Fig. 1. (a) Schematic of the MLBG structure and illustration of improved energy resolution with high-order MLBGs. (b) Theoretical diffraction efficiency of MLBGs (G1, G2, G3, G4, and G8), compared to Rh-coated grating (SLG).

Fig. 2. (a) Schematic of the ultrahigh-resolution design of the cPGM beamline and the SVLSG spectrometer using MLBG. (b) Schematic of high-resolution design of cPGM beamline and spectrometer with reduced instrument length. (c) Theoretical diffraction efficiency of gratings and transmission of the cPGM. (d) Transmission of the spectrometer. (e), (f) Energy resolution of the beamlines/spectrometer with the grating operating in different diffraction orders. Lx1 and Lx2 represent the lengths of the SVLSG spectrometer for high energy resolution and reduced-length design, respectively. M1, collimated mirror; M2, plane mirror; M3, focus mirror; MLBG, multilayer-coated blazed grating; r1, entrance arm length; r2, exit arm length; Lx, total spectrometer length; h, focal height; y, inclination angle of detector.

Fig. 3. Characterization of the fabricated MLBG structures. Cross-sectional TEM images of S1 (a) and of S2 (c) reveal the detailed internal structures. The additional dark stripes in the TEM image of sample S1 are due to it being a recoated sample. AFM images and the corresponding extracted 1D profiles of S1 (b) and S2 (d) are presented, along with deviation curves that illustrate the differences between the measured profiles (solid line) and the ideal triangle profiles (dashed line).

Fig. 4. (a) The experimental and theoretical reflectance of the first order of the reference multilayer (black spheres and black lines). The experimental (spheres) and theoretical diffraction efficiency with and without imperfections (dashed and solid lines) of the −2nd diffraction order (red) and the −3rd order (blue) of the MLBG S1. (b) The experimental (spheres) and theoretical diffraction efficiency with and without imperfections (dashed and solid lines) of the −3rd diffraction order (blue) and the −4th diffraction order (green) of the MLBG S2.

Fig. 5. Two-dimensional diffraction measurements as a function of detector angle and photon energy of the S1 at a grazing incidence angle of 3.193° in the −1st diffraction order, 2.675° in the −2nd order, and 2.175° in the −3rd order.

Fig. 6. Efficiency loss due to structural imperfections. The schematic of various structural imperfections is shown on the top. The efficiency loss caused by each structural imperfection was calculated at 2.5 keV and normalized against the efficiency of the ideal structure. The blaze angle and d-spacing were optimized to the maximum efficiency for each diffraction order, as detailed in Table 1.