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

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