A well known problem in the fabrication of aspheric optical surfaces lies in surface irregularities inherent in the figuring process. Low-spatial frequency errors (figure errors) cause distortion in the system wavefront, resulting in degradation of the point spread function. Mid-spatial frequency errors cause small-angle scattering of light (flare), which reduces image contrast. High-spatial frequency errors scatter light out of the optical beam over larger angles, reducing the energy throughput in an optical system. The Zeeko Precessions polishing is a sub-aperture process that has been developed for the control of form and texture in the production of aspheric and other optical surfaces. The Precessions process is deterministic and provides dramatic reductions in production time due to its high removal rate and repeatability. Similar to other sub-aperture finishing processes, the Precessions process is prone to leave mid-spatial frequency defects on the surface. Zeeko has developed a unicursal random tool path that does not follow a regular pattern and is non-crossing. The goal of this Phase I project is to expand on promising initial results obtained by using the random tool path. The results generated by the research project will be used to demonstrate and improve the performance of the Zeeko polisher for this critical application. We propose a study that employs the polishing methodology used by Zeeko Technologies to determine whether trial procedures using the Zeeko approach can effectively correctively finish an optic without inducing unwanted frequencies onto the surface of the part.