Mid-spatial-frequency waviness in ultra-precision machining: Real-time trajectory analysis of three machine tools

Mid-spatial-frequency (MSF) waviness — typically characterized by waviness with spatial period ranging from 0.1 mm to several millimeters — significantly impacts the optical performance of precision optics. In diamond-machined optical surfaces, trajectory variations of the machine tool can induce MSF waviness that are difficult to eliminate through conventional polishing due to their spatial frequency range. It is therefore crucial to measure and compensate for machine tool control error in real-time during the cutting process. To address this issue, we developed a real-time position capturing system (RPCS) to assess the control errors of three types of ultra-precision machine tools, with programming resolutions on linear axes ranging from 10 nm to 0.1 nm. First, we evaluated the profile accuracy of optical flat and spherical mirror on each machine tool using on-machine measurement (OMM) with a laser confocal probe, to verify linear motion accuracy. Subsequently, we manufactured three plano-elliptic optical surfaces — intended for neutron-focusing mirrors — using the respective machine tools. We then analyzed the MSF waviness of the machined mirrors and correlated it with the motion errors captured by the RPCS. Our results revealed that the machine equipped with oil hydrostatic guideways exhibited a control error of approximately 100 nm and produced MSF waviness with an amplitude around 10 nm. In contrast, machines with V–V roller guideways demonstrated significantly lower MSF amplitudes, below 10 nm. These findings demonstrate a clear correlation between guideway structure, trajectory stability, and MSF waviness, providing valuable insights for improving the precision of optics fabrication.