Refractive fringe projection profilometry for three-dimensional shape measurement

Light emitted by an object placed in a transparent protective cover will change its original propagation direction before entering a fringe projection profilometry (FPP) system due to the influence of light refraction. This Letter proposes refractive FPP for accurate three-dimensional (3D) shape measurement. The method derives a coordinate mapping between a 3D measurement space and a 2D space formed by an incident ray, a normal of a refractive interface, and an emergent ray. Based on the coordinate mapping, the equation of the emergent ray in the 3D space can be directly determined with the equation of the incident ray and used for 3D measurement without refraction error. For validation, an FPP system through a planar glass was established and used for 3D shape measurements of a ring board, a regular sphere, and two objects with complex surfaces. Experimental results demonstrate the effectiveness and accuracy of the proposed refractive FPP.