基于CGH高精度非球面检测技术研究
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摘要
计算全息（Computer-generated hologram,简称CGH）在干涉检测系统中的应用使得非球面的检测过程更为容易，不需要使用价格昂贵的参考实体和零位透镜就能产生任意需要的参考波面，而且这种方法的检测精度很高。
CGH检测非球面的技术是现代高精度非球面面形检测技术的一个主流发展方向，它能满足较低成本却实现高精度的发展要求。而且微电子产业的发展，使制作精度更高的计算全息图成为现实，极大地推动了CGH在高精度非球面检测中的应用。基于CGH高精度非球面检测技术对保障高精密仪器与光学设备的研制生产，具有重要的实际意义和应用价值。本文针对CGH非球面检测系统中各个模块对非球面检测精度的影响程度，提出了CGH的设计方法、CGH制作误差的检测消除方法以及利用双重位相计算全息图进行绝对检测非球面的测试方法，研究的目的在于提高非球面检测精度。论文主要做了如下的研究工作：
1、设计了包含主全息、对准全息、基准全息三部分的计算全息图，分析了设计辅助全息的必要性以及计算全息布局所需注意的因素。
2、分析了十种CGH制作误差对非球面检测精度的造成的影响，仿真分析了非球面曲率半径误差对检测精度的影响，提出了刻蚀深度不均匀误差和振幅误差的检测方法。由于全息片采用的离焦载频，在光轴上会存在多级衍射级次的重叠，这就可能在检测图中引入鬼像，提出了消除鬼像的实验方法。
3、提出了基于零级光检测基底误差的方法并消除了基底误差对非球面检测精度的影响，该方法对提高非球面检测精度有较大的贡献。使用该方法标定基底误差会产生残余波像差问题和球差问题，为了解决这两个问题，提出了标定光路的选用原则。
4、提出了利用莫尔条纹检测圆对称型计算全息条纹位置畸变误差的方法并消除了条纹位置畸变误差对非球面检测精度的影响。该方法是利用等倾干涉条纹和CGH上刻蚀的圆对称型条纹干涉形成莫尔条纹，通过莫尔条纹的变形信息来获取CGH上的条纹位置畸变信息，该方法对提高非球面检测精度有较大的帮助。
5、提出了用快速傅里叶变化对双重位相全息图进行分析的方法。该方法是基于双重位相全息图的衍射特性，将双重位相全息图的位相方程写成球面位相方程和非球面位相方程的一个线性组合。提出了利用光学设计软件CODE V分别建立球面波、非球面波模型的双重位相计算全息图的位相优化方法。该方法的优化结果很好，为非球面的绝对检测提供了有力支持。
6、使用Zygo公司的Verifire Asphere立式干涉仪作为非球面检测设备，对曲率半径93.86mm和144mm的非球面进行了面形检测，对CGH基底误差的检测方法、基底误差标定光路的选用原则和消除鬼像的方法作了实验验证。
Computer-generated hologram used in optical interferometric system makesthe process of aspheric testing easier. Any complex wavefront can be generated by CGH.The application of CGH in aspheric surface testing can achieve high detection accuracywithout using expensive reference surfaces or null lenses.
Aspheric surface testing based on CGH is a main development direction ofmodern high accuracy aspheric surface testing technology which can meet therequirement of low cost but high accuracy. The development of micro-electronicsindustry makes the fabrication of CGH with high accuracy become reality which hasgreatly promoted the application of CGH in high accuracy aspheric surface testing.High accuracy aspheric surface testing technology based on CGH has importantpractical significance and application value to ensure the development and productionof high precision instruments and optical equipments. Errors in the aspheric surfacetesting system can classified into CGH fabrication errors, interferometer errors, spatialfilter errors and aspheric suface errors. To improve the detection accuracy of asphericsurfaces, the design method of CGH, the measurement methods of CGH fabricationerrors and the absolute testing method for aspheric sufaces based on Twin-CGH areproposed in this paper.The purpose of the study is to improve the accuracy of asphericsurface testing.The main research work of this paper can be summarized as follows:
1. Design CGH including main CGH, alignment CGH and fiducial CGH. Analyzethe necessity of designing alignment CGH and fiducial CGH and the factors of CGHlayout.
2. Errors and uncertainties during CGH fabrication processes result in errors inthe diffraction wavefronts created by the finished hologram. The influences of CGHfabrication errors and aspheric surface curvature radius errors on aspheric surfacetesting accracy are analyzed. The method of measuring phase depth errors andamplitude errors and the experimental method of eliminating ghost image are proposed.
3. The method of measuring and eliminating the effect of substrate errors in aCGH is proposed. Using this method, the detection accuracy of aspheric surfaces can begetting better. Two problems are encountered in this method: residual wavefront errorsproblems and spherical aberrations problems. The selection principle of beam for measuring substrate errors is also proposed.
4. The method of measuring and eliminating the effect of pattern distortion errorsin a CGH is proposed. This method also has great contribution to improve the detectionaccuracy of aspheric surface testing. The equal inclination interference circular gratingand the circularly symmetric type CGH grating are equally spacing that is required inthis method.
5. This paper presents a fast Fourier transform method to analyze Twin-CGH.Twin-CGH may be written as the linear combination of two phase fuctions. Phaseoptimization method of Twin-CGH is proposed in this paper which has provided thepowerful support for the absolute testing method for aspheric sufaces. Theoptimization results by this method are very good.
