Integrability-based Free-Form Mirror Design

A considerable issue in designing catadioptric imaging systems is what shape the component mirrors should be formed. In this paper, we propose a new algorithm for a catadioptric imaging system that satisfies the desired projection using a free-form mirror. A free-form mirror expressed as an assembly of gradients is a flexible surface representation that can form various shapes including non-smooth surfaces. We improve the shape reconstruction framework in the photometric stereo scheme to design free-form mirrors. An optimal mirror shape is formed to produce the desired projection under the integrability condition that requires it to be a consistent surface. We assume various catadioptric configurations, for which actual free-form mirrors are designed. The design experiments confirm that the resulting free-form mirrors can approximate the desired projections, including non-smooth ones.