This thesis details work in developing an optimised model for the energy calibration of a Medipix All Resolution System (MARS) multi-energy computed tomography (spectral CT) scanner. The main motivation behind this research came from an unpublished internal document titled \Using Beer's law in MARS scanners" which challenged the current image reconstruction process. The document required an accurate per-pixel understanding of each of the components of the MARS scanner. The objective of my research was to work as part of the "foil group" to optimise the per-pixel energy calibration technique of the MARS multi-energy scanner using the x-ray fluorescence (XRF) technique originally worked on by Raj Kumar Panta (University of Otago). The emission of XRF is generated from the interaction between an x-ray beam and a high atomic number target. The main modification made to Panta's method in this research was to measure the XRF found outside of the primary x-ray beam. This modification aimed to increase the ratio of XRF to background photons remaining from the polychromatic x-ray beam. Initial testing of the method, however, did not consistently detect the XRF for the molybdenum and tantalum foils. Their XRF peaks were not well-defined and not consistent across the pixels. The lead XRF peak from the lead foil was clear and well-defined in each pixel. This led into an investigation for optimising the thickness of the foils used to ensure that maximum fluorescence is escaping the foil. Two stages of the model were developed: (1) assumes a monochromatic beam and calculates the optimum thickness based in the effective energy of the beam; and (2) assumes a polychromatic beam where the optimum foil thickness is calculated through numerical integration. The energy integrating model suggests a foil thickness of 50 &0x00B5;m for molybdenum, 100 &0x00B5;m for indium, and 210 m for lead. The results suggest that initial testing of the XRF method used sub-optimal foil thicknesses, explaining the low fluorescence signal. The optimal foil thickness model is being used to plan the next stage of experiments that the foil group will perform. The validity of the energy integrating model will be checked and the modified XRF technique described in this research will be automated so that minimal user intervention is required for performing the XRF energy calibration. The work in this thesis has contributed to two refereed publications. The improved energy calibration improves the image reconstruction and gives more accurate images, bringing the MARS team closer to their five-year visionary goal of extending the concept of multi-energy CT into human imaging.