It was recently shown that planar sources of entirely different states of coherence may generate fields that have the same intensity distribution throughout the far zone. With the help of a certain new correlation coefficient (which we call the coefficient of directionality), a new formulation of the underlying equivalence theorem is obtained which elucidates, in a very clear manner, the underlying physical principles involved. It is also shown that a quasihomogeneous source may always be specified that will generate the same far-zone intensity distribution as any given finite steady-state planar source. This result is illustrated by several examples. In particular a quasihomogeneous source is described that will generate the well-known Airy pattern intensity distribution.
E. Collett and E. Wolf, "New equivalence theorems for planar sources that generate the same distributions of radiant intensity," J. Opt. Soc. Am. 69, 942-950 (1979)