The fabrication of very large optical telescopes for space astronomy can be prohibitively costly due to the immense weight and size of monolithic primary mirrors. The cost of these telescopes can be reduced by the use of a segmented primary mirror. The next generation of large segmented mirrors must have little or no edge exclusion. 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 processes, the Precessions process can produce an edge effect due to the polishing spot changing when in extends beyond the edge of a part. Currently, the control software assumes no change in the spot size or shape when it moves beyond the edge. The primary goal of this Phase I project is to understand process differences at the edge and develop an approach to minimize them. Results from Phase I will provide better understanding of the polishing influence function which will serve as a foundation for a Phase II study on power spectral density (PSD) control and production of prototype optics that demonstrate advancement of the state-of-the-art in minimizing edge exclusion.