Band-resolved suppression of grinding-inherited mid-spatial-frequency errors in sapphire optics by spiral ultrasonic...

Grinding-inherited mid-spatial-frequency errors limit sapphire optics, because sub-aperture polishing couples path periodicity, contact instability, and directional texture. We demonstrate band-resolved suppression on one sapphire concave spherical optic by combining longitudinal-torsional ultrasonic vibration-assisted polishing, denoted LT-UVAP, with a radial-feed spiral path. Across three stages, the projected pitch decreased from 0.98 to 0.75 µm rev^-1, and the trajectory length increased by 56.5%, while LT-UVAP supplied coupled normal-tangential contact modulation. Laser-micrometer profiles and power spectral density analysis showed that the mid-spatial-frequency root-mean-square error decreased from 111.7 to 14.6 nm, an 86.9% reduction over the same fixed spatial-frequency band. The result shows that band-limited power spectral density can guide sapphire finishing after roughness alone no longer identifies the dominant residual.