6. Using Zygo’s Verifire Asphere interferometer as aspheric surfacetesting equipment, Φ135mm、R144mm and Φ78mm、R93.86mm aspheric surfaces aremeasured. The measurement method of CGH substrate errors and the selection of beamfor measuring substrate errors are made experimental verification.
CGH检测非球面的技术是现代高精度非球面面形检测技术的一个主流发展方向，它能满足较低成本却实现高精度的发展要求。而且微电子产业的发展，使制作精度更高的计算全息图成为现实，极大地推动了CGH在高精度非球面检测中的应用。基于CGH高精度非球面检测技术对保障高精密仪器与光学设备的研制生产，具有重要的实际意义和应用价值。本文针对CGH非球面检测系统中各个模块对非球面检测精度的影响程度，提出了CGH的设计方法、CGH制作误差的检测消除方法以及利用双重位相计算全息图进行绝对检测非球面的测试方法，研究的目的在于提高非球面检测精度。论文主要做了如下的研究工作：
1、设计了包含主全息、对准全息、基准全息三部分的计算全息图，分析了设计辅助全息的必要性以及计算全息布局所需注意的因素。
2、分析了十种CGH制作误差对非球面检测精度的造成的影响，仿真分析了非球面曲率半径误差对检测精度的影响，提出了刻蚀深度不均匀误差和振幅误差的检测方法。由于全息片采用的离焦载频，在光轴上会存在多级衍射级次的重叠，这就可能在检测图中引入鬼像，提出了消除鬼像的实验方法。
3、提出了基于零级光检测基底误差的方法并消除了基底误差对非球面检测精度的影响，该方法对提高非球面检测精度有较大的贡献。使用该方法标定基底误差会产生残余波像差问题和球差问题，为了解决这两个问题，提出了标定光路的选用原则。
4、提出了利用莫尔条纹检测圆对称型计算全息条纹位置畸变误差的方法并消除了条纹位置畸变误差对非球面检测精度的影响。该方法是利用等倾干涉条纹和CGH上刻蚀的圆对称型条纹干涉形成莫尔条纹，通过莫尔条纹的变形信息来获取CGH上的条纹位置畸变信息，该方法对提高非球面检测精度有较大的帮助。
5、提出了用快速傅里叶变化对双重位相全息图进行分析的方法。该方法是基于双重位相全息图的衍射特性，将双重位相全息图的位相方程写成球面位相方程和非球面位相方程的一个线性组合。提出了利用光学设计软件CODE V分别建立球面波、非球面波模型的双重位相计算全息图的位相优化方法。该方法的优化结果很好，为非球面的绝对检测提供了有力支持。
6、使用Zygo公司的Verifire Asphere立式干涉仪作为非球面检测设备，对曲率半径93.86mm和144mm的非球面进行了面形检测，对CGH基底误差的检测方法、基底误差标定光路的选用原则和消除鬼像的方法作了实验验证。
Computer-generated hologram used in optical interferometric system makesthe process of aspheric testing easier. Any complex wavefront can be generated by CGH.The application of CGH in aspheric surface testing can achieve high detection accuracywithout using expensive reference surfaces or null lenses.
Aspheric surface testing based on CGH is a main development direction ofmodern high accuracy aspheric surface testing technology which can meet therequirement of low cost but high accuracy. The development of micro-electronicsindustry makes the fabrication of CGH with high accuracy become reality which hasgreatly promoted the application of CGH in high accuracy aspheric surface testing.High accuracy aspheric surface testing technology based on CGH has importantpractical significance and application value to ensure the development and productionof high precision instruments and optical equipments. Errors in the aspheric surfacetesting system can classified into CGH fabrication errors, interferometer errors, spatialfilter errors and aspheric suface errors. To improve the detection accuracy of asphericsurfaces, the design method of CGH, the measurement methods of CGH fabricationerrors and the absolute testing method for aspheric sufaces based on Twin-CGH areproposed in this paper.The purpose of the study is to improve the accuracy of asphericsurface testing.The main research work of this paper can be summarized as follows:
1. Design CGH including main CGH, alignment CGH and fiducial CGH. Analyzethe necessity of designing alignment CGH and fiducial CGH and the factors of CGHlayout.
2. Errors and uncertainties during CGH fabrication processes result in errors inthe diffraction wavefronts created by the finished hologram. The influences of CGHfabrication errors and aspheric surface curvature radius errors on aspheric surfacetesting accracy are analyzed. The method of measuring phase depth errors andamplitude errors and the experimental method of eliminating ghost image are proposed.
3. The method of measuring and eliminating the effect of substrate errors in aCGH is proposed. Using this method, the detection accuracy of aspheric surfaces can begetting better. Two problems are encountered in this method: residual wavefront errorsproblems and spherical aberrations problems. The selection principle of beam for measuring substrate errors is also proposed.
4. The method of measuring and eliminating the effect of pattern distortion errorsin a CGH is proposed. This method also has great contribution to improve the detectionaccuracy of aspheric surface testing. The equal inclination interference circular gratingand the circularly symmetric type CGH grating are equally spacing that is required inthis method.
5. This paper presents a fast Fourier transform method to analyze Twin-CGH.Twin-CGH may be written as the linear combination of two phase fuctions. Phaseoptimization method of Twin-CGH is proposed in this paper which has provided thepowerful support for the absolute testing method for aspheric sufaces. Theoptimization results by this method are very good.
6. Using Zygo’s Verifire Asphere interferometer as aspheric surfacetesting equipment, Φ135mm、R144mm and Φ78mm、R93.86mm aspheric surfaces aremeasured. The measurement method of CGH substrate errors and the selection of beamfor measuring substrate errors are made experimental verification.
引文
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