Statistical properties of the field diffracted by an aperture with partially coherent illumination

The statistical properties of the electromagnetic field diffracted by a plane aperture illuminated by a fluctuating field have been studied in the Fresnel zone on the basis of the theory of partial coherence. The average power distribution and the amplitude and phase of the degree of coherence have been computed for several coherence lengths of the illuminating field ranging from 1/4 to 5 times the dimension of the aperture and for two geometries of the observation points. The obtained results indicate the limits of validity of the often assumed hypothesis of spatial stationarity and of the real Gaussian approximation for the degree of coherence of the diffracted field. It turns out also that the optimum position of a receiving phase-sensitive system placed in the field diffracted by an aperture may not be the focus of the aperture, since there the concentration of average power density is accompanied by a poor coherence of the field.