Wang Tianyi, Huang Lei, Choi Heejoo, Vescovi Matthew, Kuhne Denis, Zhu Yi, Pullen Weslin C, Ke Xiaolong, Kim Dae Wook, Kemao Qian, Tayabaly Kashmira, Bouet Nathalie, Idir Mourad
Opt Express. 2021 May 10;29(10):15114-15132. doi: 10.1364/OE.419490.
Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.
精密光学在许多先进技术应用中有着广泛需求。例如，X射线镜是同步辐射和自由电子激光设施中的关键光学元件。它们是矩形硅或玻璃基板，需要将矩形的有效孔径（CA）抛光至亚纳米均方根（RMS），以保持入射X射线波前在衍射极限下的成像能力。卷积抛光模型需要用额外数据扩展CA，通过反卷积计算驻留时间。然而，由于反卷积对边界误差和噪声非常敏感，现有的表面扩展方法很难满足亚纳米要求。一方面，在扩展过程中对CA中的面形误差建模不当，导致沿边界出现连续性问题。另一方面，不可校正的高频误差和噪声也被扩展。在本研究中，我们提出了一种新颖的稳健迭代表面扩展（RISE）方法，通过数据拟合策略解决这些问题。RISE用正交多项式对CA中的面形误差进行建模，并确保只拟合和扩展可校正误差。结合边界条件，然后提出驻留时间的迭代细化，以补偿扩展和反卷积带来的误差，这在总驻留时间增加可忽略不计的情况下，大幅降低了CA中估计的面形误差残差。据我们所知，RISE是第一种基于数据拟合的表面扩展方法，也是第一种基于迭代扩展优化驻留时间的方法。通过离子束成型从曲率半径约为173 m的球体开始制造两个椭圆圆柱体（10 mm×80 mm CA），对RISE进行了实验验证。两个CA中的面形误差分别从204.96 nm RMS和190.28 nm RMS大幅提高到0.62 nm RMS和0.71 nm RMS，这证明RISE是一种用于亚纳米级X射线镜制造的有效方法。
