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The van Cittert-Zernike theorem shows that the observation data collected by interferometers, i.e., visibilities, matches Fourier transform of the source in the sky. In theory, this means an image of the source can be revealed by applying an inverse Fourier transform to visibilities collected in an observation by an astronomical interferometer, such as a radio interferometer. In practice, accommodation must be made for noise and for less-than-ideal sampling, and the image is reconstructed using something more than mere application of the Fourier transform formula or the fast Fourier transform. The CLEAN algorithm and similar procedures are among those used for this.
The theorem was derived for an ideal: the signal (e.g., visible light or radio) is coherent, and all from the same distance, i.e., from a source or sources within a plane. Given the distance to astronomical objects, their signal is close enough to this criteria that it is practical to presume it meets the criteria.