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The resolution function of a spectrometer based on a strongly bent singlecrystal (bending radius of 10 cm or less) is evaluated. It is shown that theresolution is controlled by two parameters, (i) the ratio of the latticespacing of the chosen reflection to the crystal thickness and (ii) a singleparameter comprising crystal thickness, its bending radius, and anisotropicelastic constants of the chosen crystal. Diamond, due to its unique elasticproperties, can provide notably higher resolution than silicon. The resultsallow to optimize the parameters of bent crystal spectrometers for the hardX-ray free electron laser sources.

Resolution of a bent-crystal spectrometer for X-ray free electron laser pulses: diamond vs. silicon