Densely stacked arrays of x-ray mirrors serve as lenses for space-based x-ray telescopes. They operate at small angles of grazing incidence. Ideally they resemble thin foils, but with extremely precise shape (surface figure). The smallest forces (stress in thin-film coatings, mounting forces, gravity, thermal gradients, etc.) can distort their figure beyond tolerances. We are developing deterministic stress-based methods (ion-implantation, thermal oxide patterning, laser micro-stressing) that can counteract these forces to obtain desired mirror shapes. As part of this project we also need to develop high-accuracy metrology for cylindrical surfaces, and methods for quasi stress-free mounting. See here for more detail.