We report a small-angle neutron scattering (SANS) study of the cross-section structure of polymer-like lecithin reverse micelles in deuterated cyclohexane. We demonstrate that the application of the indirect Fourier transformation and square-root deconvolution methods to data from SANS measurements with cylindrical polymer-like micelles allows for a direct verification of the previously postulated geometrical model of flexible tubular structures with a well defined water core and a surfactant shell. By combining contrast variation experiments and data analysis performed on an absolute scale, we quantitatively deduce information on properties such as the extension of the aqueous core and the degree of water penetration into the headgroup and solvent penetration into the tail region.