Vision-ray-calibration-based monocular deflectometry with a curved screen as its display

Particularly for curved mirrors, nonplanar illumination with its shape matching the curved mirrors under test in phase measuring deflectometry (PMD) has the advantages of enlarging the measurement range, decreasing the depth range of the reflected virtual screen. In this paper, a monocular deflectometry with nonplanar illumination is proposed, which contains a camera and a curved screen. Firstly, a method of modelling the curved screen is introduced to obtain a high-accuracy model of the screen, making the transformation of the screen free from the displayed feature points. Then, in a system of monocular PMD, vision ray calibration (VRC) is used to calibrate the ray distributions in the PMD with two separate steps and an integrated step. Meanwhile, two models of the screen are introduced to the PMD. Finally, with the calibrated ray distributions and the law of reflection, the slope distributions of the specular surfaces under test (SUT) are obtained to integrally reconstruct the SUT. In simulated measurements, VRC-based mono PMDs with the two screen models are verified, respectively. In actual measurements, two specular balls with different radii and a flat mirror as SUTs are measured to verify the proposed methods. And the measurement results show high accuracy, repeatability, and stability.