X-ray mirrors are widely used for synchrotron radiation, free-electron lasers, and astronomical telescopes. The short wavelength and grazing incidence impose strict limits on the permissible slope error. Advanced polishing techniques have already produced mirrors with slope errors below 50 nrad root mean square (rms), but existing metrology techniques struggle to measure them. Here, we describe a laser speckle angular measurement (SAM) approach to overcome such limitations. We also demonstrate that the angular precision of slope error measurements can be pushed down to 20nrad rms by utilizing an advanced sub-pixel tracking algorithm. Furthermore, SAM allows the measurement of mirrors in two dimensions with radii of curvature as low as a few hundred millimeters. Importantly, the instrument based on SAM is compact, low-cost, and easy to integrate with most other existing X-ray mirror metrology instruments, such as the long trace profiler (LTP) and nanometer optical metrology (NOM). The proposed nanometrology method represents an important milestone and potentially opens up new possibilities to develop next-generation super-polished X-ray mirrors, which will advance the development of X-ray nanoprobes, coherence preservation, and astronomical physics.

Meeting the ever-increasing performance demands of X-ray beamlines at modern synchrotrons, such as Diamond Light Source (DLS), requires the use of ultra-high-quality X-ray mirrors with surface deviations of less than a few nanometres from their ideal shape. Ion beam figuring (IBF) is frequently used for creating mirrors of this precision, but achieving the highest accuracy is critically dependent on careful alignment and precise metrology of defects on the optical surface. Multiple iterations of measurement and correction are typically required, and convergence towards the requisite shape can be a slow process. DLS have designed and built an in-house IBF system that comprises a large diameter DC gridded ion source, and a 4-axis motion stage for manipulating the mirror being figured. Additionally, a slope measuring profilometer for in-situ metrology, and an imaging system for alignment, are also built into the system. The advantages of incorporating these extra components are twofold: fast metrology feedback after each figuring run will considerably reduce the time required to perform multiple figuring iterations; and alignment and indexing errors will be drastically reduced when transferring the optic. Complemented by the Optical Metrology Laboratory at DLS and at-wavelength X-ray measurements on the Test beamline B16, it is expected that this system will enable rapid development and testing of high-quality mirrors with novel designs for micro-and nano-focussing of X-rays.