Analysis of versions of the optical layout of a high-aperture imaging spectrograph based on a convex holographic diffraction grating

This paper discusses the possibility of constructing an imaging spectrograph using an aberration-corrected holographic diffraction grating deposited on a convex surface. A projection objective is used as the starting point for designing such an optical layout. It is shown that, when the simplest triplet-type objective is used, a spectrograph layout for the 400–700-nm visible range with a relative aperture of up to 1∶2.3 can be constructed that provides a spectral resolution of 2.9–7.7 nm when operated with a slit 16 mm long. A version is also considered of a spectrograph design with matching of the spectral and imaging channels, based on a six-lens projection objective.