  We present diffraction patterns from micron-sized areas of mono-crystalline
graphite obtained with an ultracold and ultrafast electron source. We show that
high spatial coherence is manifest in the visibility of the patterns even for
picosecond bunches of appreciable charge, enabled by the extremely low source
temperature (~ 10 K). For a larger, ~ 100 um spot size on the sample, spatial
coherence lengths > 10 nm result, sufficient to resolve diffraction patterns of
complex protein crystals. This makes the source ideal for ultrafast electron
diffraction of complex macromolecular structures such as membrane proteins, in
a regime unattainable by conventional photocathode sources. By further reducing
the source size, sub-um spot sizes on the sample become possible with spatial
coherence lengths exceeding 1 nm, enabling ultrafast nano-diffraction for
material science.
