New integral representation of a wave field in a continuously inhomogeneous random medium is suggested in the form of double-weighted Fourier transformation, performed simultaneously with respect to coordinates of the source and the observer. The integral representation under consideration takes into account both the diffraction effects and the multiray effects. It incorporates many results of known techniques of wave propagation description in continuously inhomogeneous media: the methods of geometrical optics, smooth perturbations, phase screen, and two-scale expansions. The method delivers new opportunities to retrieve small-scale inhomogeneous structure of ionosphere plasma from radio-sounding data and can serve as the basis for diffraction tomography of the ionosphere. ¿ 2000 American Geophysical Union