Fig. 1. Schematic of the locations of the elliptical crystal segment and detector surface relative to the X-ray source and diagnostic space. The optimized parameters are $\unicode[STIX]{x1D700}=0.9677$, $2f=600$  mm and $\unicode[STIX]{x1D702}=1.8759^{\circ }$. $\unicode[STIX]{x1D712}$ is measured from the ellipse semi-major axis to the initial X-ray trace, $\unicode[STIX]{x1D703}$ is the Bragg angle, and $\unicode[STIX]{x1D6FD}$ is the angle of the X-ray through the crossover focus.

Fig. 2. Geometry factor $Fg$ influencing the X-ray intensity reaching the linear detector versus detector position in the elliptically bent spectrometer design.

Fig. 3. Example of IP-recorded Cl spectra using the quartz (10–10) ($2d=8.512$  Å) crystal elliptical analyzer. (a) Raw spectral data recorded by IP. (b) Spectral intensity, obtained by averaging over the photon counts in the direction perpendicular to the dispersion direction of the detector, versus photon energy.

Fig. 4. Schematic of the experimental setup for the point projection of the Al $K$-edge absorption measurements.

Fig. 5. Au $M$-band spectrum from 1.54 to 3.8 keV.

Fig. 6. Experimentally measured Al transmission data with the new crystal spectrometer.