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

Tianyi Wang, Lei Huang, Hyukmo Kang, Heejoo Choi, Dae Wook Kim, Kashmira Tayabaly, Mourad Idir

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Article number8135
JournalScientific reports
Volume10
Issue number1
DOIs
StatePublished - Dec 1 2020

ASJC Scopus subject areas

  • General

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