Towards extremely high-resolution broad-band flat-field spectrometer in 'water window'

The optical design of a novel spectrometer is present, combining a cylindrically convex pre-mirror with a cylindrically concave VLS grating (both in meridional) to deliver a resolving power of 100,000-200,000 in 'water window' (2-5nm). More remarkably, unlike a typical RIXS spectrometer to obtain such high resolution by tight focusing or tiny confinement slit (<1{\mu}m), here the resolution could be achieved for an effective meridional source size of 50{\mu}m (r.m.s.). The overall optical aberrations of the system are well analysed and compensated, providing an excellent flat field at the detector domain throughout the whole spectral range. And a machine learning scheme - SVM is introduced to explore and reconstruct the optimal system with pretty high efficiency.