  We derive an analytic expression for the instrument profile of a slit
spectrograph, also known as the line spread function. While this problem is not
new, our treatment relies on the operatorial approach to the description of
diffractive optical systems, which provides a general framework for the
analysis of the performance of slit spectrographs under different illumination
conditions. Based on our results, we propose an approximation to the spectral
resolution of slit spectrographs, taking into account diffraction effects and
sampling by the detector, which improves upon the often adopted approximation
based on the root-sumsquare of the individual contributions from the slit, the
grating, and the detector pixel.
