Biconic Zernike Surface Using a Cartesian Coordinate Machine and an Analytical Solution of the Tool Path

摘要

An physical solution for obtaining a biconic Zernike surface was developed in Cartesian coordinates. The tool path for fly cutting was calculated using contact conditions and geometric relations. The software for the tool path generated G-code from optical design parameters of the biconic Zernike surface. The G-code was uploaded to a four-axis machine constructed using a nanopositioning stage, air guides, kinematic balances, and environment controls. The stage was composed of XYZ linear transfer units and a C rotational unit. The moving parts of the linear transfer units were levitated using air guides and positioning accuracy was achieved using nano-feedback devices. The weight balance of the kinematic parts and air guides were studied in the design optimization. Our machine was operated under environment controls minimizing temperature variation, pneumatic fluctuation, and external vibration. Control factors of the axes were tuned to achieve 5 nm resolution. Our experiment was implemented to obtain a copper surface of a convex F-theta surface using fly cutting.