Aspherical substrates for extreme ultraviolet lithography (EUVL) optics require an ultrahigh shape accuracy of less than 0.15 nm rms and a high-spatial frequency roughness (HSFR; spatial wavelength: less than 1 µm) of 0.12 nm rms. Generally, the ultra low expansion glass (ULE®) substrate with HSFR of 0.06–0.08 nm rms can be produced by mechanical machining methods. However, it is difficult to obtain the shape accuracy of less than 0.12 nm rms using mechanical machining methods. Therefore, ion beam figuring (IBF) may be adapted to final shape correction of the substrates for the projection optics of EUVL tools. In this study, we investigated the HSFR and machining rate of the ULE® substrate machined by a 0.3–1.0 keV Xe+ ion beam at off normal ion incidence angles and obtained the following results: the HSFRs of the ULE® substrate machined by a 1.0 keV Xe+ ion beam at a ion incidence angle of lower than 30° and a 0.3–0.5 keV Xe+ ion beam at an ion incidence angle of 0–45° are below 0.12 nm rms, which is smaller than the required HSFR specification of EUVL projection optics. From our experimental result and discussion, we concluded that the scan fine beam and tilt target mode smoothing for processing of the ULE® substrate meets the required specification of the HSFR (0.12 nm rms) of hemispherical ULE® substrates of EUVL projection optics.