  In this work we provide theoretical background for the analysis of
second-order correlation functions in experiments performed at the soft x-ray
free-electron lasers (XFELs). Typically, soft x-ray beamlines at XFELs are
equipped by the variable line spacing (VLS) monochromators. We perform
examination of the beam propagation through such VLS monochromator taking
specially into account the interplay between the finite monochromator
resolution and the exit slits width. We then provide general analysis of the
second-order correlation intensities in spectral and spatial domains. Finally,
we connect these functions with the statistical properties of the beam incoming
to the monochromator unit in the limit of Gaussian Schell-model pulses.
