Representation of a wave field in a randomly inhomogeneous medium in the form of the double-weighted Fourier transform

New integral representation of a wave field in a continuously inhomogeneous random medium is suggested in the form of double-weighted Fourier transfor mation, performed simultaneously with respect to coordinates of the source and the observer. The integral representation under consideration takes int o account both the diffraction effects and the multiray effects. It incorpo rates many results of known techniques of wave propagation description in c ontinuously 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 ionosp here plasma from radio-sounding data and can serve as the basis for diffrac tion tomography of the ionosphere.