We demonstrate a novel One-Dimensional Ion-Beam Figuring (1D-IBF) solution from Brookhaven National Laboratory. Three improvements are introduced to the new 1D-IBF system. First, the misalignment of the coordinate systems between the metrology and the 1D-IBF hardware is minimized by integrating both the sample mirror and the Beam Removal Function (BRF) mirror into a single mirror holder. The measured BRF center is then used as a reference to calibrate the coordinate correspondence. Second, a Constrained Linear Least-Squares (CLLS) algorithm with a coarse-to-fine scheme is proposed to keep the non-negativity of the dwell time as well as ensure it smoothly duplicate the required removal amount. Third, a dwell time slicing strategy is used to smooth the implementation of the dwell time in the real 1D-IBF fabrication process. Experimental results demonstrate that the proposed 1D-IBF solution reduces the residual profile errors to sub-nanometer Root Mean Square (RMS) for both flat and spherical mirrors.

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Tianyi Wang, Lei Huang, Matthew Vescovi, Dennis Kuhne, Kashmira Tayabaly, Nathalie Bouet, and Mourad Idir, "One-dimensional ion-beam figuring solution from Brookhaven National Laboratory," Proc. SPIE 11109, Advances in Metrology for X-Ray and EUV Optics VIII, 1110909 (Presented at SPIE Optical Engineering + Applications: August 11, 2019; Published: 9 September 2019); https://doi.org/10.1117/12.2526074.