Reflective imaging systems are typically limited to small field angles in order to avoid overly large obscurations or off-axis aberrations. Reflective optics are often preferred in astronomy due to the associated lower weight and cost, as well as the absence of chromatic aberrations. Although these advantages are compelling, off-axis aberrations typically limit the field of view to a few degrees, while many imaging applications require a considerably larger useful field of view. A hybrid optical-digital design could alleviate the issues associated with wide-field reflective optics by exploiting the larger design freedom inherent in such systems. In this paper we demonstrate how a holistic design approach can enable reflective imaging systems with a consistently sharp image across a wide field of view.