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, h...

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Main Authors: Tianyi Wang, Lei Huang, Hyukmo Kang, Heejoo Choi, Dae Wook Kim, Kashmira Tayabaly, Mourad Idir
Format: Article
Language:English
Published: Nature Publishing Group 2020-05-01
Series:Scientific Reports
Online Access:https://doi.org/10.1038/s41598-020-64923-3
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spelling doaj-a1b82a51f04d41bf9ba9e67a4663ca662021-05-23T11:37:39ZengNature Publishing GroupScientific Reports2045-23222020-05-0110111210.1038/s41598-020-64923-3RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrorsTianyi Wang0Lei Huang1Hyukmo Kang2Heejoo Choi3Dae Wook Kim4Kashmira Tayabaly5Mourad Idir6National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, PO Box 5000National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, PO Box 5000James C. Wyant College of Optical Sciences, the University of Arizona, 1630 E. University Blvd., P.O. Box 210094James C. Wyant College of Optical Sciences, the University of Arizona, 1630 E. University Blvd., P.O. Box 210094James C. Wyant College of Optical Sciences, the University of Arizona, 1630 E. University Blvd., P.O. Box 210094National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, PO Box 5000National Synchrotron Light Source II (NSLS-II), Brookhaven National Laboratory, PO Box 5000Abstract 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.https://doi.org/10.1038/s41598-020-64923-3
collection DOAJ
language English
format Article
sources DOAJ
author Tianyi Wang
Lei Huang
Hyukmo Kang
Heejoo Choi
Dae Wook Kim
Kashmira Tayabaly
Mourad Idir
spellingShingle Tianyi Wang
Lei Huang
Hyukmo Kang
Heejoo Choi
Dae Wook Kim
Kashmira Tayabaly
Mourad Idir
RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
Scientific Reports
author_facet Tianyi Wang
Lei Huang
Hyukmo Kang
Heejoo Choi
Dae Wook Kim
Kashmira Tayabaly
Mourad Idir
author_sort Tianyi Wang
title RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
title_short RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
title_full RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
title_fullStr RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
title_full_unstemmed RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors
title_sort rifta: a robust iterative fourier transform-based dwell time algorithm for ultra-precision ion beam figuring of synchrotron mirrors
publisher Nature Publishing Group
series Scientific Reports
issn 2045-2322
publishDate 2020-05-01
description 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 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.
url https://doi.org/10.1038/s41598-020-64923-3
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