This research is focussed on the application of Ion Beam Figuring (IBF) techniques to manufacture aspheric optical elements. IBF will be used to remove spherical aberration and defocus. This will be accomplished in several steps. An optical map of the element will be first obtained using phase measurement interferometry. This will be processed by a restoration algorithm, which is to be developed, to determine the time the ion beam source is to dwell at each location in front of the substrate. IBF will then be performed to make the aspheric element. This approach will remove a significant amount of uncertainty from the process of fabrication of aspheric optics which are now almost totally dependant on operator skill. Since these type of optics are pervasive in optical instrumentation, this research will make a significant impact on improving the productivity of the optic industry.