## 3 Results and Discussions
Figure 7 gives the measurements of phase response for two different incident angles in the large flow cell. The tested concentration of SW is 0.625 wt. %. The values of the phase difference \(\Delta\phi\) between DI and SW periods are 25 (degrees) and 35 (degrees) for the incident angles \(\theta_{i}\) 45\({}^{\circ}\) and 50\({}^{\circ}\), respectively. The trends of phase variation increased as well, as did the incident angle, similar to the simulations shown in Figure 3. The volume of the large cell requires a longer exchange time between the DI and SW liquids; the rise and fall periods also need more time to switch completely. The phase curves of the large cell are rough and include more phase tails during the exchange of liquids. To solve these issues, the smaller flow cell (Figure 6b) was adopted for comparing the phase response curves between the two flow cells. At the same flow rate of 30 sccm (mL/min) and the incident angle of 45\({}^{\circ}\), the phase curve of the small cell during the liquid exchanged is shown in Figure 8. The phase difference \(\Delta\phi\) between DI and SW is around 24.5 (degrees), which approaches the results of the large cell (Figure 7a). The phase curve is smoother with a near step change. In principle, the phase  
Figure 6: Geometrical sizes of the FBSs: (**a**) large cell and (**b**) small cell. Figure 7: Measurements of phase response for different incident angles in the large flow cell: (**a**) 45\({}^{\circ}\) and (**b**) 50\({}^{\circ}\). variations are possibly increased by increasing the incident angles over 45\({}^{\circ}\). However, the connection ports in the small cell will limit the higher incident angles. To maintain the measurement repeatability, the incident angle of 45\({}^{\circ}\) is used for the following experiments. In the optical fluidic instrument, the probe light passes through the liquids in the flow cell. Since the diameters of the inlet and outlet ports are smaller than the cover area of the flow cell. The flow speeds suddenly change between the connection pipe lines and the flow cell will cause turbulent flow [26]. The turbulent flow makes the injection liquids spend more time in the dead volume of flow cell. It will cause the incomplete exchange between two different concentrations of injection liquids. According to the phase curves shown in Figures 7 and 8, the dead-volume effects of the large cell (Figure 7) are obvious in comparison with the small cell (Figure 8). To calculate the mean values and RMSEs for the different concentrations, the measured phase variations in the central measurement period of 25 s (50 data points) are taken for the SW and HCL solutions. Figure 9a shows the list of the five concentrations of SW: e.g., 0 wt. %, 0.625 wt. %, 1.25 wt. %, 2.5 wt. %, and 5 wt. %. The mean phase change versus the concentration is a quasi-linear curve, as shown in Figure 9b. The summarized table of the mean values and RMSEs is shown in the inset. The phase variation is 135 (degrees) for the 5 wt. % change of concentration. The sensitivity of the concentration measurement is represented by the ratio of the phase difference versus the concentration change. Therefore, the sensitivity is around 2.7 \(\times\) 10\({}^{3}\) (deg./wt. %). According to Figure 9c, the liquid switching time is around 15 s to achieve a stable phase change. By considering the stable phase period as shown in Figure 9d, the best phase stability of 0.25 (degrees) is achievable. The corresponding measurement resolution is defined by the ratio of the measurement phase stability versus sensitivity. Thus, the measurement resolution of 0.0092 wt. % is achievable according to the experimental data. After the optimizations of cell size, focal position and incident angle in the SW concentration measurements, the liquid solution was further replaced by the HCL. Therein, a quasi-linear relationship between the RI and concentration within 40 wt. % was available, as provided in [20]. Figure 10 gives the phase response for different HCLs' concentrations.