Figure correction of X-ray telescope mirrors will be critical for future missions that require high angular resolution and large collecting areas. In this paper, we show that ion implantation offers a method of correcting figure errors by imparting sub-surface in-plane stress in a controllable magnitude and location in Schott D-263 glass, Corning Eagle XG glass, and crystalline silicon substrates. In addition, we can in theory achieve nearly exact corrections in Schott D-263 glass, by controlling the direction of the stress. We show that sufficient stress may be applied to Schott D-263 glass to achieve figure correction in mirrors with simulated initial figure errors. We also report on progress of a system that will be capable of correcting conical shell mirror substrates.
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