点衍射干涉仪检测技术研究
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摘要
高精密仪器与设备的发展进步，对我国未来科学技术的发展具有重要意义，而精密光学元件的加工，往往是生产此类仪器与设备的核心技术。随着高精密仪器与设备的快速发展，光学元件面形误差的要求也越来越严苛。传统的面形检测设备，如迈克尔逊干涉仪、斐索球面干涉仪，其参考波面由参考元件反射形成，检测精度必然受制于参考元件的面形精度，很难满足超高精度面形检测的要求。
本文研究的点衍射干涉仪检测技术，结构简单，采用针孔衍射产生参考波，从而摆脱了参考元件面形对检测精度的限制，极大地减少了系统误差，是超高精度检测新的发展方向。本论文的主要工作任务是研究点衍射干涉仪检测技术的关键理论与技术问题，进一步发展应用于面形测量的点衍射干涉检测技术。论文的研究工作包括以下几个部分：
(1).充分调研了现在高精度面形检测的技术手段和点衍射干涉仪检测技术的国内外研究现状，回顾了点衍射干涉仪在面形检测中的发展历史。深入研究了其基本原理，在此基础上讨论了基于针孔衍射的点衍射干涉检测技术的实验方案和工作过程,并对其中所涉及的关键问题和技术难点进行了分析，对其在高精度面形检测中的发展趋势和应用前景进行了探讨。
(2).针孔衍射波面与理想球面波的偏差是决定点衍射干涉仪检测精度的关键因素。对以往的针孔衍射波面计算方法进行了调研，分析与比较。利用有限元方法计算近场分布，再利用瑞利－索莫菲标量积分计算远场发散的方法，仿真分析与讨论了不同针孔直径、膜层厚度及系统误差引入后对衍射波面的影响。
(3).详细介绍了点衍射干涉仪测量面形的原理，对测量中使用的移相干涉术进行了相应研究，数值仿真了干涉条纹的处理过程。分析了点衍射干涉仪中主要的误差来源和分类，及其对测量结果的影响。对点衍射干涉仪能够达到的理论精度进行了理论分析。
(4).系统误差的标定是评价检测设备精度的重要手段。提出了一种新的结构实现点衍射干涉仪的“零位”测量，标定其系统误差，与传统方法相比，降低了装调难度。提出了一种CCD记录的实时图像处理计算机辅助装调的方法，设计出新的衍射模板，利用定位孔帮助聚焦斑与针孔的快速对准。提出了一种利用干涉图像中的背景光强，提取需要的位置信息，有效去除检测结果中几何误差的方法。搭建了实验平台，进行了实验验证。对标定系统所包含的系统误差进行了分析，对减少这些误差因素的方法以及检测结果和点衍射干涉仪检测精度的关系进行了探讨。
(5).搭建了点衍射干涉仪检测实验系统，对一曲率半径250mm，口径25mm的凹球面反射镜进行了测量，将其结果与ZYGO干涉仪的测量结果进行了比较分析。对实验系统主要的误差源进行了分析，讨论了提高测量精度的方法。
点衍射干涉仪原理结构简单，摆脱了参考元件的限制，在超高精度面形检测中拥有显著的技术优势。论文的这些研究成果为点衍射干涉仪的工程实现提供了理论和实验基础。
The development of the ultra precision instrument is very important in the futurescience and technology and the key to manufacture this kind of instrument is how tomanufacture the optic which is “good” enough. However, the accuracy of the traditionaloptical shop testing technology, such as Michelson inteferometry and Fizeauinterferometry, is limited by the reference wave which is produced by the reflection ofthe reference surface. The point diffraction interferometry (PDI) introduced in thisthesis not only has simple system configuration but also produces the reference wave bypinhole diffraction, so it can reach higher precision and accuracy. This thesis that isdevoted to basic research and the development of the key technology and problems ofthe point diffraction interferometry, is organized into five sections:
（1） The domestic and overseas development status about the optical testingtechnology achieving high accuracy and precision is adequately investigated andthe history of the point diffraction is also reviewed. Based on the principle of thePDI, the experimental system, working process and the application protencial arediscussed. The involved key problems and technical difficulties are analyzed.
（2） The deviation between the pinhole diffracted wave and the perfect sphericalwave is the keypoint of the accuracy of the PDI. The methods of calculating thepinhole diffracted wave are investigated and analyzed. A new way, based on FiniteElement Method (FEM) and Rayleigh-Sommerfeld scalar theory, is proposed toestimated the deviation and the influence of the system error on the diffracted waveis also numerical stimulated.
（3） The system configuration of the PDI that be used to test spherical figure andthe phase shift interfermetry are discussed. The the interferogram processing isnumerical simulated. The main errors of the PDI and the theory accuracy that thePDI can reach are analyzed.
（4） Calibration of the system errors is indispensable to estimate the accuracy of themeasurement devices. A new configuration, which is easier to make the alignment,of the null test method is proposed and set up. A method to align the focus spot ontothe pinhole with the help of two windows and a new way to calculate the relative position between the detector and the diffraction mask by processing theinformation on the intergram are proposed. The origin of the system errors and themethods to reduce those errors are analyzed. The relationship between the null testresult and the accuracy of the PDI is discussed.
（5） A PDI experiment system is set up and a convace mirror which has thediameter of25mm and the radius of250mm is tested. The testing result is comparedwith another result tested by ZYGO interferometer. The main system errors areanalyzed.
