[en] In this paper it is shown that is is possible to use intensity measurements taken in a series of planes perpendicular to some axis to produce full four-dimensional information about the cross spectral density function. This measurement of the intensity in any given plane gives a series of slices thorough the four-dimensional Fourier transform of the Brightness function. For a coherent field, this information also enables us to calculate the phase and amplitude of the electric field in any given plane. If a finite measurement range is taken, the resolution of the reconstructed field is degraded, but in the limit of measurements taken over an infinite range, the full Fresnel field can be calculated. When considering the practical application of this technique to real data, the delta function definition needs to be redefined in terms of a 'top-hat' function. This does not alter any of the central conclusions obtained using delta functions, but enables the production of an algorithm for the reconstruction of the electric field from real intensity measurements. This was applied to a simulation of the simple case of a Gaussian beam. The reconstructed phase and amplitude of the electric field so obtained were in good agreement with assumed values. 14 refs., 5 figs