针对单相机难以用于全场变形测量以及多相机在全场变形测量中复杂性等问题，提出一种利用双平面镜辅助的双相机系统来实现全场变形测量的新方法。该方法基于相机标定的坐标变换方法，即通过双平面镜实现从真实相机坐标系到虚拟相机坐标系之间的转换，进而实现从实物到虚像之间的转换。将该方法用于空心六角铝棒的热变形测量中，并与ANSYS软件的仿真结果进行比较，结果表明，该方法不但可以实现对被测件的三维重建，而且可以实现全场的变形测量，相对误差仅为0.51%，满足精度要求、效果良好。

Results and Discussions With a hollow hexagonal aluminum bar as the research object, the proposed method is used to conduct 3D reconstruction and thermal deformation research (Fig. 4). In the 3D reconstruction experiment, the maximum reconstruction deviation between the reconstructed surface and the fitted surface is about 0.004 mm, and it is mainly concentrated in the splicing area, while the deviation in other areas is relatively stable. The stereo reconstruction angle also proves that the system has stable performance and high accuracy (Fig. 6). In the thermal deformation research experiment, the proposed method can be used to obtain the average height of the first and last frame images in the vertical direction of the B and C surfaces of the part, respectively (Table 1). It can be seen that the maximum change in the height of surface B of the part is 0.5467 mm, and that of surface C is 0.5589 mm (Fig. 7). Then, the height change of surface A of the part processed by the system are directly compared with that of surfaces B and C processed by the proposed method during the cooling process, and comparison is carried out every 30 frames from frame 0 to 1290. There are 44 frames of comparison images (Fig. 8). Finally, the finite element analysis software ANSYS is used to simulate the part, and the steady-state simulation is selected. The temperature of the part rises from 20 ℃ to 310 ℃ in simulation experiments. It can be seen that the maximum thermal deformation of the part in the vertical direction is 0.5500 mm, which indicates that the thermal deformation of the part along the z direction is 550.0 μM when the temperature difference is 290 ℃ [Fig. 9 (b)].

The application of digital image correlation (DIC) technology is very extensive, and the technology has high practical value in biotechnology, civil engineering, aerospace, medical application, and other fields. With the continuous advancement of related technologies, the demand for full-field deformation measurement and 3D shape reconstruction of objects has increased accordingly. This requires the DIC technology to not only have higher measurement accuracy but also be more economical and practical, so as to make itself be applied to more fields. In recent years, many scholars have done a lot of research on the full field strain and deformation measurement by DIC, and they have made many valuable research results. Among them, the multi-camera DIC system has been proven to have high measurement accuracy, and it is feasible to achieve full field or double surface deformation measurement. However, in actual use, the system takes a long time to be built and involves a complex operation and high economic costs, and there is interference between multiple cameras. The rotation of a single camera is used to realize the full field deformation measurement of the measured object under different load conditions. In other words, the camera is continuously moved to rotate around the same measured object, and it will shoot and record in multiple different positions, so as to finally cover all the required fields of view. The system has low cost, complex operation, and low accuracy. In view of the problem that a monocular camera is difficult to be used in full-field deformation measurement and the complexity of multiple cameras in full-field deformation measurement, a new method of full-field deformation measurement by using a double-sided mirror-assisted dual-camera system is proposed.

This research adopts a coordinate transformation method based on camera calibration. In other words, the transformation from the real camera coordinate system to the virtual camera coordinate system is realized through the double-sided mirror, and then the transformation from the real object to the virtual image is realized. It is assumed that the camera coordinate system of L coincides with the world coordinate system of the binocular DIC system (Fig. 3). Therefore, the conversion relationship between the world coordinate system of the virtual binocular DIC system and that of the real binocular DIC system is equivalent to the conversion relationship between the camera coordinate systems of L′ and L. First, it is necessary to find out the positional relationship between the coordinate system o_c-x_cy_cz_c and the O₁-X₁Y₁Z₁. The rotation and translation matrices between the camera coordinate system o_c-x_cy_cz_c and O₁-X₁Y₁Z₁ can be obtained through camera calibration. Then, an intermediate coordinate system is introduced, namely, the coordinate system O₂-X₂Y₂Z₂, which is a rotating coordinate system of O₁-X₁Y₁Z₁. According to the imaging law of the plane mirror and the nature of the Euler angle, the rotation and translation matrices from the coordinate system o_v-x_vy_vz_v to the coordinate system O₂-X₂Y₂Z₂ can be obtained, and then the rotation and translation matrices from the coordinate system o_v-x_vy_vz_v to the coordinate system O₁-X₁Y₁Z₁ can be obtained. Finally, the conversion relationship between the real camera coordinate system and the virtual camera coordinate system can be calculated by synthesizing the above results.

A new method of full field deformation measurement using a double-sided mirror-assisted binocular DIC system is proposed. With a hollow hexagonal aluminum bar as the measuring object, the thermal deformation results of three outer surfaces are measured during the cooling process from 310 ℃ to 20 ℃, and they are compared with the simulation results of the finite element software. The results show that the change curves of the three outer surfaces of the part along the height direction basically coincide with the simulation results, and the absolute error between the calculated average thermal deformation values of A, B, and C surfaces along the height direction of the part by using the proposed method and the simulation results is 2.8 μm. The relative error is only 0.51%. It can be seen that the proposed method not only overcomes the limitation that a monocular camera cannot realize full field measurement but also discards the complexity of a multi-camera DIC system.