基于平移旋转的球面绝对检测技术研究
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摘要
随着现代电子工业技术的飞速发展，光学系统对光学元件的面形质量要求愈加严格，例如极紫外（EUV）投影曝光系统要求其核心光学元件的面形误差均方根值（rms）在0.1nm以内。检测能力制约着加工能力，高精度的加工必然要求有更高精度的检测能力。作为高精度面形误差检测的主要手段，干涉检测技术的基本原理是通过分析参考光与被测光之间产生的干涉条纹而获得被测面的面形误差信息，其实质是将参考面作为理想的检测标准进行的相对检测，面形误差检测精度主要受到参考面面形质量的影响。绝对检测技术可以有效剔除参考面面形误差，得到被测面的绝对面形误差分布信息，实现高精度的面形误差检测。平移旋转绝对检测技术是球面面形误差绝对检测领域的通用技术，它属于零位测量（即在检测过程中，被测面和参考面始终处于共焦位置关系），且可以标定发散镜头，一直是当前光学检测领域的前沿课题和研究热点。
本论文研究的主要目的就是在高重复性干涉仪基础之上，进行平移旋转绝对检测技术的算法研究、理论误差分析以及实验验证，完成标准镜参考面面形误差的标定，从而提高面形误差的检测精度。
被测面的面形误差可分为旋转对称和旋转非对称两部分，旋转非对称面形误差的检测是其面形误差检测中相当重要的一部分。论文第二章介绍了多种旋转法检测被测球面旋转非对称面形误差的基本原理，分析了其中存在的理论误差，并提出了相应的改进方法，最后对各种旋转法进行了对比分析。
平移旋转算法是平移旋转绝对检测技术的核心，也是本论文研究工作的核心和关键问题。分析了平移旋转算法的特点，并对其进行了分类总结。分析了传统的平移旋转算法，针对其存在的理论误差，提出了改进算法，有效提高了算法检测精度；然后将Zernike多项式拟合扩展至全口径面形误差，提出了基于Zernike多项式全口径拟合的平移旋转算法；同时针对现有平移旋转算法计算量大、计算速度受到一定限制的问题，提出了平移旋转快速算法；最后，为进一步提高平移旋转绝对检测技术的检测精度，提出了基于像素点未知量的平移旋转算法，将算法检测精度提高至像素级，并给出了初步实验验证。
平面作为球面的特殊情况，介绍了其传统绝对技术三平板法的基本原理，然后将平移旋转法应用于平面的绝对检测，并与传统的三平板法进行了实验对比分析，分析了各自存在的问题。
为直接验证平移旋转绝对检测技术的有效性，进行了以不同质量（相同F数）的标准镜检测同一被测球面的验证性实验。此外，进行了以平移旋转法、双球面法、随机球法等三种不同的绝对检测技术检测标定同一标准镜参考面面形误差的标定实验，通过交叉对比实验结果，验证了绝对检测技术的有效性。
论文最后介绍了旋转平移参数（旋转中心、旋转角度和平移量）的精确确定方法，分析了影响平移旋转算法检测精度的主要误差，并进行了理论仿真和基于实验数据的分析。
With the rapid development of modern electronics industry, high-precision opticshave been widely employed in optical systems, eg. Surface deviation of the opticsused in the EUV must be better than rms0.1nm. The manufacture accuracy is limitedby the testing accuracy, and it certainly requires much higher accuracy of testing.Interferometric testing is the main method to test surface deviation; its result isactually the deviation of tested surface compared to the reference surface. It is relativemeasurement. The absolute testing methods can remove the reference surfacedeviation to get the absolute surface deviation of the tested surface. As a generalabsolute testing method, the shift-rotation method belongs to null-test method, and isthe key technology in surface metrology.
Based on the high repeatability of interferometers, the thesis is dedicated to solvethe key theoretical algorithm, error analysis and technical problems of absolute testingmethod of shift-rotation, and further promote the accuracy of measurements bycalibrating the surface deviation of the reference surface.
The surface deviation of any optical surface can be divided into rotationallysymmetric and asymmetric components. And there are many different absolute testingmethods that are based on Zernike polynomials fitting methods, to measure therotationally asymmetric surface deviation. We introduce the principles of the methods,and analysis the theoretical errors. And we further propose a new method withtheoretical and experimental comparisons.
The shift-rotation algorithm is the key of the absolute testing technologies, and itis the key content of the thesis. We briefly introduce different shift-rotation methods,and give corresponding comments.
The traditional shift-rotation employs the N-position method, and it suffers thekN order angular terms errors missed by N-position method when calculates therotationally symmetric surface deviation. An optimized absolute testing method ofshift-rotation is presented in this thesis. It considers the missingkN order errors.As a result, it is more accurate than the traditional method. Experimental absolute results of spherical surfaces are given.
A simple and reliable data-reduction method of absolute shift-rotation method ispresented, which relies on the decomposition of the surface deviation into rotationallyasymmetric and symmetric components. The rotationally asymmetric surfacedeviation can be simply obtained by N-position method. After that, thetwo-dimensional (2D) problem of estimating the other rotationally symmetric surfacedeviation can be simplified to a one-dimensional (1D) problem. Experimentalabsolute results of spherical surfaces are given.
A pixel-level spatial frequency solution of shift-rotation method is also presentedin the thesis. With the well-organized absolute procedures, the absolute surfacedeviation of the test and reference surface can be obtained accurately with pixel-levelspatial frequency resolution. Experimental absolute results of flat surfaces are given.
The absolute testing methods of flats are also introduced in the thesis. Comparedwith the traditional three-flat testing method, the shift-rotation method has its ownadvantages. With theoretical analysis, the experimental results are given.
