Huang Lei, Wang Tianyi, Nicolas Josep, Vivo Amparo, Polack François, Thomasset Muriel, Zuo Chao, Tayabaly Kashmira, Wook Kim Dae, Idir Mourad
Opt Express. 2019 Sep 16;27(19):26940-26956. doi: 10.1364/OE.27.026940.
Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for "Calibrate, and then Stitch", calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for "Stitch, and then Calibrate", stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in - and -directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexible option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.
拼接干涉测量是通过从重叠的子孔径收集干涉数据并将这些数据拼接在一起以提供完整的表面图来进行的。在拼接干涉测量中，用于精确重建表面形貌时，测量子集数据中系统误差的传播是主要误差源之一。在这项工作中，我们利用捕获子集数据的冗余性，提出了两种二维（2D）自校准拼接算法，通过原位估计可重复的高阶附加系统误差来克服这个问题，特别是在测量X射线镜的应用中。第一种算法称为CS（“校准，然后拼接”的缩写），通过最小化重叠子集的去倾斜差异来校准参考的高阶项，然后拼接减去参考的子集。第二种算法称为SC（“拼接，然后校准”的缩写），先拼接一个临时结果，然后根据测量子集和临时拼接结果的去倾斜差异来校准参考。在x和y方向的二维扫描实现中，引入步长随机化以生成非均匀间隔的子集，这可以减少在均匀间隔子集中常见的周期性拼接误差。对低阶项的正则化提供了一个高度灵活的选项，可添加由另一个系统获取的曲率和扭曲。进行了数值模拟和实验以验证所提出的方法。所有结果表明，在拼接干涉测量中，可以从二维冗余重叠数据中检索二维高阶可重复附加系统误差。
