻点连接算法.电子与信息学报.2005,27(2)266-268.
[105].廖洋.基于相位恢复的长焦距光学镜面面形在位检测技术研究.[硕士论文].长沙:国防科技大学,2009、11.
[106].刘崇.非球面环形子孔径拼接干涉测试方法研究.[硕士论文].南京:南京理工大学,2009、5.
[107].陈善勇.非球面子孔径拼接干涉测量的几何方法研究.[博士论文].长沙:国防科技大学,2004、6.
[108]. Elssner K-E,Burow R,Grzanna J, Spolaczyk R. Absolute sphericity measurement. AppliedOptics,1989,28(21):4649-4661.
[109]. S. O’Donohue, G. Devries, P. Murphy, G. Forbes, P. Dumas. New methods forcalibrating systematic errors in interferometric measurements[J].SPIE,2005,5869:58690T-1-58690T-9.
[110]. Cheng W.M, Lin Y.L, Chen M.Y. Accuracy analysis of multiaperture overlap-scanningtechnique(MAOST)[J].SPIE,1993,2003:283-288.
[111].白剑,程上彝.大口径镜面的多孔径拼接技术[J].光学学报,1997,17(7):953-956.
[112]. Wang Q, Chen J B, Zhu R H, et al. A new technique fortesting large optical flat[C]. SPIE,2003,1993:389-397.
[113].张蓉竹,《ICF系统光学元件高精度波前检测技术研究》,四川大学博士论文,2003,4.
[114].PaulMurphy,JonFleig,GregForbes.Subaperturestitchinginterferometryfortestingmildaspheres[J].SPIE,2006,6293:62930J-1-62930J-10.
[2].H.J.Tiziani,S.Reichelt,C.Prub.etal.TestingofAsphericSurfaces.SPIE.2001,4440:109-11.
[3].李国.新型非球面超精密加工装置数控系统的研究:[哈尔滨工业大学硕士论文].哈尔滨:哈尔滨工业大学.2006.
[4].李圣怡,戴一帆.超精密加工技术的发展及对策.中国机械工程,2000,11(8):7-10.
[5].P.R.Hannah,R.D.Day,D.Hateh.Computercontrolledprecisionopticalpolishing on the diamond turning machine.ASPE 8th Annual Meeting,Seattle,Washington.1993(11).
[6].N.Bueseher,T.ADow,A.Sohn,etal,Live AxisTurning.httP://www.asPe.net/Publieations/Annual_2005/PAPERS/IPRMOT.
[7].P.A.MeKeown,W.J.Wills-Moren,R.F.J.Read,etal.ThedesignandDevelopmentofalargeultra-PrecisionCNCdiamondturningmachine.MaterialsAndManufacturingProcesses,1986,1(l):133-157.
[8].罗松保,张建明,非球面曲面的超精密加工与测量技术的研究.制造技术与机床,2003,(9):55-62.
[9].韩成顺,张龙江,董申,等.大型光学非球面零件超精密切削新方法.哈尔滨工业大学学报,2007,39(7):1062-1064.
[10].H.Yin,T.Kun,Y.J.Zhu,etal.Fabricationofmicroglasslensmouldbyusing.ultra-Precisionmicro-grindingProeess.ProceedingofSPIE,2009,7282:6-11.
[11].左巍,辛科,赵广木.高陡度非球面光学元件加工技术研究.现代制造工程,2009,(7):l-5.
[12].王贵林,李圣怡,戴一帆.光学非球面复合加工机床的设计与精度分析.中国机械工程,2004,15(02):99-102.
[13].闫锋,范镝,张斌智,等.一种SIC非回转对称非球面的加工与检测.光电工程,2009,36(3):135-139.
[14].宁博.Gram-Schmidt正交基的行列式表示法.高等数学研究,2007,10(1),113.
[15].孙卓明,江莹.Schmidt正交化过程的改进.上饶师范学院学报。2003,15(6),15-18.
[16].唐建国.LU分解与广义Schmidt正交化方法,大学数学.2005,21(4),95-99.
[17].鄢静舟,雷凡.用Zernike多项式进行波面拟合的几种算法[J].光学精密工程,1999,7(5):119-128.
[18].单宝忠,王淑岩,牛憨笨等. Zernike多项式拟合方法及应用[J].光学精密工程2002,10(3):318-323.
[19].惠梅,牛憨笨.运用泽尼克多项式进行物面波前数据拟合.光子学报,1999,28(12):1113-1116.
[20].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.
[21].李新南,张明意,大口径光学平面的子孔径拼接检验研究.光学技术.2006.7:514-517.
[22].张蓉竹,杨春林,石奇凯,等.子孔径拼接干涉检验及其精度分析.光学学报,2003.23(10):1241-1244.
