IOE OpenIR  > 光电技术研究所博硕士论文
干涉面形绝对检测不确定度评估方法研究
全海洋1,2
Subtype博士
Thesis Advisor伍凡 ; 侯溪
2017-05
Degree Grantor中国科学院研究生院
Place of Conferral北京
Degree Discipline光学工程
Keyword光学检测 干涉计量 绝对检测 三平板绝对检测 不确定度评估
Abstract

以投影光刻物镜为代表的现代高端光学系统已经将光学元件干涉面形检测推向了“极限”,光学元件面形质量要求达到均方根值(rms)纳米甚至亚纳米级别。这给面形检测提出了极大的挑战,使得传统的检测手段已经不能满足现代高端光学元件研制的需求,相应的面形检测结果不能充分发挥其指导加工的作用。一个完整的面形检测结果应该包括被测面形的最佳估计值和描述该检测结果分散性的测量不确定度。测量不确定度评估方法的研究是干涉面形检测中的研究难点,是寻求减小不确定度途径中必须经历且必不可少的一步。

绝对检测技术将系统误差(主要指参考面面形误差)从相对测量结果中分离出来,可突破参考标准固有的精度限制,因此有望实现最小不确定度的检测。但是绝对检测本身的不确定度也必须加以评估。本论文正是针对绝对检测结果的不确定度需要准确评估的需求,以探索一种适用于干涉面形绝对检测不确定度评估的通用方法为主要目的,主要开展了以下研究内容:

1、充分调研国内外现行的几种不确定度评估方法,对比两种适用于面形检测的自上而下和自下而上不确定度评估方法,分析比较其各自的优缺点及其适用范围;系统分析几种常用的干涉面形绝对检测技术,包括三平板法及其扩展方法、双球面法、随机球法、平移旋转法和逆向优化法,并从测量装置、测量人员、测量方法、测量环境四大方面分析各种绝对检测技术的不确定度来源。

2、对绝对检测的模型建立、模型求解、模型误差传递和不确定度评估这几个方面进行系统研究。使用一个通用的线性回归模型来描述整个绝对检测过程,并引入了三种绝对检测模型的求解算法,包括最小二乘法、极大似然估计法和矩阵迭代法。介绍了两种绝对检测误差传递和不确定度评估的方法:基于正态统计分布假设的测量不确定度评估方法和基于蒙特卡洛误差传递的不确定度评估方法。

3、文中系统研究了三平板法绝对检测技术。提出了一种通用的三平板平面绝对检测方法,即采用通用迭代优化算法来求解三平板模型,该通用迭代算法可以实现像素空间分辨率的检测,实施简单、收敛快速且迭代重构精度高,同时不需要太大的存储空间和运算量。设计仿真实验和实测实验来验证该算法的有效性。并详细分析了三平板测量过程中的主要不确定度源。

4、研究了一种不确定度评估的拟蒙特卡洛方法,用于处理小样本情况下测量不确定度的准确评估,具有不需要对总体分布做任何假设的优势。该方法针对每个像素点的面形进行评估,其评估的面形结果及其不确定度都用矩阵图表示,因此评估结果更加完整,而不单单是rms值这样的单值指标。该方法是《测量不确定度评定与表示》(GUM法)的补充,为GUM法评估结果提供了一种验证方法。以通用三平板绝对检测技术为例,同时使用GUM法和拟蒙特卡洛法对测量结果进行了不确定度评估,同时设计了多种交叉对比实验来验证不确定度评估结果的可靠性。

5、系统分析了三平板法绝对检测的误差分配原则和精度保证措施。针对立式工况下重力变形问题提出了一种基于模型的重力变形补偿技术,为零重力变形的提取提供了思路。基于模型的重力变形补偿技术借助于有限元模型和实测旋转差分检测数据,通过迭代优化算法来分离旋转差分检测过程中的调整误差,进而实现实际工况下重力变形的准确提取。并设计实验验证了基于模型的重力变形补偿方法的有效性。

6、提出可以通过优化测量条件配置使得绝对检测在消除模型误差的同时抑制测量噪声,从而降低测量不确定度。仿真分析了单次旋转角度测量和多次旋转角度测量的优化配置问题。并通过设计实验得到单次旋转和多次旋转的独立重复测量精度分别为0.35 nm rms和0.24 nm rms,验证了多次旋转角度优化配置后实现了测量不确定度的降低。

