計算型光譜儀以一組具差異化光譜響應的編碼元件將入射光譜調製為編碼強度訊號，再藉由演算法反推原始光譜，本研究以超穎介面（metasurface）作為光譜編碼器並結合壓縮感知（compressed sensing）進行重建，在沿用本實驗室先前製程技術與超穎介面結構設計之基礎上，自量測架構、量測矩陣可信度、過完備字典與重建演算法四個面向對系統進行系統性改進與驗證，並以非相干性為準則設計新一代超穎介面編碼器。在量測架構上，改採背向入射以抑制高階繞射所致之單元間串擾，實測影像與嚴格耦合波分析法（RCWA）模擬皆證實高階繞射受有效抑制，而各單元之有效編碼響應完整保留；實驗量測矩陣與模擬高度一致，並以四種LED光源驗證前向一致性。在光譜重建上，本研究依據相干性理論設計三組過完備高斯原子字典，其中，全域相干性一致字典Ψ3於重建保真度與表示稀疏度均不劣於其餘二者之前提下，具備最佳之計算效率；於求解器比較中，Woodbury矩陣求逆引理將ADMM之單步成本壓至與FISTA同一數量級，其更低的迭代次數因而轉化為約13倍更短之線上運算時間，故選定「Ψ3字典搭配ADMM」作為線上重建組合。最後，針對硬體相干性偏高之瓶頸，本研究以最小化最壞情況相干為準則自候選單元庫選取64單元之新設計，將量測通道數由49提升至64，並使最壞情況相干改善約8 %、平均相干亦同步降低約6 %。然而，新編碼器目前僅以RCWA模擬建立並評估，其相干性改善尚待實體製作與端到端閉環驗證證實。

A computational spectrometer uses encoding elements with different spectral responses to turn an incident spectrum into a set of coded intensity signals, and then recovers the original spectrum by computation. This keeps the device small while still giving good spectral resolution. This work uses a metasurface as the spectral encoder, together with compressed-sensing reconstruction. Using the same fabrication process and metasurface dimensions as an earlier study in our group, the system is improved and checked in four parts, namely the measurement setup, the reliability of the measurement matrix, the overcomplete dictionary, and the reconstruction algorithm, and a new encoder is designed using an incoherence criterion. For the setup, a back-side-incidence configuration is used to reduce the crosstalk between units caused by high-order diffraction; both measured images and rigorous coupled-wave analysis (RCWA) show that high-order diffraction is clearly reduced, while each unit's useful encoding response is fully kept. The experimental measurement matrix matches the simulation well, and forward consistency is confirmed with four LED sources. For reconstruction, three overcomplete Gaussian dictionaries are designed from coherence theory; the globally coherence-equalized dictionary attains the best computational efficiency while degrading neither reconstruction fidelity nor representation sparsity. In the solver comparison, ADMM needs far fewer iterations than FISTA, and the Woodbury identity holds its per-iteration cost at the FISTA level, making the online runtime about thirteen times shorter, so this dictionary with ADMM is chosen for online reconstruction. Finally, to deal with the high hardware coherence, a 64-unit design is chosen from a candidate library by minimizing the worst-case coherence, raising the number of channels from 49 to 64 and improving the worst-case coherence by about 8% and the average coherence by about 6%.

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