We report measurements of propagating capillary waves on a liquid water surface at T=5 degrees C with x-ray photon correlation spectroscopy. The experiment has been performed under grazing incidence conditions with an incoming x-ray beam below the critical angle of total external reflection. In the q region investigated the measured intensity-intensity autocorrelation functions of the liquid water surface were found to be heterodyne signals, i.e., a combination of first- and second-order correlation functions g(1)(tau) and g(2)(tau).

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 ͑XPCS͒. 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.

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