Fringe projection profilometry is generally used to measure the 3D shape of an object. In oblique-angle projection, the grating fringe cycle is broadened on the reference surface. A well-fitted, convenient, and quick cycle correction method is proposed in this study. Based on the proposed method, an accurate four-step phase shift method is developed. Comparative experiments show that the fringe projection profilometry based on the novel phase shift method can eliminate cycle error and significantly improve measurement accuracy. The relative error of the measurement is less than 1.5%. This method can be widely employed for measuring large objects.

As the number of codewords adopted in phase-coding fringes increases, the solution of fringe orders leads to many mistakes. Consequently, errors of the unwrapped phase occur. Thus, increasing the codeword approach in a phase-coding fringe remains a challenge. In this paper, a modified stair phase-coding fringe is designed, and a new phase unwrapping algorithm based on shifting fringe order is presented. The main idea of this method is that the width ratio between the sinusoidal fringe and each stair phase of phase-coding fringe is set to 1: n. The fringe order retrieved from the phase-coding fringe can be multiplied by the shift itself, thereby assisting phase unwrapping. This method adopts fewer codewords to replace the usual large number. As such, the approach gains two merits. One is that it guarantees a high measurement accuracy. The other is that it allows the measurement of isolated objects with complicated shapes. The experiments demonstrate that the proposed method is simple but effective.

In panoramic three-dimensional (3D) shape measurement based on a turntable, the point cloud registration accuracy is greatly affected by the calibration of the rotating axis. To improve the calibration accuracy of the rotating axis, a calibration method based on an auxiliary camera is proposed. The calibration procedure uses a checkerboard and an auxiliary camera. Firstly, the checkerboard is rotated on the turntable to determine the rotation axis, and is used to calibrate the relative orientation of the auxiliary camera and the measurement camera, so that the two cameras have the same world coordinate system. Then, the origin point of the coordinate of the rotation axis is obtained by the auxiliary camera, and the Z -axis direction is taken as the direction of the rotation axis. Finally, the 3D shape of the multi-view is measured by the fringe projection system, and the rotation registration is completed according to the rotation axis vector. The proposed method does not need to reconstruct the 3D coordinates of multiple points when the rotating axis is calibrated. The experimental results show that the proposed method effectively improves the calibration accuracy of the rotation axis vector, and reduces the complexity of the calibration process.

Phase measuring deflectometry (PMD) is widely used to measure the surface of specular objects. The planar screen used in traditional PMD systems have the drawbacks of a small field of view of measurement and a large virtual image depth range. This problem can be effectively solved by using the curved screen. As the arc structure of the curved screen is different to the planar structure required in Zhang’s method, the existing methods mainly rely on the stereo vision of two cameras to obtain the screen position. This paper presents a novel PMD based on a curved screen and single camera. A method of calibrating a curved screen by constructing a virtual planar screen is presented. The method only needs one camera to calibrate the curved screen directly with high accuracy. In addition, the change from planar screen to curved screen makes the traditional phase-gradient-height relation invalid. Based on the comprehensive analysis of space optical path models, a novel phase-gradient-height relation is presented. The relation is a general formula. It can be used for any curved screen, including the planar screen. Simulation and quantitative comparison experiments verify the accuracy and reliability of the proposed calibration method. The measurement results of concave mirror show that the proposed method has higher accuracy and a larger field of view in measuring specular objects than traditional methods.