The application of the double weighted Fourier transform (DWFT) method is suggested for extracting the linear integral of the electron density in the inhomogeneous plasma from microwave or IR sounding data. The virtue of DWFT is its ability to localize the measured linear integral in the area, narrow as compared with the radius of the Fresnel zone, that is to realize super-Fresnel resolution. The advantages of the DWFT method are illustrated, firstly, by numerical simulation of a wave propagation through the Gaussian inhomogeneity in conditions of weak scattering, when a small angle Born approximation is applicable, and secondly, by theoretical estimates of resolution in conditions of strong scattering. The method under discussion promises to be helpful for studying the fine structure of turbulent plasma.