The development of third-generation synchrotron sources has stimulated efforts toward high-resolution monochromators. A good knowledge of grating efficiency is needed to achieve an optimal compromise between resolution and photon flux. Because simple geometric models fail to describe correctly the gratings properties in the UVtosoft-X-ray range, we have developed a simulation software based on differential theory. A simplified R-matrix propagation algorithm assures the numerical stability of the code for deep gratings. Our numerical results are compared with previous research on deep gratings. Experimental and numerical studies have been performed on some test cases at a synchrotron source. Very good agreement between numerical prediction and measurement has been found.
We have developed at LURE a code to predict the efficiency of gratings. The code is based on differential theory and uses a simplified R-matrix propagation algorithm to obtain numerical stability on the whole range from visible to hard x-rays. Experimental and numerical studies have been performed on some test cases at a synchrotron source. A good agreement between numerical prediction and measurements has been found. The code is a rigorous application of electromagnetic theory and gives exact results as long as accurate optical constants can be attributed to grating materials. Such rigorous calculations provide an important tool for the optical engineering of modern synchrotron monochromator gratings. We give an example of application of this code to the engineering of a modern beamline and for the optimization of harmonic rejection.
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