For certain Fourier-based Synthetic Aperture imaging methods, spherical waves need to be approximated by composing several planar-wave-segments. In this work we propose a new conic segmentation method (CSM) in contrast to the rectangular segmentation method (RSM) found in the literature. We compared CSM and RSM by convergence studies of image quality using the structural similarity index on imaging results of synthetic data, runtime measurements of C++ implementations, as well as theoretical analysis regarding time complexity, phase continuity and phase errors. It can be shown that CSM has an inferior runtime scaling behavior compared to RSM. The convergence studies, however, show faster image quality convergence of CSM with respect to the number of segments. Hence, the runtime overhead of CSM can be compensated, since fewer segments are necessary to achieve sufficient image quality. Moreover it can be shown that CSM introduces less phase errors in the near field of the transmitters and avoids discontinuity artifacts as opposed to RSM. Therefore, CSM is a simple technique to avoid discontinuity artifacts and near-field distortions, while having no effective runtime overhead.