Abstract
Rigorous dynamical theory calculations show that four-beam diffraction (4BD) can be activated only by a unique photon energy and a unique incidence direction. Thus, 4BD may be used to precisely calibrate X-ray photon energies and beam positions. Based on the principles that the forbidden-reflection 4BD pattern, which is typically an X-shaped cross, can be generated by instant imaging using the divergent beam from a point source without rocking the crystal, a detailed real-time high-resolution beam (and source) position monitoring scheme is illustrated for monitoring two-dimensional beam positions and directions of modern synchrotron light sources, X-ray free-electron lasers and nano-focused X-ray sources.
Highlights
X-ray diffraction from crystals is generally based on Bragg’s law of two-beam diffraction (2BD), 2d sin =, where is the Bragg angle, is the X-ray wavelength, and d is the spacing of the diffracting lattice planes
X-ray absorption edges of elements have been widely used for wavelength calibration, for double-crystal monochromators (DCMs) of synchrotron beamlines
Motivated by the phasespace (1D) beam position monitor system based on element K-edge absorption (Samadi et al, 2015, 2019a,b), here we propose a new scheme that can accurately monitor 2D source positions and directions and at the same time can calibrate the wavelengths of the X-ray beams
Summary
Bragg’s law of 2BD is mainly a one-dimensional (1D) equation that is unable to generate two-dimensional (2D) diffraction patterns required for precise determination of the 2D position and direction of an X-ray beam in space To overcome these problems, it has been proposed to use multiple-beam diffraction to calibrate photon energies Motivated by the phasespace (1D) beam position monitor system based on element K-edge absorption (Samadi et al, 2015, 2019a,b), here we propose a new scheme that can accurately monitor 2D source positions and directions and at the same time can calibrate the wavelengths of the X-ray beams This scheme is based on forbidden-reflection four-beam diffraction (4BD) from crystals with cubic structures, which has to be activated by a unique photon energy and a unique beam direction. The 4BD method will be suited for diagonstic applications of modern synchrotron light sources, XFELs, and nano-focused beams that have small 2D source sizes
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