Propagation of spatial coherence in fast pulses

Diffraction and interferometry with fast pulses are analyzed for the case that the fields are partially correlated in time and in space. This generalizes a previous work[Schoonover et al., J. Mod. Opt. 55, 1541 (2008)], where only the temporal correlations of pulsed fields were considered in a Young's interferometer. The meaning of the interferograms is addressed for measurements taken in the near, Fresnel, and far zones of the source. It is shown that single-shot measurements cannot generally be used to infer statistical properties of the source, rather, data averaged over many pulses must be used.