Bi-prism-based single-bilateral-telecentric-camera stereo-DIC for accurate underwater 3D deformation measurement: Implementation of a parametric model

Full-field surface shape and deformation measurements of submerged objects using stereo-digital image correlation (stereo-DIC) remains challenging due to the light ray refraction occurred on the interface of two different transparent media (e.g., air, glass and water). In this work, we proposed an underwater full-field 3D deformation measurement method based on the bi-prism-based single-bilateral-telecentric-camera (SBTC) stereo-DIC, which adopts a parametric model to establish the mathematical relationship between the image points and their corresponding object points by taking the refraction into account in the ray-tracing process. The key parameters (e.g., bi-prism/glass orientation and position) of the parametric model were calibrated by a one-step calibration. To verify the correctness and effectiveness of the proposed method, translation tests with a rotated bi-prism and underwater translation tests were performed. Experimental results indicate that the proposed parametric model can effectively handle the imperfect system configuration and the unavoidable light ray refraction that occurred on the optical path, thus allowing high-accuracy underwater deformation measurement. Compared with the existing underwater deformation measurement approaches, the proposed method can not only deliver displacement measurement with higher accuracy, but also is free of any assumptions on the configuration of the camera system or the refractive interface.