Nano-precision metrology of X-ray mirrors with laser speckle angular measurement

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.