General formulae have been calculated for the intensity distribution in a grating spectrograph with various types of grating errors, with aperture diffraction, with proper aberrations and with amplitude filters. The calculations were based on the theory of contrast transfer for the optical image formation. This theory permits the calculation of the spectral distribution of the light falling into the entrance slit from the measured intensity distribution with the aid of the Fourier theorem. In this way, a maximum of information can be obtained. The theory can also be applied to less conventional spectrographs where the limit of resolution does not depend on the aperture diffraction in the usual way.