## 4 Relative Uncertainty Analysis for Scattering-Rate Measurement System
### Calibration of Detector  
In the measurement, the detector usually obtains the current intensity, while the physical quantity received by the detector is always expressed as the luminous flux in the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**System Component** & **Parameter** & **Specifics/Design Values** \\ \hline \multirow{3}{*}{Laser} & Wavelength for Measurement & 1064 nm \\  & Wavelength for aiming & 532 nm \\  & Power Stability & \(\pm\)0.19\% \\ \hline \multirow{4}{*}{Integrating Sphere} & Inner Surface Diameter & 100 mm \\  & Incident Beam Opening Diameter & 20 mm \\ \cline{1-1}  & Sample Opening Diameter & 15 mm \\ \cline{1-1}  & Detector Opening Diameter & 12 nm \\ \cline{1-1}  & Diffuse Reflectance of Inner Wall & 96\% \\ \hline \multirow{2}{*}{CCD Camera} & Focal Length of Aiming Optical System & 6–60 mm \\  & \(f\)-Number & 1.4 \\ \hline \multirow{4}{*}{Infrared Detector} & Sensor & InSb and HgCdTe \\  & Response Band & 1–13 μm \\ \cline{1-1}  & Response Time & 50 ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main technical parameters of the system.  
simulation analysis. In order to obtain the surface reflectance of the coating, the calibration relationship between the output laser power and the detector photocurrent intensity should be established firstly according to Equation (13). In addition, the corresponding model was established in TracePro according to the technical parameters of the measurement system, in order to ensure the consistency and comparability between the simulation model and the actual measuring system. The specific simulated parameters were as follows: the opening radius of integrating sphere was 50 mm, the opening radius of incident beam was 10 mm, the radius of sample opening was 6.5 mm and the radius of measuring opening was set to 7.5 mm. The diameter of incident beam was 2 mm. The laser power increased from 0 to 1 W with an interval of 50 mW. The inner wall reflectivity of the integrating sphere was set to 96%. The scattering model employed the standard Lambert's law setting.  
Figure 11 shows the calibration results between the output detector photocurrent intensity and the simulated luminous flux. The laser power in TracePro was consistent with the experimental laser power, and the adjustment range of both was 0-1 W. In the experiment, the output laser at 1064 nm was sampled once per second for 10 s, and then the average value of ten samples had been taken. After stabling the laser power, the photocurrent value measured by the infrared detector was recorded by consecutive reading five times and taking the mean value. It could be seen from Figure 11a that the simulated luminous flux received by the detector and the detector photocurrent intensity were linearly related to the incident laser power. Figure 11b presents the calibration relationship between the detector photocurrent intensity and the simulated luminous flux, which can be expressed by the following equation:  
\[I_{out}=0.817\Phi_{d} \tag{14}\]  
where \(I_{out}\) is the responding detector photocurrent intensity to the luminous flux; \(\Phi_{d}\) is the simulated luminous flux received by the detector. Equation (14) indicates that the simulated luminous flux of 1 mW corresponds to the detector photocurrent intensity of 0.817 uA.  
Figure 11: Detector calibration results: (**a**) variations of simulated luminous flux and experimental current intensity with incident laser power; (**b**) calibration relationship between the experimental current intensity and the simulated luminous flux.