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We have built a 45-cm long x-ray deformable mirror of super-polishedsingle-crystal silicon that has 45 actuators along the tangential axis. Afterassembly the surface height error was 19 nm rms. With use of high-precisionvisible-light metrology and precise control algorithms, we have actuated thex-ray deformable mirror and flattened its entire surface to 0.7 nm rmscontrollable figure error. This is, to our knowledge, the first sub-nanometeractive flattening of a substrate longer than 15 cm.

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