Clusters consisting of hundreds to thousands of atoms are accelerated by an electric field and impinge upon the material surface, enabling ultra-precision polishing, surface figure or film thickness trimming. Compared with conventional plasma beams, this technique offers advantages, including low induced damage and negligible thermal effects. Its applications encompass polishing of superhard materials (e.g., diamond), complex curved surfaces and optical components, removal of damaged layers on functionally structured surfaces, and ultraprecision trimming of semiconductor thin films.