Focus in Catadioptric Imaging Systems

Catadioptric imaging systems consisting of conventional lens based cameras and mirrors are widely used in many vision applications. Most of the prior work in this area has focused either on aspects of mirror design or the application it is being used for. In contrast, little attention has been paid to the aspect of sharp image formation. In this paper we study how reflections in curved mirrors affect image formation from the perspective of lens focus. In particular we answer the question "How and where must the lens focus when imaging reflections in curved mirrors?". Using caustics to model the reflections, we show that the space of infinite scene depth is compressed within a finite volume which we call the "caustic volume". Analysis of the caustic volume is presented for common catadioptric systems. We also present a framework to derive the "optimal" focal plane at which to focus the lens for sharp image formation along with experimental verification.