Double-mirror catadioptric sensors with ultrawide field of view and no distortion

Abstract

We compute a family of double-mirror catadioptric sensors with ultrawide field of view and no distortion. The two concentric mirrors are rotationally symmetric, and the inside mirror is a revolved conic section. The mapping between the object and the image planes was linear, hence the lack of distortion. The equations describing the outer mirror were determined by the projection induced by the inside mirror and the rectifying property of the sensor. Solving the resulting nonlinear ordinary differential equations yielded the cross section of the secondary mirror. The sensors we present require no further digital processing.