Form Error Compensation for Freeform Mirrors Made of Aluminum Silicon Alloy in Ultra-Precision Diamond Turning

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.