Distortion correcting method when testing large-departure asphere
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摘要: 在高数值孔径（NA）投影光刻物镜中，随着数值孔径的增加，非球面的偏离度越来越大。对这种大偏离度非球面进行亚纳米量级的检测，一直是光学检测的一大难题。本文首先对一偏离度超过500 μm的偶次高次非球面进行了计算全息图（Computer-Generated Hologram，CGH）设计，设计出了满足高精度面形检测和刻蚀加工要求的CGH。然后，针对此设计方案，定量分析了CGH的成像畸变及畸变对像差分析的影响。分析结果表明，不同径向位置的成像倍率偏差（畸变）最大达到了2.7:1，并且由于畸变的存在，低阶像差衍生出了明显的高阶像差。最后，针对用CGH检测大偏离度非球面时出现的成像畸变，提出了采用光线追迹与最小二乘法相结合的成像畸变的校正方法，并通过实验验证了此方法的准确性。实验结果表明，畸变校正之后相对剩余残差小于0.2%，可以满足高精度非球面检测加工的要求。Abstract: With the increase in numerical aperture, the aspheric departure is also increasing in the high-NA projection objective. It is a problem to test the large-departure asphere in nanometers in the optical metrology. For an asphere with aspheric departure exceeding 500 micrometers, firstly, we design a CGH to satisfy the demands of high precise testing and etching fabrication. Secondly, the imaging distortion and the effect of distortion on aberration are analyzed quantitatively. The analysis results show that the maximum magnification deviation is 2.7:1 for the different radial positions, and the low order aberrations will generate high order aberrations obviously. Lastly, we propose the ray trace and least square method to correct the imaging distortion when testing large-departure asphere with CGH, and verify the precision of the method through the experiments. The results show that the relative residue is less than 0.2% after correcting, and the precision will satisfy the demands of high precise optical testing and fabrication.
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Key words:
- computer-generated hologram /
- CGH /
- distortion /
- asphere testing
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图 2 用CGH检测非球面的光路图和CGH刻线的空间频率
Figure 2. Light path of testing asphere with CGH and spatial frequency of CGH
图 4 非球面不同的径向位置在CCD上的分辨率
Figure 4. CCD resolution for the different radial positions of asphere
图 5 非球面倾斜0.001度时，分别以非球面和参考面为光阑，仿真获得的干涉图与Zernike系数；(a)以非球面为光阑时的干涉图；(b)以参考面为光阑时的干涉图；(c)以非球面为光阑时的Zernike系数；(d)以参考面为光阑时的Zernike系数
Figure 5. Interferograms and Zernike coefficients generated by simulation when the asphere and reference surface are set as stop respectively, and the tilt of asphere is set 0.001 degree; (a) Interferogram when the asphere is set as stop. (b) Interferogram when the reference surface is set as stop. (c) Zernike coefficients when the asphere is set as stop. (d) Zernike coefficients when the reference surface is set as stop
图 6 采用不同的拟合阶数进行拟合时的剩余残差
Figure 6. Fitting residuals when using different fitting orders
图 7 (a)带有标记点的干涉图；(b)在干涉图中提取标记点坐标
Figure 7. (a) Interferogram with fiducials; (b) Extracting the coordinates of fiducials on the interferogram
图 9 (a)畸变校正之前的干涉图；(b)畸变校正之后的干涉图
Figure 9. (a) Interferogram before correcting distortion; (b) Interferogram after correcting distortion
表 1 非球面参数
Table 1. Parameters of asphere
D R K A4 A6 A8 144 297.510 0 -1.363×10-7 6.488×10-12 -7.002×10-16 A10 A12 A14 A16 A18 4.057×10-19 -1.505×10-22 3.533×10-26 -4.479×10-30 2.358×10-34 
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