Two intensity functions are defined for partially coherent light: one in a space domain and a second one in a spatial-frequency domain. Moreover, a quantity is introduced that can be considered a measure of the overall degree of coherence of the partially coherent light. It is then shown that the following uncertainty principle can be formulated when the partially coherent light is spatially quasi-stationary: the product of the effective widths of the two intensity functions has a lower bound, and this lower bound is inversely proportional to the overall degree of coherence.
http://www.opticsinfobase.org/abstract.cfm?URI=josa-72-10-1437