The PDI, which has got rid of the limitation of the reference surface, is prior toother measurement instruments in ultra precision figure testing. The research in thisthesis will be the theory and experiment foundation of the application of the PDI.
本文研究的点衍射干涉仪检测技术，结构简单，采用针孔衍射产生参考波，从而摆脱了参考元件面形对检测精度的限制，极大地减少了系统误差，是超高精度检测新的发展方向。本论文的主要工作任务是研究点衍射干涉仪检测技术的关键理论与技术问题，进一步发展应用于面形测量的点衍射干涉检测技术。论文的研究工作包括以下几个部分：
(1).充分调研了现在高精度面形检测的技术手段和点衍射干涉仪检测技术的国内外研究现状，回顾了点衍射干涉仪在面形检测中的发展历史。深入研究了其基本原理，在此基础上讨论了基于针孔衍射的点衍射干涉检测技术的实验方案和工作过程,并对其中所涉及的关键问题和技术难点进行了分析，对其在高精度面形检测中的发展趋势和应用前景进行了探讨。
(2).针孔衍射波面与理想球面波的偏差是决定点衍射干涉仪检测精度的关键因素。对以往的针孔衍射波面计算方法进行了调研，分析与比较。利用有限元方法计算近场分布，再利用瑞利－索莫菲标量积分计算远场发散的方法，仿真分析与讨论了不同针孔直径、膜层厚度及系统误差引入后对衍射波面的影响。
(3).详细介绍了点衍射干涉仪测量面形的原理，对测量中使用的移相干涉术进行了相应研究，数值仿真了干涉条纹的处理过程。分析了点衍射干涉仪中主要的误差来源和分类，及其对测量结果的影响。对点衍射干涉仪能够达到的理论精度进行了理论分析。
(4).系统误差的标定是评价检测设备精度的重要手段。提出了一种新的结构实现点衍射干涉仪的“零位”测量，标定其系统误差，与传统方法相比，降低了装调难度。提出了一种CCD记录的实时图像处理计算机辅助装调的方法，设计出新的衍射模板，利用定位孔帮助聚焦斑与针孔的快速对准。提出了一种利用干涉图像中的背景光强，提取需要的位置信息，有效去除检测结果中几何误差的方法。搭建了实验平台，进行了实验验证。对标定系统所包含的系统误差进行了分析，对减少这些误差因素的方法以及检测结果和点衍射干涉仪检测精度的关系进行了探讨。
(5).搭建了点衍射干涉仪检测实验系统，对一曲率半径250mm，口径25mm的凹球面反射镜进行了测量，将其结果与ZYGO干涉仪的测量结果进行了比较分析。对实验系统主要的误差源进行了分析，讨论了提高测量精度的方法。
点衍射干涉仪原理结构简单，摆脱了参考元件的限制，在超高精度面形检测中拥有显著的技术优势。论文的这些研究成果为点衍射干涉仪的工程实现提供了理论和实验基础。
The development of the ultra precision instrument is very important in the futurescience and technology and the key to manufacture this kind of instrument is how tomanufacture the optic which is “good” enough. However, the accuracy of the traditionaloptical shop testing technology, such as Michelson inteferometry and Fizeauinterferometry, is limited by the reference wave which is produced by the reflection ofthe reference surface. The point diffraction interferometry (PDI) introduced in thisthesis not only has simple system configuration but also produces the reference wave bypinhole diffraction, so it can reach higher precision and accuracy. This thesis that isdevoted to basic research and the development of the key technology and problems ofthe point diffraction interferometry, is organized into five sections:
（1） The domestic and overseas development status about the optical testingtechnology achieving high accuracy and precision is adequately investigated andthe history of the point diffraction is also reviewed. Based on the principle of thePDI, the experimental system, working process and the application protencial arediscussed. The involved key problems and technical difficulties are analyzed.
（2） The deviation between the pinhole diffracted wave and the perfect sphericalwave is the keypoint of the accuracy of the PDI. The methods of calculating thepinhole diffracted wave are investigated and analyzed. A new way, based on FiniteElement Method (FEM) and Rayleigh-Sommerfeld scalar theory, is proposed toestimated the deviation and the influence of the system error on the diffracted waveis also numerical stimulated.
（3） The system configuration of the PDI that be used to test spherical figure andthe phase shift interfermetry are discussed. The the interferogram processing isnumerical simulated. The main errors of the PDI and the theory accuracy that thePDI can reach are analyzed.
（4） Calibration of the system errors is indispensable to estimate the accuracy of themeasurement devices. A new configuration, which is easier to make the alignment,of the null test method is proposed and set up. A method to align the focus spot ontothe pinhole with the help of two windows and a new way to calculate the relative position between the detector and the diffraction mask by processing theinformation on the intergram are proposed. The origin of the system errors and themethods to reduce those errors are analyzed. The relationship between the null testresult and the accuracy of the PDI is discussed.
（5） A PDI experiment system is set up and a convace mirror which has thediameter of25mm and the radius of250mm is tested. The testing result is comparedwith another result tested by ZYGO interferometer. The main system errors areanalyzed.
The PDI, which has got rid of the limitation of the reference surface, is prior toother measurement instruments in ultra precision figure testing. The research in thisthesis will be the theory and experiment foundation of the application of the PDI.
引文
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