Single-viewpoint, catadioptric cone mirror omnidirectional imaging theory and analysis

Abstract

A family of catadioptric imaging systems has been developed that can achieve omnidirectional viewing with a single planar imager while still being able to recover perspective images, provided that they satisfy the single-viewpoint (SVP) constraint. It has been shown that the only mirror shapes that can have SVP when paired with a sole focusing planar imager camera are the surfaces of revolution of conic section curves. However, the special case of such a surface, the cone-shaped mirror itself, has not been deemed a viable SVP mirror shape. We present a comprehensive imaging theory of the cone mirror in its SVP configuration. We show that the SVP, cone mirror catadioptric system not only is practical but also has unique advantages for certain applications. The detailed theory explains why and how a practical SVP cone configuration can be set up, the merits and weaknesses of such systems, and how one can remedy the weaknesses to create a workable imaging system. We also derive the tolerance formula for estimating effects of alignment errors. A prototype has been constructed, and experimental results validate our theory.