Systematic search for spherical crystal X-ray microscopes matching 1–25 keV spectral line sources

Spherical-crystal microscopes are used as high-resolution imaging devices for monochromatic x-ray radiography or for imaging the source itself. Crystals and Miller indices (hkl) have to be matched such that the resulting lattice spacing d is close to half the spectral wavelength used for imaging, to fulfill the Bragg equation with a Bragg angle near 90° which reduces astigmatism. Only a few suitable crystal and spectral-line combinations have been identified for applications in the literature, suggesting that x-ray imaging using spherical crystals is constrained to a few chance matches. In this paper, after performing a systematic, automated search over more than 9 × 10⁶ possible combinations for x-ray energies between 1 and 25 keV, for six crystals with arbitrary Miller-index combinations hkl between 0 and 20, we show that a matching, efficient crystal and spectral-line pair can be found for almost every He_α or K_α x-ray source for the elements Ne to Sn. Finally, using the data presented here it should be possible to find a suitable imaging combination using an x-ray source that is specifically selected for a particular purpose, instead of relying on the limited number of existing crystal imaging systems that have been identified to date.