本研究提出一套共面偵測分束器式光柵干涉儀，此套干涉儀採用「雙繞射式」的光路設計進行系統開發，透過光柵與反射鏡的搭配使通過光柵後的繞射光束再次穿過光柵形成二次繞射，用以引進加倍的的相位變化量，可有效提升干涉儀的量測靈敏度。此外，亦透過「Littrow光路」的設計概念，使繞射光束得以沿原路徑返回，使干涉儀能於單一偵測架構下提供面內位移及面外位移之量測訊息，同時亦藉由側向分束器(Lateral Displacement Non-Polarized Beamsplitter, LBS)的使用，在共用光學元件的情況下形成第二個偵測架構，而後可針對同一個待測光柵表面進行量測，用以形成「共面偵測光路」，每組偵測架構皆具備面內位移及面外位移的量測能力，藉由比對兩組偵測架構的量測結果即可回推出光柵於x軸及z軸的旋轉角度變化量。
由實驗結果證明，此套共面偵測分束器式光柵干涉儀可在不改變光學架構下，提供四自由度位移及旋轉角度的量測資訊，其面內、面外位移(x軸向及z軸向)及旋轉角(θx軸向及θz軸向)之解析度分別可達0.7 nm、1.2 nm及40.8 nrad、50.5 nrad；重複性分別優於0.6 nm、0.8 nm、8.3 nrad及10.2 nrad；穩定度於開放式環境歷時10分鐘的條件下分別優於8 nm、14 nm及100 nrad、200 nrad。由上述實驗結果驗證此套共面偵測分束器式光柵干涉儀具備優異的量測性能，日後可廣泛應用於各式需進行多自由度位移及角度量測等場合中。

In this study, a four-degree-of-freedom grating interferometer based on coplanar detection design is proposed. The proposed interferometer is adopted “double-diffraction” as the core technique. Through the combination of grating and mirrors, the diffraction beams are passed through the grating again to form the second diffraction, which can induce the double phase variation and can improve the sensitivity of the system effectively. In addition, through the design concept of “Littrow optical path”, the diffraction beams can return along the original path so that the proposed interferometer can provide the measurement information of in-plane and out-of-plane displacement under a single detection configuration. Also, by the use of a lateral displacement non-polarized beamsplitter (LBS), the second detection configuration is formed and the measurement can be obtained to form “coplanar detection optical path”. Therefore, each detection configuration has capabilities of measuring in-plane and out-of-plane displacement. By comparing the measurement of the two detection configurations, the measurements of θx-axis and θz-axis can be obtained.
The experimental results show that the four-degree-of-freedom grating interferometer can provide the measurement information of four-degree-of-freedom displacement and rotation angle without changing the optical configuration. The resolutions for displacement (x-axis and z-axis) and rotation angle (θx-axis and θz-axis) are approximately 0.7 nm, 1.2 nm, 40.8 nrad and 50.5 nrad, the repeatabilities are better than 0.6 nm, 0.8 nm, 8.3 nrad and 10.2 nrad, the stabilities are better than 8 nm, 14 nm, 100 nrad and 100 nrad in ten minutes. The superior performance demonstrates that the proposed interferometer can be widely used for various precision measurement systems.

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