## 2 Theoretical Analysis of Reflection Error Correction for Ambient Radiation of Turbine Blade
### Simulation Results and Analysis of Dynamic Reflection Model  
Based on the geometric models of the suction surface of the target blade, the suction surface and the pressure surface of the upper rotor blade, and the adjacent three guide vanes in Figure 4, the ambient radiation reflected by the trailing edge of the suction surface of the target blade is analyzed. First, the radiation angle factors between the three guide vanes and point \(P_{0}\) shown in Figure 6 are calculated. Equation (15) is used to calculate the radiation angle factor of the adjacent blades to the target blade at different angles \(\varphi\). In order to judge whether radiation can reach the target blade, the radiation angle of the panel and whether other blades block the panel radiation are considered in the calculation. Figure 6 illustrates the change in radiation propagating from the adjacent blades to point \(P_{0}\) on the target blade when the target blade rotates and uses different colored shadows to distinguish the radiation propagating from different adjacent blades to \(P_{0}\) on the target blade. The guide vanes are distributed periodically; therefore, we take the process of rotating the blade from the position to another position as a cycle, as shown in Figure 6a-c, and use the reflection model for analysis. The target blade rotates 6 degrees in one cycle. Figure 7 shows the simulation results of the reflection model; that is, the angle factor distribution between the target blade and guide vanes 1, 2, and 3 at different angles (\(\varphi\) = 0\({}^{\circ}\), 2\({}^{\circ}\), 4\({}^{\circ}\), and 6\({}^{\circ}\)). In Figure 7, the \(x\)-axis is close to the trailing edge of the blade, and its positive direction is from the tip to the root of the blade. The \(y\)-axis is close to the tip, and its positive direction is from the trailing edge to the leading edge. Figure 7 shows that during rotation of the target blade, the position where the most intense radiation from the three guide vanes is received is the trailing edge of the target blade suction surface. This is because the distance between the guide vanes and the trailing edge is the smallest compared with other parts of the target blade suction surface. However, due to the shape of the target blade and the shielding of the upper rotor blade, the radiation of the three guide vanes cannot reach the leading edge of the suction surface of the target blade, so the radiation angle factor is almost zero. Figure 6: Changes in radiation propagating from adjacent blades to point \(P_{0}\) when the target blade moves at (**a**) \(\varphi\) = 0\({}^{\circ}\), (**b**) \(\varphi\) = 3\({}^{\circ}\), and (**c**) \(\varphi\) = 6\({}^{\circ}\). The peak of the radiation angle factor between rotor blade 2 and the target blade is located near the protrusion of the blade surface. As rotor blades 1 and 2 are arranged at a certain angle in the engine, the peak position of the radiation angle factor deviates to the root side of the target blade at the protrusion of the suction surface. According to the above simulation results, the reflected radiation and temperature measurement error of the target blade are simulated and calculated. The relative position coordinates of point \(P_{0}\) are (0.5, 0.66), the target blade temperature is 1100 K, the guide vane temperature is 1000 K, the upper rotor blade temperature is the same as the target blade temperature, the target blade emissivity is 0.58, and the wavelength of radiation temperature measurement is 1550 nm. The ratio of the reflected energy on the surface of the target blade to the total energy received by the radiation pyrometer and the temperature measurement error caused by reflection are calculated. The relationship between them and the angle of the target blade is shown in Figure 9a.