The uncertainty principle for partially coherent light tells us that the product of the effective widths of the space-domain intensity and the spatial-frequency-domain intensity has a lower bound and that this lower bound is inversely proportional to the overall degree of coherence of the light. The nature of the partially coherent light for which the lower bound can be reached is derived.
http://www.opticsinfobase.org/abstract.cfm?URI=josa-73-10-1320