X-ray optics of doubly curved diffractors II

Abstract

A general equation is derived for x-ray diffractors with arbitrary toroidally curved surface and planes when used with a point source. This equation, which gives the locus of points on a curved diffractor’s surface for a given deviation from the Bragg angle, is shown to yield the appropriate equations for all of the crystal diffractor geometries that were previously discussed by Wittry and Sun [J. Appl. Phys. 67, 1633 (1990)]. Two examples are given of the use of the general equation to design diffractors with improved collection solid angle over a range of Bragg angles. The x-ray collection solid angle and focusing properties of these two examples are given.

Design of a doubly-curved crystal to improve X-ray fluorescence analysis of aerosol particles

“…Wittry et al have discussed a wide range of possible shapes of singly and doubly-curved crystals [1,[12][13][14][15][16][17]. Here, we only present two special cases of doubly-curved crystals.…”

“…A general equation for arbitrary toroidally curved surfaces is derived in [17]. For the geometries of interest here, the respective formulae are…”

“…Using these normalized coordinates, the angular deviations for different geometries can be calculated following [13,16,17]. A general equation for arbitrary toroidally curved surfaces is derived in [17].…”

High Definition X‐Ray Fluorescence: Principles and Techniques

“…Use of focusing geometries for producing a point image from a point X-ray source for analytical use was described and investigated during the 1950s [20,21]. In the 1980s and 1990s, the X-ray optical properties of DCC optics were systematically studied by using a ray tracing method [22][23][24][25][26]. Fabrication and application of DCC optics were also reported in the early 1990s by Wittry et al [27,28].…”

Microanalysis by monochromatic microprobe x-ray fluorescence—physical basis, properties, and future prospects

“…15,16 The geometry considered here is the Johann point-focusing geometry; this has the Johann geometry in the focal circle plane and axial symmetry along the source-image line. Like the normal Johann geometry, this geometry does not satisfy point-to-point focusing exactly and the image of an ideal point source on the focal circle is broadened by the geometrical aberration.…”