摘 要
由於鍍膜設備的進步使漸變折射率薄膜的製程變得容易，使漸變折射率光學薄膜的設計將會成為重要的課題，而多種設計方法中以傅立葉轉換法最能夠以物理方式推導與理解，不需使用嘗試錯誤或迭代的方式得到結果，所以可快速正確的得到初階折射率分佈與較正確的光譜圖，再由傅立葉轉換法所得的結果作耦合層設計或經由修正輸入之穿透率值得到最佳的結果，而本論文之工作主要分為兩項，一是使用射頻離子束濺鍍方法並利用靶材Ta靶與SiO2靶混合出折射率由2.2變化至1.48且低吸收之光學混合膜，且可有效控制折射率之間隔至0.03以下；二是利用傅立葉轉換之數學式撰寫成電腦程式作漸變折射率光學薄膜之光學成效設計，既是將欲達成之穿透率光譜用傅立葉轉換，轉換成折射率對光學厚度之變化圖，並且能完成初步之自動化鍍膜控制程式，得到預期之光學成效，證明漸變折射率光學鍍膜之可行性。

Abstract
The gradient-index optical thin film design will become an important topic, since the fabrication of gradient-index optical thin film is easier. Furthermore, among the several methods, only the Fourier transform methods can used as a physical means to explain and understand. Thus it is unnecessary to used try and error or substitution method to derive results, so it is fast and accurate to derive a first step refractive index distribution and correct transmittance spectrum. Then Fourier transforms is used to obtain a result for coupled layer design or modify input transmittance spectrum to get the best design. This thesis has two parts, part one is the use of radio frequency ion beam sputtering and moving target coat composite thin film of refractive index continuously varied from 2.2 to 1.48 and low absorption by Ta and SiO2 targets, to effect the control refractive index to a lower interval of 0.03; Part two is to design optical performance of gradient-index optical thin film by using mathematics formula of Fourier transform to write a computer program. That is transform the transmittance spectrum to a refractive index vs. optical thickness curve by Fourier transform, and finish the first step of an automatic coating control program. To obtain the expected optical performance, the proven moving target method for coating gradient-index optical thin film is practical.

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