  The resolution function of a spectrometer based on a strongly bent single
crystal (bending radius of 10 cm or less) is evaluated. It is shown that the
resolution is controlled by two parameters, (i) the ratio of the lattice
spacing of the chosen reflection to the crystal thickness and (ii) a single
parameter comprising crystal thickness, its bending radius, and anisotropic
elastic constants of the chosen crystal. Diamond, due to its unique elastic
properties, can provide notably higher resolution than silicon. The results
allow to optimize the parameters of bent crystal spectrometers for the hard
X-ray free electron laser sources.
