本研究提出一套創新的四自由度共路徑式線性光學尺，具備同時量測面內或面外的位移及旋轉角量測能力。此套線性光學尺結合干涉術、光柵干涉術、分光技術及共路徑式光路等技術優勢進行系統開發，具備高靈敏度、高穩定度、高容忍度、精密的位移量測和自行校正能力，且已成功將系統微小化。
此套四自由度共路徑式線性光學尺，其系統光路架構簡單、架設快速和低成本的優勢。此外，只需要一個稜鏡和光柵的組合便可得到面內或面外的位移資訊。此套系統以「共路徑式光路」為設計核心，主要是藉由稜鏡角度的設計，使雷射光源入射至稜鏡後，會產生一道穿透光P光及一道折射光R光，並以斜向入射的方式入射至光學尺尺身(光柵)，會使得穿透光P光及折射光R光的繞射光相互疊合形成干涉，當光柵產生面內或面外位移時，我們藉由光偵測器接收干涉訊號的相位變化，進而回推光柵之物理量。為了進一步提升此系統的量測能力，我們利用分光的技術，讓系統於光柵上形成兩個偵測點，使此套線性光學尺系統可以同時量測位移及旋轉角，並且能夠自行補償因旋轉角對量測所造成的誤差，賦予系統具備自行校正能力。
由實驗結果證明，此套四自由度共路徑式線性光學尺的位移與旋轉角的解析度分別可達10 nm與200 nrad，重複度可達3.6 nm 與71 nrad，穩定度於30分鐘內之條件下優於30 nm與1000 nrad，速度極限可達8800 μm/s，具備優異的量測性能及商品化之開發潛力，可廣泛應用於各式需精密量測的場合中。

An innovative four-degree-of-freedom common path linear encoder with the ability to simultaneously measure both in and out of plane displacements and rotations is proposed in this study. This linear encoder combines the advantages of interferometry, grating interferometry, beam splitting techniques and common optical path design to develop a system with high sensitivity, high stability, high tolerance, precise displacement measurement and self-correction capability, and has been successfully miniaturized.
The four-degree-of-freedom common path linear encoder has the advantages of simple configuration, quick set up and low cost. In addition, only one set of prism and grating is needed to obtain both in-plane and out-of-plane displacement information. The system is designed around the core of a common optical path configuration, focusing mainly on the angle of the prism. This causes the laser light source entering the prism to split into a transmission P beam and a refracted R beam. The P and R beam are then incident onto the optical scale (grating) at an oblique angle and diffracted, causing the diffracted P and R beams to overlap forming interference. When the grating is displaced in and in-plane or out-of-plane direction, the phase change of the interference signal received by a photodetector can be used to obtain the grating displacement value. To further enhance the measurement capability of this system, beam splitting was utilized to form two detection points on the grating, allowing the linear encoder system to measure displacement and rotation simultaneously, while compensating for measurement alignment errors, and give the system the ability to self-correct.
The experimental results show that the resolution of the displacement and rotation angle of the four-degree-of-freedom common path linear optical scale can reach 10 nm and 200 nrad, respectively. The repetition rate can reach 3.6 nm and 71 nrad, and the stability is within 30 minutes. Under the condition of better than 30 nm and 1000 nrad, the speed limit can reach 8800 μm/s. It has excellent measurement performance and potential of commercial development, and can be widely used in various occasions where precision measurement is required.

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