干涉面形绝对检测不确定度评估方法研究

发布时间：2018-01-16 07:32

本文关键词：干涉面形绝对检测不确定度评估方法研究　出处：《中国科学院光电技术研究所》2017年博士论文　论文类型：学位论文

【摘要】：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。
[Abstract]:The modern high-end optical system in projection lithography lens have been represented by the optical element surface to interference detection limit, optical component surface quality requirements to the RMS value (RMS) nano or even sub nanometer level. The surface presents a great challenge to the traditional means of detection, detection has been unable to meet the demand for high-end modern optical element is developed, the corresponding surface detection results can not fully play its guiding role. A machining surface integrity test results should include the best estimate of measured surface values and describe the detection results of dispersion measurement uncertainty. Study of measurement uncertainty evaluation method is difficult study on interference surface detection, is seeking to reduce the uncertainty in the way of experience and must be an essential step. The absolute detection system error (mainly refers to the reference surface error) from Isolated relative measurement results, the accuracy limit can break the inherent reference standard, it is expected to achieve the minimum uncertainty of detection. But the absolute detection uncertainty itself must also be evaluated. This paper is the uncertainty of the need to accurately assess the demand for absolute detection results, to explore a suitable intervention absolute flatness detection method of uncertainty evaluation as the main purpose, the main research contents are as following: 1, full investigation and evaluation method of several existing domestic and foreign uncertainty degree evaluation method applicable to the comparison of two kinds of surface shape detection of top-down and bottom-up uncertainty, analyzed and compared their advantages and disadvantages and their application the scope of system analysis; the absolute detection technology of several commonly used interference surface, including three plate method and the expansion method, double sphere method, random sphere, translation and rotation and the reverse. The method, and the measuring device, measuring, measurement method, measurement environment four aspects of absolute detection technology analysis of various sources of uncertainty in.2, established on the absolute detection model of solving the model, the model of error transfer and uncertainty evaluation of several aspects of this system. Using a general linear regression model to describe the absolute detection process, and introduces the algorithm for solving three kinds of absolute detection model, including least squares, maximum likelihood estimation method and matrix iteration method. The transfer and the method of uncertainty evaluation of two kinds of errors: absolute measurement uncertainty evaluation method and uncertainty evaluation method based on Monte Carlo error transfer.3 the measurement of normal statistical distribution based on the assumption, this paper studies three plate method of absolute detection technology. Propose an absolute detection method of a general three plane, i.e. A general iterative optimization algorithm to solve the three plate model, the general iterative algorithm can achieve spatial resolution pixel detection, simple implementation, fast convergence and high precision iterative reconstruction, and does not require storage space and computing quantity is too large. Simulation experiments and field experiments to verify the effectiveness of the algorithm and a detailed analysis of the three. The tablet in the measurement of the main uncertainty sources of.4, a Quasi Monte Carlo method for uncertainty evaluation, for the case of small sample measurement uncertainty to accurately assess the degree, which do not need to make any assumptions on the overall advantages. The distribution of surface shape for each pixel of the methods are evaluated the surface shape of the evaluation results and uncertainty with matrix diagram, so the evaluation results are more complete, not just the RMS value of this single value index. This method is the evaluation of uncertainty in measurement. With said > (GUM) supplement provides a verification method for the evaluation result of GUM method. In general three tablet absolute detection technology as an example, using GUM method and Quasi Monte Carlo method on the measurement results of uncertainty evaluation, and designed a variety of cross contrast experiments to verify the reliability of.5 uncertainty the evaluation results, the error distribution principle and means to guarantee the accuracy of a systematic analysis of the three plate method of absolute measurement. Aiming at the problem of deformation under the condition of vertical gravity presents a deformation model based on gravity compensation technology, extracting deformation as zero gravity has provided the thinking model of gravity deformation compensation technology. With the help of the finite element model and measured rotating differential detection based on the data, through the iterative optimization algorithm to separate the rotation error adjustment in the process of detection, so as to realize the accurate extraction of the actual conditions of gravity deformation. And design The.6 test is to verify the effectiveness of the compensation method of the deformation model based on gravity, can put forward the measurement of noise suppression in the model error and absolute measurement conditions through the optimization of configuration makes, so as to reduce the measurement uncertainty. Simulation analysis of the optimized configuration of single rotation angle measurement and rotation angle measurement and the design. The independent measurement accuracy of single rotation and multiple rotations were 0.35 nm rms and 0.24 nm rms, have proved the rotation angle optimization is achieved after the measurement uncertainty is reduced.

【学位授予单位】：中国科学院光电技术研究所
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O436.1

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