In order to restrain the mid-spatial frequency error in magnetorheological finishing (MRF) process, a novel part-random path is designed based on the theory of maximum entropy method (MEM). Using KDMRF-1000F polishing machine, one flat work piece (98 mm in diameter) is polished. The mid-spatial frequency error in the region using part-random path is much lower than that by using common raster path. After one MRF iteration (7.46 min), peak-to-valley (PV) is 0.062 wave (1 wave =632.8 nm), root-mean-square (RMS) is 0.010 wave and no obvious mid-spatial frequency error is found. The result shows that the part-random path is a novel path, which results in a high form accuracy and low mid-spatial frequency error in MRF process.
Mid-high spatial frequency errors are often induced on optical surfaces polished by computer-controlled optical surfacing (CCOS) processes. In order to efficiently remove these errors, which would degrade the performances of optical systems, the ability of a CCOS process to correct the errors have been investigated based on the convolution integral model in view of the availability of material removal. To quantify the ability, some conceptions, such as figure correcting ability and material removal availability (MRA), have been proposed. The research result reveals that the MRA of the CCOS process to correct a single spatial frequency error is determined by its tool removal function (TRF), and it equals the normalized amplitude spectrum of the Fourier transform of its TRF. Finally, three sine surfaces were etched using ion beam figuring (IBF), which is a typical CCOS process. The experimental results have verified the theoretical analysis. The employed method and the conclusions of this work provide a useful mathematical basis to analyze and optimize CCOS processes.
