We use a scattering model for image formation to demonstrate how to simulate images formed by ring-shaped illumination. The description assumes weakly scattering samples, such as phase objects of broad interest in live cell imaging, which also makes no angular approximations and covers forward and backward scattering, single-angle and angle-averaged illumination, as well as monochromatic and broadband light. The numerical experiments reveal the image formation behavior that is consistent with recent experiments reported in the literature, which shows this model can be applied to different imaging systems that are based on ring-shaped illumination with good performance, by considering the incident as a plane wave incident originating at the ring aperture.