## 3 Experiments  
### [PERSON]'s Modulus Measurement of a Homogeneous Phantom  
3D displacements and strains of a phantom under compression were measured by the DVC-based 3D OCE technique. A homogenous phantom was made by mixing food-grade translucent 45-degree silica gel and titanium dioxide (TiO\({}_{2}\)) scatterer with a diameter of 1 \(\upmu\)m and density of 0.5 mg/mL. The phantom was cut into a \(l_{x}=4.24\) mm, \(l_{y}=4.24\) mm and \(l_{z}=11.60\) mm cube shown as Figure 3a and was set on the surface of the force sensor of the loading device shown in Figures 1a and 3b. The phantom was preloaded for about 5 min until the reading of the force sensor became stable at 1.072 N. Then, the first 3D OCT image was taken as shown in Figure 3d. The phantom was compressed by 0.046 N immediately after the first image was taken, and the second 3D OCT was taken. This procedure took less than 1 s, thus, tissue relaxation was neglected. The phantom was compressed for \(-41.0\)\(\upmu\)m reading from the translation of the optical window. The phantom was scanned 4 mm in both the width and length directions. The ROI was marked out with a blue cube shown in Figure 3d. It is 64.7 \(\upmu\)m below the top surface of the phantom as shown in Figure 3c. 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 3d. The number of DVC computed points was \(M=9\times 9\times 5=405\). The step lengths in the \(x,y\) and \(z\) directions were 17 voxels. By calibration, the dimensions of the ROI were \(Lx=Ly=2861.1\)\(\upmu\)m, and \(Lz=844.1\)\(\upmu\)m. The average of the correlation coefficient of the ROI was tested to be 0.659. Figure 2: A flow chart of the layered VFM. All components of displacements and strains obtained by the DVC are shown in Figure 4. It can be seen from Figure 4c that the value of displacement in the \(z\)-direction decreases from the top to the bottom, which corresponds to theory. The mean value of the displacement on the top surface is \(-42.7\)\(\upmu\)m. So, the relative error for the \(z\)-direction displacement measurement is \(4.1\%\) compared with the imposed displacement of \(-41.0\)\(\upmu\)m. The displacements in the \(x\) and \(y\) directions shown in Figure 4a,b change diagonally, probably because the sample was slightly tilted and the OCT scanning direction was not strictly parallel with the edge of the sample. Each of the strains shown in Figure 4d-i is supposed to be a constant, and therefore the variations of the results demonstrate measurement errors. Figure 4f shows that the values are fairly constant except a thin top layer. The bigger values on the top portion, are possibly induced by the friction between the glass window and the top surface of the sample. The mean value of the \(\varepsilon_{z}\) of the whole ROI is \(-0.39\%\) as shown in Figure 4f. While the applied strain is \(-41.0\)\(\upmu\)m/\(11.60\) mm \(=-0.35\%\), thus the relative measurement error is \(11.4\%\). If the top portion with bigger values is excluded, the relative measurement error becomes \(5.7\%\). The measurement error for shear strains shown in Figure 4g-i is within \(0.2\%\). Figure 4: 3D deformation measurement of the homogeneous phantom. (**a**–**c**) 3D displacements in the \(x\), \(y\) and \(z\) directions respectively; (**d**–**f**) 3D normal strains in the \(x\), \(y\) and \(z\) directions respectively; (**g**–**i**) 3D shear strains. Figure 3: A sample of homogeneous phantom. (**a**) A photo of the phantom; (**b**) a photo of the phantom under compression; (**c**) a 2D OCT image of the phantom, where the ROI is marked with a blue rectangle; (**d**) a 3D OCT image of the phantom, where the ROI is marked with a blue cube. The full-field strain \(\varepsilon\) obtained in Figure 4d-i and virtual strains \(\varepsilon^{*(i)}\) were then utilized to form the coefficient matrix \(\mathbf{A}\) of VFM in Equation (11).