超高精度非球面面形检测技术研究
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摘要
在光学设计中，单个球面可以供优化的自由度只有曲率半径；而非球面除了顶点曲率半径之外，还有二次曲面常数和高阶项系数。由于非球面比球面拥有更多设计自由度，所以在高NA投影光刻物镜中，都普遍采用非球面元件来减小系统的复杂度，并提高系统的成像质量。虽然非球面有优良的光学性质，但是非球面检测，特别是超高精度非球面面形检测，一直是光学检测领域的一个难题，也是制约非球面元件应用的关键因素。对于非球面偏离度较小的非球面，可以采用环带拼接法或子孔径拼接法进行检测，但检测精度往往受制于机械定位误差和干涉仪的非共光路误差。如果非球面是二次曲面，也可以采用无像差点法进行检测，但往往会引入中心遮拦；而高次非球面，则采用零位补偿法进行检测。对于高NA投影光刻物镜而言，非球面度往往比较大，并且对面形精度要求极为苛刻(RMS为亚纳米量级)，对于如此高精度的非球面，一般只能采用零位补偿法进行检测。
针对高NA投影光刻物镜对超高精度非球面面形检测的需要，本论文以计算全息图(Computer-Generated Hologram, CGH)和补偿镜为零位补偿器，主要开展了以下研究内容：
1、高精度CGH设计。分析了CGH的工作原理、工作模式和衍射效率，给出了CGH相位和空间频率的计算方法；针对高NA投影光刻物镜中的一高次偶次非球面，详细论述了零位补偿CGH和辅助调节CGH的设计方法，并重点分析了衍射鬼像的产生机理和剔除方法；基于Matlab软件平台，利用论文所论述的方法，编写了CGH设计软件，利用该软件实现对光刻物镜中的非球面所需CGH的设计。
2、用CGH对非球面检测的误差分析及标定方法。系统分析了CGH的基底误差、CGH的刻蚀误差、CGH和非球面的调节误差、CGH的成像畸变和温度压强波动等对非球面检测精度的影响；针对CGH基底误差，给出了基底的标定方法；针对CGH的成像畸变，建立了畸变校正模型，并实现了对CGH成像畸变的高精度校正；针对CGH和非球面的调节误差(球差和彗差)，提出了误差控制的方法；采用非线性最小二乘算法，在测量非球面面形的同时，也实现了对非球面顶点曲率半径的高精度测量。同时，考虑到整个系统的轴对称性，采用多角度平均的方法，实现了对非球面旋转非对称面形的绝对标定，进一步提高了非球面的检测精度。
3、高精度补偿镜的设计及公差分配。论文提出采用平行光入射的补偿镜设计方案，与其他设计方法相比，该设计方案便于调节(不用调节补偿镜的轴向距离和偏心)，避免了补偿镜的调节误差对非球面测量精度的影响。另外，由于在光学加工和装配过程中采用了“光学复算”的方法，在满足非球面检测精度的情况下，使补偿镜的曲率半径加工公差、中心厚加工公差和透镜间隔装配公差变的相对宽松，方便补偿镜的加工和装配。
4、检测结果的比对和实验验证。针对一抛物面，分别采用无像差点法和CGH法进行了高精度检测；通过对比二者的检测结果，从实验上验证了CGH法的准确性。
In optical design, the radius of curvature (ROC) is used as the only variable parameterfor optimizing a sphere surface. By contrast, a conic constant and many high-orderaspheric coefficients can be used as variables for optimizing an aspheric surface.Therefore, aspheric surfaces are commonly used in the high numerical aperture (NA)projection objectives to decrease the complexity and to improve the imagingperformance. However, its applications are limited by the testing level despite ofmany superior optical features. Especially the ultra-precision aspheric surface testinghas become a challenge that we have to deal with. Usually, Annular stitching orsub-aperture stitching method can test an asphere with a mild departure from the bestfit radius (BFR), but the testing precision is restricted by the mechanical positioningerror and the retrace error of the interferometer. Stigmatic null testing can test a conicsurface, but with the center usually obscured. Thus, null lens compensator is the bestchoice for testing a high-order aspheric surface. Furthermore, the testing precisionshould be less than1nm RMS in order to meet the surface precision requirements ofasphere elements in high NA projection objectives.
Aiming at the requirements of ultra-precision aspheric surface testing in high NAprojection objectives, this dissertation focuses on the research of computer-generatedhologram (CGH) and null lens as compensators and contains the following sections:
1. Designing high precise CGH. The thesis analyses the CGH working principle,CGH working modes and diffraction efficiency; gives the calculatingmethods of CGH phase and CGH spatial frequency. For a general even highorder asphere in high-NA projection objectives, the thesis discusses thedesign method of null CGH and alignment CGH in detail, and then analysesthe reason how the diffracting ghosts turn up, and proposed a method toavoid them. According to the methods described in this thesis, a programbased on Matlab platform is compiled to complete the CGH design for theaspheres in the high-NA projection objective.
2. Error analysis of aspheric testing with CGH and calibrating methods. Thethesis analyses the substrate error, etching error, alignment error betweenCGH and asphere, imaging distortion and the influence of temperature andpressure fluctuation. The thesis gives the calibration methods for thesubstrate error of CGH and builds a model to correct the imaging distortion of CGH precisely. The thesis also gives an effective method to restrict thealignment errors such as spherical aberration and coma. Using the nonlinearleast-square method, the vertex radius of curvature is acquired whenmeasuring the aspheric surface. To improve the testing precision, therotational asymmetric surface is calibrated absolutely using the multi-angleaveraging method.
