Ray-tracing-based three-dimensional profilometry using fringe projection

A fringe projection system, in special application scenarios, is used for three-dimensional (3D) shape measurement through a transparent medium. The light refraction caused by the medium gives rise to erroneous 3D data in conventional fringe projection methods. In this work, we propose ray-tracing-based 3D profilometry using fringe projection. The method uses phase information for seeking the homologous points between camera images and projector images pixel by pixel. Equations of light rays emitted from each point pair are identified with the law of flat refraction. A midpoint of skew lines common perpendicular algorithm is developed for calculating the intersections of these equations, which are 3D shape data without refraction error. For validation, a fringe projection system through a transparent glass was set up and applied for 3D shape measurements. The results verify the effectiveness and accuracy of the proposed ray-tracing-based 3D profilometry.