  A reciprocal relationship between the autocovariance of the light intensity
in the source plane and in the far-field detector plane is presented in a form
analogous to the classical van Cittert - Zernike theorem, but involving
intensity correlation functions. A "classical" version of the reciprocity
relationship is considered first, based on the assumption of circular Gaussian
statistics of the complex amplitudes in the source plane. The result is
consistent with the theory of Hanbury Brown - Twiss interferometry, but it is
shown to be also applicable to estimation of the source size or the spatial
resolution of the detector from the noise power spectrum of flat-field images.
An alternative version of the van Cittert - Zernike theorem for intensity
correlations is then derived for a quantized electromagnetic beam in a coherent
state, which leads to Poisson statistics for the intrinsic intensity of the
beam.
