本研究提出一套「雙自由度共路徑式散斑干涉儀」，此套系統以氦氖雷射(Laser)、偏振片(P)、電光調制器(EOM)、平行分束器(BD)、沃拉斯頓稜鏡(WP)、圓柱透鏡(CL)及光感測器(PD)等光學元件建構出外差光源模組、散斑干涉模組及訊號解調模組，可直接於單一偵測面上形成兩組位移偵測架構，用以進行精密位移及角位移量測，並形成共路徑式光路，能有效降低光學元件的使用數量及裝置誤差，具低成本的開發優勢。
依據此套共路徑式散斑干涉儀的量測原理，我們透過氦氖雷射及電光調制器的搭配來形成外差光源模組，使雷射光束可載於特定的頻率上，能有效降低環境低頻擾動對干涉儀之量測結果所造成影響。而後，透過BD、WP及CL的搭配建構出獨特的共路徑式散斑干涉模組，使系統在形成兩組偵測架構的同時，其參考光束及量測光束於空間中皆行經相同的光學元件及路徑，當環境存在擾動時，其擾動量將於干涉訊號中相互抵消或補償，能有效降低環境擾動對干涉儀之量測結果所造成的影響，使系統具備優異的穩定性。此外，透過兩組CL元件的搭配及擺放，即能使四道外差偏振光束以特定的角度成對入射至待測粗糙面(於本研究中使用鋁合金平板)上形成散射，其散射光將於空間中相交疊形成干涉，而後由兩光偵測器所接收，形成兩組偵測架構。最後，透過光感測器(PD)及訊號擷取卡(DAQ)將兩組偵測架構之干涉訊號輸入至鎖相解調軟體中，形成訊號解調模組，每組偵測架構皆具備面內位移的量測能力，當待測粗糙面沿著面內方向進行角位移運動時，藉由比較兩組偵測架構的量測結果之差異，即可藉由三角函數回推出待測粗糙面的角位移變化量，使此套共路徑式散斑干涉儀系統具備量測面內位移及角位移的能力。
為了進一步驗證此套「雙自由度共路徑式散斑干涉儀」我們將粗糙待測表面架設於商用精密定位平台(Physik Instrumente, P562.6CD)上，並進行一系列嚴謹的驗證實驗，包括位移、解析度、重複性、隨機位移及穩定度量測實驗，同時使用商用干涉儀(Keysight 5517B)加以驗證。首先，由不同波型及行程及的位移及角位移運動量測實驗結果可知，本研究所提出之雙自由度共路徑式散斑干涉儀的量測結果與電容式位移計及商用干涉儀的量測結果相符，驗證此套散斑干涉儀具備精密的位移及角位移量測能力。而後，由微小行程位移(5 nm)及角位移(600 nrad)運動實驗的量測結果可知，此套共路徑式散斑干涉儀的位移及角位移量測解析度(1σ)分別可達3.08 nm及312.68 nrad，驗置此套散斑干涉儀具備高解析度。由來回步階實驗結果可知，此套散斑干涉儀的位移及角位移量測重複性分別為0.41 nm及0.15 μrad，驗證此套散斑干涉儀具備高重複性。由30分鐘穩定度量測結果可知此套散斑干涉儀在靜止的狀態下進行30分鐘的量測實驗，其穩定度可控制在12.78 nm及695.52 nrad，驗證此套散斑干涉儀具備高穩定性。由上述實驗結果證明本研究所開發之「雙自由度共路徑式散斑干涉儀」具備優異的位移及角位移量測能力，同時具備高解析度、高穩定度及高重複性，日後可廣泛應用於各式精密位移量測的場合中。

This study proposes a Two Degree-of-freedom Common-path Speckle Interferometer. It is composed of heterodyne light source module, speckle interference module and signal demodulation module, which can be used for precise displacement and angular displacement measurement. The common-path speckle interferometer's optical path consists of a he-ne laser, a polarizer (P), an electro-optic modulator (EOM), a beam displacer (BD), a Wollaston prism (WP), a cylindrical lens (CL), and a photodetector (PD). Two sets of displacement detection structures can be directly formed on a single detection surface, which can effectively reduce the number of optical elements used and installation errors, and has the advantage of low-cost development.
Based on the measurement principle of this set of common-path interferometer, we use a combination of a he-ne laser and an electro-optic modulator to form a heterodyne light source, enables the laser beam to be modulated at a specific heterodyne frequency. This approach effectively reduces the impact of low-frequency environmental disturbances on the interferometer measurement results. Then, by BD, WP, and CL construct a unique common-path interferometric setup, the system achieves two distinct detection schemes, with both the reference and measurement beams passing through the same optical components and path in space. In the presence of environmental disturbances, the disturbances are mutually cancelled or compensated in the interference signal. This design effectively reduces the impact of environmental disturbances on the interferometer measurement results, ensuring the system possesses outstanding stability. Furthermore, by employing two sets of CL elements and arranging them appropriately, four heterodyne polarized beams are incident on the test rough surface (In this study, an aluminum alloy plate was used as the test rough surface.) at specific angles, forming scattering. The scattered light interferes when the beams overlap in space and is then detected by two photodetectors, creating two sets of heterodyne speckle interferometric detection schemes. Each detection scheme has the capability to measure in-plane displacement. When the test rough surface undergoes displacement or angular motion in the in-plane direction, the measurement results from the two detection schemes are compared, enabling the determination of the displacement or angular displacement change of the test rough surface. This common-path heterodyne speckle interferometer system possesses the ability to measure both displacement and angular displacement changes, providing a dual-degree-of-freedom measurement capability.
In order to further validate the " two degree-of-freedom common-path speckle interferometer," we set up the rough test surface on a commercial precision positioning platform (Physik Instrumente, P562.6CD) and conducted a series of rigorous verification experiments, including displacement, resolution, repeatability, random displacement, and stability measurements. At the same time, we used a commercial interferometer (Keysight 5517B) for comparison and verification. Firstly, The results from displacement and angular displacement motion measurements using different waveforms, different stroke lengths, and random waveforms show that the measurement results of the proposed dual-degree-of-freedom common-path speckle interferometer are consistent with those of the capacitive displacement sensor and the commercial interferometer. This validates the precise measurement capability of the speckle interferometer for both displacement and angular displacement. Then, the results from small stroke displacement (5 nm) and angular displacement (600 nrad) motion experiments indicate that the displacement and angular displacement measurement resolutions (1σ) of this common-path speckle interferometer are 3.08 nm and 312.68 nrad, respectively, validating its high resolution capability. The results from back-and-forth step experiments show that the displacement and angular displacement measurement repeatability of this speckle interferometer are 0.41 nm and 0.15 μrad, respectively, confirming its high repeatability. The 30-minute stability measurement results demonstrate that this common-path speckle interferometer can maintain its measurement values within 12.78 nm and 695.52 nrad while in a static state during the 30-minute measurement experiment. This verifies the high stability capability of the speckle interferometer. Based on the above experimental results, it is evident that the " two degree-of-freedom common-path speckle Interferometer " developed in this study possesses excellent displacement and angular displacement measurement capabilities, along with high resolution, stability, and repeatability. Its wide-ranging applications in various precision displacement measurements are promising for the future.

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