Thin mirror surface figure correctability using ultrafast laser stress figuring (ULSF): from X-ray optics to thin shells for deformable mirrors

Ultrafast laser stress figuring (ULSF), in which ultrafast laser-generated bending moments permanently deform mirror substrates, has been previously demonstrated to flatten 100 mm-diameter mirror substrates by ~5 μm RMS to ~10 nm RMS flatness. For significantly larger magnitude or higher spatial-frequency corrections, however, a substrate cannot be fully corrected due to limited space available in the substrate. A predictive model of the magnitudes and spatial frequencies that ULSF is capable of correcting is needed to implement ULSF for mirror substrate manufacturing. To this end, corrections of randomly generated surface maps were simulated, using linear optimization of the correctable RMS height error, to understand the capabilities of ULSF correction. This paper describes the mechanics of ULSF and the optimization process to minimize achievable height error. We also report on the ULSF process capabilities gleaned from the simulations.