Spherical, cylindrical, and lamellar microstructures were examined by (SANS) in the binary system water (D2O)/pentaethylene glycol mono-perdeutero-n-dodecyl ether (C(12)D(25)E(5)) and in the ternary system (D2O)/pentaethylene glycol mono-n-dodecyl ether (C(12)E(5))/perdeuterated n-octane (C8D18). A model-independent picture of the structures emerges from Fourier transformation of the measured SANS spectra. The data analysis makes no a priori assumptions about the type of structure. Rather, the pair distribution functions obtained are so unique that an unambiguous assignment of the local geometry is possible. The different structures for a given mixture are obtained by changing temperature. For water-rich samples the sequence of spherical, cylindrical, and planar structures is obtained with increasing temperature. For oil-rich samples the same sequence occurs as a function of decreasing temperature. As an important additional result, the scattering length density profile normal to the interface is obtained. The interfacial profile is found to be rather diffuse, apparently because of solvent penetration.