習用共路徑架構具有高穩定度、高解析度、架構簡單的優點。不過共路徑架構大多是將雷射聚焦在光柵上進行繞射，雷射聚焦在光柵上光點直徑僅有約0.1mm，聚焦光束設計造成光學尺對光柵製造品質、與光柵上髒污變得非常敏感，產生難以補償的量測誤差。
本文提出了一種非聚焦共路徑雷射光學尺(Non-focused common-path Laser Encoder，以下簡稱NFCPLE)，在沒有將雷射聚焦情況下可有效克服過往共路徑架構遇到的瓶頸，NFCPLE對於光柵本身品質要求也較類似架構來得低。另外IC-Haus LSC感測器減少了光學元件數目，可減少光學元件之間的對位誤差。
本研究利用商用HP5529A干涉儀進行NFCPLE量測性能實驗評估，並進行誤差分析。實驗結果顯示，在10mm行程內，商用HP5529A干涉儀與NFCPLE的平均差量為185.31nm。而NFCPLE於三小時系統穩定度量測中產生漂移量為3.8±0.5nm，解析度約1.6±0.5 nm。綜合本研究的實驗評估與分析，可知NFCPLE在超精密機械應用相當有潛力。

Commonly usedcommon-path configuration.called (CPLE) has the advantages of high stability, high-resolution. ButCPLE almost is focused laser on grating.The focusedlaseron the grating is only about 100 mm in diameter. The optical scale is sensitive to grating manufacturing quality and grating dirty because of focused laser designed.
This study proposes a non-focused common-path laser encoderdevice called (NFCPLE). NFCPLE can effectively overcome the problems in the past CPLE without focused laser design.NFCPLE compared with CPLE for the grating quality requirements is also much low.MoreoverIC-Haus LSCphotodetector reduces optical elements. With this technique, the effect of optical element error can be greatly reduced.
In this study, NFCPLE conduct experimental evaluation of performance test and error analysis with HP5529A interferometer for offset evaluation, it is displayed in the analysis and the experimental results. In the displacement of 10 mm,the average differential of NFCPLE was 185.31nm with HP5529A interferometer. The time dependent drift of NFCPLE was measured for a period of three hour and was found to be 3.8 ± 0.5 nm with 1.6 ± 0.5 nm resolution.  It is therefore shown that NFCPLE has enormous potential forfuture development.

目錄
中文摘要.........................................................................................................................I
英文摘要.......................................................................................................................II
目錄..............................................................................................................................III
圖目錄...........................................................................................................................V
表目錄........................................................................................................................VII
符號表.......................................................................................................................VIII
第一章緒論....................................................................................................................1
1.1前言........................................................................................................1
1.2文獻回顧................................................................................................2
1.3研究動機..............................................................................................14
1.4研究目的..............................................................................................14
1.5章節介紹..............................................................................................14
第二章原理與方法......................................................................................................16
2.1NFCPLE系統架構..............................................................................16
2.2干涉基本原理......................................................................................18
2.3都卜勒頻率偏移..................................................................................19
2.4相位調解..............................................................................................23
2.5相位重建..............................................................................................23
第三章實驗與結果......................................................................................................28
3.1實驗架設..............................................................................................28
3.2IC Haus LSC感測器...........................................................................30
3.3IC Haus LSC旋轉...............................................................................32
3.4資料擷取卡..........................................................................................34IV 

3.5複合式定位平台..................................................................................34
3.6位移量測..............................................................................................35
3.6.1 10 mm量測..................................................................................36
3.6.2100 mm量測................................................................................37
3.6.3 1 mm量測...................................................................................39
3.6.410 mm量測.................................................................................40
3.7系統穩定度量測..................................................................................42
3.8對位公差量測......................................................................................44
第四章誤差分析..........................................................................................................46
4.1系統誤差..............................................................................................46
4.1.1餘弦誤差......................................................................................46
4.1.2光柵髒汙影響..............................................................................47
4.1.3光柵誤差......................................................................................49
4.1.4光學非線性..................................................................................51
4.2隨機誤差..............................................................................................51
4.2.1材料熱變形..................................................................................51
4.2.2電子雜訊......................................................................................52
4.2.3 訊號誤差 ......................................................................................52
第五章結論與研究建議..............................................................................................54
5.1結論......................................................................................................54
5.2未來研究建議......................................................................................54
附錄A訊號處理演算法.............................................................................................55
A.1訊號校正處理演算法..........................................................................55
參考文獻......................................................................................................................67

