An imaging spectrograph concept optimized for extended far-ultraviolet emission sources is presented. Although the design was originally developed for FIMS aboard the first Korean science satellite STSAT-l launched on September 27, 2003, no rigorous theoretical background of the spectrograph design has been published. The spectrograph design employs an off-axis parabolic cylinder mirror in front of a slit that guides lights to a diffraction grating. The concave grating provides moderate spatial resolution over a large field of view. This mapping capability is absent in most astronomical instruments but is crucial to the understanding of the nature of a variety of astrophysical phenomena. The aberration theory presented in this paper can be extended to holographic gratings in order to improve the spatial as well as the spectral resolutions.