Effective spatial and angular correlations in beams of any state of spatial coherence and an associated phase-space product

We study effective spatial and angular correlations in beams of any state of spatial coherence, and we introduce a phase-space product, Q, which takes these correlations into account. This phase-space product is shown to reduce to the conventional beam-quality factor M-2 when the beam is spatially fully coherent. We also determine the lower bound for the value of Q and demonstrate that it is attained for all Gaussian Schell-model beams. (C) 2001 Optical Society of America.