Phase unwrapping is the key problem in building the elevation map of a scene from interferometric synthetic aperture radar (SAR) system data. Phase unwrapping consists in the reconstruction of the phase difference of the radiation received by two SAR systems as a function of the azimuth and slant range coordinates. The data available to reconstruct the phase difference are a measure of the difference module 2/spl pi/. The authors propose a phase unwrapping method that makes use of the equivalent, in a discrete space, of the irrotational property of a gradient vector field. This property is used first to locate the areas where the discrete vector field estimated from the available data must be corrected, and then, with the knowledge of some a priori information, to perform the correction needed to obtain a useful estimate of the discrete gradient of the phase difference function, from which the phase difference function is reconstructed. The use of the fast Fourier transform makes it possible to have a fast algorithm, that is to process an image of N pixel in O(NlogN) elementary operations. Tests of the method proposed here on real and simulated data are presented.