Optical fringe-reflection deflectometry with bundle adjustment

Abstract

Liquid crystal display (LCD) screens are located outside of a camera's field of view in fringe-reflection deflectometry. Therefore, fringes that are displayed on LCD screens are obtained through specular reflection by a fixed camera. Thus, the pose calibration between the camera and LCD screen is one of the main challenges in fringe-reflection deflectometry. A markerless planar mirror is used to reflect the LCD screen more than three times, and the fringes are mapped into the fixed camera. The geometrical calibration can be accomplished by estimating the pose between the camera and the virtual image of fringes. Considering the relation between their pose, the incidence and reflection rays can be unified in the camera frame, and a forward triangulation intersection can be operated in the camera frame to measure three-dimensional (3D) coordinates of the specular surface. In the final optimization, constraint-bundle adjustment is operated to refine simultaneously the camera intrinsic parameters, including distortion coefficients, estimated geometrical pose between the LCD screen and camera, and 3D coordinates of the specular surface, with the help of the absolute phase collinear constraint. Simulation and experiment results demonstrate that the pose calibration with planar mirror reflection is simple and feasible, and the constraint-bundle adjustment can enhance the 3D coordinate measurement accuracy in fringe-reflection deflectometry.