Journal Article Research Support, Non-U.S. Gov't free-electron laser free-electron lasers ptychography wavefront sensing FEL FEL diagnostics FERMI Gaussian beams Kirkpatrick–Baez WISEr X-ray free-electron lasers X-ray optics XFELs active optics system coherent diffraction imaging coherent mode propagation cross correlation diffraction gratings elliptical mirrors extreme-ultraviolet polarimetry four-wave-mixing groove placing error holography magnetic materials non-linear optics orbital angular momentum of light pump–probe pump–probe experiments