本研究提出一套創新的六自由度外差式散斑干涉儀，用以進行精密位移及旋轉角度量測。此套外差式散斑干涉儀系統結合外差干涉術、散斑干涉術、對稱式光路和分光技術等技術之優勢，具備高解析度、大量測範圍及六自由度的量測性能。
此套六自由度外差式散斑干涉儀由外差光源模組及三組對稱式偵測架構所組成，每一組偵測架構皆可提供雙自由度的位移量測訊息。我們藉由電光調變器及氦氖雷射所構成的外差光源模組來產生外差光源，再透過光柵、Wollaston prism(WP)元件、及聚焦透鏡的使用來建構出創新的對稱式光路，使系統易於架設及校正。當外差光源先後通過光柵、WP元件及聚焦透鏡後，參考光及量測光將以對稱角度入射並交疊於一待測平面(紙面)後形成散射及干涉，再利用光電感測器來接收其干涉光強訊號。當待測平面沿著面內方向產生位移變化時，由待測平面到外差光源和由光感測器到待測平面的相對距離會隨入射角和觀察角發生改變，光的電場在相對距離發生兩次改變時，會因為都卜勒效應而隨之改變，我們可以藉由光感測器所量測到的散射光之相位變化量來回推待測平面之位移量變化量。
為了驗證此套六自由度外差式散斑干涉儀的可行性及其量測性能，我們分別使用商用六軸定位平台及長行程步進平台來進行多項實驗，並將干涉儀的量測結果與平台內建的電容式位移計與光學編碼器所量得的結果相比較。由實驗結果證明，本研究所開發的六自由度外差式散斑干涉儀可準確地提供六自由度的位移及旋轉角度量測訊息，其實際量測解析度約為10 nm及5 μrad，三軸向位移(x, y, z)之重複性為0.4 nm、0.4 nm、1.8 nm，三軸向旋轉角(θx, θy, θz)之重複性為2 μrad、3.5 μrad 、1.58 μrad，量測速度極限約為110 μm/s，具備優異的量測性能，可廣泛應用於機密機械、自動化光學檢測及工具機業等場合中。

In this study, a novel six-degree-of-freedom (DOF) heterodyne speckle interferometer for displacement and rotation angle precision measurement is proposed. The proposed system is combines the advantages of heterodyne interferometry, speckle interferometry, symmetrical optical path design and beam splitting technique, and possesses high resolution, large measurement range and multi-dimensional measurement capability.
The proposed six-DOF heterodyne speckle interferometer consists of a heterodyne light source and three sets of symmetrical measurement configurations, with each set providing two-DOF in-plane displacement information. The heterodyne light source is produced by means of an electro-optic modulator and a helium-neon laser, and the innovative symmetrical optical path configuration is constructed with a grating, a Wollaston prism, and a focusing lens, making the system easy to set up and calibrate. When the heterodyne light passes through the grating, WP and focusing lens, the reference and measurement light will be incident at a symmetrical angle and overlap on a measured plane to form scattering and interference, the intensity of which is then acquired by a photodetector. When in-plane motion occurs for the measure plane, its distance to the light source and the photodetector will change with the angle of incidence and the angle of observation, and the electric field of the beams will change due to the Doppler effect. The displacement and rotation angle of the measured plane can then be derived from the phase shift of the speckle pattern received by the photodetector.
To verify the feasibility and performance of the system, we used a commercial six-DOF positioning stage and a long-stroke stepping stage to carry out a number of experiments, and the system measurement results are compared with the results of the built-in capacitive displacement sensor and the optical encoder of the stages. The results show that the six-DOF heterodyne speckle interferometer can accurately provide measurement data of six-DOFdisplacement and rotation, the measurement resolution is about 10 nm, the repeatability of the x, y and z-axis displacement is 0.4 nm, 0.4 nm, 1.8 nm, the repeatability of θx, θy and θz axis rotation is 2 μrad, 3.5 μrad 1.58 μrad, and the measurement speed limit of the system is about 110 μm/s. This system displays excellent measurement performance and can be widely applied in fields such as precision manufacturing, automated optical measurement and machine tool industry.

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