Cylindrical Optic Polishing Dwell Time Optimization

The Constellation-X x-ray telescope consists of replicated grazing incidence optics. The polishing of the "master' mandrel is accomplished by moving a polishing tool along a helical path on the surface of this almost cylindrical surface. The measurement of the surface is, however, performed along "axial" scan lines which intercept this helical path. This approach to polishing and measuring permits a relatively simple scheme to be implemented for the determination of the optimal dwell times of the polishing tool. These optimal dwell times are determined by a deconvolution which approaches the problem as a linear programming problem and uses the simplex method. This 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.