High-accuracy cross-media 3D measurement based on a ray model with unknown refractive

In certain contexts, such as the conservation and restoration of relics, measurements must be carried out with the objects placed inside protective enclosures to ensure their preservation. This paper addresses the scenario in which an unknown refractive medium exists between the camera and the object under measurement and proposes a general-purpose calibration and reconstruction method. This method uses a ray model to directly determine height and lateral coordinates through phase information, achieving three-dimensional (3D) measurement without refraction errors. The method first establishes a mapping relationship between each pixel on the imaging plane and the emitted light rays then establishes a mapping between phase and height. Thus, when the phase is known, the height and lateral coordinates can be directly determined. To validate this method, we constructed a fringe projection profilometry (FPP) system using a glass box and a high-precision display calibration target. We performed 3D measurements on a standard plane and a regular sphere. The experimental results demonstrate the proposed technique's significant effectiveness and measurement accuracy.