A merit function is proposed and applied to design holographic concave gratings for moderate-resolution monochromators. To justify the validity of the merit function, imaging properties of gratings used for the coma-correction Seya-Namioka monochromator, designed by the present authors, Noda, and Takahashi, are compared through ray tracing and their aberration-correction mechanisms are also analyzed. The capability of the merit function is well demonstrated in the design of holographic gratings for another two moderate-resolution monochromators with different requirements. All the results obtained show that the merit function is not only straight and effective but also manages to balance various aberrations of the concave holographic grating very well.
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