臺灣博碩士論文加值系統

本篇論文提出如何應用數位全像顯微術(Digital Holographic Microscopy, DHM)以其非接觸、非侵入與非破壞的特性對光學元件的物理特性執行定量的檢測。有別於無透鏡數位全像術，DHM利用複合透鏡(Objective Lens, OL)來收集物體的光波並放大待測物體的尺寸。當物體光波向前傳遞通過OL後，物體光波將含有一個二次相位項(Quadratic Phase Term)，即所謂的失焦像差(Defocus Aberration)。通過OL向前傳遞的物體光波與參考光波在全像平面上進行干涉並由CCD記錄全像片。所以利用DHM架構所記錄的全像片不僅包含零階、物體光波及其共軛項資訊，同時也包含一個二次相位項。即使在零階與物體共軛光波等干擾項已從全像片消除的情況下，若是以數值演算法則模擬參考光波入射全像片的繞射過程，直接重建物體的波前，則被重建的物體波前仍然含有二次相位項（失焦像差）。因著重建的物體波前的相位分佈仍然含有一個二次相位項，即其真正的相位分佈被遮蔽，所以待測物體的形狀、輪廓以及表面起伏高低便無法重建。
為了移除OL所引起的失焦像差並重建物體波前真正的相位分佈，我們應用實體的方式(Physical)補償因著OL的存在所帶進的二次相位項，以便對光學元件的物理特性執行定量的檢測。這個方法是在OL後面引進一個補償的透鏡，使得OL的後焦點和透鏡的前焦點以共焦方式安置，藉以補償OL所產生的二次相位項，如此CCD所記錄的物體光波資訊將不再含有失焦像差。同時藉著光學運算子符號法(Optical Operator)的分析，可以證明當物體光波通過OL與補償透鏡所組合而成的DHM光路後，將不再含有二次相位項。
我們利用Mach-Zehnder干涉儀架構來實現同軸和離軸的全像光路，同時提出任意雙相位步進方法(Arbitrary Phase-Step Digital Holography, APSDH)來抑制干擾，即零階和共軛影像。至於離軸架構，則利用Chen等人所提出增加第二個重建平面空間地濾除多餘的干擾項，然後在第一個重建平面重建物體的波前。為了展現相位補償的效果，我們執行沒有和具有相位補償（修正）的DHM方案的實驗並證實修正的DHM方案能夠補償OL所產生的失焦像差。在使用數值演算法則消去那些干擾影像之後，明顯地亮度對比和相位對比諸影像的確呈現沒有失焦像差和模糊現象。利用離軸和同軸修正的DHM方案光學諸特性與諸結果在文中也簡短地回顧與討論。此外我們也展示如何應用修正的離軸DHM光路，在不需要切割（破壞）一片完整LLA的前題下，去實際量測一個62 LPI的圓柱透鏡陣列單一透鏡的寬度，並且與規格值比較誤差只有3.17%。這個提議方案可以應用於DHM、相位物體量測與光學精密度量。

