Yanjun Fu

To address the problems of fringe compression in optical mirror measurement, this paper shows a method for phase measuring deflectometry of spiral fringes in polar coordinates. This method modulates the phase in 2 linearly independent directions in polar coordinates. Furthermore, spiral stripes have the unique property of spiral arms increasing with radius. It can solve the fringe compression problem at the convex mirror’s edge. Due to the periodicity of angles in polar coordinates, phase errors occur where the phase is zero. Therefore, this study studies a solution of extracting the wrapped phase boundary instead of the absolute phase boundary and dealing with the phase error points, effectively solving this problem. When the tangential and radial gradient data of the surface under test were obtained, we used an accurate calculation for Zernike polynomial surface reconstruction in polar coordinates. That algorithm no longer uses the traditional Cartesian pixel arrangement to obtain the sampling points, but reconstructs the horizontal and vertical pixels. The polar pixel matrix is used to obtain the fan pixel arrangement. On that basis, the geometric and numerical errors of traditional pixel arrangements can be avoided using Zernike polynomial surface reconstruction in polar coordinates. The experimental results demonstrate that the proposed method can improve measurement accuracy.

In traditional calibration methods for line-structured light vision sensors, the use of two-dimensional planar targets usually requires multiple placements of the target in the measurement space to capture more images to improve the final calibration accuracy, which complicates the calibration process. We propose a new calibration method for line structured light vision sensors (LSLVS) based on freely placeable circular targets. The circular target only needs to be placed freely twice, and the camera captures the images of the circular target and the optical strip. Based on the geometrical relationship of the circle under the camera projection and the nature of the vanishing line, the target plane is first reconstructed, and then multiple three-dimensional points on the target plane are obtained according to the perspective projection relationship, and finally the reconstruction of the optical plane is completed. Compared with the traditional calibration method, this method can be applied to measurements in a limited space, and it does not need sophisticated auxiliary equipment to control the target motion during the whole calibration process, which makes the calibration process more simplified. The final experimental results show that the method can reach an accuracy of 0.0523 mm when only two images are used and can be effectively applied to the line structured light measurement system.

In the existing binocular fringe projection methods, the continuous phase is commonly employed for performing 3D scene reconstruction. However, this method has phase ambiguity issues that require the addition of patterns or the utilization of embedded signals to be solved. However, this approach not only leads to the introduction of cumbersome steps but also fails to accurately reconstruct objects without obvious features. To effectively overcome these challenges, an active stereo 3D measurement method was proposed that eliminated the need for phase unwrapping. More specifically, the proposed method first applied binary processing to the wrapped phase map, followed by extracting phase order lines, and assigning symbolic labels to the phase intervals between them, accomplishing thus rough matching. Finally, based on the region block matching, the phase values were used to refine the disparity map. The proposed method was evaluated using a standard sphere with a diameter of 60 mm, and the root-mean-square error of the proposed method is 0.053 mm.