  High harmonic generation (HHG) is an established means of producing coherent,
short wavelength, ultrafast pulses from a compact set-up. Table-top
high-harmonic sources are increasingly being used to image physical and
biological systems using emerging techniques such as coherent diffraction
imaging and ptychography. These novel imaging methods require coherent
illumination, and it is therefore important to both characterize the spatial
coherence of high-harmonic beams and understand the processes which limit this
property. Here we investigate the near- and far-field spatial properties of
high-harmonic radiation generated in a gas cell. The variation with harmonic
order of the intensity profile, wavefront curvature, and complex coherence
factor is measured in the far-field by the SCIMITAR technique. Using the
Gaussian-Schell model, the properties of the harmonic beam in the plane of
generation are deduced. Our results show that the order-dependence of the
harmonic spatial coherence is consistent with partial coherence induced by both
variation of the intensity-dependent dipole phase as well as finite spatial
coherence of the driving radiation. These findings are used to suggest ways in
which the coherence of harmonic beams could be increased further, which would
have direct benefits to imaging with high-harmonic radiation.
