干涉儀相位移動器之精密校正法

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姓名

周厚丞(Hou-Cheng Chou) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

干涉儀相位移動器之精密校正法
(The precise calibration of the phase-shifting adapter in interferometer)

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摘要(中)

現今高精密度的製造業要求更加準確、精確和迅速的量測學，而相移干涉學正是目前許多工業所倚重的一門量測的學問，相移精度對於相移干涉術之量測，是最可代表樣品之可靠度。對利用相移干涉術來量測樣品之干涉儀而言，不準確的相移會在計算物體相位上而產生誤差，如此，無法準確的得到物體的表面資訊。
本系統之相位移動器由三個壓電致動器所構成，由於壓電致動器本身之差異與結構上受到不同應力的影響，在移動的過程中會產生移動不均勻的問題；為了提高其精準度，本文章提出一種有效提升精確度的校正方法，從理論推導出壓電致動器位移與條紋斜率之關係，接著主要是利用傅立葉轉換後，在空間頻率座標上之訊號為兩個脈衝函數值，並藉由兩點之連線求得其斜率，再由輸入電壓與條紋斜率變化之關係，得知各PZT之間的差異，來完成校正各PZT之工作，再藉由五步相移將其相位值計算出來，可發現此方法的確改善移動不均勻的現象，未經校正時，相位移誤差之RMS值為3.492 deg，約為0.0194λ，而經校正後，相位移誤差之RMS值最好可降低至0.062 deg，約為0.0034λ，證明出此方法有效的提升相位移動的精確度。

摘要(英)

The precision of phase-shift to the measurement of phase-shift interferometry may most represent reliability of a sample. It is represented the reliability of the sample that the measurement of the phase-shift accuracy for the phase-shift interferometry.
In this thesis, a method to calibrate a phase-shifting adapter (PSA) with three piezoelectric ceramics based on the relationship between the displacement of PZT and the slope of interference fringe is proposed to increase the testing precision of phase-shifting interferometer. The unequal movement of the PSA is improved by this method.
The paper proposed that the relations between shifting and the slope of interference fringe for phase-shifting adapter. Subsequently used flat plate interferogram as a sinusoidal wave and transferred from Fourier transform. Signals in frequency domain were two values of pulse functions, and calculated the slope by connecting the points. Before the phase-shifting adapter is calibrated, the RMS of phase shift error is 0.3492 deg, which is equal to 0.0194λ. After the phase-shifting adapter is calibrated, the RMS of phase shift error is 0.0621 deg, which is equal to 0.00004λ.It is found that this method really improved the phenomenon of moving unevenness, and advanced precision of phase-shift effectively.

關鍵字(中)

★ 誤差分析
★ 相移校正
★ 快速傅立葉轉換
★ 相移干涉術

關鍵字(英)

★ noise analysis
★ phase shift calibration
★ phase shifting interferometry
★ fast fourier transform

論文目次

中文摘要................................................................................................................I
英文摘要..............................................................................................................II
誌謝.....................................................................................................................III
目錄.....................................................................................................................IV
圖目錄..............................................................................................................VIII
表目錄..............................................................................................................XIV
第一章緒論.......................................................................................................1
1.1 前言..........................................................................................................1
1.2 研究目的與動機......................................................................................2
第二章相移干涉系統.......................................................................................4
2.1 基本干涉原理..........................................................................................4
2.1.1 光干涉原理......................................................................................5
2.1.2 相移干涉技術..................................................................................7
2.1.3 各式相移演算法..............................................................................9
2.1.3.1 三步相移演算法......................................................................9
2.1.3.2 四步相移演算法....................................................................10
2.1.3.3 Carré演算法..........................................................................10
2.1.3.4 五步相移演算法....................................................................11
2.1.4 相移量與CCD之誤差分析...........................................................12
2.1.4.1 三步相移理論誤差................................................................12
2.1.4.2 四步相移理論誤差................................................................14
2.1.4.3 五步相移理論誤差................................................................15
2.1.4.4 CCD之理論誤差...................................................................16
2.1.5 相位展開與重建技術....................................................................17
2.2 壓電致動器之工作原理........................................................................19
2.2.1 壓電材料........................................................................................19
2.2.2 壓電原理及現象............................................................................21
2.2.3 壓電應用........................................................................................23
2.3 干涉條紋之分析....................................................................................23
2.3.1 光學像差分析................................................................................23
2.3.2 影像快速傅立葉轉換....................................................................26
2.3.3 濾波器的分析................................................................................29
2.3.4 條紋斜率計算................................................................................29
第三章相移精度文獻探討.............................................................................32
3.1 各演算法之比較....................................................................................32
3.1.1 線性誤差分析................................................................................32
3.1.2 非線性誤差分析............................................................................33
3.2 校正相位移動裝置................................................................................35
3.2.1 光學條紋投射器之步進馬達........................................................35
3.2.2 干涉儀之相位移動器....................................................................37
3.3 計算相位變化........................................................................................38
第四章提升相位移動器精確度之理論.........................................................40
4.1 建立壓電致動器之空間分佈................................................................40
4.1.1 一般分佈情形................................................................................40
4.1.2 特殊分佈情形................................................................................43
4.2 條紋斜率分析........................................................................................51
4.2.1 傅立葉空間分析............................................................................51
4.2.2 分析條紋斜率之極限....................................................................53
4.3 提升相位移動器精確度之方法............................................................57
第五章模擬之研究.........................................................................................59
5.1 模擬光學雜訊........................................................................................59
5.1.1 雜訊分析........................................................................................59
5.1.2 光學像差之影響............................................................................66
5.2 模擬PZT移動情形................................................................................69
5.3 模擬五步相移法....................................................................................70
第六章實驗與分析.........................................................................................72
6.1 實驗系統與架構....................................................................................72
6.2 實驗步驟................................................................................................77
6.3 實驗結果................................................................................................82
6.3.1 校正分析........................................................................................86
6.3.2 校正後結果....................................................................................90
6.4 實驗誤差分析........................................................................................92
6.4.1 空氣擾動與環境振動....................................................................92
6.4.2 非線性移動現象與磁滯現象........................................................94
6.4.3 其他誤差影響..............................................................................100
第七章結論與未來展望...............................................................................103
7.1 實驗結論..............................................................................................103
7.2 未來展望..............................................................................................104
參考文獻...........................................................................................................106
附錄一...............................................................................................................112
附錄二...............................................................................................................115
附錄三...............................................................................................................116

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指導教授

歐陽盟(Mang Ou-Yang)

審核日期

2007-7-24

推文