[23].李国培,于瀛洁,陈明仪.误差均化的拼接技术.光学精密工程,2001.9(6):561-564.
[24].杨力.先进光学制造技术[M].北京:科学出版社,2001.
[25].潘君骅.光学非球面的设计、加工与检测[M].江苏:苏州大学出版社,2004.
[26].杨志文.光学测量[M].北京:北京理工大学出版社,1995.
[27].普里亚耶夫.光学非球面检验[M].北京:科学出版社,1982.
[28].庞永杰.计算全息法检测凹非球面研究[D]: [硕士论文].昆明:昆明理工大学,2008.
[29].王美成,廖广兰,史铁林.小型非球面光学元件测量技术研究[J].计测技术,2007,27(4):1-4.
[30]伍凡.大口径透镜凸面零检验的补偿器设计.应用光学.1996,17(5):511-515.
[31] Jeng-dang Kuang.The Testing of a General Rotationally Symmetrical Aspherical Surface byUsingaNullLensinaZygoInterferometerMeaurment.1994,(13):85-90.
[32]伍凡,陈强.F/1.3抛物面零检验补偿器设计.光电工程.2004,31(1):12-15.
[33] B PHildebrand,K AHaines.Interferometric measurement using the wavefront reconstructiontechniques[J].Appl.Opt.1966.5(1):172-173.
[34]吴震.光学干涉测量技术[M].北京:中国计量出版社,1995.
[35] M.Mauro,P.Luca,M.Alessandro.Testing aspheric surfaces using mulitiple annularinterferograms[J].Opt.Eng.,1993,32(5):1073-1079.
[36] Y.J.Fan,K.G.Struik,P.C.Mulders et al..Stitching interferometry for the measurement ofasphericsurfacesannalsoftheCIRP[C].1997,46(1):459-462.
[37] S.Aric,I.K.Will,T.Marc.Magnet orheological finishing and sub-aperture stitchinginterferometryoflargeandlightweightoptics[C].SPIE,2004,5494:81-90.
[38] T.Marc,D.Paul,F.Greg.Sub-aperture approaches for aspheric polishing andmetrology[C].SPIE,2005,5638:284-299.
[39]王孝坤,张学军,王丽辉等.环形子孔径拼接干涉检测非球面的数学模型和仿真研究[J].光学精密工程,2006,14(4):527-532.
[40] SUZUKI M.KANAYA M,Application of Moire topography measurement methods inindustry.Opt&Lasereng,1988,8(3):171-188.
[41].Jun-ichi Kato, Ichirou Yamaguchi, Toru Nakamura, et al. Video-rate fringe analyzer based onphase-shiftingelectronicmoirépatterns.[J].Appl.Opt.,1997,36:8403-8412.
[42].程仕东,张学军等.基于相移电子莫尔条纹的深度非球面检测[J].光学精密工程,2003,11(3):250-256.
[43].DeAngelisM.DeNicolaS.FerraroP.Analysisofmoiréfringesformeasuringthefocallengthoflenses[J].OpticsandLasersinEngi-neering,1998,30:279—286.
[44]郝群,丁凌,栗孟娟,朱秋东.用于数字莫尔干涉术的莫尔滤波合成法[J].光学技术,2006,32(1):81-84.
[45]杨国光.近代光学测试技术,第一版.浙江:浙江大学出版社,1997年.
[46]谢建平,明海,徐继泽,吴云霞。一种新的莫尔条纹法[J],中国科技技术大学学报,1990,2(1):99-103.
[47]施宇清.用莫尔测偏法在线快速测非球面表面形貌。振动、测试与诊断,2002,22(1):16-19.
[48]马平,周绍林,胡松,徐文祥.莫尔条纹分析及其在光刻对准中的应用,光电工程,2010,37(7):103-106.
[49]吴玲玲,吴国俊,仓玉萍,陈良益.基于Talbot-Moiré法测量透镜焦距的莫尔条纹的图像处理.光子学报,2010,39(9):1723-1726.
[50]曹向群,黄维实.莫尔技术的现状和展望(综述).光电工程.1990(3):48-56.
[51]满玉春,张学军.子区域拼接数字莫尔条纹非球面检测的理论分析[J].光学精密工程,2008,16(3):420-425.
[52]蔡伟建,李津蓉.利用莫尔偏转法测量轴对称相位物体.传感技术学报,2007,20(2):442-445.
[53] CHENG Shi-dong, ZHANG Xue-jun, ZHANG Zhong-yu, ZHANG Feng. Deep aspherictesting based on phase-shift electronic Moirépatterns.Optics and PrecisionEngineering.2003,11(3):251-254.
[54]王学礼.基于莫尔理论的大面积快速高精度3D测量技术研究.[博士学位论文],西安:西安交通大学,2000.
[55]郝煌栋,赵洋,李达成.光学投影式三维轮廓测量技术综述.光学技术.1998(5):57-60.
