Proposed high energy electron-positron linear colliders require a high ux of positrons. To achieve this a number of new positron source designs have been proposed. One of these is an undulator-based positron source, which is the baseline positron source design for the International Linear Collider. The undulator-based positron source for the International Linear Collider uses a helical undulator to produce a intense photon beam that generates positrons through the pairproduction mechanism. As a helical undulator is used the photon beam is polarised and this results in polarised positrons being produced. This thesis investigates the undulator-based positron source design and aims to optimise it for positron production at the International Linear Collider. To do this the undulator is studied in detail as there is a large scope to design a bespoke undulator for positron production. As the particle physics community is interested in having a high positron polarisation the undulatorbased positron source needs to be optimised for yield and polarisation. In order to optimise the design of the helical undulator we derive an analytical equation for the radiation produced by a helical undulator. This is done to provide some understanding of how the dierent undulator parameters aect the photon spectrum produced by a helical undulator. In addition to the analytical equation, new software is used to calculate the photon spectra produced by non-ideal undulators in order to evaluate how a realistic undulator-based positron source would function. Using suggestions proposed in this thesis we could expect to see an increase in positron yield of of 10:9% and an increase in positron polarisation from 21:93% to 41:93 %.