本研究提出一套創新的六自由度聚焦式雷射光學尺量測技術，其系統架構簡單，架設與校正容易，可用以進行精密位移及旋轉角度量測。此套量測技術的開發主要是以「光柵干涉術」為技術核心，輔以外差調制技術及自行設計的「聚焦式光路」，除可使雷射光學尺系統具備高靈敏度、高解析度與高穩定度等量測性能之外，亦使系統具備高可調性及低裝置誤差等技術優勢，深具商品開發潛力。
此套雷射光學尺主要是藉由光束偏移器(Beam Displacer, BD)、聚焦透鏡及光柵等元件的配合，成功地建構出「聚焦式光路」架構，可使雷射光束通過BD元件後形成偏振態相互垂直（p偏振光與s偏振光）而行進方向相互平行的兩道光束，而後藉由聚焦透鏡將p偏振光與s偏振兩光束聚焦至光柵後形成繞射，透過選擇合適的光柵週期及聚焦長度後，即可使p偏振與s偏振之繞射光於空間中部分重疊，其重疊區域將產生干涉條紋，當光柵於面內方向移動時，將因為都卜勒移頻效應使各繞射階光引入相位變化，藉由量測干涉訊號的相位變化量，即可回推待測光柵的面內位移量。
此外，於研究中我們透過適當地改變光柵與聚焦透鏡間的距離，使聚焦於光柵的兩道入射光產生離焦的效果，如此即可於單一的偵測架構下建立兩個干涉訊號的偵測區域，當光柵於面內方向產生旋轉角度時，兩偵測區域所引入的相位變化量將有所差異，並利用三角函數及兩偵測區域的干涉訊號相位變化之關係式，即可回推光柵於面內方向所產生的旋轉角度變化量。接著，本研究亦可藉由二維光柵的使用及BD元件的加入，使此套聚焦式雷射光學尺於單一偵測架構中，同時具備三自由度面內資訊的量測能力(即x, y, θz)。最後，透過分光技術的使用亦能有效延伸此套聚焦式雷射光學尺的量測能力，使其可在不改變光學系統架構下同時提供六自由度的量測訊息(x, y, z, θx, θy, θz)。
為了驗證此套聚焦式雷射光學尺量測技術的可行性，本研究進行了一系列的實驗，包括六自由度位移及旋轉角、解析度、重複度、穩定度、速度極限及靈敏度測試等實驗，並將聚焦式雷射光學尺的量測結果與商用感測器的量測結果相比較，用以驗證雷射光學尺的量測性能。由實驗結果證明，本研究所開發的聚焦式雷射光學尺可同時提供六自由度位移及旋轉角度量測訊息，其位移與旋轉角之實際解析度分別可達3 nm與50 nrad，重複度可達0.8 nm 與15 nrad，穩定度於5分鐘內之條件下優於20 nm與1200 nrad，速度極限可達1800 μm/s，靈敏度約為108˚/μm，由以上實驗結果可驗證此套系統具備精準的位移及旋轉角度量測能力。

In this study an innovative six-degree-of-freedom focusing type laser encoder is proposed. This measurement system has a simple configuration, is easy to set up and calibrate, and can be used for precision displacement and rotation measurement. The development of this measurement technique is mainly based on grating interferometry, and is combined with the heterodyne modulation technique and a novel focusing type optical path. In addition to possessing high sensitivity, high resolution and high stability, the system also has the technical advantages of high adjustability and low installation error, and has great potential for commercial development.
The laser encoder mainly consists of a beam displacer (BD), a focusing lens and a grating, combining to form a focusing type optical path configuration, which allows the laser beam to pass through the BD element to form a two parallel beams polarized perpendicularly to one another. The two beams are then focused onto the grating by a focusing lens to form diffraction, and by selecting an appropriate grating period and a focusing length, the diffracted beams can be overlapped, and the overlapping area will form interference fringes. When the grating moves in an in-plane direction, phase change will be introduced into the interference pattern to Doppler shifting. By measuring the phase variation of the interference signal, the phase change can be used to calculate the in-plane displacement of the measured grating.
In addition, by increasing the distance between the grating and the focusing lens a certain amount, the two focused beams on the grating will be defocused, so that two interference signals can be detected under a single detection system. In the measurement area, when the grating produces a rotation in the in-plane direction, the phase change amount introduced by the two detection areas will be different, and the relationship between the trigonometric function and the phase change of the interference signals of the two detection areas can be used. The amount of change in the angle of rotation produced by the grating in the in-plane direction. This study can also utilize two-dimensional gratings and the addition of BD components to expand the measurement capabilities of this focusing type laser encoder into a three-degree-of-freedom in-plane motion (x, y, θz) interferometer, while still remaining a single detection system. Finally, to extend the measurement capability of the proposed system, beam splitting can be used to expand the system into a six-degree-of-freedom measurement information without changing the optical system configuration (x, y, z, θx, θy, θz).
In order to verify the feasibility of this set of focusing type laser encoder, this study carried out a series of experiments, including displacement and rotation in six degrees-of-freedom, resolution, repeatability, stability, speed limit and sensitivity tests. The measurement results of the focusing type laser encoder were compared with those of a commercial precision displacement sensor to verify the measurement performance of the focusing type laser encoder. The experimental results show that the focused laser encoder can provide six-degree-of-freedom displacement and rotation measurement information. The actual resolution of displacement and rotation can reach 3 nm and 50 nrad, respectively. For repeatability it can reach 0.8 nm and 15 nrad respectively, the stability is better than 20 nm and 1200 nrad in 5 minutes, and the speed limit is 1800 μm/s. Finally, the sensitivity is about 108˚/ μm. The above experimental results prove that the system has great displacement and rotation measurement capabilities.

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