$\hat{O}_{{_{\mathrm {{D}}}}}$ (see Fig. \[fig002\]) and its spectral transmittance function (b). D$_{{_{\mathrm {{D}}}}}$ is an example of an in-line four-crystal CDDW-type dispersing optic, comprised of collimating (C), dispersing (D$_{{_{1}}}$, D$_{{_{2}}}$), and wavelength-selecting (W) crystals in a ($\pi+$,$0-$,$0+$,$0-$) scattering configuration. With the crystal parameters provided in Table \[tab1\] of Appendix \[cddwoptic\], the dispersing element D$_{{_{\mathrm {D}}}}$ features a spectral transmission function with a $\Delta E_{{_{\cup}}}=8.8$ meV bandwidth (b), a cumulative angular dispersion rate ${{{\mathcal D}}_{\cup_{{_{{D}}}}}} = -25 ~\mu$rad/meV, and a cumulative asymmetry factor ${b_{\cup_{{_{{D}}}}}} = 1.4$. The sharp line in (b) presents the 0.1-meV spectral resolution of an x-ray echo spectrometer, designed for use with 9.1-keV photons. []{data-label="fig003"}](cddw-pi+0-0+0-comb-art.pdf){width="50.00000%"}

![Dispersing element D$_{{_{\mathrm {{R}}}}}$ (a) of the refocusing system $\hat{O}_{{_{\mathrm {{R}}}}}$ (see Fig. \[fig002\]) and its spectral transmittance function (b). Similar to D$_{{_{\mathrm {{D}}}}}$ in Fig. \[fig003\], D$_{{_{\mathrm {{R}}}}}$ is an example of the in-line four-crystal CDDW-type dispersing optic, but, in a ($\pi+$,$\pi+$,$\pi-$,$0-$) scattering configuration. With the crystal parameters provided in Table \[tab1\] of Appendix \[cddwoptic\], the dispersing element D$_{{_{\mathrm {D}}}}$ features a spectral transmission function with a $\Delta E_{{_{\cup}}}=5.5$ meV bandwidth (b), a cumulative angular dispersion rate ${{{\mathcal D}}_{\cup_{{_{{D}}}}}} =
  -43 ~\mu$rad/meV, a cumulative asymmetry factor ${b_{\cup_{{_{{D}}}}}} =
  0.36$, and ${{{\mathcal D}}_{\cup_{{_{{D}}}}}}/{b_{\cup_{{_{{D}}}}}} 