Revisited grating efficiency maps: predicting diffraction grating performance by use of image analysis programs

Soft X-ray monochromator designers know very well the program, which M. Neviere developed in order to predict the diffraction efficiencies of reflection gratings by use of the rigorous differential method. Infact it is used frequently for the grating parameter optimisation. Here a simple analytical equation is presented, which predicts for perfect grating profiles diffraction efficiencies, which correspond within 10% to the results with the more rigorous Neviere approach. This empirical equation, which is based on plausible assumptions, facilitates very much systematic studies, which can then easily be presented in the form of isoefficiency maps, which are valid rather generally and which can be further evaluated in simple image analysis programs. Infact such maps will allow one to identify the optimum grating parameters for a given application in a glimpse.