Approaching ultimate resolution for soft x-ray spectrometers

We explore the potential performance of soft x-ray spectrometers based on the use of varied-line-spacing spherical diffraction gratings (VLS-SG). The quantitative assessment is based on an optimization procedure to obtain both negligible optical aberrations at full illumination of the grating and a quasi linear focal curve. It involves high-order optical aberration cancellation to calculate the focal curves. We also examine the validity of small divergence closed-form formulas describing the light path function. Optimizing the optical and geometric parameters gives an ultimate resolving power, at 930 eV, of between 10 800 for a 3 m long instrument and 34 000 for an 11 m spectrometer according to the Rayleigh criterion. Typical fabrication tolerances would scale these values down by about 10%. The findings are validated by ray-tracing simulations. (C) 2012 Optical Society of America