It is shown that, among all partially coherent wave fields having the same informational entropy, the product of the effective widths of the intensity functions in the space and the spatial-frequency domains takes its minimum value for a wave field with a Gaussian-shaped cross-spectral density function. Furthermore, it is shown how this minimum value is related to the informational entropy and how this informational entropy is related to other quantities that can measure the overall degree of coherence of the partially coherent wave field.
http://www.opticsinfobase.org/abstract.cfm?URI=josaa-3-8-1243