Optimization of single-point diamond turning processes for single crystal calcium fluoride: A surrogate model for surface roughness prediction

Single-crystal calcium fluoride (CaF₂) is essential in high-level optical systems due to its excellent optical properties, including high penetration, laser damage resistance, and low dispersion across ultraviolet and infrared wavelengths. However, CaF₂ is soft, brittle, and its anisotropic nature makes predicting surface roughness (R_a) during lens manufacturing challenging. Traditionally, operators rely on manual adjustments and measurements to achieve desired surface finishes, a process that is both time-consuming and costly. This study addresses these challenges by developing a model to predict surface roughness in ultra-precision machining of CaF₂. The machining depth was set to 200 nm to maintain ductile cutting conditions. A central composite design (CCD) experiment gathered data on three critical machining parameters: spindle speed, feed rate, and tool rake angle. The surface roughness prediction models were then constructed using a synthetic artificial neural network (S-ANN), response surface methodology (RSM), and kriging. Evaluation results showed that the S-ANN model achieved the highest accuracy (97.4% accuracy, 0.907 nm error), outperforming the RSM (90.4% accuracy, 1.343 nm error) and kriging (87.1% accuracy, 1.931 nm error) models. The S-ANN model’s performance is suitable for practical application, offering an effective method to predict CaF₂ R_a, significantly reducing costs associated with single-point diamond turning.