Computer-controlled cylindrical polishing process for development of grazing incidence optics for the hard x-ray region

The focusing performance of shell optics for the hard X-ray region strongly depends on their axial mid-spatialfrequency- range figure errors. This paper presents the development of a deterministic computer-controlled polishing process to minimize these axial figure errors on cylindrical shaped mandrels from which the mirror shells are replicated. A mathematical model has been developed to simulate the residual surface figure errors due to the polishing process parameters and the polishing tools used, along with their non-conformance to the mandrel. We present design considerations of a large-size polishing lap where the experimentally determined process variables have been used for optimizing the lap configuration and the machine operational parameters. Furthermore, the developed model is capable of generating a corrective polishing sequence for a known surface error profile. Practical polishing experiments have been performed to verify the model and to determine its ability to correct known axial figure errors through polishing machine control.