Effect of slope errors on the performance of mirrors for x-ray free electron laser applications

In this work we point out that slope errors play only a minor role in the performance of a certain class of x-ray optics for X-ray Free Electron Laser (XFEL) applications. Using physical optics propagation simulations and the formalism of Church and Takacs [Opt. Eng. 34, 353 (1995)], we show that diffraction limited optics commonly found at XFEL facilities posses a critical spatial wavelength that makes them less sensitive to slope errors, and more sensitive to height error. Given the number of XFELs currently operating or under construction across the world, we hope that this simple observation will help to correctly define specifications for x-ray optics to be deployed at XFELs, possibly reducing the budget and the timeframe needed to complete the optical manufacturing and metrology.