[56]李田泽,李会贞.基于莫尔干涉技术相位物体测试系统及其分析.山东工程学报.1999(2):35-43.
[57]Seung-WooKim(MEMBERSpIE),Geno-SooHan.Aeelerated phase-measuring algorithmof least squares for Phase shifting interferometry.Optical Engineering.November1997(36):3101-3106.
[58]P.Hariharan,B.eoreb,T.Eiju.Digitalphase-shiftinginterferometry:asimpleerror-compensatingphaseealculation.AppiedOpties.July1987:504-2505.
[59]李霖,赵宏.一种基于相移技术的物体表面三维轮廓测量方法.仪器仪表学报.2003(3):41-43.
[60]马少鹏,金观昌,代树红.应用时域相位解包方法的三维形貌测量系统.光学技术.28(5).2002.
[61]S.Chan , A.Asundi , Phase-shifting digital system for profile measurement.SPIE.Vo12354:444-452.
[62]HaiXiaShang,HuiMinXie,FuLongDai.APPlieationofphaseshiftingTeehniqueforSEMseanningmoiremethodinmemes.SPIE.50(58),2003:417-422.
[63]Zhang,Yonglin.Automatie36003-Dobjeetusingshearinginterferometer&virtualgrating.SPIE.vo12899:162-168.
[64]B.Bhushan,J.C Wyant,and C.LKoliopoulos.Measurement of surface topogranhpy of magnetictapesbyMiraunterferometryAppl.Opt.1985(24):1489-1497.
[65] J.E Greiveenkamp,J.Hbruning .Phase Shifting Interferometry.Optical Shoptesting,1992:201-595.
[66]D.Malacara.Interferogramanalysisforopticaltesting.MareelDekker ,newYork 1998.
[67]朱日宏,陈进榜,王青,等。移相干涉术的一种新算法:重叠平均法。光学学报,199414(2):1288-1293.
[68]李田泽,李会贞.基于莫尔干涉技术相位物体测试系统及其分析.山东工程学报.1999(2):35-43.
[69]李霖,赵宏.一种基于相移技术的物体表面三维轮廓测量方法.仪器仪表学报.2003(3):41-43.
[70]P.Hariharan,BeOreb,T.Eiju.Digitalphase-shiftinginterferometry:asimpleError-compensatingPhaseealculation.APPied OPties.July1987:504-505.
[71]钱克矛,续伯钦,伍小平.光学干涉计量中的位相测量方法,实验力学.2001(3)
[72]孙仲康.离散傅立叶变换及其应用.第一版.北京:人民邮电出版社,1982年
[73]王世一.数字信号处理.第一版.北京:北京理工大学出版社,1997年.
[74]罗军辉,冯平等,matlab在图像处理中的应用.北京:机械工业出版社,2005。
[75]林爱英,谷小青,郑宝周.用频率采样法设计FIR滤波器。现代电子技术,2010,17:85-88.
[76]]J.M.Huntley,Noise-immunephaseunwrappingalgorithm,Appl.Opt.1989,28:3268-3270.
[78].J.A.Quiroga,A.Gonzalez-Cano,andE.Bernabeu,Stablemarriagesa1gorithmforPreproeessingphasemapswithdiseontinuitysourees,Appl.Opt.1995,34:5029-5038.
[79]. Zhijun wang and Shusun li.Phase unwrapping through aBranch-cut-based cut-bridging andwindow-patehingmethod.Appl.Opt.1999,38(5):805-814.
[80].D.J.Bone,fourierfringeanalysis:thetwo-dimensionalphaseunwrappingproblem,Appl.Opt,1991,30(25):3627-3632.
[81].Suxianyu,ChenWenjing.Reliability-guidedphaseunwrappinga1gorithm:a review,OpticsandLasersinEngineering,2004,42:245-261.
[82].J.Meneses,T.GharbiandP.Humbertphaseunwapping algorithmforImageswith highnoisecontentbasedonalocalhistogram.Appppl.Opt.2005,44(7):1207-1215.
[83].Jin-JungChyou,Shean-JenChen,andYi-KuangChen,two-dimensionalPhase unwrapping with a multiehannel least-mean-squarealgorithm.Appl.Opt.2004 ,43(30):5655-5659.
[84]. Miguel Arevalillo Herraez,Jessus.Botieario,Miehael J.Lalor,And David R.Burton,Agglomerative eclustering-based approach for Two-dimensional Phaseunwrapping.Appl.Opt.2005,44(7):1129-1140.
[85].杨磊,赵拥军,王志刚.最小生成树相位解缠中冗余去除算法.遥感学报.200610(6):779-884.
[86].穆冬朱兆达张焕春.干涉SAR最小二乘二维相位展开法的改进.现代雷达.2001,23(2):23-26.
