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.
Highlights
As the third and fourth generation X-ray synchrotron sources is rapidly developing toward fully diffraction limited X-ray sources, the requirement of mirror specifications in terms of smoothness and shapes has drastically increased
To obtain a complete calculation result in the Clear Aperture (CA), the Dwell Grid (DG) should be always larger than the outline perimeter of the CA with the radius of the Beam Removal Function (BRF)
To apply Fast Fourier Transform (FFT), zd(x, y) and t(x, y) must have the same sampling interval[13], a mismatch typically exists between practical metrology sampling and Ion Beam Figuring (IBF)’s motion control resolution
Summary
As the third and fourth generation X-ray synchrotron sources is rapidly developing toward fully diffraction limited X-ray sources, the requirement of mirror specifications in terms of smoothness and shapes has drastically increased. Ion Beam Figuring (IBF)[4], as a highly deterministic CCOS technique, has been applied for the ultra-precision finishing of optical surfaces[5,6,7,8,9,10]. Zhou et al proposed a Truncated SVD (TSVD) algorithm[17], in which only the largest k singular values were kept Both the computational and memory burdens of SVD are too heavy, restricting its wider applications in calculating large dwell time maps. The computation speed has been largely increased, the piston adjustment has to be performed multiple times to guarantee the non-negativity of the dwell time map. The computational burden became even heavier due to the introduction of the constraint matrices
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