A mid-high spatial frequency error suppression method based on the pseudo-random path with spatial MABF mapping for complex surface

Abstract

Optical lenses, mirrors and other precision optical components will inevitably produce mid-high spatial frequency errors in polishing, which will cause light scattering in different degrees, and seriously affect the imaging performance of the optical system such as contrast and reflectivity. The pseudo-random path has high direction randomness, effectively suppressing the machined surface's periodic polishing marks. In this study, a mesh surface pseudo-random path planning method based on the Matrix Angle Based Flattening (MABF) algorithm is proposed to suppress the mid-high spatial frequency errors generated in the polishing process of free-form surface, and it extended the application scope of the pseudo-random path planning method from the plane to the complex surface. Firstly, to improve the computational efficiency and reduce the deformation of the mesh in the parameterization process, an improved Angle-based Flattening (ABF) algorithm called the MABF algorithm is proposed. Then, a pseudo-random path planning method for complex surfaces is proposed based on spatial mapping. This method mainly includes pseudo-random path planning in the parameterized plane, path inverse mapping and NURBS smoothing processing. The pseudo-random path obtained by this method has the advantages of smooth and uniform distribution. Simulation results show that the MABF algorithm is superior to the ABF algorithm in computing efficiency and error control. Simulations and experiments are conducted to verify the feasibility of the proposed path planning method in complex surface polishing and the effectiveness of suppressing mid-high spatial frequency errors.