本文探討光譜儀的系統中，利用光柵方程式將入射光分光後，會形成一階及二階以上的光波，設計高通濾波主要是先前所開發的二階線性漸變濾波器(second-order Linear Variable Filter,LVF)，二階線性漸變濾波片為了保留光譜儀系統中光柵分光後一階的光波，而濾除二階及二階以上的光波，探討二階線性漸變濾波器(second-order Linear Variable Filter,LVF)的穿透頻譜圖模擬設計。
本研究使用薄膜厚度理論，建立於線性漸變濾波片上，於目標製程上加入蒸鍍機台相關之製程參數、擋板高度設計等，利用數值運算軟體Matlab模擬基板上之膜厚分佈及輪廓，判斷膜厚分佈中，相對厚度25%至75%為最佳線性度，利用此結果，找出不同擋板高度下，所求得線性漸變區寬度，應用於線性漸變濾波片穿透率光譜之表現。
本實驗應用於可見光波段(400-1000nm)與短波紅外光波段(900-1700nm)進行膜堆設計，使用於業界廣泛使用的光學鍍膜設計軟體TF-Calc，以低通對稱膜堆設計並優化，接著分析高通濾波以及低通濾波線性漸變濾波片之線性變化，得知臨界波長λ_C相對應相對厚度，求得R平方值，確保線性度的可能性。調整相對厚度，呈現對應之穿透光譜之表現，定義線性漸變區相對厚度中間為50%，選定光譜儀偵測器之寬度，得出高通濾波與低通濾波線性漸變區寬度，由得知的線性漸變區寬度找出不同擋板高度下之線性漸變濾波片。
為了達到帶通濾波線性漸變之效果，高通濾波線性漸變濾波片需與低通濾波線性漸變濾波片重疊，針對不同高低通濾波之膜堆設計，能呈現不同半高全寬(Full Width at Half Maximum)之大小與帶通濾波最高穿透率之波長位置，並且分析帶通濾波片光譜分辨力(Resolving Power)之解析度。

The grating equations split the incident light and generate first-order and the above of the second-order wavelengths in a spectrometer system.Previously the development of a second-order linear variable filter (LVF) was mainly designed high pass filtering.In order to reserve a first-order after the grating split it eliminates second-order and the above of second-order wavelengths in a spectrometer system.A second-order linear variable filter is discussed in the simulation and design of transmission spectrum.
The research is used for the design of distribution for thin film thickness which building on a second-order linear variable filter.The use of numerical operation Matlab simulated the distribution for thin film thickness and profile because of matlab is added to the fabricated parameters and designing the height of mask in a coating machine.The relative thickness 25% to 75% is the best linearity judging by the distribution for thin film.The result of different the height of local mask get the wide of linear variation which is applied to the performance of transmission spectrum.
The experiment designed the stack of thin film and used a software for optical film design.Based on designing the stack of thin film and optimization,it analysed the linear variation of low pass filtering and high pass filtering on visible near-infared (VNIR) and short wavelength infared (SWIR).The critical wavelength correspond to the relative of thickness and get the value of the R square.It assured that the relative of 25% to 75% have the probability of the linearity.The definition of the center relative thickness is 50% in the area of linear variation.If you choose the wide of detector,you can get linear variable wide of low pass filtering and high pass filtering.The wide of linear variation find the different of the height of the local mask on a second-order linear variable filter.
In order to achieve the effect of linear variable band pass filtering,the high pass filtering overlaps the low pass filtering.With the design of film stack for the difference of high pass and low pass filterings,it performs the difference of full width at half maximum and the position of the best transmittance in a band pass filtering and analyzes the resolution of the band pass filter.

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