## 3 Design, Simulation and Implementation for Scattering Measurement System
### Modeling for Three-Hole Integrating Sphere  
The integrating sphere models with spherical-missing plate and sample plate were established respectively. In this model, there were three holes, named incident beam opening, measuring opening and sample opening, on the surface of the integrating sphere. The measuring opening and the sample opening were respectively fitted with the detector and the sample plate, while the incident beam opening was empty.  
Figure 5 shows a geometric model of integrating sphere with the spherical-missing plate and the sample plate. In Figure 5a, the contact position between the spherical-missing plate and the hole of the integrating sphere was a part of the sphere. When the spherical-missing plate and the integrating sphere coincided, the integrating sphere just formed a complete sphere, which was used to measure the background current noise. In Figure 5b, the reference sample plate in contact with the sample opening of the integrating sphere was a plane plate, which was used to provide reference calibration.  
Figure 4: Simulation results of aiming-and-positioning system with and without light-emitting diode (LED) ambient light: (**a**) without LED and (**b**) with LED.  
Figure 5: Geometric model of three-hole integrating sphere: (**a**) with spherical-missing plate and (**b**) with sample plate.  
The TracePro was employed to achieve accurate simulation by using more tracing rays. However, with the increase of the tracing rays number, the effect of improving the accuracy for the results would be weaker. In the meantime, it would also cause a heavy computing burden for simulation. Therefore, in order to ensure the accuracy and efficiency of the results, we investigated the simulation effect for different numbers of tracing rays, and the results are shown in Figure 6. It could be seen from the Figure 6 that the simulated results fluctuated greatly when the number of tracing rays was small, which led to the low accuracy of the simulated results at this stage. With the increase of the tracing rays number, the simulated results gradually tended to be stable. After the number of tracing rays reached at 47,000, the simulated results only fluctuated in a small range.  
According to Figure 6, the simulation results for tracing rays number could be divided into three intervals, namely 1000-20,000, 21,000-46,000 and 47,000-80,000. The standard deviation for these three sections of data could be obtained respectively to investigate the stability of the calculation results. The calculation results showed that the variation coefficient of simulated luminous flux was respectively 1.25%, 0.37% and 0.15% in the ranges of 1000-20,000, 21,000-46,000 and 47,000-80,000. Obviously, the luminous flux received by the detector fluctuated greatly in the range of 1000-20,000. At the range from 21,000 to 46,000, the simulated results were relatively stable, but there were still large fluctuations. When the number of tracing rays was more than 46,000, the standard deviation of simulated results was lower and more stable. Therefore, in this paper, 50,000 of tracing rays was chosen for high credibility results and short simulation time.