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29 December 2023 Reference surface self-calibration stitching algorithm based on Legendre polynomials for testing synchrotron radiation flat mirrors
Yong Liu, Xibo Gao, Zubo Hu, Shuai Xue, Shanyong Chen, Cheng Huang, Chunyang Du, Hao Hu, Yifan Dai, Xiaoqiang Peng, Linfeng Wang
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Proceedings Volume 12976, Eighth Asia Pacific Conference on Optics Manufacture and Third International Forum of Young Scientists on Advanced Optical Manufacturing (APCOM and YSAOM 2023); 1297625 (2023) https://doi.org/10.1117/12.3009617
Event: 8th Asia Pacific Conference on Optics Manufacture & 3rd International Forum of Young Scientists on Advanced Optical Manufacturing, 2023, Shenzhen, China
Abstract
X-ray mirrors play a critical role in transmitting and focusing beams in advanced light source devices like synchrotron radiation (SR) and free electron laser (FEL) light sources. The Root-Mean-Square (RMS) value of surface shape accuracy required for these mirrors is typically sub-micro radian/sub-nanometer, and their aperture can be hundreds of millimeters or even meters. To achieve this accuracy, deterministic figuring is required and surface figure error is the premise. Interferometric stitching test is commonly utilized. However, interferometric test obtains the surface figure error relative to the reference surface. To obtain the absolute surface figure error of X-ray mirrors, it is crucial to obtain the surface figure error of the reference surface before or during stitching measurement and separate it from the stitching result. To achieve this, a reference surface self-calibration interferometric stitching algorithm based on Legendre polynomial fitting is reported. The algorithm fits the reference surface by orthogonal Legendre polynomials in the rectangular domain, and the polynomial coefficients are expressed as interlocking terms in the stitching algorithm. The fitting coefficients are optimized and fitted together with the free compensation terms, i. e. the translation and tilt terms. The paper established the theoretical model of the algorithm and conducted simulations on an X-ray mirror with a length of 300 mm. A two dimensional stitching interferometry device was built. An X-ray mirror with a length of 300 mm was tested utilizing the proposed method. The short-term repeatability was preliminarily analyzed.
(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Yong Liu, Xibo Gao, Zubo Hu, Shuai Xue, Shanyong Chen, Cheng Huang, Chunyang Du, Hao Hu, Yifan Dai, Xiaoqiang Peng, and Linfeng Wang "Reference surface self-calibration stitching algorithm based on Legendre polynomials for testing synchrotron radiation flat mirrors", Proc. SPIE 12976, Eighth Asia Pacific Conference on Optics Manufacture and Third International Forum of Young Scientists on Advanced Optical Manufacturing (APCOM and YSAOM 2023), 1297625 (29 December 2023); https://doi.org/10.1117/12.3009617
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KEYWORDS
Mirror surfaces
Mirrors
Calibration
Stitching interferometry
Simulations
Synchrotron radiation
X-rays
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