is realistic), and designed for use with 9.1-keV and 4.6-keV photons. The signal in echo spectrometers is enhanced by at least three orders of magnitude compared to what is possible with the standard scanning-IXS-spectrometer approach.

X-ray echo spectrometers require a combination of the CDDW dispersing elements and focusing optics as major optical components. Such components have been experimentally demonstrated recently [@SSM13; @SSS14]. Implementation of x-ray echo spectrometers is, therefore, realistic.

Acknowledgments
===============

Stimulating discussions with D.-J. Huang (NSRRC) are greatly appreciated. S.P. Collins (DLS) is acknowledged for reading the manuscript and for valuable suggestions. Work at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357.

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