## 2 Characterization of CCD Cameras
### Assessment of Intensity of Radiation from Measured Data of CCD Cameras
#### 2.1.2 Far-Infrared Camera  
The far-infrared camera used in this study is a bolometer-type camera that can obtain the illuminance data \(D_{\mathrm{f,obj}}\) proportional to the radiation energy from the temperature changes caused by the temperature exchange of the radiation between the camera sensor and the object observed in environmental experiment by the camera. Through calibration experiments, the temperature of the observed object \(T_{\mathrm{s}}\) and the intensity of the radiation emitted from the material \(i_{\mathrm{f,obj}}\) can be derived from the illuminance data obtained by this far-infrared camera. This makes it possible to evaluate the heat exchange between the environment and the human body. The system of the calibration experiments conducted in this study is shown in Figure 3.  
In the calibration experiment, the temperature of the pseudo-blackbody \(T_{\text{b}}\) varied, and the illuminance data \(D_{\text{f,obj}}\) were measured with the far-infrared camera. The energy \(Q_{\text{b}}\) of the total radiation exchanged between the blackbody and the camera sensor is given by following equation:  
\[Q_{\text{b}}=\varepsilon\sigma(T_{\text{b}}^{4}-T_{\text{s}}^{4})A_{\text{b}}F_ {\text{b}\rightarrow\text{s}}, \tag{6}\]  
where \(\varepsilon\) is the emissivity of the camera sensor, and \(A_{\text{b}}\) is the area of the blackbody surface observed by the camera sensor, \(F\) is the view factor from the observed object to the camera sensor, and the subscript \"s\" refers to the camera sensor. In other words, if we can show that the measured illuminance data \(D_{\text{f}}\) are proportional to \(Q_{\text{b}}\), we can evaluate the radiation energy with the far-infrared camera. Figure 4 shows the measured luminance data \(D_{\text{f,obj}}\) as a function of the heat exchange between the two black bodies represented by \(\sigma(T_{\text{b}}^{4}-T_{\text{s}}^{4})\) with the camera sensor temperature being \(T_{\text{s}}\). The plotted data are the average value of the central area of the blackbody sample, and the error bars are its standard deviation. This averaging process is detailed in the Supplementary Materials (Section SA). The measured irradiance data have a linear relationship with the exchanged radiation energy with the coefficients \(C_{\text{f}}\) and \(C_{\text{f}}^{\prime}\) for the linear approximation. These coefficients were calculated using the least-squares method. The correlation coefficient \(r^{2}\) is shown in the figure. Then, the intensity of radiation from the observed object \(i_{\text{f,obj}}\) can be expressed by the following equation:  
\[i_{\text{f,obj}}=\frac{D_{\text{f,obj}}}{\pi\cdot C_{\text{f}}}-\frac{C_{ \text{f}}^{\prime}}{\pi\cdot C_{\text{f}}}+\frac{\sigma T_{\text{s}}^{4}}{\pi} \tag{7}\]  
Figure 3: Experimental system used for far-infrared light camera calibration. Figure 2: Measurement results for calibration experiment of (**a**) visible-light camera and (**b**) near-infrared light camera. Evaluation of the Exchange of Radiation between the Human Body and the Surrounding Environment Structures  
It was shown in Section 2.1 that the intensity of radiation, \(i_{\rm p}\), emitted from a point \(p\) on a measured area with cameras can be given by the equations as derived from the measured illuminance data \(D\). Section 2.2 describes how to evaluate the radiant energy exchange between the human body and its surroundings, taking into account the radiant energy going from the point \(p\) measured by the camera on to the human body. Here, we treat the human body as a subscript \"hb\". The energy \(dQ_{\rm p\tohb}\) of radiation per unit time from a small area \(dS\) on the image measured by the camera toward the human body is expressed as follows:  
\[dQ_{\rm p\tohb}=\pi(i_{\rm p}-i_{\rm hb})F_{\rm P\tohb}dS, \tag{8}\]  
where \(F_{\rm P\tohb}\) is the morphological coefficient of viewing the human body from the position of the small area, and \(i_{\rm hb}\) is the intensity of radiation emitted from the human body.