Trajectory optimization method of variable pitch spiral matrix for intermediate frequency error

Magnetorheological polishing can efficiently remove low-frequency errors on the surface of optical elements, but it also introduces intermediate-frequency errors. The existence of intermediate-frequency errors has a serious impact on the performance of the optical system, which must be effectively controlled. The commonly used grating trajectories and spiral trajectories were studied. It was found that the regular polishing trajectory caused the convolution process to be inconsistent with the actual removal process, which would introduce symmetrical iterative errors. The iterative error is an important factor in the deterioration of the intermediate frequency error. Based on the research of grating trajectory and spiral trajectory, a trajectory optimization method for variable pitch spiral matrix trajectory was proposed to reduce the intermediate frequency error of optical components. The trajectory retained the advantages of simplicity and ease of the grating trajectory and the spiral trajectory by disrupting the pitch of the spiral matrix trajectory, and also changed the randomness between the trajectory lines. Through the power spectrum analysis of the surface shape before and after processing, it was verified that the trajectory can effectively reduce the intermediate frequency error of the surface, and the intermediate frequency convergence efficiency of the grating line and the spiral line is comprehensively improved by 26.59%.