Conception of Diffractive Wavefront Correction for XUV and Soft X-ray Spectroscopy

We present a simple and precise method to minimize aberrations of mirror-based, wavelength-dispersive spectrometers for the extreme ultraviolet (XUV) and soft x-ray domain. The concept enables an enhanced resolving power $ E/\Delta E $E/ΔE, in particular, close to the diffraction limit over a spectral band of a few percent around the design energy of the instrument. Our optical element, the "diffractive wavefront corrector" (DWC), is individually shaped to the form and figure error of the mirror profile and might be written directly with a laser on a plane and even strongly curved substrates. Theory and simulations of various configurations, like Hettrick-Underwood or compact, highly efficient all-in-one setups for $ {{\rm TiO}_2} $TiO spectroscopy with $ E/\Delta E \mathbin{\lower.3ex\hbox{$\buildrel{\displaystyle{\lt}}\over{\smash{\displaystyle\sim}\vphantom{_x}}$}} 4.5 \times {10^4} $E/ΔE∼<4.5×10, are addressed, as well as aspects of their experimental realization.