X-ray free-electron lasers (XFELs) generate sequences of ultra-short spatially 
coherent pulses of X-ray radiation. A diffraction focusing spectrometer (DFS), 
which is able to measure the whole energy spectrum of the radiation of a single 
XFEL pulse with an energy resolution of ΔE/E 2 × 10(-6), is proposed. This is 
much better than for most modern X-ray spectrometers. Such resolution allows one 
to resolve the fine spectral structure of the XFEL pulse. The effect of 
diffraction focusing occurs in a single-crystal plate due to dynamical 
scattering, and is similar to focusing in a Pendry lens made from a metamaterial 
with a negative refraction index. Such a spectrometer is easier to operate than 
those based on bent crystals. It is shown that the DFS can be used in a wide 
energy range from 5 keV to 20 keV.