We establish the groundwork for a phase theory applicable to multiple aperture systems. To do this, we define ideal behavior as the phase behavior of an off-axis piece of a system that has rotational symmetry. Then we examine the phase behavior of a more general system that has only a single plane of symmetry. This system represents a branch of a multiple aperture system. Comparison of the two systems leads to conditions for which the plane symmetric system has ideal behavior. As a result of this comparison, design rules that are commonly applied to multiple aperture systems appear naturally, including the well- known requirement that the exit pupil is a scaled copy of the entrance pupil. The phase theory that we present is cohesive, provides useful design guidelines, and can be considered an addition to wave aberration theory.