School of Science Department of Physics 57 Department of Physics Fourier Optics Supervisor: ALTMAN Michael Scott / PHYS Student: NGUYEN Xuan Tan / PHYS-IRE Course: UROP1100, Fall In earlier models of low energy electron microscopy (LEEM) image formation theory, the spread in the energy of the imaging electron beam was modelled as a Gaussian function to reflect the imperfect temporal coherence of electron sources in experiments. However, this simplification of the energy spread function may be unable to provide an accurate simulation of an image formed in LEEM, especially at the limits where effects caused by chromatic aberrations dominate those induced by wave aberrations. In this report, we will provide a method to calculate the image formed by a source of arbitrary energy spread function, based on the existing Gaussian model. Then, simulated images of the Gaussian spread and that of a cold field emission source are compared to examine the validity of the former one. The Geometry and Physics of Wrinkling Supervisor: ALTMAN Michael Scott / PHYS Student: FONG Ching / SSCI Course: UROP1000, Summer This article aims to study the effect on the geometry of uniaxial-constrained monolayer graphene when subjected to current flow upon a series of tabletop experiments. It is observed that the potential gradient of the graphene is non-uniform over the region where it is suspended. To explain this, we proposed the geometry is non-Euclidean over the region, and it is governed by both the uniaxial-constraint and minimization of the energy of the sp2 bonded carbon by the Keating model. In other words, by minimizing the energy functional, one may obtain the geometry of the suspended monolayer graphene via optimization methods.