[87].杨锋涛,吕晓旭,王殿元,江长双.基于二阶差分的加权最小费用流相位展开算法.激光技术.2006,30(6):667-673.
[88].宋芳,苏显渝.InSAR中基于干涉图质量参数的相位展开.激光杂志.2006,27(3):32-34.
[89].刘景峰,李艳秋,刘克.含噪声包裹相位图的加权最小二乘相位展开算法研究.光学技术.2008,34(5):643-646.
[90].宋芳,苏显渝.可靠性排序在InSAR相位展开中的应用.光电子.激光。2005,16(1):9-13.
[91].毛志杰,廖桂生,刘向阳,戴继光。基于最小费用流的InSAR干涉相位展开算法。2008,24(6):491-495.
[92].Richard M.Goldstein,Howare A.Zebker,and Charles L.Werner.Satellie radar interferometry:two-dimensionalphaseumwrapping.radioscience.1988,(23)4:713-720.
[93] R.Cusaek,J.M.Huntley,H.T.Goldrein,Improved noise immune phase Unwrappingalgorithm.Appl.Opt.1995,34(5):781-789.
[94]B.GutmannandH.Weber,Phaseunwrappingwiththebraneh-cutmethod:c1ustering of diseontinuity sources and reverse simulatedannealing , Appl.Opt.1999 ,38:5577-5593.
[95]J.R.Buekland J.M.Huntley,andS.R.E.Turner,UnwrappingnoisyphaseMapsbyUseofaminimum-cost-matehingalgorithm,Appl.Opt.1995,34:5100-5108.
[96]D.J.Bone,Fourier fringe analysis: the two-dimensional Phase unwrapping Problem,AppliedOptics.1991,30:36273632.
[97].Y.Xu and C.Ai,Simple and effective Phase unwrapping technique,Interferometry TechniquesandAnalysis,Proc.SPIE,vol.2003,PP.254-263,1993.
[98].杨锋涛,罗江龙,刘志强,吕晓旭,相位展开的6种算法比较。激光技术2008,32(3):323-326.
[99]. D.C.Ghiglia,L. A.Romero.Robust two-dimensional weighted and unweighted Phaseunwrappingthatusefasttransformsanditerativemethods.J.Opt.Soe.Am.A,1994,11(l):107-117.
[100].S.M.Song,S.Napel,etal,phaseunwrappingofMRphaseimagesusingpassionequation,IEEETtans.OnImageProcessing,1995,l4:.667-676.
[101].M.D.PrittandJ.S.Shipman,Least-squarestwodimensionalphaseunwrappingusingFFTs,IEEETrans.Geosei.RemoteSens.1994,32:706-708.
[102].M.D.Pritt,PhaseunwrappingbymeansofmultigridtechniquesforInterferometricSAR,IEEETrans.Geosei.RemoteSess.1996:34:728-738.
[103].G.Fornaro,G..Franeeschetti,and R.Lanari Interferometrie SAR Phase unwrapping usingGreenformulation,IEEET.rans.Geosei.RemoteSensing,1996,34:720-727.
[104]李绍恩,向茂生,吴一戎.一种新的相位展开算法—最近相邻点连接算法.电子与信息学报.2005,27(2)266-268.
[105].廖洋.基于相位恢复的长焦距光学镜面面形在位检测技术研究.[硕士论文].长沙:国防科技大学,2009、11.
[106].刘崇.非球面环形子孔径拼接干涉测试方法研究.[硕士论文].南京:南京理工大学,2009、5.
[107].陈善勇.非球面子孔径拼接干涉测量的几何方法研究.[博士论文].长沙:国防科技大学,2004、6.
[108]. Elssner K-E,Burow R,Grzanna J, Spolaczyk R. Absolute sphericity measurement. AppliedOptics,1989,28(21):4649-4661.
[109]. S. O’Donohue, G. Devries, P. Murphy, G. Forbes, P. Dumas. New methods forcalibrating systematic errors in interferometric measurements[J].SPIE,2005,5869:58690T-1-58690T-9.
[110]. Cheng W.M, Lin Y.L, Chen M.Y. Accuracy analysis of multiaperture overlap-scanningtechnique(MAOST)[J].SPIE,1993,2003:283-288.
[111].白剑,程上彝.大口径镜面的多孔径拼接技术[J].光学学报,1997,17(7):953-956.
[112]. Wang Q, Chen J B, Zhu R H, et al. A new technique fortesting large optical flat[C]. SPIE,2003,1993:389-397.
[113].张蓉竹,《ICF系统光学元件高精度波前检测技术研究》,四川大学博士论文,2003,4.
[114].PaulMurphy,JonFleig,GregForbes.Subaperturestitchinginterferometryfortestingmildaspheres[J].SPIE,2006,6293:62930J-1-62930J-10.