## 2 Experimental Approach
### Development of Temperature Measurement Method Using pNIPAM Solution  
A temperature measurement method is developed based on the refractive index of a pNIPAM solution measured by SPRi, particularly the angular modulation. The refractive index of the pNIPAM solution is estimated by finding the SPR angle with a fixed condition of the prism, gold film thickness, and wavelength. The temperature of the gold film, \(T_{s}\), is controlled using a heating plate, and the thermocouple is attached to the gold film to measure the temperature. Figure 2 depicts reflectance curves of the pNIPAM solution with different surface temperatures. The reflectance decreases with the increase of the incidence angle, and it shows a minimum at the SPR angle. Interestingly, the SPR angles for temperatures of 21.1 \(\pm\) 0.2 \({}^{\circ}\)C and 24.3 \(\pm\) 0.2 \({}^{\circ}\)C are the same, which means temperature measurements are not meaningful due to no corresponding reflectance variations at given incidence angles. Moreover, the reflectance curves shift to the right with an increase of temperature, as in Figure 2a,b. The refractive indices corresponding to each temperature are listed in Table 1. The refractive index increases with the temperature of the pNIPAM solution showing the same tendency with [PERSON] et al. (2018). The refractive index of the pNIPAM solution drastically increases when the temperature is higher than 29.3 \({}^{\circ}\)C near the LCST. However, it is impossible to predict the SPR angle near the LCST through the reflectance curve in the present experimental setup. This is because the reflectance is indistinguishable at a higher refractive index with a different incident angle. Thus, the reflectance of the pNIPAM solution is measured with a temperature range of 24.3 \({}^{\circ}\)C to 29.3 \({}^{\circ}\)C.  
Figure 1: (**a**) Picture of the present surface plasmon resonance imaging (SPRi) experimental setup and (**b**) schematic of temperature measurement using a poly(\(N\)-isopropylacrylamide) (pNIPAM) solution, left: for the evaluation of pNIPAM solution, center: droplet temperature measurement, right: cross-sectional schematic of multi-layer.  
A correlation between reflectance and refractive index at a specific incidence angle is derived based on reflectance results obtained by converting intensities of experimental images. Figure 3 shows the relation between the reflectance, refractive index, and temperature of the pNIPAM solution when the incidence angle of the light to the gold film is 75\({}^{\circ}\). The curve fitted equations are obtained from experimental results as follows:  
\[n_{p}\ =\ 0.02806R+1.352 \tag{2}\]  
\[T\ =\ -2.39621\times 10^{5}+3.52117\times 10^{5}n_{p}-1.29341\times 10^{5}n_{p}^{2} \tag{3}\]  
where \(n_{p}\) is the refractive index of a pNIPAM solution, \(R\) is reflectance, and \(T\) is the temperature of a pNIPAM solution. From the experimental images using the SPRi system, the calibrated reflectance of the pNIPAM solution is obtained, and subsequently, the temperature distribution is calculated from Equations (2) and (3).  
\begin{table}
\begin{tabular}{c c} \hline
**Temperature** (\({}^{\circ}\)**C**) & **Refractive Index** \\ \hline
21.1 \(\pm\) 0.2 & 1.3549 \\
24.3 \(\pm\) 0.2 & 1.3549 \\
26.1 \(\pm\) 0.1 & 1.3557 \\
27.5 \(\pm\) 0.2 & 1.3573 \\
28.2 \(\pm\) 0.2 & 1.3580 \\
28.8 \(\pm\) 0.2 & 1.3595 \\
29.3 \(\pm\) 0.2 & 1.3610 \\ \hline \end{tabular}
\end{table}
Table 1: Refractive index of pNIPAM solution (10 wt%).  
Figure 2: (**a**) Reflectance curve of pNIPAM solution considering the incidence angle of light and temperature, (**b**) magnified reflectance curve near the SPR angle.