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Updated: May 26, 2026

Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic
Published on: August 25, 2016
Design of a general point focusing crystal geometry for x-ray spectroscopy
Sayyed Jalal Pestehe1, Golamreza Askari Germi
1Department of Physics, University of Tabriz, Tabriz, Iran. sjpest@tabrizu.ac.ir
Abstract:
A nearly exact general equation for geometrical angular deviations from the Bragg angle over entire curved crystal surfaces is derived using a toroidally curvilinear coordinate system and applied on the nine conventional crystal geometries. Although the derived formula confirms Wittry's results for the first five cases, it shows considerable differences for the more important cases, such as 45° point focusing, general point focusing, and Berreman geometries. The effective scattering areas for the mentioned cases have been derived, plotted, and interpreted. A point-to-point focusing crystal geometry is introduced, and it is shown that it approaches Wittry's and spherical plane-spherical Johansson geometries as θ(B) → 90° and θ(B) → 0°, respectively.
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