The results of an experimental study at the KISI-Kurchatov synchrotron source of a new phase-contrast imaging scheme for micro-objects using a nanofocusing compound refractive lens are presented. Visualization with submicron spatial resolution of a Fresnel zone plate, with the width of outer zones less than 0.5 µm, has been demonstrated. It was found that in the conducted experiments the main contribution to the instrumental function, which limits spatial resolution, is due to the vibrations of the optical scheme elements. The possibility of using the proposed scheme to determine the beam transverse size at the focus of the compound refractive lens, considering the instrumental function, is shown.