Cylindrical optic figuring dwell time optimization

Abstract

The Constellation-X, grazing incidence, x-ray telescope may be fabricated from replicated segments. A series of mandrels will serve as the 'masters' in the replication processes. Diamond turning (milling) followed by abrasive figuring followed by a super polishing are the steps currently envisioned in making just one (of many) mandrel. The abrasive figuring of a mandrel is accomplished by moving a grinding tool along a helical path on this almost cylindrical surface. The measurement of the surface is, however, performed along 'axial' scan lines which intercept this helical path. This approach to figuring and measuring permits a relatively simple scheme to be implemented for the determination of the optimal dwell times of the figuring tool. These optimal dwell times are determined by a deconvolution which approaches the problem in a linear programming context and uses the Simplex Method. The approach maximizes the amount of material removed at any point subject to inequality constraints. The effects of using these 'optimum' dwell times is to significantly improve the tools effectiveness at removing the higher spatial frequencies while staying (strictly) within the bounds and constraints imposed by the hardware. In addition, the ringing at the edges of the optic, frequently present in deconvolution problems, is completely eliminated.