3. Designing high precise null lens and tolerance analysis. Compared to otherdesigns, the design which uses the parallel beam illuminating the null lenscould be easily aligned (need not to take the axial and decenter alignment)and avoid the alignment errors for aspheric surface testing. Furthermore, thefabricating tolerance of ROC and center thickness, and the aligning toleranceof spacing will be much loosened by using the optical redesign method in thefabricating and aligning process. This will be very favorable for opticalfabrication and alignment.
4. The results comparing and experimental verification. A paraboloid is testedprecisely using stigmatic null test and CGH null test respectively. Theprecision of CGH is verified experimentally by comparing the two testingresults.
针对高NA投影光刻物镜对超高精度非球面面形检测的需要，本论文以计算全息图(Computer-Generated Hologram, CGH)和补偿镜为零位补偿器，主要开展了以下研究内容：
1、高精度CGH设计。分析了CGH的工作原理、工作模式和衍射效率，给出了CGH相位和空间频率的计算方法；针对高NA投影光刻物镜中的一高次偶次非球面，详细论述了零位补偿CGH和辅助调节CGH的设计方法，并重点分析了衍射鬼像的产生机理和剔除方法；基于Matlab软件平台，利用论文所论述的方法，编写了CGH设计软件，利用该软件实现对光刻物镜中的非球面所需CGH的设计。
2、用CGH对非球面检测的误差分析及标定方法。系统分析了CGH的基底误差、CGH的刻蚀误差、CGH和非球面的调节误差、CGH的成像畸变和温度压强波动等对非球面检测精度的影响；针对CGH基底误差，给出了基底的标定方法；针对CGH的成像畸变，建立了畸变校正模型，并实现了对CGH成像畸变的高精度校正；针对CGH和非球面的调节误差(球差和彗差)，提出了误差控制的方法；采用非线性最小二乘算法，在测量非球面面形的同时，也实现了对非球面顶点曲率半径的高精度测量。同时，考虑到整个系统的轴对称性，采用多角度平均的方法，实现了对非球面旋转非对称面形的绝对标定，进一步提高了非球面的检测精度。
3、高精度补偿镜的设计及公差分配。论文提出采用平行光入射的补偿镜设计方案，与其他设计方法相比，该设计方案便于调节(不用调节补偿镜的轴向距离和偏心)，避免了补偿镜的调节误差对非球面测量精度的影响。另外，由于在光学加工和装配过程中采用了“光学复算”的方法，在满足非球面检测精度的情况下，使补偿镜的曲率半径加工公差、中心厚加工公差和透镜间隔装配公差变的相对宽松，方便补偿镜的加工和装配。
4、检测结果的比对和实验验证。针对一抛物面，分别采用无像差点法和CGH法进行了高精度检测；通过对比二者的检测结果，从实验上验证了CGH法的准确性。
In optical design, the radius of curvature (ROC) is used as the only variable parameterfor optimizing a sphere surface. By contrast, a conic constant and many high-orderaspheric coefficients can be used as variables for optimizing an aspheric surface.Therefore, aspheric surfaces are commonly used in the high numerical aperture (NA)projection objectives to decrease the complexity and to improve the imagingperformance. However, its applications are limited by the testing level despite ofmany superior optical features. Especially the ultra-precision aspheric surface testinghas become a challenge that we have to deal with. Usually, Annular stitching orsub-aperture stitching method can test an asphere with a mild departure from the bestfit radius (BFR), but the testing precision is restricted by the mechanical positioningerror and the retrace error of the interferometer. Stigmatic null testing can test a conicsurface, but with the center usually obscured. Thus, null lens compensator is the bestchoice for testing a high-order aspheric surface. Furthermore, the testing precisionshould be less than1nm RMS in order to meet the surface precision requirements ofasphere elements in high NA projection objectives.
Aiming at the requirements of ultra-precision aspheric surface testing in high NAprojection objectives, this dissertation focuses on the research of computer-generatedhologram (CGH) and null lens as compensators and contains the following sections:
1. Designing high precise CGH. The thesis analyses the CGH working principle,CGH working modes and diffraction efficiency; gives the calculatingmethods of CGH phase and CGH spatial frequency. For a general even highorder asphere in high-NA projection objectives, the thesis discusses thedesign method of null CGH and alignment CGH in detail, and then analysesthe reason how the diffracting ghosts turn up, and proposed a method toavoid them. According to the methods described in this thesis, a programbased on Matlab platform is compiled to complete the CGH design for theaspheres in the high-NA projection objective.
2. Error analysis of aspheric testing with CGH and calibrating methods. Thethesis analyses the substrate error, etching error, alignment error betweenCGH and asphere, imaging distortion and the influence of temperature andpressure fluctuation. The thesis gives the calibration methods for thesubstrate error of CGH and builds a model to correct the imaging distortion of CGH precisely. The thesis also gives an effective method to restrict thealignment errors such as spherical aberration and coma. Using the nonlinearleast-square method, the vertex radius of curvature is acquired whenmeasuring the aspheric surface. To improve the testing precision, therotational asymmetric surface is calibrated absolutely using the multi-angleaveraging method.
3. Designing high precise null lens and tolerance analysis. Compared to otherdesigns, the design which uses the parallel beam illuminating the null lenscould be easily aligned (need not to take the axial and decenter alignment)and avoid the alignment errors for aspheric surface testing. Furthermore, thefabricating tolerance of ROC and center thickness, and the aligning toleranceof spacing will be much loosened by using the optical redesign method in thefabricating and aligning process. This will be very favorable for opticalfabrication and alignment.
4. The results comparing and experimental verification. A paraboloid is testedprecisely using stigmatic null test and CGH null test respectively. Theprecision of CGH is verified experimentally by comparing the two testingresults.
引文
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