An apparatus and methods for small-angle electron beam scattering measurements in a reflection or a backscattering mode are provided. The apparatus includes an electron source, electron collimation optics before a sample, electron projection optics after the sample, a sample stage capable of holding the sample, and a electron detector module. The electrons emitted from the source are collimated and positioned to impinge nanostructures on the sample. The signals resulting from the interactions between the impinging electrons and the nanostructures are further magnified by the electron projection optics to reach a sufficient angular resolution before recorded by the electron detector module.