Phase-Shifted Quasi-Elliptical Fringe Patterns for Underwater 3-D Imaging

The development of robust fringe patterns for an underwater imaging is challenging due to the unique physical properties of the underwater environment. A line in the image plane, when projected through a flat refractive interface, deforms which introduces errors in both calibration and reconstruction procedures. In this paper, we present a novel image formation model, based on the axial camera model, which utilizes phase shifted quasi-elliptical fringe patterns for the underwater imaging. When projected through flat refractive interfaces, deformed elliptical fringe patterns produce concentric cones of camera rays in the outmost medium, each uniquely identified by its radius encoded in the phase. Triangulation is then achieved by computing ray-cone intersections, with extraneous solutions filtered out since more than one viable solutions exist. The proposed quasi-elliptical fringe pattern was experimentally evaluated by imaging calibration objects and performing 3D reconstruction, wherein quantitative results demonstrate the feasibility of the proposed method.