Correlations of light in the deep Fresnel region : an extended Van Cittert and Zernike theorem

We derive an extension of the Van Cittert and Zernike theorem (VCZT), which holds very near to planar quasihomogeneous radiation sources. This derivation is based on paraxial propagation of the Wigner distribution function of the scalar field. We identify a critical distance from the source. Below this distance (deep Fresnel region) the field autocorrelation function is invariant upon propagation and the propagated field contains information about the correlation properties of the radiation source. Beyond the critical distance, the classical VCZT theorem is found to hold and no information about the source correlation can be recovered. The transition between the two regimes is described analytically for a simple case