## 3 Critical Technical Approach
### Design Method for Optical Filters Addressing Power-Spectrum Nonlinearity Characteristics  
In a Sun outage interference simulation system, the spectral characteristics of the solar radiation background are among the core parameters determining the realism of interference reconstruction. To achieve high-fidelity reproduction of the solar spectral distribution within the communication band (1540-1560 nm), as illustrated in Figure 3, the light source must spectrally match the actual solar spectral radiance to ensure effective spectral-domain coupling between the signal and interference beams. However, conventional spectral filter design is typically based on static source spectra, which makes it unsuitable for handling the nonlinear spectral response of laser sources under varying power levels [27; 28]. To address this, a spectral filter design strategy based on the co-optimization of laser power-spectrum characteristics is proposed. Using the standard solar spectral radiance in the communication band as the target function, the filter's wavelength-dependent transmittance \(T(\lambda)\) is optimized to modulate the original laser output \(L_{\text{source}}(\lambda,P)\), producing the desired output spectrum \(L_{\text{source}}(\lambda,P)\cdot T(\lambda)\). To achieve spectral shape consistency  
Figure 3: Standard solar spectrum. Figure 2: Schematic diagram of large-aperture far-field beam homogenization optics. (The red annotations highlight the critical steps in the proposed homogenization method.) under normalization conditions, the filter's transmittance must satisfy a spectral matching Equation (4):  
\[\frac{L_{\text{source}}(\lambda,P)\cdot T(\lambda)}{\text{Max}[T(\lambda)\cdot L_{ \text{source}}(\lambda,P)]}=\frac{L_{\text{solar}}(\lambda)}{\text{Max}[L_{ \text{source}}(\lambda)]} \tag{4}\]  
a spectral uniformity index \(U_{L}\) is introduced as the evaluation metric for filter performance, as defined in Equation (5):  
\[U_{L}=\frac{2*\text{Min}(L_{j}^{i}\cdot T_{i})}{\text{Min}(L_{j}^{i}\cdot T_{ i})+\text{Max}(L_{j}^{i}\cdot T_{i})} \tag{5}\]  
where Min [] denotes the minimum operator, and Max [] denotes the maximum operator. The spectral response at each wavelength point \(\lambda_{\text{i}}\) (i-th index) was measured under different power levels \(P_{\text{j}}\) (j-th index). To achieve optimal matching performance, the filter design problem is formulated as a linear programming optimization, with the objective of minimizing the normalized error function. The following constraints are applied as Equation (6):  
\[\left\{ \begin{array}{l}U_{L}\geq 80\%\\ \text{Min}_{\lambda_{\text{i}}}[T(\lambda_{i})]\geq\varepsilon\ \ (\varepsilon=0.2)\\ 0\leq T(\lambda)\leq 1\end{array} \right. \tag{6}\]  
where the first constraint ensures that the spectral uniformity exceeds 80%; the second guarantees sufficient energy utilization efficiency; the third defines the physical bounds of the transmittance values. The actual transmittance design of the spectral filter is given by Equation (7):  
\[T_{\text{i}}(\lambda_{i})=\frac{L_{\text{solar}}(\lambda_{i})}{L_{\text{ source}}(\lambda_{i},P_{\text{j}})}\cdot\frac{\text{Max}[L_{\text{solar}}( \lambda_{i})]}{\text{Max}[L_{\text{source}}(\lambda_{i})]} \tag{7}\]  
The final optimization objective is to minimize the normalized spectral error function, which is expressed as Equation (8):  
\[\text{Min}(\sum_{j=1}^{m}\sum_{i=1}^{n}\left|\frac{L_{\text{source}}(\lambda_{ i},P_{\text{j}})\cdot T(\lambda_{i})}{\sum L_{\text{source}}(\lambda_{i},P_{ \text{j}})\cdot T(\lambda_{i})}-\frac{L_{\text{solar}}(\lambda_{i})}{\sum L_ {\text{source}}(\lambda_{i})}\right|) \tag{8}\]  
This strategy extends the spectral reconstruction process from traditional static design to a dynamic power-spectrum co-optimization approach. By precisely controlling the transmittance across the full spectral range, the system maintains a stable and solar-like spectral distribution over a broad range of output power levels.