Clear imaging specular surface and fringe patterns by using a concave mirror in phase measuring deflectometry

Phase measuring deflectometry (PMD) has been widely used to measure three-dimensional (3D) shape of specular objects because of its advantages of non-contact, large dynamic range, high-precision and fast-acquisition. However, due to the limited depth of field (DOF) of a camera lens, a liquid crystal display (LCD) screen and a tested specular object cannot be clearly imaged together, which affects the measurement accuracy. To tackle this issue, this paper proposes a novel PMD method of auxiliary imaging LCD screen by using a concave mirror. The LCD screen and a reference are in the same plane via the center of the concave mirror, and are perpendicular to the optical axis of the mirror. Both the LCD screen and the reference are symmetric each other through the optical axis, so that the imaging of one is the location of the other. Based on the imaging principle of concave mirror, the LCD screen is reflected and an inverted real image of the equal size is formed at the reference, and then reflected into the camera by the reference mirror during calibration. During the measuring procedure, a tested specular object is placed at the position of the reference. The displayed fringe patterns on the LCD screen are modulated by the tested specular object and the deformed fringes are captured by the camera. After phase calculation from the captured fringe patterns, 3D shape of the tested specular object can be obtained. The proposed PMD method can avoid the limited DOF of the camera lens, because fringe patterns displayed on the LCD screen and the tested specular surface can be clearly imaged together at the same position. Some simulated experiments on measuring specular objects have been carried out and the results demonstrate that the proposed PMD method can effectively and accurately measure 3D shape of specular surfaces.