Effects of source size and wavefront propagation on the energy resolution of a bent-crystal polychromator

Polychromators, or elliptically bent diffracting crystals that focus a broad-bandwidth X-ray beam onto a sample, have become a common device at synchrotron beamlines specializing in X-ray absorption spectroscopy (XAS) because they allow a full absorption spectrum to be collected in one shot. Such a device is being planned for the XAS beamline I20 of the Diamond Light Source. A bent silicon crystal diffracting 7 keV X-rays with the (1 1 1) reflection is taken as a model for the simulations of this report. Instrumental resolution is determined by the demagnification of the source, the spread of the diffracted beam during propagation and the pixel size of the position-sensitive detector placed behind the sample. The first is calculated by geometrical optics. The second is calculated by a full wave-optical treatment, which includes Takagi–Taupin integration to find the diffracted amplitude at the crystal's surface and Huygens–Fresnel propagation of the diffracted wave to the sample or detector. This sets the polychromator's intrinsic energy resolution. The pixel size of the detector is then added to find the total instrumental resolution at various sample–detector distances.