Instead, the use of undulators would be more favourable as they emit a line spectrum which is even tunable. As far as synchrotron radiation at larger photon energies in the soft X-ray range is concerned, the latter suppression strategy for the principle diffraction order with filters could be used as well at bending-magnet sources, which emit a continuous spectrum. In this case, interferences by integer multiples of the respective wavelength need to be absent or need to be eliminated by appropriate means such as filters. This strategy is regularly applied when the incident light from laboratory line sources, emitting smaller photon energies from the visible spectral range up to the vacuum ultraviolet (VUV), is dispersed at close to normal incidence. According to equation (2) the use of the second ( n = 2) or even higher orders can then help to reduce the achievable spectral resolution at least twofold (see, for example, Born & Wolf, 1980 ). Where Δ ϕ is the intrinsic beam angular divergence limited by the finite source size s and given by the ratio of this size s and the source distance L. Without any requirement for a sophisticated grating exchange scheme, a related instrument promises to be sufficiently stable for the needs imposed by the improvements in source point stability at diffraction-limited storage rings. This would allow operation of a single highly efficient grating over a larger photon energy interval at a modern synchrotron radiation source, e.g. The performance in terms of transmission and spectral resolving power can be very similar to the performance of a grating with a larger groove density, which would otherwise have to be used for accessing the same energy range. The principle finding is that, by operation of gratings with lower groove densities, and thus with higher efficiencies, in higher order diffraction, one can extend the tuning in existing instruments with mechanical/optical limitations to larger photon energies. The predictions are then verified by use of rigorous calculations. The related systematic study could make profitable use of a recently introduced simple analytical equation for the prediction of the diffraction efficiency of blazed gratings with an ideal sawtooth profile. This study will thus address the feasibility of efficient diffraction of soft X-rays in the second order at reflection gratings when operated at grazing angles of incidence. A similar routine operation in monochromators for the soft X-ray range is not reported yet. The fact that a diffraction grating can provide twofold-smaller bandwidth when operated in second-order diffraction is long known and applied routinely in the laboratory for spectroscopy in the visible and ultraviolet spectral range.
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