The radiant intensity from planar sources of any state of coherence

A new formula is derived for the radiant intensity from any steady, finite, primary or secondary planar source of any state of coherence. It expresses the radiant intensity as a two-dimensional spatial Fourier transform of a quantity that represents a correlation function of the field in the source plane, averaged over the area of the source. The formula may be regarded as a natural counterpart for fields generated by partially coherent sources to the well-known two-dimensional Fourier transform relation between the field distributions in the plane of a finite coherent source and in the far zone. Some implications of the new formula are discussed. An alternative expression is also obtained that is applicable when the the source is a primary one and it is shown to imply that the radiant intensity is then a boundary value on two real axes of an entire analytic function of two complex variables.