The exploration of the structure, composition and bonding states at the nanoscale are key to the understanding of advanced materials. Transmission electron microscopes have been widely used to study materials under high spatial resolution, and when equipped with electron energy-loss spectrometers, can provide elemental composition and identify bonding states with atomic resolution. Currently, the attainable energy resolution is limited to values in the range of 0.2 - 0.5 eV by mainly two factors: the energy spread of the primary beam and the energy resolution of the spectrometer, with the beam energy spread typically being the greater limiting factor. As a result, the relatively wide zero-loss-peak (ZLP) buries many features of interest, including band-gaps, dielectric function maps, and phonons in the energy spectrum range below 1 eV. Thus, there is significant interest in improving the energy resolution into the 10 - 100 meV regime by reducing the energy spread of electron sources and thereby minimizing the ZLP. A reduction of the energy spread to less than 100 meV is also useful for improving the spatial resolution as a result of the simultaneous reduction in chromatic aberrations, in particular at lower primary energies. Electron Optica proposes to develop a novel monochromator that reduces the energy spread of commonly used electron sources into the 10-50 meV range. The design of the monochromator accommodates existing electron sources and is suitable for both transmission and scanning electron microscopes. The monochromator utilizes an electrostatic electron mirror combined with a beam separator and a knife- edge aperture. Electrons emitted by the source are deflected off the beam axis towards the mirror. The beam separator disperses the electrons by heavily bending the trajectory of the lower energy electrons. As the electrons proceed towards the mirror, the knife edge stops the higher or the lower energy tail of the energy distribution, pending on its position. After reflection in the mirror, the remaining energy tail is stopped on the same knife edge. Consequently, the electron beam that passes back into the column is characterized by a lower energy spread. The use of a knife edge as the energy selecting device is key: it makes for a more reliable aperture when compared to the narrow, often sub-micrometer slits needed in existing monochromators. Here, it is the optics, rather than the slit width, that sets the ultimate energy resolution. After the double pass through the monochromator, the energy dispersion introduced by the beam separator vanishes due to the symmetry in the design. The proposed research will focus on achieving the requisite reduction in energy spread while minimizing optical aberrations. A detailed electron-optical analysis of the key monochromator components, such as the beam separator, the mirror, and the gun, will be performed using state-of-the-art simulation software. All the proposed work will be carried out by Electron Optica, Inc. The goal of the phase I research is to design a monochromator that will be prototyped in phase II.