High precision edge extrapolation technique in continuous phase plate magnetorheological polishing

In order to improve the edge quality of the continuous phase plate in magnetorheological polishing and realize the full aperture polishing of the components, the edge extrapolation of the original error profile must be carried out. In view of the shortcoming of the existing edge extrapolation algorithm, a two-dimensional Gerchberg bandlimited extrapolation algorithm was proposed to realize the edge extrapolation technique that was frequency domain matching for continuous phase plate. Firstly, Zoom Fourier transform was applied to the original error profile to get its high and low cutoff frequencies. Then, the modified two-dimensional Gerchberg extrapolation algorithm was used to fill data in extrapolation region around the original region to get the same spectral structure as the original region. At last, an magnetorheological polishing experiment was performed on a 100 mm100 mm continuous phase plate element with complex frequency spectrum structure. The experimental results show that the edge processed by the method is more regular and the edge effect radius is reduced from 5 mm to 2 mm, and the residual error RMS is reduced from 19.3 nm to 9.7 nm. It indicates that the modified Gerchberg edge extrapolation technique can obviously improve the edge quality and the overall convergence precision of continuous phase plate.