本研究提出一套「循環式線性光學尺(CLE)」，此套光學尺是由雷射二極體、光柵(G)、側向位移分光鏡(LBS)、偏極化分光鏡(PBS)、反射鏡(M)、偏振片(P)及IC光偵測器所組成，具光路架構簡單、元件取得容易和低成本的開發優勢。此套線性光學尺主要是透過創新的光路設計使參考及量測光分別行經相同的光學元件及路徑後相疊合形成干涉，建構出所謂的「循環式光路」，當外界環境存在擾動時，參考及量測光束皆會感受到相同的擾動量，其擾動量將於干涉訊號中相互抵消或補償，可有效提升光學尺的穩定度及準確度。
根據此套循環式線性光學尺的量測原理，我們使用雷射二極體做為系統光源，而後使光束穿過一偏極化分光鏡(PBS)形成穿透(p偏振)及反射(s偏振)光束，此兩道光束將以對稱的方式斜向入射至反射式光學尺(光柵元件)後形成繞射，建構出對稱式光路，而後，我們透過一個反射鏡使p偏振光的第負一階(-1st)繞射光束(Ep-1)及s偏振光的第正一階(+1st)繞射光束(Es+1)再次入射至光學尺形成第二次繞射，建構出雙(再)繞射式光路，兩次繞射的p偏振及s偏振雙繞射光束(E2s+1及E2p-1)將引入雙倍的相位變化量，能有效提升系統的靈敏度。再者，此兩道雙繞射光束將分別沿著對方的行進路徑前進，而後回到原偏極化分光鏡相疊合形成干涉，並由IC光偵測器所接收，建構出創新的循環式光路，即當外界環境存在擾動時，兩道雙繞射偏振光束皆會感受到相同的擾動量，其擾動量將於干涉訊號相互抵消或補償，可使系統具備優異的穩定性。當光學尺沿著面內方向移動時，IC光偵測器量到的干涉訊號將產生相對應的變化，藉由分析干涉訊號的變化量即可回推光學尺的位移量。此外，基於相同的設計概念，我們藉由側向位移分光鏡的使用建構出第二組偵測架構，其亦具備位移的量測能力。而後，透過比較兩組偵測架構的量測資訊，我們即可回推光學尺的位移及角位移變化量，使此套循環式線性光學尺具備雙自由度位移(x軸)及角位移(θz)的量測能力。
為了進一步驗證此套創新的「循環式線性光學尺」的可行性及量測性能，我們分別將其架設於商用精密定位平台(Physik Instrumente, P562.6CD)及長行程電控位移平台(Sigmakoki, SGSP26-150)上，而後進行了多項嚴謹的驗證實驗。首先，由不同行程、不同波形及隨機波形的位移及角位移運動量測實驗結果可知，我們所提出的循環式線性光學尺的量測結果與電容式位移計、線性光學尺及雷射干涉儀的量測結果相符，驗證此套循環式線性光學尺具備精密的位移及角位移量測能力。由小行程位移(3 nm)及角位移(80nrad)運動實驗的量測結果可知，此套循環式線性光學尺的位移及角位移量測解析度(1)分別為1.1 nm及29.8 nrad，驗證此套光學尺具備高解析度。由來回步階運動的實驗結果可知，此套光學尺的位移及角位移量測重複性(1)分別為0.19 nm及0.26 nrad，驗證此套光學尺具備高重複性。由30分鐘的穩定度量測結果可知，此套光學尺的位移及角位移量測穩定度分別為19 nm及502 nrad，驗證此套光學尺具備高穩定度。由上述實驗結果證明此套「循環式線性光學尺」具備高解析度、高重複性、高穩定度之量測能力，日後可廣泛應用於各式需要精密位移及角位移的量測場合。

A Two-degree-of-freedom of Cyclic type linear encoder (CLE)is proposed in this study. The CLE is composed of laser diode (LD), grating (G), lateral beam splitter (LBS), polarization beam splitter (PBS), mirror (M), polarizer (P), and IC. It has the advantages of simple structure, component obtain easily, andn low cost. The CLE is mainly through the innovative optical path to make the reference and measurement beam respectively travel through the same optical element and path in the space and overlap to form interference. The “Cyclic Optical Path” can be constructed. When there is disturbance in the external environment, the refernce and measurement beams will sense the same disturbance, and the disturbance would be compensated in the interference signal, so that can enhance the stability and accuracy of the CLE effectively.
According to measurement principle of the proposed CLE, we us LD as the CLE’s light source. The light beam of LD is passed through the PBS to form transmitted (p-polarized) and reflected (s-polarized) beams. These two beams will incident on a reflective grating at a symmetrical angle and then diffracted. The symmetrical Optical Path can be constructed. Then, through a mirror, we make the first negative first order (-1st) diffracted beam (Ep-1) of p-polarized and the positive first-order (+1st) diffracted beam (Es+1) of s-polarized incident on the grating again to form the second time diffraction, The double diffraction optical path can be constructed. The p-polarized and s-polarized double-diffracted beams (E2s+1 and E2p-1) diffracted twice will introduce double the amount of phase change, which can effectively improve the sensitivity of the system. Furthermore, these two double-diffracted beams will travel along each other’s paths and then return to the original PBS to form interference. The interference will be received by the IC. The innovative “Cyclic Optical Path” can be constructed. When there is disturbance in the external environment, both double-diffracted polarized beams will feel the same amount of disturbance, and the disturbance will cancel or compensate each other in the interference signal, the corresponding diffracted beams will sense the same disturbance, and the disturbance would be compensated for in the interference signal, so that the proposed system can has higher stability. When the CLE moves along the in-plane direction, the interference signal measured by the IC will produce a corresponding change, and the displacement of the optical scale can be deduced by analyzing the variation of the interference signal. In addition, based on the same design concept, we constructed a second set of detection structures by using a lateral displacement beam splitter, which also has the ability to measure displacement. Then, by comparing in-plane displacement variation measured by these two detection configurations, we can deduce the displacement and angular displacement variation of the optical scale, so that the CLE has the measurement capability of two-degree-of-freedom displacement (x-axis) and angular displacement (θz).
In order to verify the feasibility and measurement performance of a innovative CLE, we set it up on a commercial precision positioning stage (Physik Instrumente, P562.6CD) and a long-stroke electronically controlled displacement stage (Sigmakoki, SGSP26-150), and then conducted a number of rigorous verification experiments. First of all, from the displacement and angular displacement motion measurement results of different strokes, different waveforms and random waveforms, The results of the measurement experiment show that the CLE proposed by us are consistent with the measurement results of the capacitive sensor, linear encoder and laser interferometer, which verifies that the CLE has precise displacement and angular displacement measurement capabilities. From the measurement results of small stroke displacement (3 nm) and angular displacement (80 nrad) motion experiments, it can be seen that the measurement resolution (1) of displacement and angular displacement of the CLE are 1.1 nm and 29.8 nrad respectively, which verifies that the CLE has high resolution. From the experimental results of the back-and-forth step motion, it can be seen that the measurement repeatability (1) of displacement and angular displacement of the CLE are 0.19 nm and 0.26 nrad respectively, which verifies that the CLE has high repeatability. From the 30-minute stability measurement results, it can be seen that the measurement stability (1) displacement and angular displacement of the CLE are 19 nm and 502 nrad in a 30-minute measurement experiment in a static state, which proves that the CLE has high stability. The above experimental results prove that the CLE has high-resolution, high-repeatability, and high-stability. The proposed CLE can be further applied to fields which need various precise displacement and angular displacement in the future.

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