Suppression of mid-frequency errors in optical manufacturing by longitudinal-torsional hybrid ultrasonic vibration (<italic>invited</italic>)

ObjectiveMid-spatial frequency (MSF) errors tend to accumulate during the polishing of hard and brittle optical materials due to the periodic superposition between tool influence functions and deterministic scanning paths, and they are difficult to suppress using conventional polishing strategies. This study proposes a longitudinal-torsional composite ultrasonic vibration-assisted trajectory regulation approach to enhance trajectory complexity and spatial uniformity, thereby improving removal stability and suppressing MSF errors in optical surface manufacturing.MethodsA polishing strategy incorporating longitudinal-torsional composite ultrasonic vibration was developed, and a kinematic model describing abrasive motion under coupled longitudinal and torsional vibrations was established. The influence of vibration amplitude and phase on the spatial expansion and distribution of polishing trajectories was systematically analyzed. Trajectory uniformity and complexity under raster-1, raster-2, and spiral scanning modes, with and without vibration, were quantitatively evaluated using information entropy. Polishing experiments were conducted on fused-silica specimens using an AGM1600 five-axis CNC system. Surface topography was measured by a Zygo interferometer, and MSF characteristics were analyzed in the frequency domain using power spectral density (PSD).Results and DiscussionsThe introduction of longitudinal-torsional vibration increased trajectory entropy by approximately 33%-34% for all scanning paths, rising from 5.108 to 6.812 for raster path 1, from 5.167 to 6.857 for raster path 2, and from 5.231 to 7.021 for the spiral path. Under identical processing times, the RMS form error was reduced from 0.176λ to 0.014λ for raster scanning 1 and from 0.191λ to 0.013λ for spiral scanning. SEM observations revealed that polishing without vibration resulted in pronounced directional removal features, including linear grooves, brittle pits, and localized debris, indicating strong trajectory-dependent accumulation. In contrast, longitudinal-torsional vibration effectively disrupted these features, leading to more homogeneous micro-plastic deformation. Three-dimensional surface measurements further confirmed this trend: without vibration, raster scanning paths produced strong linear textures with Sa values of 1.56 nm and 1.54 nm, while the spiral scanning path exhibited weaker but still periodic patterns (Sa=1.38 nm). With vibration, surface textures became significantly randomized, and Sa decreased to 1.23 nm, 1.21 nm, and 0.98 nm for raster-1, raster-2, and spiral scanning paths, respectively. PSD analysis demonstrated that pronounced MSF peaks that were obvious without vibration, especially along the Y-direction for raster scanning, were effectively suppressed after introducing longitudinal-torsional vibration, yielding smoother spectra while preserving low-frequency convergence. Among all paths, the spiral scanning combined with vibration exhibited the strongest MSF suppression.ConclusionsA longitudinal-torsional composite ultrasonic vibration-assisted trajectory regulation strategy was proposed to suppress MSF errors in optical polishing. Kinematic analysis and information entropy-based evaluation demonstrated that the introduction of torsional vibration induces nonlinear trajectory expansion, significantly enhancing spatial complexity and uniformity. The experimental results confirm that increased trajectory entropy is directly associated with effective MSF attenuation, improved form convergence, reduced surface roughness, and suppressed MSF PSD peaks. This study provides a physically grounded, entropy-guided approach for high-precision polishing of optical surfaces.