A path towards next generation x-ray gratings: compensation of substrate errors by a variation of the local line density

Diffraction gratings are key components in experiments with UV, VUV and soft x-ray radiation at synchrotron radiation and free-electron laser (FEL) facilities. They areused in monochromators to produce beams with narrow energy distribution, and in analyzers to provide high-resolution spectral analysis of scattered radiation. Today, such diffraction gratings consist of a large number of periodic grooves (typically tens to thousands per millimeter) arranged on the reflecting surface on a plane or concave substrate. The performance of the grating is also ultimately limited by the surface quality of the substrate. For best spectral resolution, the substrates need to be ultra-precise and superpolished, with typical lengths of 100 – 300 mm and shape errors of 1-2 nanometers, slope errors in the order of 100 nrad, and a roughness in the Angstrom scale. Today, the line patterns of x-ray gratings are mostly produced either by holographic exposures of interfering laser beams into a photo resist, or by ruling machines that imprint the grating groves in a line-by-line manner into a soft metal layer. As an alternative to these established methods, we present a strategy of grating fabrication by electron-beam lithography (EBL). This technique can expose arbitrary patterns with high resolution and placement accuracy at a speed sufficient for x-ray grating fabrication. We have performed optical metrology of a low-cost grating substrate, which served as the basis for an aligned exposure of a corrected grating pattern to yield a laminar grating with a constant deflection angle along the substrate surface. We have confirmed that the effects of slope errors were strongly compensated over an extended wavelength range by using synchrotron radiation in the soft x-ray range. This work shows a path for circumventing the limited availability of high quality reflective substrates to obtain gratings with performance beyond what is possible today.