【作者】 满玉春；

【导师】 张学军；

【作者基本信息】 中国科学院研究生院（长春光学精密机械与物理研究所） ， 光学工程， 2011， 博士

【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更多还原

【Abstract】 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_regionphaseshiftingdigitalmoirépatternsIntroduced 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.DigitalmoirépatternsfilterprocessingThis 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.unwrappingIntroduced several common unwrapping technology,through digital moirépatterns filtering processing,on the basis of the phase launched by partition methodandresidualpointcentrifugedtheoryrealizeunwrappingprocessing.4.phasesplicingandpolynomialfittingReference 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.TestingexamplesThe 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.更多还原