光譜儀系統中，根據光柵方程式將入射光分光後，偵測器上會產生高階光波干擾，二階線性漸變濾波器(second-order Linear Variable Filter, LVF)目的為濾除光譜儀系統中光柵分光後二階以上光波。本研究為探討LVF的設計流程開發，可主要分為三個部分。
第一部份為膜層厚度分佈設計，以基板上加擋板的LVF製作方式，定義擋板高度、基板位置、尺寸與蒸鍍腔內配置的結構參數，建立理論模型，模擬出基板上薄膜二維及三維的厚度分佈，並以數值軟體Excel與MATLAB計算與分析。接著變動擋板高度數值，可得出在LVF膜層相對厚度0%至100%的水平位置距離與擋板高度之關係。
光譜儀系統中光柵和偵測器皆會對光波穿透率造成影響，故在第二部分，會使用包含以上變數的效能運算匹配式，計算LVF對於高階光波的透射率規格。再把本研究膜層結構設計的對稱膜堆設計原則，與前述LVF規格，套入光學鍍膜軟體 Essential Macleod，模擬應用波段為400 – 1000 nm的LVF膜層結構，包括膜層的物理厚度(physics thickness)、光學厚度(optical thickness)，以及穿透頻譜圖等結果。接著使用三種方式推導出基板上漸變膜層的穿透頻譜可知，以先模擬出膜層相對厚度50%的穿透頻譜，再利用軟體改變膜層厚度至相對厚度25%和75%的方式，其穿透頻譜表現最能接近實際應用情況。再改變應用波段至900 – 1700 nm，得岀膜層結構與穿透頻譜圖。
最後部分，配合實際光譜儀案例，在兩個波段範圍：可見光波段(400 – 1000 nm)，近紅外光波 (900 - 1700 nm)，設計兩組LVF，搭配解析度為1.5 nm及3 nm的光柵和規格為8 μm/pixel size及25 μm/pixel size的偵測器，設計出能與其匹配的LVF，驗證本研究所開發之設計流程。

According to the grating function, high order wavelength interference occurs on the detector in a spectrometer system. A second-order linear variable filter (LVF) is used for the purpose of eliminating these high order wavelengths. Development of design process for LVF is discussed in this thesis, which can be divided into three major parts. The first part is the design of distribution for LVF thin film thickness, by using the manufacturing of adding a mask on the substrate. It starts with building a theory model for simulating two and three-dimension thin film thickness distribution, then uses numerical calculation software such as Excel and MATLAB to analysis the results. These show the relationship between the horizontal distances from 0% to 100% relative thickness position and the mask heights.
In a spectrometer system, grating and detector also affect the optical transmission. So an equation includes these factors will be introduced in the second part and is used for calculating the transmission of high order wavelengths about LVF. Substituting the results above and the symmetric multilayers design, which is the method of constructing thin film structures in this thesis, into the optical coating design software, Essential Macleod, to simulate physics thickness, optical thickness and transmission spectrum of thin film layers.
Then uses three different ways to derived transmission spectrum in different relative thickness positions applied in 400 – 1000 nm wavebands. The results show that the way approaches the real situation most, is simulating the transmission spectrum at the 50% relative thickness position of LVF first, then keep the same thin film structures and change the relative thickness to 25% and 75%. Then repeats the process above but changes wavebands to 900 -1700 nm, outputs the thin film structures and the transmission spectrum.
Two wavebands are introduced in the third part, including visible and near-infrared wavelengths, to verify the design process developed. With two 1.5 nm and 3 nm resolution gratings and two 8μm and 25μm pixel size detectors, the process is worked.

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