Ion beam figuring is suitable for the final correction of the surface figure error of aspherical substrates using an extreme ultraviolet lithography tool. In ion beam figuring, however, the machined surfaces of substrates become rougher than the unprocessed surfaces. Moreover, the surface is positively charged due to the positive charges of impinging ions. In this experiment, a Si layer was deposited by ion beam sputtering on a Zerodur (R) substrate with a depth of similar to 300 nm; then, this was machined by an Ar+ ion beam with energies in the range of 3-10 keV. The mid-spatial-frequency roughness of the surface machined to a depth of less than 50 nm was comparable to that of an unprocessed surface. The high-spatial-frequency roughness (HSFR) of the unprocessed surface was 0.21 nm rms, whereas the average HSFRs of the surface machined up to a depth of 50 nm were 0.25, 0.33, 0.39, and 0.59 nm root mean square at energies of 3, 5, 7, and 10 keV, respectively. The HSFR of the machined surface increased with the ion beam energy. (C) 2008 American Vacuum Society.