本研究提出一套以「雙繞射」為設計概念進行系統開發的雙繞射式雷射光學尺，用以進行位移及旋轉角量測。此套雙繞射式雷射光學尺系統整合外差干涉術、光柵干涉術、雙繞射光路及分光技術等設計概念進行開發，使系統具備高解析度、高穩定度及六自由度的量測能力。
此套雙繞射式雷射光學尺系統透過「雙繞射」的光路設計，除可使通過光柵後的繞射光再次穿過光柵，用以引入加倍的相位變化量，有效提升雷射光學尺的系統解析度之外，亦可解決傳統雷射光學尺存在離焦偵測之問題，即當光柵產生面外方向移動時，系統仍可持續提供正確的面內位移量測訊息。此外，藉由光柵、分光鏡與反射鏡的配合，使系統於單一偵測架構下即具備雙自由度位移及旋轉角度的量測能力。為了進一步延伸此套雙繞射式雷射光學尺的量測能力，我們藉由分光技術的運用成功建構出三組偵測架構，使雷射光學尺系統具備六自由度(x, y, z, θx, θy, θz)的精密量測能力。
為了驗證本研究所提出的雙繞射式雷射光學尺之可行性及其系統性能，我們分別使用商用六軸微定位平台及長行程定位平台進行多項實驗，並將雷射光學尺的量測結果與平台內建的電容式位移計及線性光學尺所量測到的結果相比較。由實驗結果證明，此套雙繞射式雷射光學尺量測技術可在不改變光學架構下，同時提供六自由度位移及旋轉角度的量測資訊，其位移與旋轉角度的解析度分別可達2 nm與300 nrad，重複性分別優於1.7 nm及51 nrad，量測速度極限可達150 μm/s，具備優異的量測性能，可廣泛應用於精密量測、工具機業及自動化光學檢測等場合中。

In this study, a resolution-enhanced laser encoder with “double diffraction” as its primary design concept for precision measurement of displacement and rotation is proposed. The double-diffraction-type laser encoder is developed by combining heterodyne interferometry, grating interferometry, double diffraction optical configuration, as well as the beam splitting technique. It has the capability of measuring in six degrees-of-freedom (DOF) with high resolution and stability.
The proposed system takes advantage of a “double diffraction” optical configuration, which directs diffracted light to pass through a grating twice without additional optical components, thereby doubling the phase change induced by grating displacement, effectively improving the resolution of the laser encoder. In addition, the design of the optical path configuration of the system can overcome the problem of defocusing of conventional laser encoders, that is when the grating moves in the out-of-plane direction, the proposed laser encoder can continue to provide accurate in-plane displacement measurement information. Furthermore, through the incorporation of mirrors and a beamsplitter, the system is given the ability to measure in 2 DOFs, both displacement and rotation, using only a single detection structure. To extend the measurement capability of the resolution-enhanced laser encoder, we combined three detection structures into one measurement system possessing the ability to perform simultaneous precision measurement in six DOFs (x, y, z, θx, θy, θz).
In order to verify the feasibility and performance of the proposed laser encoder, a commercial 6-DOF precision positioning stage, as well as a long-stroke nano-displacement stage were used in conjunction with the system to perform several experiments, with the measurement results obtained from the proposed system compared with the built-in capacitive sensor of the commercial six DOF precise position stage, as well as the built-in linear encoder the long-stroke nano-displacement stage. As displayed in the results, the proposed resolution-enhanced laser encoder has the ability to perform precision displacement and rotation measurement in six DOFs without needing to change the optical configuration, as well as overcoming the defocusing problem inherent to laser encoders. The resolution of the displacement measurement system is twice that of conventional laser encoders. The system resolutions for displacement and rotation measurement are 2 nm and 300 nrad, and the repeatability are better than 1.7 nm and 51 nrad, respectively. The maximum velocity for displacement measurement can reach 150 μm/s. The proposed laser encoder is well-suited for applications within precision manufacturing, tool machine industry, automatic optical measurement, nanotechnology, semi-conductor technology and other related fields.

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