The manufacturing requirements for extreme ultraviolet lithography (EUVL) projection lenses are highly stringent, demanding ultra-precise control over surface height and slope profile to achieve optimal imaging quality. Nevertheless, the current technology lacks the explicit capability to control the two-dimensional (2D) surface slope of optics. Focusing on the ultra-precision machining technology based on slope profile, a partial derivative exchange decoupling (PDED) method is proposed to approximately calculate the vector removal coupling problem within the 2D slope-based figuring (SF) model, specifically addressing the interplay between the slope removal function and the slope error. Furthermore, the fusion figuring (FF) model accomplishing the dual monitoring of both surface height accuracy and slope profile accuracy is proposed innovatively. Through simulation experiments, the modification results of the fusion, slope-based, and height-based figuring (HF) models are systematically compared and analyzed, demonstrating the effectiveness and superiority of the fusion figuring model. In actual manufacturing experiments, the FF model improves RMS convergence for slope errors by over 20% and for height errors by nearly 10% compared to the HF model. The research results successfully achieve a notable level of convergence in optics machining and provide a new approach with ultra-precision and stability for the fabrication of complex optics requiring precise control of both surface and slope accuracy.
