Metrology on KB mirrors for an x-ray free electron laser oscillator

The European XFEL is a large x-ray free-electron laser facility in the Hamburg area of Germany, designed to provide a transversally fully coherent x-ray radiation with outstanding characteristics, such as high repetition rate, ultra-short wavelength (down to 0.05 nm), short pulses in the femtosecond scale, and high average brilliance. However, it has a rather poor longitudinal coherence, which is a characteristic of single-pass self-amplified spontaneous emission free-electron laser (SASE FEL) amplifiers (Kim et al., Technical Report, SLAC National Accelerator Laboratory, Menlo Park, CA, 2019). Similarly to visible light lasers, the use of an x-ray cavity to reflect and recirculate the x-ray beam through a gain medium (here a set of undulators) would produce FEL pulses with full three-dimensional coherence, nearly constant pulse-to-pulse stability, and higher spectral flux compared to the SASE process [Bahns et al., 14th International Particle Accelerator Conference, PUBDB-2023-03074 (Koordination des XFEL-Beschleunigers, 2023)]. A proposed setup for an x-ray Free Electron Laser Oscillator (XFELO) is built with a pair of diamond Bragg crystals and four silicon mirrors in KB geometry to create two ideal retroreflectors. Each pair of silicon mirrors needs to be aligned precisely perpendicular to each other with precision <100 μrad to ensure the principle of the retroreflector, according to simulations. The mirror surface roughness and shape error have to be of outstanding quality, specified to less than 0.3 nm rms and 3 nm P-V. The metrology and alignment of these systems were done at European XFEL using a 12 in. aperture Fizeau interferometer. To achieve the required angular precision, an optical rotational setup was built using an auxiliary mirror and the alignment was done in iterative steps with sequential interferometric measurements. In addition, the influence of the mechanical mount on the mirrors' surface was also investigated and monitored during the mounting and alignment process.