AUTHOR=Zhang Yunyang , Huang Qiushi , Yan Shuai , Yu Jun , Huang Handan , He Yumei , Luo Hongxin , Liu Zhi , Zhang Zhong , Wang Zhanshan TITLE=High-Precision Ion Beam Figuring of X-Ray Plane Mirrors for the Bendable KB Focusing System JOURNAL=Frontiers in Physics VOLUME=Volume 10 - 2022 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.865411 DOI=10.3389/fphy.2022.865411 ISSN=2296-424X ABSTRACT=Two trapezoidal plane mirrors with 240mm length were fabricated by ion beam figuring (IBF) technology for application in bendable KB focusing system. The correction of surface height and slope errors in different spatial frequency range of the mirrors was studied systematically. After one to two iterations of IBF, the figure height error of vertical focusing mirror (VFM) and horizontal focusing mirror (HFM) were improved from 32.4nm and 65.4nm to 2.7nm and 7.2nm (RMS), respectively. If the best-fit sphere of surface profile was subtracted, the residual two dimensional height errors were only 1.1 nm and 1.2 nm (RMS). The slope errors in the low spatial frequency range were corrected much faster than the middle frequency ones (f=~1mm-1) which make the low frequency slope error much smaller. After IBF, the two dimensional slope errors of the two mirrors calculated with the spatial interval of 1mm and 10mm were reduced to approximately 0.29 μrad and 0.08 μrad, respectively. Full spatial frequency characterization of the VFM before and after IBF showed that the low frequency figure errors (f<1mm-1) was significantly reduced while the middle and high frequency morphology (f>1~2mm-1) remain almost the same as before etching. The fabricated plane mirrors were applied in the hard X-ray Microfocusing beamline in Shanghai Synchrotron Radiation facility which realized a focal spot of 2.4 μm × 2.8 μm at 10 keV.