On smart optimization of blazed soft X-ray gratings

The first attempts to calculate the diffraction efficiencies of gratings in the soft X-ray range were made on a scalar model. The results were simple analytical equations, that always severely overestimated the performance of real objects. In this respect, computer programs were found to be more successful, which rigorously consider all diffracted and refracted waves. Consequently soft X-ray gratings are presently optimized using these tools, which requires rather extensive calculations for any instrument optimization as general trends are not immediately obvious. Here it will be shown that the results of the rigorous calculations for gratings with blaze or sawtooth profile can be approximated rather well with a simple analytical equation. This equation contains three multiplicative factors, which deal independently with the effect of the reflectivity, the blaze angle and the groove density. This opens the possibility to initially ignore the effects of the blaze angle and thus to start an optimization in a very general way. Such optimization can be based on isoreflectivity curves and it can then provide `blaze maximum efficiency maps', i.e. simple images. In these latter images, one can identify directly the optimum parameters for a grating, i.e. the groove density providing best efficiency for a requested spectral resolving power. Only successively will the blaze angle have to be fixed. Its choice is then not the result of an extensive optimization process but of a simple calculation applied for the photon energy at which maximum efficiency performance is requested. The maps presented here are used for the optimization of a medium-resolving-power soft X-ray monochromator, which can scan the photon energy range 300-2000eV.