Static tool influence function for fabrication simulation of hexagonal mirror segments for extremely large telescopes.

We present a novel simulation technique that offers efficient mass fabrication strategies for 2m class hexagonal mirror segments of extremely large telescopes. As the first of two studies in series, we establish the theoretical basis of the tool influence function (TIF) for precessing tool polishing simulation for non-rotating workpieces. These theoretical TIFs were then used to confirm the reproducibility of the material removal foot-prints (measured TIFs) of the bulged precessing tooling reported elsewhere. This is followed by the reverse-computation technique that traces, employing the simplex search method, the real polishing pressure from the empirical TIF. The technical details, together with the results and implications described here, provide the theoretical tool for material removal essential to the successful polishing simulation which will be reported in the second study.