Digital image correlation (DIC) technology is a processing method commonly employed for image matching, and meanwhile after nearly forty years of development, its accuracy, efficiency, practicality, and other aspects have yielded significant improvement. With the development and progress of science and technology, DIC technology for three-dimensional (3D) measurement should also be economical and practical, with the utilization of relatively simple devices for a full range of functions. DIC measurement systems with the assistance of the camera and external equipment can also be realized with multiple viewpoints and multi-directional measurements, on which many scholars have carried out thorough research. Among them, the single camera system has a flexible field of view adjustment and simple optical path, but features poor stability and low accuracy. The multi-camera system requires the adoption of multiple cameras, and the calibration process is complicated. Although the multi-camera measurement system can improve the range and accuracy of 3D measurement, it is difficult to be widely leveraged in 3D full-field measurement due to the high requirements of environmental conditions and the expensive cameras. Given the shortcomings of the existing single-camera and multi-camera systems, we propose a dual-camera 3D reconstruction method assisted by a dual-plane mirror.

We put forward a visual 3D measurement method assisted by a dual-plane mirror, which is to analyze the virtual and real correspondences of the corner points in the mirror surface and thus obtain the reflection transformation matrix. Meanwhile, the virtual and real transformations of the object surface are completed by the reflection transformation matrix, and the 3D full-field measurements are realized finally. Additionally, this method avoids spraying diffuse spots on mirrors to take up the spatial resolution of the camera, making the solution of the reflection transformation matrix easy and efficient. Firstly, the image information of the front surface and the back side surface of the object is acquired simultaneously by the dual-camera DIC measurement system (Fig. 1). Secondly, the calibration plate is placed in front of the plane mirror, and the dual cameras can observe the real calibration plate and the virtual image in the mirror at the same time (Fig. 4). The midpoint method based on the common vertical line is adopted to determine the 3D coordinates of the corner points in space (Fig. 5), and the specific positions of the dual-plane mirrors are finally determined by changing the position of the calibration plate several times. Finally, the reflection transformation matrix is solved by the mirror position equation, and then the 3D reconstruction of the object is completed.

To verify the accuracy of the proposed method, we conduct static and dynamic experiments on the measured parts respectively. In the static experiments, the 3D contour of the game coin is reconstructed, and in the dynamic experiments, the thermal deformation of the five-side aluminum column is investigated (Fig. 6). By employing the proposed method, the dual-mirror equation and reflection transformation matrix can be obtained under the mirror angle of 108° (Table 1). The front and back contours of the ordinary game coin are reconstructed in three dimensions, the theoretical thickness of the game coin is 1.80 mm, and the measured thickness is around 1.75 mm (Fig. 9). The reconstruction method of spraying diffuse spots on the mirror surface is compared to verify the 3D reconstruction accuracy of the proposed method (Fig. 9), and the 3D reconstruction of the game coin by the proposed method is found to be better than that of spraying diffuse spots on the mirror surface. Meanwhile, the proposed method avoids taking up the spatial resolution of the camera by spraying diffuse spots on the mirror surface, with higher accuracy.

Aluminum column 3D reconstruction and thermal deformation measurement results are shown. Firstly, the reconstruction results of the surface profile of the five-side aluminum column are obtained by the proposed method (Fig. 10), the real height of the aluminum column is 70.00 mm±0.01 mm, and the average measurement height is 70.0035 mm, which is a sound measurement effect. Secondly, the average height change of the five outer surfaces of the aluminum column can be obtained during thermal deformation (Table 2). The thermal deformation displacement cloud map of the outer surfaces is shown in Fig. 11 and the height change of different surfaces in the cooling process is illustrated in Fig. 12. To more intuitively demonstrate the accuracy of the proposed method of real-virtual transformation, we compare and analyze the deviation values of the height change obtained by the two methods at each node (Fig. 13), which shows that the proposed method has higher measurement accuracy.

We propose a dual-plane-mirror assisted visual DIC 3D full-field measurement method. The static experiment results indicate that the proposed method is better than the reconstruction method of spraying diffuse spots on mirrors for the 3D reconstruction of game coins with higher accuracy. The results of dynamic thermal deformation experiments indicate that when the temperature of the five-side aluminum column is reduced from 330 to 20 ℃, the height change of the outer surfaces of the column is basically consistent with the simulation results of the finite element software, and the deviation values of the height change measured by the proposed method are smaller than those of the method of spraying diffuse spots on mirrors. Since the proposed method can avoid spraying diffuse spots on mirrors to take up the spatial resolution of the camera, it features simple operation, high measurement accuracy, and sound application perspectives.