The thesis presents how to apply the Digital Holographic Microscopy (DHM) with its non-contact, non-invasive and non-destructive characteristics to measure the physical characteristics of the optical components quantitively. In contrast with lensless digital holography, DHM uses an Objective Lens (OL) to collect the object wave and magnify the dimensions of object under test. When the object wavefront passes OL and propagates forward, then object wavefront will contain a quadratic phase term, the so called defocus aberration. The propagating object wavefront will interfere with the reference wave at the hologram plane and the interference pattern be captured by CCD. Thus the holograms recorded with DHM setup will not only the information of the zero order, object wavefront and its conjugate term, but also a quadratic phase term. Even the blur, i.e. zero order and wavefront conjugate terms, had been removed; if the hologram is directly reconstructed using numerical algorithms, then the reconstructed object wavefront will still include a quadratic phase term (defocus aberration). Since the phase information of the object wavefront contains a quadratic phase term, thus the absolute phase distribution of object wavefront had been masked, therefore the shape, profile and surface roughness of the object under test can not be reconstructed.
To remove the defocus aberration due to OL and reconstruct the exact phase distribution of the object wavefront, we use a physical mean to compensate the quadratic phase term due to OL and then the physical characteristics of the optical components can be measured quantitively. The proposed scheme is that an offset lens is inserted after OL, the OL and offset lens are separated such that their foci are common and together (confocal), to physically compensate for the quadratic phase term due to OL, thus the recorded holograms which were captured by CCD will not contain the defocus aberration no longer. Meanwhile, through the analysis of the optical operator, it can be shown that the inverted and magnified object wavefront, which has passed through the OL and compensation lens configuration, will not carry and contain the quadratic phase term anymore.
We exploit the Mach-Zehnder interferometry to implement the in-line and off-axis DHM optical setups, and the arbitrary phase-step digital holography (APSDH) to suppress the blur, i.e. zero-order and twin-image terms. For the off-axis configuration, we use Chen et al. method which is the second reconstruction plane added to spatially filter the unwanted terms, and then numerically reconstruct the object wavefront at the original plane. For demonstrating the effect of the phase compensation, the optical experiments without and with phase compensation (modified) DHM scheme are conducted, and verified that the modified scheme can satisfactorily compensate for the defocus aberration due to OL. After using the numerical algorithms to eliminate those blur, obviously the reconstructed magnitude- and phase-contrast images do present no defocus aberration and blur. Moreover, optical characteristics and reconstruction results which were obtained from in-line and off-axis modified DHM are briefly reviewed and discussed. Furthermore, we also demonstrate how to implement off-axis setups, without cutting (destruction) the whole piece LLA (lenticular lens array), to measure the pitch of a 62 LPI (lenticular per inch) LLA, and the error is about 3.17% when compared the nominal value. The suggested scheme can be applied to DHM, phase object measurement, and optical metrology.

誌謝 ii
摘要 iii
ABSTRACT v
目錄 vii
表目錄 ix
圖目錄 x
1. 緒論 1
1.1 研究動機與目的 1
1.2 數位全像術文獻回顧 2
1.3 數位全像顯微術文獻回顧 6
1.4 研究方法與規劃 9
1.5 論文內容編排 10
2. 數位全像術之理論基礎 12
2.1 零階項抑制之方法 14
2.1.1 典型的方法 14
2.1.2 Chen等人的方法 14
2.1.3 Kreis與Juptner方法 15
2.2 同軸方式消除干擾(In-Line Scheme for Removing the Blurring) 15
2.2.1 固定相位調變方法(Fixed Phase-Shifting Method) 16
2.2.2 任意兩步相位步進方法(Arbitrary Two Phase-Step Method) 18
2.2.2.1 工作原理-共軛影像的抑制 20
2.2.2.2 未知的相位步進的估計 21
2.2.2.3 任意相位步進數位全像術的重建能力 25
2.2.2.4 同軸架構電腦模擬與討論 25
2.3 離軸方式消除干擾(Off-Axis Scheme for Removing the Blurring) 29
2.3.1 空間濾波(Spatial Filtering, SFL) 30
2.3.2 空間頻譜濾波(Spatial Spectrum Filtering, SSF) 31
2.3.3 第二個重建平面加入(The Addition of Second Reconstruction Plane) 33
2.3.4 離軸架構電腦模擬與討論 34
3. 數位全像顯微術－數位全像術的應用 39
3.1 基本方式－複合透鏡加入 39
3.2 修正方式－複合透鏡加上補償透鏡 40
3.3 光學系統分析－使用運算子方法 41
4. 實驗結果與討論 44
4.1 任意兩步相位調變全像術實驗結果與討論 44
4.2 離軸數位全像顯微術實驗結果與討論 47
4.3 同軸數位全像顯微術實驗結果與討論 58
5. 結論與未來工作 68
6. 參考文獻 70
7. 發表論文 82

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