為達到微型光譜儀技術完全自主之目的，本研究主要目的為開發二階線性漸變濾波片通用設計流程，此設計流程演算法適用於任何機型之蒸鍍系統，可自由調控模型參數，進而可模擬加入擋板後基材上膜厚分布情形，以利設計任何規格之二階線性漸變濾波片。本文所開發之二階線性漸變濾波片通用設計流程，於單次製程可量產151片之線性漸變濾波片，有別於其他文獻僅能少量生產，使製造成本大幅降低。
線性漸變濾波片可應用於光柵光譜儀，實際擺放於光譜儀偵測器前方，以濾除不必要之高階繞射之光譜，達到正確光譜解析之效果。為達漸變濾波效果，其光學薄膜厚度需呈漸變，故本研究設計局部擋板結構，將其固定置於基材上方，利用擋板遮蔽效應蒸鍍出線性漸變之膜厚。
本文首先依蒸鍍腔體幾何結構建立三維理論模型及光跡模擬模型，計算加入擋板後基材上膜厚分布，並將二組模型所得結果進行分析比較。研究結果顯示，於LVF漸變區域內二組模型之計算膜厚與實際蒸鍍膜厚分布極為吻合。3D理論模型中，理論模型及光跡模計算結果幾乎吻合，〖RMSD〗_((R-T))平均值為0.94%。〖RMSD〗_((E-T) )平均值為6.45%，〖RMSD〗_((E-R) )平均值為6.76%，兩組模型均能精準預測蒸鍍膜厚分布。且漸變區(25%-75%膜厚)輪廓趨近於線性，漸變區輪廓之線性回歸數R^2均大於等於0.9903，表示LVF於漸變區域線性度極佳，與設計目標相符。
薄膜輪廓差異較大為膜厚轉折處，實際蒸鍍膜厚轉折處成圓弧狀。為修正理此誤差，本文採用高斯摺積之方法，使理論模型之計算逼近實際膜厚分布。以h=10mm為例，未修正前之RMSD為7.24%，修正後之RMSD降低為1.44%，此方法可大幅提升修正後之理論膜厚與量測之吻合度。
為驗證線性漸變濾波之特性，本研究架設光譜量測系統，針對濾波片各線性位置進行光譜量測。另使用Essential Macleod模擬軟體計算LVF之濾波效能，以比較理論與模擬之差異，並作為理論與模擬架構修正之參考。在線性漸變區內，其臨界波長λ_C與LVF空間位置呈線型關係(以h=10mm為例R2=0.9962)，驗證LVF實際可達理論設計之線性漸變濾波效能。本研究另以SEM觀察LVF漸變區之多層膜剖面結構，觀測結果顯示多層膜之各膜層堆疊平整，因漸變區內其各膜層呈現完整之薄膜結構，使其達到LVF漸變濾波效能。

This study proposes a generalized design process for order-sorting linear variable filter (LVF). In this design procedure, parameters used in theoretical model are adjusted according to the evaporator geometry to calculate the three-dimensional thin film thickness distribution on the substrate with a local mask. A novel method capable of high-volume high-precision production of LVFs. A total of 151 pieces of LVFs can be fabricated in a single batch and the process is much simpler than the previously reported methods. The LVF is placed on a linear detector sensor in the spectrometer to eliminate the overlapping orders of diffraction generated by the grating.
A local mask on top of the substrate positioned on a rotating substrate holder inside an evaporation chamber. This process generates a thin film thickness gradient on the substrate. The gradient thickness variation is controlled by adjusting the height of the local mask.
A theoretical analytical model and a ray tracing simulation model based on the geometry of a commercial coater and the local mask are developed to obtain the profiles of LVFs. The results of theoretical model and ray tracing simulation show good agreement with the evaporated profile. The averaged root-mean-square deviation is 0.94% between ray tracing and theoretical model, 6.45% between evaporation and theoretical model, and 6.76% between evaporation and ray tracing, respectively. This indicates that the proposed theoretical model and ray tracing simulation both predict the evaporated thin film profile of LVF with high precision. Within the 25%–75% thin film thickness range, the thickness profiles of the three models are linear. The coefficients of determination of linearity are greater than or equal to 0.9903.
Phenomenologically, compensating for the discrepancy between the theoretical and evaporation curves in the regions of thickness >75% and <25% is achieved by convoluting the theoretical thickness function with a Gaussian distribution. For the case of h=10mm, the result shows that the root-mean-square deviation between the evaporation and theoretical profiles reduces from 7.24% to 1.44% after applying the Gaussian convolution technique.
A spectrum measurement system is setup to measure the thin film transmittance at various locations on the LVF to evaluate the performance of linear variable filtering. The calculated transmittance of the LVF is obtained by Essential Macleod thin film software and the result is compared with the measurement. The experimental result shows that within the range of LVF zone, the critical wavelength presents a linear relationship with the position along the gradient thickness direction as predicted by the thin film transmittance calculation.
Within the LVF zone, cross-section of multilayer thin film observed by a scanning electron microscope shows smooth and solid film stacking between layers, which indicates the effectiveness of local mask thin film fabrication method.

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