This paper is concerned with the history, properties, development, application, and prospects of soft X-ray (2—300 Å) VLS spectrometers, i.e., spectrometers with reflection diffraction gratings whose spacing varies monotonically across the aperture according to a prescribed law (so-called Varied Line-Space (VLS) gratings). An important feature of grazing-incidence VLS spectrometers is that the spectrum is formed on a nearly flat surface perpendicular (or slightly inclined) to the diffracted beams, making them perfectly compatible with modern CCD detectors. VLS spectrometers are employed for the spectroscopy of laboratory and astrophysical plasmas, including the diagnostics of relativistic laser-produced plasmas, for measuring the linewidth of an X-ray laser, for recording the high-order harmonics of laser radiation, and the registering the emission of fast electric discharges and other laboratory X-ray sources. Instruments with VLS gratings are employed to advantage in reflectometry/metrology, X-ray fluorescence analysis, and microscopy with the use of synchrotron, free-electron laser, and laser-produced plasma radiation, as well as in SXR emission spectroscopy, combined with an electron microscope (SXES). Recent years have seen the active development of VLS spectrometers dedicated to the investigation of the electronic structure of different materials and molecules by resonant inelastic X-ray scattering (RIXS) spectroscopy with synchrotron radiation. Among recent trends is the development of VLS gratings with a multilayer reflective coating and extension of the operating spectral range towards 'tender' X-rays ($\hbar \omega \sim& 1.5—6 keV), some projects aiming to achieve a resolving power $\lambda /\delta \lambda \sim 10^5$ in the region $\hbar \omega \sim 1$ keV.
Keywords: soft X-ray radiation, aperiodic reflection diffraction grating (VLS grating), flat-field spectrometer, scanning spectrometer/monochromator, stigmatic (imaging) spectrometer PACS:07.60.−j, 07.85.−m, 07.85.Fv, 07.85.Nc, 07.87.+v, 42.79.−e (all) DOI:10.3367/UFNe.2020.06.038799 URL: https://ufn.ru/en/articles/2021/5/d/ Citation: Ragozin E N, Vishnyakov E A, Kolesnikov A O, Pirozhkov A S, Shatokhin A N "Soft X-ray spectrometers based on aperiodic reflection gratings and their application" Phys. Usp.64 495–514 (2021)