High-energy electron radiography (HEER) has been proposed for time-resolved imaging of materials, high-energy density matter, and for inertial confinement fusion. The areal-density resolution, determined by the image intensity information is critical for these types of diagnostics. Preliminary experimental studies for different materials with the same thickness and the same areal-density target have been imaged and analyzed. Although there are some discrepancies between experimental and theory analysis, the results show that the density distribution can indeed be attained from HEER. The reason for the discrepancies has been investigated and indicates the importance of the uniformity in the transverse distribution beam illuminating the target. Furthermore, the method for generating a uniform transverse distribution beam using octupole magnets was studied and verified by simulations. The simulations also confirm that the octupole field does not affect the angle-position correlation in the center part beam, a critical requirement for the imaging lens. A more practical method for HEER using collimators and octupoles for generating more uniform beams is also described. Detailed experimental results and simulation studies are presented in this paper.