Calculations of the xhyphen;ray optics of four types of doubly curved diffractors are described and the results are compared with similar results for singly curved diffractors (Johann and Johansson geometry). In these calculations the locus of points on a curved diffractorrsquo;s surface is determined for a given deviation from the Bragg angle when the diffractor is used at Bragg angles ranging from 15 to 75 degrees. The six cases discussed include cylindrical, spherical, and toroidal geometries. The calculations are used as a basis for comparing the collection efficiency and the spectral resolution when these diffractors are used in scanning monochromators. It is shown that doubly curved diffractors are superior to singly curved ones and that a diffractor with spherical planes and toroidal surface provides the best performance of all of the diffractors considered if a wide range of Bragg angles must be covered.
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