To prove the validity of shift-rotation method, we measure a same testes sphericalsurface with two different sphere transmissions (same F number, but differentqualities). Then we prove the validity of the absolute testing methods withexperiments. With three different absolute testing methods, two-sphere method,random-average-testing method and shift-rotation method, we calibrate the samespherical reference surface and make comparisons.
Finally, we introduce a method to determine the shift and rotational parameters,and give error analysis of the shift-rotation method.
本论文研究的主要目的就是在高重复性干涉仪基础之上，进行平移旋转绝对检测技术的算法研究、理论误差分析以及实验验证，完成标准镜参考面面形误差的标定，从而提高面形误差的检测精度。
被测面的面形误差可分为旋转对称和旋转非对称两部分，旋转非对称面形误差的检测是其面形误差检测中相当重要的一部分。论文第二章介绍了多种旋转法检测被测球面旋转非对称面形误差的基本原理，分析了其中存在的理论误差，并提出了相应的改进方法，最后对各种旋转法进行了对比分析。
平移旋转算法是平移旋转绝对检测技术的核心，也是本论文研究工作的核心和关键问题。分析了平移旋转算法的特点，并对其进行了分类总结。分析了传统的平移旋转算法，针对其存在的理论误差，提出了改进算法，有效提高了算法检测精度；然后将Zernike多项式拟合扩展至全口径面形误差，提出了基于Zernike多项式全口径拟合的平移旋转算法；同时针对现有平移旋转算法计算量大、计算速度受到一定限制的问题，提出了平移旋转快速算法；最后，为进一步提高平移旋转绝对检测技术的检测精度，提出了基于像素点未知量的平移旋转算法，将算法检测精度提高至像素级，并给出了初步实验验证。
平面作为球面的特殊情况，介绍了其传统绝对技术三平板法的基本原理，然后将平移旋转法应用于平面的绝对检测，并与传统的三平板法进行了实验对比分析，分析了各自存在的问题。
为直接验证平移旋转绝对检测技术的有效性，进行了以不同质量（相同F数）的标准镜检测同一被测球面的验证性实验。此外，进行了以平移旋转法、双球面法、随机球法等三种不同的绝对检测技术检测标定同一标准镜参考面面形误差的标定实验，通过交叉对比实验结果，验证了绝对检测技术的有效性。
论文最后介绍了旋转平移参数（旋转中心、旋转角度和平移量）的精确确定方法，分析了影响平移旋转算法检测精度的主要误差，并进行了理论仿真和基于实验数据的分析。
With the rapid development of modern electronics industry, high-precision opticshave been widely employed in optical systems, eg. Surface deviation of the opticsused in the EUV must be better than rms0.1nm. The manufacture accuracy is limitedby the testing accuracy, and it certainly requires much higher accuracy of testing.Interferometric testing is the main method to test surface deviation; its result isactually the deviation of tested surface compared to the reference surface. It is relativemeasurement. The absolute testing methods can remove the reference surfacedeviation to get the absolute surface deviation of the tested surface. As a generalabsolute testing method, the shift-rotation method belongs to null-test method, and isthe key technology in surface metrology.
Based on the high repeatability of interferometers, the thesis is dedicated to solvethe key theoretical algorithm, error analysis and technical problems of absolute testingmethod of shift-rotation, and further promote the accuracy of measurements bycalibrating the surface deviation of the reference surface.
The surface deviation of any optical surface can be divided into rotationallysymmetric and asymmetric components. And there are many different absolute testingmethods that are based on Zernike polynomials fitting methods, to measure therotationally asymmetric surface deviation. We introduce the principles of the methods,and analysis the theoretical errors. And we further propose a new method withtheoretical and experimental comparisons.
The shift-rotation algorithm is the key of the absolute testing technologies, and itis the key content of the thesis. We briefly introduce different shift-rotation methods,and give corresponding comments.
The traditional shift-rotation employs the N-position method, and it suffers thekN order angular terms errors missed by N-position method when calculates therotationally symmetric surface deviation. An optimized absolute testing method ofshift-rotation is presented in this thesis. It considers the missingkN order errors.As a result, it is more accurate than the traditional method. Experimental absolute results of spherical surfaces are given.
A simple and reliable data-reduction method of absolute shift-rotation method ispresented, which relies on the decomposition of the surface deviation into rotationallyasymmetric and symmetric components. The rotationally asymmetric surfacedeviation can be simply obtained by N-position method. After that, thetwo-dimensional (2D) problem of estimating the other rotationally symmetric surfacedeviation can be simplified to a one-dimensional (1D) problem. Experimentalabsolute results of spherical surfaces are given.
A pixel-level spatial frequency solution of shift-rotation method is also presentedin the thesis. With the well-organized absolute procedures, the absolute surfacedeviation of the test and reference surface can be obtained accurately with pixel-levelspatial frequency resolution. Experimental absolute results of flat surfaces are given.
The absolute testing methods of flats are also introduced in the thesis. Comparedwith the traditional three-flat testing method, the shift-rotation method has its ownadvantages. With theoretical analysis, the experimental results are given.
To prove the validity of shift-rotation method, we measure a same testes sphericalsurface with two different sphere transmissions (same F number, but differentqualities). Then we prove the validity of the absolute testing methods withexperiments. With three different absolute testing methods, two-sphere method,random-average-testing method and shift-rotation method, we calibrate the samespherical reference surface and make comparisons.
Finally, we introduce a method to determine the shift and rotational parameters,and give error analysis of the shift-rotation method.
引文
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