We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry. The beam is focused by a fixed curvature mirror system optimized for high flux density under conditions of partial coherence. The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation. In view of imaging applications, the magnified in-line image of a test pattern formed under conditions of partial coherence is analyzed quantitatively. Finally, additional coherence filtering by use of x-ray waveguides is demonstrated. By insertion of x-ray waveguides, the beam diameter can be reduced from typical values of 200 nm to values below 15 nm. In proportion to the reduction in the focal spot size, the numerical aperture (NA) of the projection imaging system is increased, as well as the coherence length, as quantified by grating interferometry.