We present a rigorous description of the effects of partial coherence and detector resolution on intensity autocorrelation functions as they can be measured by x-ray photon correlation spectroscopy (XPCS). Based on the Huygens-Fresnel propagation law and on the first Born approximation, we derive a general expression for the normalized intensity autocorrelation function. We calculate how the mutual coherence function of the x-ray beam propagates from an aperture to the sample and how it propagates after the scattering process to the detector area and consequently influences the intensity autocorrelation function. We illustrate our calculation with examples of XPCS intensity autocorrelation functions of liquid surfaces calculated for grazing incidence geometry.