Other Abstract

Modern high-end optical systems, especially the lithographic objective lens system, have taken interferometrical surface figure measurement of optics to the extreme. The surface figure specification requires to nanometer rms even sub-nanometer rms, which is a huge challenge for surface figure testing. Traditional test techniques can not work. Thus the test result can not be the guidance to optical fabrication. As GUM says, a complete statement of the result of a measurement includes an approximation or estimate of the value of the measurand, as well as information about the uncertainty of measurement. Study on the uncertainty evaluation of surface figure testing is a hard problem. But it is the right key to improve measurement uncertainty.

Absolute test, i.e., test procedures that enable separation of systematic errors (mainly the reference errors) from the relative test datas, can break through the limitation of reference standards. So it is possible to reach the lowest uncertainty. However, the measurement uncertainty of the absolute test itself should be accurately evaluated. Aiming at the requirements of uncertainty evaluation in absolute test, this dissertation focuses on the research of a generally universal uncertainty evaluation approach for absolute test and contains the following sections:

1. The domestic and overseas development status about the uncertainty evalucation is investigated. Both the top-down approach and bottom-up approach are compared with each other, aims to find the applicability of each method using in surface figure measurement. Various absolut test techniques are compared and analyzed, including the three-flat test and its variants, two-sphere test, random-ball test, shift-rotation test and reverse optimization. For each test technique, the four main sources of uncertainty are analyzed: measurement instrument, people, method and procedure, and environment.

2. The following parts are systematically studied, forward modeling for absolute test, inverse model solution for the model, and error propagation and uncertainty evaluation. A universal linear regress model is used to express the whole absolute test process. Three main model solvers are introduced: least squares estimator (LSE), maximum likelihood estimator (MLE), and iterative methods. Uncertainty evaluation methods based on normal distribution hypothesis and Monte Carlo error propagation are presented.

3. A generalized iterative method for absolute measurement of optical flats has been discussed. Both simulation results and experimental results demonstrated that the generalized method can correctly reconstruct absolute figures with pixel-level spatial resolution; are easy to understand and implement; and computationally efficient. Also it saves much computational costs and memory space requirements. For three-flat test, several sources of uncertainty are analyzed systematically.

4. A quasi-MCM is proposed to estimate the uncertainty of absolute test, which can handle the uncertainty problems with small samples, without any assumption of the probability distribution. Quasi-MCM estimates the surface figure at every pixel, which makes the absolute test result and its uncertainty both matrices. Thus the evaluation is more complete compared with other methods using single value like rms.Taking the three-flat test as an example, both GUM and Quasi-MCM are used to evaluate the measurement uncertainty of the three-flat test result. To prove the reliability of the uncertainty evaluation, several independent cross-check experiments are designed.

5. Both error allocations and accuracy guarantees for three-flat test are analyzed. As to the sag problem introduced by gravity for a horizontally mounted optical flat, a reverse optimization method based on the FEM model and the real difference rotation test result is proposed. Experimental results demonstrated that this reverse optimization method can effectively reconstruct the sagging information due to gravity.

6. Through sensitivity analysis of reconstruction error and rotation angle, it is noticed that some surface error terms cannot be reconstructed by the one-angle rotation model. By adding measurements with additional rotation angles, the error terms that cannot be estimated can be compensated and the measurement uncertainty is improved as well. Both simulation and experimental results indicate that the proposed iterative optimization method is effective for solving the three-flat problem with pixel-level spatial resolution and the measuring precision of two separate measurements for multiple rotations is 0.24 nm rms, while the result is 0.35 nm rms for one-angle rotation.

Language中文
Document Type学位论文
Identifierhttp://ir.ioe.ac.cn/handle/181551/8097
Collection光电技术研究所博硕士论文
Affiliation1.中国科学院光电技术研究所
2.中国科学院大学
Recommended Citation
GB/T 7714
全海洋. 干涉面形绝对检测不确定度评估方法研究[D]. 北京. 中国科学院研究生院,2017.
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