Objective Full-field thickness-direction strain measurement within a large deformation range is of significance for mechanical performance testing of materials. Based on a multispectral digital image correlation compact setup, we measure the full-field thickness-direction strain of transparent hyperelastic materials. By pre- fabricating two different fluorescent speckle patterns on the front and back surfaces of the transparent sample and combining them with an auxiliary prism and a single color camera assembly, synchronous observation of thickness deformation on one side of the sample is achieved by employing four virtual cameras. To accurately calculate thickness deformation, we firstly adopt refraction distortion correction based on Snell law and the positional relations of the four virtual cameras to reconstruct and unify the surface topography coordinates of the front and back surfaces of the sample. Furthermore, by utilizing the inverse distance weighting interpolation method, the frontal and back surface three-dimensional scattered data in a local coordinate system in any loading condition is interpolated to generate uniformly and symmetrically distributed interpolation points, establishing a one-to-one correspondence between points on the front and back surfaces. Finally, strain within the thickness is calculated point by point to determine the distribution of full-field thickness-direction deformation. This method is successfully applied to the large deformation stretching experiment of an upconversion fluorescence-responsive disulfide crosslinked polyurethane (DSPU) elastomer. Methods We research a single-camera multispectral digital image correlation system. First, as shown in Fig. 1(a), the object's image is projected onto the left and right sides of the sensor by adjusting the position and angle of the outer flat mirror. Different colored fluorescence speckle patterns are applied to the front and back surfaces of the transparent sample, and two corresponding color channels of the 3CCD camera are adopted to record the images of the two relative surfaces, thus achieving the operation of a four-virtual-camera stereo perspective imaging system. Then, we leverage the 3D-DIC algorithm to reconstruct the front and back surfaces of the 3D object. Furthermore, for the convenience of statistical and computational analysis of thickness information, as shown in Fig. 4, we transform the 3D data in the global coordinate system into a new local coordinate system. In the new coordinate system, to determine the one-to-one correspondence between the point cloud coordinates of the front and back surfaces, we employ a 3D discrete data interpolation method. During the interpolation, we adopt the same parameters to generate uniformly and symmetrically distributed interpolation points. By performing statistical analysis and calculations on all interpolation point coordinates, we obtain the full-field thickness-direction strain distribution of the material. Results and Discussions We characterize the uniform and non-uniform full-field thickness of transparent thin plates and semicylinders. The results show that the system has excellent accuracy, with a relative error of less than 1%. By carrying out uniaxial tensile experiments, we obtain the full-field thickness-direction strain distribution of an upconversion fluorescence-responsive DSPU elastomer and establish the corresponding strain variation trend at calculation points. The feasibility of a single-camera multispectral digital image correlation compact device for measuring full-field thickness-direction strain in transparent hyperelastic materials is verified. As shown in Fig. 8, the material's thickness undergoes a maximum variation of 62% before rupture, and throughout the process, the thickness-direction strain is uniformly distributed without distinct necking features. As shown in Fig. 9, the full-field thickness-direction strain curve displays nonlinearity, including an elastic stage and a hardening stage. In the elastic stage, the thickness-direction strain rapidly increases with the rising load, while in the hardening stage, when the load reaches a certain value, the material starts to harden, which results in lower growth of thickness-direction strain and ultimately failure. Conclusions We propose a single-camera multispectral three-dimensional digital image correlation measurement device, which features low cost, compact design, and easy implementation. The relative error in thickness measurement accuracy verification experiments is less than 1%. By conducting uniaxial tensile experiments, we obtain the full-field thickness-direction strain distribution characteristics of DSPU elastomers. Although local issues such as internal material defects and defocusing of back surface speckles lead to slight non-uniformity in the overall strain distribution, the proposed compact multispectral digital image correlation device overcomes the limitation of traditional 3D-DIC techniques that can only provide the deformation information of a single surface. Additionally, by combining fluorescent speckles and multispectral imaging technologies, low-cost and high-precision full-field thickness-direction deformation measurement is achieved to provide accurate and reliable thickness deformation information for transparent hyperelastic materials. Meanwhile, since the system utilizes a single camera and prism combination imaging, the spatial resolution of sampled images is somewhat reduced. Therefore, optical system improvements are required to enhance imaging resolution.
