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Title: RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors

Abstract

With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using themore » dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.« less

Authors:
 [1];  [1];  [2];  [2];  [2];  [1];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)
  2. Univ. of Arizona, Tucson, AZ (United States). College of Optical Sciences
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1631025
Report Number(s):
BNL-215948-2020-JAAM
Journal ID: ISSN 2045-2322
Grant/Contract Number:  
SC0012704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Volume: 10; Journal Issue: 1; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Wang, Tianyi, Huang, Lei, Kang, Hyukmo, Choi, Heejoo, Kim, Dae Wook, Tayabaly, Kashmira, and Idir, Mourad. RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors. United States: N. p., 2020. Web. doi:10.1038/s41598-020-64923-3.
Wang, Tianyi, Huang, Lei, Kang, Hyukmo, Choi, Heejoo, Kim, Dae Wook, Tayabaly, Kashmira, & Idir, Mourad. RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors. United States. https://doi.org/10.1038/s41598-020-64923-3
Wang, Tianyi, Huang, Lei, Kang, Hyukmo, Choi, Heejoo, Kim, Dae Wook, Tayabaly, Kashmira, and Idir, Mourad. Mon . "RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors". United States. https://doi.org/10.1038/s41598-020-64923-3. https://www.osti.gov/servlets/purl/1631025.
@article{osti_1631025,
title = {RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors},
author = {Wang, Tianyi and Huang, Lei and Kang, Hyukmo and Choi, Heejoo and Kim, Dae Wook and Tayabaly, Kashmira and Idir, Mourad},
abstractNote = {With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using the dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.},
doi = {10.1038/s41598-020-64923-3},
url = {https://www.osti.gov/biblio/1631025}, journal = {Scientific Reports},
issn = {2045-2322},
number = 1,
volume = 10,
place = {United States},
year = {2020},
month = {5}
}

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