Picometre-level surface control of a closed-loop, adaptive X-ray mirror with integrated real-time interferometric feedback.

We provide a technical description and experimental results of the practical development and offline testing of an innovative, closed-loop, adaptive mirror system capable of making rapid, precise and ultra-stable changes in the size and shape of reflected X-ray beams generated at synchrotron light and free-electron laser facilities. The optical surface of a piezoelectric bimorph deformable mirror is continuously monitored at 20 kHz by an array of interferometric sensors. This matrix of height data is autonomously converted into voltage commands that are sent at 1 Hz to the piezo actuators to modify the shape of the mirror optical surface. Hence, users can rapidly switch in closed-loop between pre-calibrated X-ray wavefronts by selecting the corresponding freeform optical profile. This closed-loop monitoring is shown to repeatably bend and stabilize the low- and mid-spatial frequency components of the mirror surface to any given profile with an error <200 pm peak-to-valley, regardless of the recent history of bending and hysteresis. Without closed-loop stabilization after bending, the mirror height profile is shown to drift by hundreds of nanometres, which will slowly distort the X-ray wavefront. The metrology frame that holds the interferometric sensors is designed to be largely insensitive to temperature changes, providing an ultra-stable reference datum to enhance repeatability. We demonstrate an unprecedented level of fast and precise optical control in the X-ray domain: the profile of a macroscopic X-ray mirror of over 0.5 m in length was freely adjusted and stabilized to atomic level height resolution. Aside from demonstrating the extreme sensitivity of the interferometer sensors, this study also highlights the voltage repeatability and stability of the programmable high-voltage power supply, the accuracy of the correction-calculation algorithms and the almost instantaneous response of the bimorph mirror to command voltage pulses. Finally, we demonstrate the robustness of the system by showing that the bimorph mirror's optical surface was not damaged by more than 1 million voltage cycles, including no occurrence of the `junction effect' or weakening of piezoelectric actuator strength. Hence, this hardware combination provides a real time, hyper-precise, temperature-insensitive, closed-loop system which could benefit many optical communities, including EUV lithography, who require sub-nanometre bending control of the mirror form.