Future X-ray telescopes require significant amounts of optical area. To accommodate this in a grazing incidence design, extremely thin mirrors are formed in concentric shell configurations. A slumping technique has been demonstrated with such thin, lightweight shells. However, the optical surface is found to contain a significant amount of mid-spatial frequency errors. It is proposed to demonstrate a sub-aperture figuring technique that does not impart mid-spatial frequencies to the optical substrate geometries planned for integration into next-generation X-ray telescopes. Reactive Atom Plasma (RAP) is a sub-aperture, atmospheric pressure, non-contact figuring technology that relies on a deterministic gas-phase etching of the optical surface with high material removal rates. RAP has already been demonstrated as a very credible approach for fabricating the lightweight wedges required for the assembly of such mirrors. RAP is especially suitable for damage-free processing of extremely lightweight mirrors given the non-contact operation, and its ability to ameliorate sub-surface damage. The tool footprint is a Gaussian and hence has a limited capability to both impart mid-spatial errors, as well as to fix them. In phase 1, we plan on demonstrating the ability of the RAP process to impart minimal mid-spatial errors into the optical surface while a figuring demonstration using adjustable footprints is planned for phase 2.