Sub-nanometer flattening of a 45-cm long, 45-actuator x-ray deformable mirror

We have built a 45-cm long x-ray deformable mirror of super-polished single-crystal silicon that has 45 actuators along the tangential axis. After assembly the surface height error was 19 nm rms. With use of high-precision visible-light metrology and precise control algorithms, we have actuated the x-ray deformable mirror and flattened its entire surface to 0.7 nm rms controllable figure error. This is, to our knowledge, the first sub-nanometer active flattening of a substrate longer than 15 cm.
Comment: Revised version accepted by Applied Optics 24 Apr 2014