UROP Proceedings 2020-21

School of Science Department of Physics 66 Department of Physics Fourier Optics Supervisor: ALTMAN Michael Scott / PHYS Student: LO Tsz Yu / PHYS Course: UROP1100, Fall The aim of the project is to study the relationship between the feature of the image and the object under different setting of the Low Energy Electron Microscope (LEEM). This is meaningful as knowing those relationship can help us to have better observation when using the LEEM. In this project, the Fourier Optics approach is used for the calculation of image formation. The image of an amplitude object, step phase objects and sinusoidal phase objects are calculated using different setting of the LEEM, such as aperture diameter and defocus. The image resolution is first evaluated as a function of the contrast aperture for a phase object. Those calculation showed that there is an optimum aperture such that the resolution is minimized. The contrast produced by the sinusoidal phase object also depends on the aperture size, but is independent of aperture size if it exceeds the optimum size. The result also showed that the having a little defocus can also help better observation. Fourier Optics Supervisor: ALTMAN Michael Scott / PHYS Student: LO Tsz Yu / PHYS Course: UROP2100, Spring A program for simulating images of two-dimensional objects in low energy electron microscopy was implemented. The comparison of images of amplitude and phase objects simulated by this program to results published in reference indicated that the simulation program is working properly. We then used the program to simulate circular and square objects with sizes below and slightly above the instrumental resolution. We found that intensity line scans through the objects in the simulated images may have one or two intensity peaks depending upon their size and the defocus value. These observations may be used to determine the sizes and possibly the shapes of objects below the instrumental resolution. Fourier Optics Supervisor: ALTMAN Michael Scott / PHYS Student: NGUYEN Xuan Tan / SSCI Course: UROP1000, Summer The current model of Fourier optics used in low energy electron microscopy (LEEM) was successful in predicting image formation with high accuracy. However, there are certain assumptions that limit its scope of application to electron sources of high temporal and spatial coherence with Gaussian energy distribution. This report provides a generalisation to spatially and temporally more extended sources by taking into account second-order Taylor expansion of the phase shift caused by source extension. The energy distribution is generalised by a combination of N Gaussian sources, which can be utilised to fit a generic energy distribution. A comparison is made to examine the validity of the current Fourier optics model for the Fowler-Nordheim energy distribution.