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Salient features of the theory and practice of radio interferometry are presented with special attention to assumptions and to the specifically two-dimensional aspects of the subject. The measurable quantity on an interferometer record is defined as complex visibility by generalization from an analogous quantity in optical interferometry. Subject to conditions on antenna size and symmetry, the observed complex visibility is equal to the normalized two-dimensional Fourier transform of the source distribution, with respect to certain variables S. and S, which are defined. This transform is in turn identically equal to the complex degree of coherence Â¿ between the field phasors at the points occupied by the interferometer elements. The correlation between the instantaneous fields, and that between the instantaneous intensities are less general parameters which are, however, deducible from Â¿. A theorem is proved according to which only certain discrete stations on a rectangular lattice need be occupied for full determination of a discrete source distribution. Procedures in interferometry are discussed in the light of this result and an optimum procedure is deduced. Current practice is considered over-conservative, e.g, independent data in the case of the sun are obtainable only at station spacings of about 100 wavelengths on the ground, a fact which has not hitherto been taken into account.