## 4 Discussion  
The 3D OCE method based on DVC and VFM has been developed in this study. Experimental results demonstrate that this method can obtain the 3D displacements, strains and constitutive parameters including Young's modulus and Poisson's ratio of layered materials. The Young's modulus of the homogenous phantom obtained by the DVC and VFM based 3D OCE method is \(\sim\)1% different from the value measured by a tensile test, which demonstrates the effectiveness of the new method. For the compressive loading experiments conducted in this paper, the theoretical strain distribution in the depth direction and the shear strains can be estimated. These distributions and analyses show the relative error is about 10%. Errors are also observable at the edges shown in Figure 4g-i. Reasons for the strain measurement errors include: (1) the influence of the glass window on the top of the specimen including the friction with the specimen and the slant compression; (2) the boundary effect of the polynomial fitting; (3) the influence of noise, which is unavoidable in laser interferometry. The measurement can be improved by improving the loading device, optimizing the virtual fields and applying data processing techniques to reduce noise. The Poisson's ratio can be easily calculated from the DVC results or by the VFM. The results obtained by the two methods are very close, which can be further verified by other experimental methods such as tensile testing. A complete friction boundary condition was employed at both the top and bottom surfaces. This is reasonable, because the maximum ratio of shear stress to compressive normal stress on the top surface of the phantom is \(\sim\)0.02 at the four corners, calculated by simulation. Generally, the static friction coefficient that is the ratio of the maximum static shear stress to normal stress between the glass and different rubbers is larger than 0.2 [28], which would be similar to the coefficient between the silica gel phantom and the glass. Because the shear stress is 10 times less than the maximum static shear stress, the complete friction boundary conditions can be applied in Equation (20). The OCT noise will affect the gray value of speckle images and then affect the accuracy of DVC and VFM. Above all, the OCT noise will affect the correlation coefficient in DVC. The correlation coefficient decreased from 0.8 to 0.6 with the depth increasing in the experiment of the homogeneous phantom. Because the scattering light intensity decreases with the increase of depth, the information of the sample is reduced dramatically. The OCT noise will cause the results of DVC to no longer be reliable in deep regions. Hence, only the shallow regions were used. Furthermore, the OCT noise can mask the gray value of speckle images. It will result in matching errors even in the samples without any motion or deformation as the stationary experiment showed that the sensitivities of our system were 0.05 voxels and 0.2% for displacement and strain measurement, respectively. If the matching errors exist, the strains inputted into the VFM will lead to errors in the calculation of the constitutive parameters. By combining noise resistant methods, such as the ZNSSD criterion [20], the local ternary quadratic polynomial fitting method, and the linear VFM method [23], the experimental results will be insensitive to noise. The 3D strain maps not only provide the necessary input, but also enable more automatic and accurate segmentation of the double-layer materials. This is important for the successful performance of the proposed VFM method. Although the interface was estimated as a series of broken lines, it is reliable because most of the purple dashed line is located at the blue curve in Figure 7b. The interface can also be described more accurately in the future work to improve the computing accuracy through finer meshing.