圖目錄
圖1-1麥克森干涉光路[5].......................................................................3
圖1-2反射式雷射光學尺[8]...................................................................4
圖1-3光學尺結合Littrow裝置示意圖[9].............................................5
圖1-4反射式繞射光學尺[10].................................................................6
圖1-5外差光柵干涉儀架構圖[11].........................................................7
圖1-6繞射式雷射光學尺[12].................................................................8
圖1-7雷射光學尺結合Littrow架構[13]...............................................9
圖1-8外差光柵干涉儀一維位移量測結構圖[14]...............................10
圖1-9擬共光程位移量測系統[15].......................................................11
圖1-10線性繞射式雷射光學尺[16].....................................................12
圖2 -1NFCPLE雷射光學尺架構示意圖............................................18
圖2 -2入射波方向與光柵移動方向反向...........................................20
圖2 -3入射波方向與光柵移動方向同向...........................................20
圖2 -4 位移一光柵週期之訊號..........................................................22
圖2 -5一組訊號校正為正交訊號.......................................................23
圖2 -7經過相位重建的tan-1函數.....................................................26
圖2 -8未經相位重建的位移值...........................................................26
圖2 -9經相位重建的位移值...............................................................27
圖3 -1NFCPLE實驗架構....................................................................29
圖3 -2NFCPLE干涉條紋....................................................................29
圖3 -3IC-Haus LSC..............................................................................31
圖3 -4IC-Haus LSC感測器電路示意圖.............................................31
圖3 -5LSC兩感測器間距離................................................................32VI 

圖3 -6條紋與感測器夾角0度...........................................................33
圖3 -7條紋與感測器夾角30度.........................................................33
圖3 -8條紋與感測器夾角60度.........................................................33
圖3 -9LabVIEW程式前置面板.........................................................34
圖3 -10複合式定位平台示意圖.........................................................35
圖3 -1110um位移運動........................................................................37
圖3 -12100um位移運動......................................................................38
圖3 -131 mm位移運動........................................................................40
圖3 -1410 mm位移運動......................................................................41
圖3 -153小時靜態量測(HP5529A V.S .NFCPLE).............................42
圖3 -16三小時靜態量測溫度變化.....................................................43
圖3 -17NFCPLE穩定度量測..............................................................43
圖3 -18機械運動偏擺.........................................................................45
圖4 -1光柵貼附於移動平台的不平行示意圖...................................47
圖4 -2污漬在光柵上...........................................................................48
圖4 -3共路徑雷射光學尺讀取污漬光柵...........................................48
圖4 -4非聚焦共路徑雷射光學尺讀取污漬光柵...............................48
圖4 -5繞射儀架構示意圖...................................................................49
圖4 -6正負一階閃耀角沿入射光路徑射出.......................................50
圖4 -7繞射儀量測點示意圖...............................................................50
圖4 -8未去除直流項之呂薩加圖形...................................................52
圖4 -9等速位移時，直流項不為零而交流項相等示意圖...............53
圖A-1無偏離圓心之正橢圓座標圖形...............................................55
圖A-2實際訊號座標圖形...................................................................56
圖A-3反正切函數圖形.......................................................................65
圖A-4反正切函數運算流程圖...........................................................66VII 

表目錄
表1 -1文獻回顧....................................................................................13
表2 -1角度轉換關係表.......................................................................25
表3 -1系統使用元件...........................................................................30
表3 -2複合式平台規格.......................................................................35
表3 -310um量測實驗環境參數..........................................................36
表3 -410um實驗結果..........................................................................36
表3 -5100um量測實驗環境參數........................................................37
表3 -6100um實驗結果........................................................................38
表3 -71 mm量測實驗環境參數..........................................................39
表3 -81 mm實驗結果..........................................................................39
表3 -910mm量測環境參數.................................................................40
表3 -1010 mm實驗結果......................................................................41
表3 -113小時穩定度測試結果...........................................................44
表3 -12對位公差實驗結果.................................................................45
表4 -120mm銦鋼繞射儀結果............................................................50
表4 -2實驗元件熱膨脹係數[32].........................................................51

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