# Quantitative Optical Coherence Elastography for Robust Stiffness Assessment
## 5 Results
### qOCE Assessment of Stiffness on PDMS Samples with Different Thicknesses  
We further demonstrated qOCE assessment of stiffness on stiff and soft PDMS samples that had different thicknesses. The stiff sample was made with a 10:1 base-to-agent ratio, corresponding to a stiffness of approximately 2.6 MPa. The soft sample was made with a 20:1 base-to-agent ratio, corresponding to a stiffness of approximately 1.0 MPa. The thicknesses of stiff and soft phantoms were 6 mm (thick), 4 mm (medium) and 2 mm (thin). To acquire qOCE data, we translated the probe axially to compress the sample. Reaction force and depth resolved sample displacement were obtained at the end of the compression process. We then normalized the displacement (\(d(z)\)) with the reaction force (\(F\)), as shown in Equation (4). The resultant \(m_{qOCE}(z)\) curves for stiff and soft samples are shown in Figure 7a,b (dashed lines), respectively. Using the experimental data (\(m_{qOCE}(z)\)) and the analytical \(M_{R}(z)\) expressed in Equation (5), we were able to fit the linear model of Equation (6) to extract the elastic modulus. Notably, experimental data within a depth range of 0-330 \(\upmu\)m was used in the fitting. With the elastic modulus (\(E\)) extracted, we show the fitting results (\(M_{R}(z)/E\)) as solid lines in Figure 7a,b. The consistency between the experimental results and the fitted analytical function validates the effectiveness of the simplified material model for qOCE measurement within a limited depth range. The elastic moduli obtained from the stiff sample with large, medium and small thickness are shown in Figure 7c (green bars) in comparison with the value from literature (red bar). The elastic moduli obtained from the soft sample with large, medium and small thickness are shown in Figure 7d (green bars) in comparison with the value from literature (red bar). Figure 7c,d suggest that our method allows accurate stiffness assessment despite variations of sample thickness. Figure 6: _Cont._  
Figure 6: (**a**) elastic moduli obtained using \(m_{qOCE}(z)\) in consistent with the known material stiffness; (**b**) the relationship between apparent stress and apparent strain results in an overestimation of stiffness; (**c**) the relationship between reaction force and indenter displacement results in an underestimation of stiffness. Figure 7: (**a**) experimental results (\(m_{qOCE}(z)\)) from qOCE characterizations for stiff samples (\(E\) = 2.6 MPa) with different thicknesses, and curve fitting results; (**b**) experimental results (\(m_{qOCE}(z)\)) from qOCE characterizations for soft samples (\(E\) = 1.0 MPa) with different thicknesses, and curve fitting results; (**c**) elastic moduli obtained from the stiff sample with large, medium and small thickness (green bars) in comparison with the value from literature (red bar); (**d**) elastic moduli obtained from the soft sample with large, medium and small thickness (green bars) in comparison with the value from literature (red bar). As shown in Figure 7a,b, the displacement field extracted from qOCE measurement does not have a linear dependency on depth. In other words, the strain field extracted is not spatially uniform. This is partially due to OCT signal attenuation with depth. As the depth increases, the OCT signal becomes overwhelmed by noise and the Doppler phase shift extracted from OCT signal cannot provide effective motion tracking. Regardless of OCT signal characteristics, a non-uniform strain field is established within the sample because the sample is compressed by an indenter with a finite dimension. The strain field is also affected by the geometry of the sample, which can be observed in Figure 7b. Moreover, the spatial variation of displacement/strain also depends on the mechanical properties (Figure 7a versus Figure 7b).