近年來，精密機械業對於能提供高精度的量測設備需求正逐年攀升，透過具備優異量測性能的量測設備對工具機台進行位移、旋轉角和幾何誤差量測與校正，以維持高製造精度。然而，大多數的量測設備無法同時提供多自由度的位移或旋轉角度的量測資訊，即無法準確地量測被測物體在各個自由度上的運動狀態或偏差。
本論文開發一套創新的「循環式光柵干涉儀」，可用以進行精密位移(x, z)及旋轉角度(θx, θy, θz)量測，具備優異的幾何誤差量測能力。此套系統是以「循環式」光路做為技術核心進行開發，當外界環境存在擾動時，其擾動量將於干涉訊號中相互抵消，能有效提升系統的穩定性。於此同時，此套獨特的「循環式」光路亦能克服常見光柵干涉儀無法進行面外位移量測之缺點，經干涉訊號的加減運算後，即能使干涉儀於單一偵測架構下即具備雙軸向(x, z)位移之量測能力；透過「雙繞射式」光路設計，使繞射光束兩次入射至光柵元件，藉此引入兩倍的相位變化量，可有效提升系統的靈敏度及解析度；藉由「共面偵測式」光路設計，建構出三組偵測架構，每組偵測架構皆具備面內(x)與面外(z)位移的量測能力，由各偵測架構之間所獲得的位移量測結果的比對，即可進一步回推待測光柵於三軸向(θx, θy, θz)的旋轉角度變化量。如此，即能使系統在不改變光學架構的情況下，進行幾何誤差量測。
由實驗結果可知，此套「循環式光柵干涉儀」可同時提供雙軸向(x, z)位移、三軸向(θx, θy, θz)旋轉角度及幾何誤差量測資訊，其於各軸向位移及旋轉角度的解析度分別為1.2 nm、1.5 nm、14.6 nrad、25 nrad及16.5 nrad；重現性分別優於1.9 nm、2.4 nm、10.3 nrad、10.8 nrad及9.5 nrad。此外，此套系統於30分鐘的量測穩定度亦分別優於16.7 nm、36.4 nm、590 nrad、722 nrad及494 nrad。由上述的量測結果證明此套「循環式光柵干涉儀」具備優異的量測性能，日後可廣泛應用於各式需進行位移、旋轉角度及幾何誤差量測之場合中。

In recent years, the demand for high-precision measurement equipment in the precision machinery industry are increasing year by year. Measurements of displacement, rotation angle or geometric error for machine tools are carried out through the measurement equipment with excellent measurement performance to maintain high manufacturing accuracy. However, most measurement equipment cannot provide measurement information of displacement or rotation angle of multiple degrees of freedom simultaneously, that is, cannot accurately measure the motion state or deviation of the measured object in each degree of freedom.
In this thesis, an innovative cyclic grating interferometer is developed for precise displacement (x, z), rotation angle (θx, θy, θz) and geometric error measurements. The proposed system is developed with a “cyclic optical path” as the core technology, therefore, when there are disturbances in the external environment, the disturbances would be canceled in the interference signal, which can effectively improve the stability of the proposed system. Meanwhile, the proposed “cyclic optical path” can also overcome the shortcomings of common grating interferometers that cannot perform out-of-plane displacement measurement. After the addition and subtraction of the interference signals, the proposed interferometer is able to measure biaxial (x, z) displacements under a single detection configuration. Moreover, through a “double diffraction optical path” design, the corresponding diffraction beams are incident on the grating twice, thereby introducing double amount of phase change, which can enhance the measurement sensitivity and resolution of the system. Meanwhile, through the design concept of coplanar detection configuration, each set of detection configuration has the ability to measure in-plane (x) and out-of-plane (z) displacements simultaneously. By comparing the measurement results obtained between the detection configurations, the rotation angle variation of the grating to be measured in the three axes (θx, θy, θz) can be further obtained. In this way, the proposed system has the ability to measure geometric errors without changing the optical configuration.
It can be seen from the experimental results that this set of “cyclic grating interferometer” can simultaneously provide biaxial displacement (x, z), triaxial rotation angle (θx, θy, θz) and geometric errors measurement information. The measurement resolution of displacement and rotation angle in each axis (x, z, θx, θy, θz) is 1.2 nm, 1.5 nm, 14.6 nrad, 25 nrad and 16.5 nrad while the measurement reproducibility is better than 1.9 nm and 2.4 nm, 10.3 nrad, 10.8 nrad and 9.5 nrad. In addition, the measurement stability of this system in 30 minutes is better than 16.7 nm, 36.4 nm, 590 nrad, 722 nrad and 494 nrad, respectively. The measurement results demonstrate that the proposed cyclic grating interferometer has excellent measurement performance and can be widely used in various occasions where displacement, rotation angle and geometric errors measurements are required in the future.

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