Fig. 1. Structural schematics of concave VLS grating with or without pre-diverged convex mirror and their ideal resolving power (corresponding to A1 and A2). (a) Single concave VLS grating spectrometer system; (b) high-resolution spectrometer with pre-diverged convex mirror; (c) variations of A1 and A2 with Mc at different spacings d

Fig. 2. Spectralimaging distributions (according to ray-tracing software) for three different sets of d and Mc, corresponding to dots x, y, and z in Fig. 1(c). (a) Mc=-0.39, d=800 cm, Qa=1.13; (b) Mc=-0.304, d=534 cm, Qb=0.51; (c) Mc=-0.20, d = 300 cm, Qc≈0.61

Fig. 3. Variations of Q value and ideal resolving power of A2 with d and Mc. (a) Variation of Q value; (b) variation of A2; (c) variation of Q value at various photon energies

Fig. 4. Actual structure and performance analysis of spectrometer. (a) Schematic layout of system design for grating spectrometer with enhanced resolving power and spectral intensity; (b) coordinate distributions of optimized meridional and sagittal focal curves in principal plane with respect to center of grating at coordinate (0, 0); (c) calculated results of major factors which influence resolving power of spectrometer; (d) corresponding resolving powers of Fig. 4(c)

Fig. 5. Ray-tracing results for spectrometer with parameters in table 1. (a) Overall spectral distribution at optimal detector plane for full energy range (0.6-1.5 keV); (b) ray-tracing result under energy of 0.6 keV and resolving power of 70440; (c) ray-tracing result under energy of 1.0 keV and resolving power of 48650; (d) ray-tracing results under energy of 1.5 keV and resolving power of 33010