Optical imaging for non-self-luminous objects surrounded by complex scattering environments is scientifically challenging and technologically important. We propose a non-invasive imaging method by externally sending the illuminating light through the scattering medium and by detecting and analyzing the speckle patterns. The imaging of the object is recovered by extending the application scope of the Fourier-domain shower-curtain effect. It is found that the imaging depth is substantially extended and that faster imaging restoration is realized with the improved illumination scheme assisted with optical lenses, hence making it possible to apply the non-invasive optical imaging technique for practical applications.