Metal mirrors will be widely used in the coming decades. Therefore, as one of the enabling technologies for metal optical freeform surface manufacturing, ultra-precision (UP) diamond turning error compensation has become a research hotspot. However, for the tool offset error and tool radius error, which are the main errors in UP diamond turning, no precise and efficient calculation method has been found in the literature. In this study, a more precise and efficient algorithm was developed and validated in three ways using on-machine measurement data and profilometer measurement data. After one compensation, the tool offset error can be reduced to below 0.1 μm, and the tool radius error can be reduced to below 1 micrometer, which will significantly improve the UP turning accuracy and efficiency of optical parts.

A complex curved reflector made from a 40% silicon–aluminum alloy (AlSi40) can meet the requirements of optical systems operating across the infrared, near-infrared, and visible bands. It enables an athermalization design with simplified alignment and assembly, while offering high manufacturing efficiency and low costs. This makes it ideal for widespread use in high-end optical systems. As an enabling technology for the fabrication of AlSi40 freeform mirrors, error compensation in ultra-precision (UP) diamond turning is currently a research hotspot; however, current error compensation methods still have considerable room for improvement in terms of both accuracy and manufacturing efficiency. To address this issue, this study proposes an efficient and highly accurate method: a polar grid is defined in the machining coordinate system, and the corresponding surface point cloud is calculated. Using measured point clouds from reference spheres and freeform form error in the measurement coordinate system, mounting pose errors and form error with measurement error removed are determined via least squares. Machining error at grid points is then calculated via coordinate transformations and bicubic spline interpolation, and applied to correct cutter contact points (CCPs). Cutter location points (CLPs) are finally obtained using piecewise cubic spline fitting and a bisection method. With this method, average form error of four AlSi40 substrates improved from RMS 114.8 nm to 47.9 nm, and for four AlSi40 substrates with nickel–phosphorus (NiP)-plated surfaces, from RMS 71.3 nm to 31.1 nm. The compensated accuracy meets near-infrared stellar tracker requirements without polishing, greatly enhancing freeform mirror manufacturing efficiency.