基於Talbot效應之疊紋式角度量測系統開發

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姓名

陳旭東(Syu-Dong Chen) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

基於Talbot效應之疊紋式角度量測系統開發
(Measurement of angular displacement system based on Talbot effect and moiré method)

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摘要(中)

本論文提出一套新穎且架設簡易的角度量測技術-「基於Talbot 效應成像之疊紋式
角度量測系統」。本系統可分為兩部分：疊紋量測光路系統與相位分析系統。疊紋量測光路系統是將兩相隔特殊距離之雙光柵，以夾具等機構安裝於待測平台上，系統光源He-Ne Laser 搭配擴束鏡以準直光入射光柵機構，產生的疊紋影像依Talbot 效應成像於CCD。當待測平台產生角度旋轉時，裝配於一體的光柵組機構連帶產生旋轉，利用疊紋將光柵相對變化物理量放大的效果，搭配疊紋相位分析系統，便可計算待測平台旋轉角度，具有arcsec 級角度量測解析度。
本系統核心元件為兩片光柵週期介於50 ~ 200 m 之線性光柵，製作難度不高，
搭配Talbot 效應成像疊紋影像無須額外透鏡或光學元件輔助，實現高精度低成本的角度量測裝置。系統的量測解析度可藉由調整光柵間距及光柵週期來改變，具有多種組合，可依不同情況選擇適當配置。代表性的組合為200 m 光柵週期搭配1 倍Talbot距離之光柵間距(12.64 cm)，具有0.36 arcsec 角度解析度，1.06°/ arcsec 角度靈敏度，±6°量測範圍與1.36°/s 理論量測速度。

摘要(英)

We proposed a new method based on the moiré technique and Talbot effect to measure the angular displacement. The measurement system is divided into two parts, the optical
moiré system and the phase analysis system. In the first part, the collimated He-Ne laser beam is expanded by the beam expander (BE) and is forward incident into the two linear amplitude gratings, which placed symmetrically by a centre of the precision rotation stage. These two gratings can be regarded as the a spatial modulator. After passing through the gratings, the spatial modulated light beam forms a moiré pattern and is captured by the CCD camera. By adjusting the distance D between the two gratings to meet the Talbot image distance (Zt ), the clear and high contrast moiré pattern can be obtained. When the rotation stage provides a rotation, the relative displacement between these two gratings results in the phase shifting of the moiré pattern. The phase analysis by the subfringe integration
arithmetic (SIA). Here, the period of moiré pattern is then divided into four areas, A, B, C and D for further analysis. By means of calculating the intensity integration of the four areas with SIA, the variation of phase shift of the moiré pattern can be obtained, and the rotation angle can be determined. This is the second part of this system.
Clearly, the experimental results demonstrate that the measurement range of our system can achieve ±6°. Considering the high-frequency noise, the measurement resolution of the system is about 0.36 arcsec.

關鍵字(中)

★ Talbot 效應
★ 疊紋
★ 角度量測

關鍵字(英)

★ angular displacement,
★ moiré method
★ Talbot effect
★ phase detection

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 ix
符號說明 x
第一章緒論 1
1.1研究背景 1
1.2 文獻回顧 1
1.2.1光學式角度量測文獻回顧 2
1.2.2疊紋效應文獻回顧 10
1.2.3疊紋式角度量測文獻回顧 11
1.3 研究目的 14
1.4 論文架構 15
第二章基礎理論 16
2.1光柵的Talbot效應 16
2.2疊紋效應 18
2.2.1疊紋基本原理 18
2.2.2疊紋位移理論 21
2.2.3疊紋縮放理論 22
2.3亞條紋積分法 23
2.4小結 26
第三章系統架構 27
3.1元件介紹 27
3.2疊紋式角度量測系統 29
3.2.1雙光柵旋轉架構 30
3.2.2光柵Talbot成像系統 31
3.2.3系統量測範圍 32
3.3疊紋相位分析 34
3.3. 疊紋資訊子陣列拓展 34
3.3.2.疊紋相位位移判斷 36
3.4小結 38
第四章實驗結果與討論 39
4.1系統架構設置 39
4.2系統量測範圍與角度步階實驗 40
4.2.1光柵週期200 m 41
4.2.2光柵週期100 m 49
4.2.3光柵週期50 m 55
4.3系統量測速度 61
4.4實驗討論 63
4.4.1疊紋訊號對比度分析 63
4.4.2相同光柵週期不同間距D 70
4.4.3不同光柵週期相同間距D 70
4.5小結 74
第五章誤差分析 75
5.1系統誤差 75
5.1.1解相系統之相位誤差 75
5.1.2光柵引入角度誤差 83
5.1.3間距D引入角度誤差 84
5.2隨機誤差 85
5.2.1環境擾動 85
5.2.2光學元件與夾具材料熱特性 87
5.2.3電子雜訊 88
5.3小結 89
第六章結論與未來展望 90
參考文獻 91

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指導教授

李朱育(Ju-Yi Lee)

審核日期

2014-8-8

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