Normal-incidence imaging spectrograph based on an aperiodic spherical grating for the vacuum spectral region

The possibility of astigmatism compensation in a wide wavelength range in normal incidence schemes based on a spherical diffraction grating with variable groove density has been considered. Two schemes imaging spectrographs with dimensions of about $1$ and $5$ m for the wavelength ranges $820$–$1690$ and $980$–$1520$ $\mathring{\mathrm{A}}$ that operate in the first external and first internal diffraction orders, respectively, have been calculated. It has been shown that the advantage of the external order of diffraction is a wide (more than an octave) spectral range at relatively compact sizes of the device. Schemes operating in internal orders of diffraction have better imaging characteristics, but large dimensions of the device are required to maintain the width of the wavelength range at the octave level. A comparison of the above schemes with schemes based on gratings with curvilinear grooves has been carried out. It has been shown that the variable line-spaced gratings yield a gain in the limiting spatial resolution, while the gratings with curvilinear grooves allow the achievement of a better limiting spectral resolution. The schemes of the considered type can be applied in the soft X-ray range when using diffraction gratings with a multilayer coating.