## 2 Theoretical Modified Model of Scattering Characteristics on Coating Surface  
As shown in Figure 1, it is assumed that the reflection law of the material inside the integrating sphere follows [PERSON]'s law of diffuse reflection, so the illuminance at any point inside the integrating sphere consists of two parts: one is the illuminance generated by the light source directly irradiating a point \(a\); and the other is the superimposed illuminance generated at the point \(a\), excluding the contribution of illuminance caused by directly irradiating from the light source to point \(a\). For any point \(a\) in the integrating sphere, the illuminance \(E_{0}\) produced by directly irradiating from the light source can be expressed as follows:  
\[E_{0}=\frac{\phi}{4\pi r^{2}} \tag{1}\]  
where \(\phi\) is the total luminous flux of the light source, and \(r\) is the radius of the integrating sphere. The illuminance \(E_{1}\) after one time reflection can be represented as follows: \(E_{1}=\frac{\rho\cdot\phi}{4\pi r^{2}}\), where \(\rho\) is the coating reflectivity on the inner wall of the integrating sphere. The illumination \(E_{2}\) produced by secondary reflection can be expressed as \(E_{2}=\frac{\rho^{2}\cdot\phi}{4\pi r^{2}}\). Then, one can infer that the illuminance \(E_{\text{n}}\) after the \(n\)th reflection is \(E_{n}=\frac{\rho^{n}\cdot\phi}{4\pi r^{2}}\). Therefore, the total illumination produced at point \(a\) can be written as follows:  
\[ \begin{array}{ll}E&=E_{0}+E_{1}+E_{2}+\cdots+E_{n}+\cdots\\ &=\frac{\phi}{4\pi r^{2}}+\frac{\phi\cdot\phi}{4\pi r^{2}}+\frac{\rho^{2}\cdot \phi}{4\pi r^{2}}+\cdots+\frac{\rho^{n}\cdot\phi}{4\pi r^{2}}+\cdots\\ &=\frac{\phi}{4\pi r^{2}}+\frac{\phi\cdot\phi}{4\pi r^{2}}(1+\rho^{1}+\rho^{2} +\cdots+\rho^{n}+\cdots)\\ &=\frac{\phi}{4\pi r^{2}}+\frac{\phi}{4\pi r^{2}}\frac{\rho^{2}}{1-\rho}\\ \end{array}  \tag{2}\]  
Figure 1: Schematic diagram of illumination composition inside integrating sphere. where the first term in Equation (2) is the illuminance produced by the light source directly irradiating at the point, and the second term is the sum of the illuminance produced by the light reflected by other points. For a single-hole integrating sphere, when the laser enters the integrating sphere from the hole, it will not directly irradiate the point outside the incident position. Therefore, Equation (2) can be simplified as follows:  
\[E=\frac{\phi}{4\pi r^{2}}\cdot\frac{\rho}{1-\rho} \tag{3}\]  
For the three-hole integrating sphere, as shown in Figure 2, the laser enters into the integrating sphere from hole \(a\) to hole \(b\). The hole \(b\) is blocked by the measured coating sample. The laser incident on the material surface is reflected many times in the integrating sphere and finally reaches the port of detector window c. With photoelectric signal conversion module, the detector converts the collected illumination into current signal. After calculation by using the data-processing module, the measurement results are output by a display module. It is assumed that the average spectral reflectance of the diffuse reflective coating material in integrating sphere is \(\rho\) and the total radiation flux of the laser source entering the integrating sphere is \(\phi_{0}\). As the light on the inner surface of integrating sphere reaches equilibrium after several times of diffuse reflection, the radiation flux distribution in the inner cavity is uniform and the illuminance is equal everywhere. As a result, the illuminance at any point in the integrating sphere is as follows:  
\[E=\frac{\sum\phi}{A} \tag{4}\]  
where \(\sum\phi\) represents the sum of the radiation fluxes after multiple reflections in the inner cavity of the integrating sphere, and \(A\) is the surface area of the integrating sphere inner wall. Since the divergence angle of the laser source used in the experiment is rather small (-1 mrad), it can be approximately considered as a parallel light.