## 3 Critical Technical Approach
### Stray Light Suppression Analysis and Structural Design Based on BRDF Modeling
#### 3.3.1 Scattering Characterization Modeling and Energy Attenuation Mechanism Analysis  
This study adopts a modeling approach based on the Bidirectional Reflectance Distribution Function (_BRDF_) to characterize the scattering properties of components [31]. For  
Figure 4: Raw spectral radiance distribution of the fiber laser across different output power levels. Figure 5: Designed spectral transmittance profile with tolerance envelope for the custom spectral shaping filter. mirror-like reflective surfaces, the directional scattering characteristics are described using the ABg model, as expressed by the following Equation (9):  
\[BRDF=\frac{\text{A}}{\text{B}+|\sin\theta_{s}-\sin\theta_{i}|^{g}} \tag{9}\]  
where \(\theta_{i}\) and \(\theta_{s}\) denote the incident and scattering angles, respectively; A, B, and g are model fitting parameters; \(\Delta n\) is the refractive index difference between incident and scattering media; and \(\lambda\) is the wavelength of the incident light. The total energy loss due to surface scattering is governed by the Total Integrated Scatter (_TIS_), which can be approximated as a function of the root-mean-square surface roughness \(\sigma\) using Equation (10). This model provides a quantitative basis for analyzing the impact of surface quality on system background radiation and supports surface manufacturing quality control. \[TIS=(\frac{2\pi\Delta n\sigma\cos\theta_{i}}{\lambda})^{2} \tag{10}\]  
To address secondary stray light generated by non-ideal internal cavity reflections, this study introduces a path-level modeling approach and proposes a reflective light trap structure to suppress energy return. The designed U-shaped light trap is internally coated with a high-absorption material, where the single-bounce absorptance is \(\gamma\). If a ray undergoes n reflections along the primary path, the residual energy ratio can be expressed as Equation (11):  
\[\eta=(1-\gamma)^{2n+1} \tag{11}\]  
The scattering behavior of the light trap's inner surfaces is modeled using an improved micro-surface \(BRDF\) formulation [32], expressed in Equation (12), where \(g(\theta_{i},\varphi_{r})\) denotes the polynomial fitting function (g\({}_{0}=0.01\)), which can be expressed as Formula (13), \(G\) is the geometric shadowing function, \(F\) represents the Fresnel reflection term, the exponential term describes the surface distribution function (\(\alpha=0.5\)), and the final term \(k\cos\theta_{i}\) accounts for diffuse reflection. \[BRDF(\theta_{i},\varphi_{i},\theta_{r},\varphi_{r})=g(\theta_{i},\varphi_{r}) \cdot\frac{G(\theta_{i},\varphi_{i},\theta_{r},\varphi_{r})}{\cos\theta_{i} \cdot\cos\theta_{r}}\cdot F\times\exp(-c^{2}\alpha^{2})+k\cos\theta_{i} \tag{12}\]  
\[g(\theta_{i},\varphi_{r})=\frac{\text{P}_{1}\cdot\varphi_{r}^{6}+\text{P}_{2} \cdot\varphi_{r}^{5}+\text{P}_{3}\cdot\varphi_{r}^{4}+\text{P}_{4}\cdot \varphi_{r}^{3}+\text{P}_{5}\cdot\varphi_{r}^{2}+\text{P}_{6}\cdot\varphi_{s} +\text{P}_{7}-g_{0}}{\text{q}_{1}\cdot\theta_{i}^{3}+\text{q}_{2}\cdot\theta _{i}^{2}+\text{q}_{3}\cdot\theta_{i}+\text{q}_{4}}+g_{0} \tag{13}\]  
The theoretical modeling described above supports the subsequent experimental analysis of energy path contribution ratios, surface roughness tolerance evaluation, and structural optimization of the light trap. Table 1 systematically defines all variables, constants, and operators used in Equations (1)-(13), along with their physical meanings and units where applicable.