Segmented apertures are playing an increasingly important role in telescope and beam director design as aperture sizes increase an d as active optics are employed to overcome wavefront distortions due to atmospheric effects and to mirror and structural deformations. This paper provides a comprehensive look at the effects of phase errors and of the contributions of edges and gaps so as to provide guidance for controlling optical losses. In particular, while diffraction from the segments is smeared by turbulence with ground-based systems, it persists with space paths, and the resulting multiple images of a single source can be misinterpreted as dim objects. The effects have been modeled in the past, but finite numerical integration scales can confuse the issue by producing mathematical artifacts. Closed-form solutions have therefore been generated for particular cases to facilitate interpretation, and guidelines have been developed from them to assist prediction with more general situations.