Key technology of vector removal decoupling in a slope-based figuring model and application in continuous phase plate fabrication

For the high-precision fabrication of a continuous phase plate (CPP), a combined decoupling algorithm of single-step decoupling based on the Clairaut–Schwarz theorem and global decoupling by stagewise iteration is proposed. It attempts to address the problem of the low accuracy and limitation of the existing slope-based figuring (SF) model in two-dimensional applications caused by the vector removal coupling between the tool slope influence function and the material removal slope due to the inherent convolution effect in the SF model. The shortcomings of CPP interferometry and the application bottleneck of the Hartmann test in traditional height-based figuring model are studied. The generation mechanism of vector removal coupling is analyzed and compensated. A CPP of 85 mm × 85 mm was successfully machined by the decoupled slope-based figuring model, and the root mean square (RMS) of the surface height error accounted for 6.01% of the RMS of the design value. The research results can effectively improve the convergence and certainty of CPP fabrication using the slope-based figuring model.