In this thesis, the Omega-k algorithm used for processing stripmap synthetic aperture radar (SAR) data is explored in detail. While the original Omega-k algorithm does not achieve the same SNR as a matched filter, a modification is presented which enables the algorithm to nearly achieve that SNR. It is shown that the focused point spread function obtained when the Omega-k algorithm is used differs in important ways from the output of a modified version of the matched filter. Spread out sidelobes and a stretched mainlobe are observed when the data is processed by the Omega-k algorithm. These differences may increase the potential interference between some nearby scatterers; however, the amplitude of the resulting sidelobes is lower than that observed for the matched filter, and the potential interference between other nearby scatterers is reduced. The details of a discrete implementation of the algorithm are also presented. Two methods for mixing the frequency domain signal to baseband are compared, and one is shown to potentially reduce the required accuracy of the interpolation kernel. Finally, the errors associated with the key approximation used by the algorithm are explored through simulation, and it is shown that the approximation is sufficiently accurate for a particularly demanding configuration.