## 3 Experiments
### [PERSON] and [PERSON]'s Modulus Measurement of a Double-Layer Phantom  
A double-layered phantom was made by mixing 1 \(\upmu\)m and 0.5 mg/mL TiO\({}_{2}\) scatterer with 15-degree silica gel for the bottom layer and 0-degree silica gel for the top layer. The dimensions of the double-layer phantom were \(l_{x}\) = 4.20 mm, \(l_{y}\) = 4.00 mm and \(l_{z}\) = 1.90 mm. A compression experiment was conducted following the same procedure as the homogeneous phantom. The double-layer phantom was preloaded for 1.320 N, then compressed by 0.247 N as read from the force sensor. The phantom was scanned 4 mm along both the width and length directions, before and after deformation. A 3D and a 2D OCT image of the phantom are shown in Figure 5a, from which the interface of the two layers can be observed. The ROI is marked with a blue cube or rectangle, which is 99.3 \(\upmu\)m below the top surface of the phantom as shown in Figure 5 aii. The average of the correlation coefficient of the ROI was tested to be 0.581. The coordinate was built with the origin \(O\) at the bottom left corner of the ROI, and the three axes were along the three edges of the ROI as shown in Figure 5a. The number of computed points was \(M\) = 9 \(\times\) 9 \(\times\) 5 = 405. The step lengths were 17 voxels in the \(x\) and \(y\) directions, and 8 voxels in the \(z\)-direction. The computed dimensions were \(Lx\) = \(Ly\) = 2861.1 \(\upmu\)m and \(Lz\) = 397.2 \(\upmu\)m. The 3D displacements of the ROI with the defined coordinate system are shown in Figure 5b-d. The 2D images are the cross-sections along the dashed lines on the 3D images. The distributions of 3D strains are shown in Figure 6. From the 3D display of \(\varepsilon_{z}\) in Figure 6c, the interface of the two layers can be observed. Strain-gradients were then calculated to segment the two layers automatically. Based on the abrupt change of the strain-gradient, the interface can be determined, which is drawn with dashed lines in Figure 6 ci,cii. The strain-gradients of \(\varepsilon_{z}\) in the \(z\)-direction of the cross-section in Figure 6 ci,cii are plotted on their cross-sectional OCT images as shown in Figure 7. For accuracy of computation in the VFM, broken lines simulated the physical interface between two layers, the blue curves shown in Figure 7. Although the physical boundary is recognizable in the phantom, the interfaces of most biological tissues are invisible. Hence, the automatic estimation of the boundary is necessary. The location of the minimum of the strain-gradient is where the interface of the two layers, i.e., the purple dashed lines as shown in Figure 7a,b, shows a good agreement with the physical boundary. After the full-field strain \(\varepsilon\) of the double-layer phantom was obtained, the constitutive parameters were calculated by the VFM. Because the errors of \(\varepsilon_{x}\) are large on the left boundary as shown in Figure 6a, the values of the left two columns were dropped out during VFM calculation. Then \(Lx\) became: \(Lx\) = 2225.3 \(\upmu\)m. The number of computed points became \(M\) = (9 \(-\) 2) \(\times\) 9 \(\times\) 5 = 315 in the VFM. The boundary conditions were the same as that of the homogenous phantom test, where the displacements in the \(x\) and \(y\) directions on the top and bottom surfaces were approximated as zeros, considering the friction on the contact surfaces. The value of \(z_{t}\) = 496.5 \(\upmu\)m obtained from OCT imaging as shown in Figure 5 aii; \(z_{b}\) = \(z_{t}\)-\(l_{z}\) = \(-\)1404.0 \(\upmu\)m; \(T_{0}\) = \(-\)0.247 N/(4.20 \(\times\) 10\({}^{-3}\) m \(\times\) 4.00 \(\times\) 10\({}^{-3}\) m) = \(-\)14,702 Pa. The full-field strain \(\varepsilon\) and virtual strains \(\varepsilon^{\bullet(i)}\) were input to Equation (17).