## 2 Characterization of CCD Cameras
### Assessment of Intensity of Radiation from Measured Data of CCD Cameras
#### 2.1.1 Visible Camera and Near-Infrared Camera  
For this calibration experiment, a sunlight simulator (San-ei Electronics Co., Ltd., XES-50S2-TT) with a wavelength distribution similar to that of sunlight reaching the ground was used as a known value of radiation intensity. The light from the sunlight simulator was shone on a standard diffuse reflector (hemispherical reflectance at visible and near-infrared wavelengths (\(\lambda\) = 0.25-2.5 \(\upmu\)m) \(\rho_{\text{ref}}\) = 0.99), and the reflected light was measured by the visible camera or near-infrared camera as shown in Figure 1. This experimental setup was selected because the reflected intensity of the light source can be derived numerically and the value of \(i\) can be known. In general, solar energy reaching the ground \(E_{\text{ground}}\) [W/m\({}^{2}\)] is about 1.0 kW/m\({}^{2}\)[26]. Assuming that the wavelength distribution of the solar energy \(E_{\text{b}}\) [W/m\({}^{2}\)] has the same distribution as the Planck function [27] due to the solar temperature \(T_{\text{sun}}\) [K], the relationship between \(E_{\text{ground}}\) and \(E_{\text{b}}\) is as follows using the constant value \(R\) [-] and Stefan-Boltzmann constant \(\sigma\) [W/m\({}^{2}\cdot\)K\({}^{4}\)]:  
\[\frac{1}{R}=\frac{E_{\text{ground}}}{\int_{0}^{\infty}E_{\text{b}}(\lambda,T_{ \text{sun}})}=\frac{E_{\text{ground}}}{\sigma T_{\text{sun}}^{4}} \tag{1}\]  
Figure 1: Experimental system for visible and near-infrared light camera calibration. The spectral reflected intensity \(i_{\mathrm{dr},\lambda}\) from the standard diffuse reflector exposed to the solar simulator is given by the reflector \(\rho_{\mathrm{dr}}\). Then, \(i_{\mathrm{dr}}\) can be obtained by integrating \(i_{\mathrm{dr},\lambda}\) over the range of visible wavelengths or near-infrared wavelengths, as shown below. \[i_{\mathrm{dr},\lambda}\approx\frac{E_{\mathrm{b}}(\lambda,T=T_{sun})}{\pi \cdot R}\cdot\rho_{\mathrm{dr}},(\rho_{\mathrm{dr}}\approx 1) \tag{2}\]  
\[i_{\mathrm{dr}}=\int i_{\mathrm{dr},\lambda}d\lambda \tag{3}\]  
Referring to the camera's catalog specifications [28], the visible-light camera used in this study has a linear relationship between the energy of the incident radiation \(Q_{\mathrm{v}}\) on the camera's sensor and the camera's luminance data \(D_{\mathrm{v}}\). On the other hand, the near-infrared camera [29] has a logarithmic relationship between the incident radiation \(Q_{\mathrm{n}}\) and the camera's luminance data \(D_{\mathrm{n}}\). However, these catalog specifications do not guarantee the evaluation of light sources containing light of various wavelengths, such as sunlight. Therefore, it becomes necessary to measure the camera luminance data \(D\) in response to changes in solar light energy. In this study, we used neutral density (ND) filters (SIGMAKOKI CO., LTD., MAN-25-1-70) to change the light energy of the solar simulator without changing the wavelength distribution as shown in Figure 1. In this method, \(D_{\mathrm{obj}}\) measured was compared to the reflection data \(D_{\mathrm{dr}}\) measured from the white diffuse reflector with ND filters, where the observed object was assumed to be a gray body with hemispherical isotropic reflections. The measurement results of this calibration experiment are shown in Figure 2. The vertical axis shows the raw data of the camera luminance data \(D\). The horizontal axis, \(i\), is the value taken with respect to \(i_{\mathrm{dr}}\), the value obtained by integrating Equation (3) over the wavelength range in which each camera can measure. The plotted data are the average value of the central area of the diffuse reflector, and the error bars are its standard deviation. This averaging process is detailed in the Supplementary Materials (Section SA). As can be seen from the graph, the luminance data \(D\) obtained by the cameras decreases as the light intensity is reduced by the ND filters.