同調性X光繞射成像技術是一個極具潛力的新一代X光顯微術，此技術與傳統的X光繞射不同，其最大的差異點在於使用高同調性X光做為光源，使用高同調性的X光做為光源可以使我們藉由干涉來得知非週期性樣品的結構，我們甚至可以在布拉格點上量測晶體的三維繞射圖紋來獲得高解析度的材料三維應變場及缺陷資訊，此技術可廣泛應用於半導體異質接面應力分析、半導體材料結構分析等，並以非破壞性方式提供高解析度的應變場以及缺陷資訊，此技術提供了我們許多的研究非週期性樣品以及晶體結構的可能性，所以近年來延伸出了多種形式的同調性X光繞射成像技術來研究不同領域的難題。

本論文示範如何使用同調性X光繞射來進行四氧化三鐵奈米粒子之成像，其內容包括演算法、模擬、儀器以及量測結果分析，提供使用同調性X光繞射成像顯微術之量測方法的經驗。

Coherent X-ray diffraction imaging has a great potential for a new generation of X-ray microscopy. This technique is different from traditional X-ray diffraction. Because the light source is highly coherent, we can measure non-periodic structure by interference. We can even use the interference pattern of a crystal to obtain high-resolution three-dimensional strain field and defect information. This technique can be widely used in semiconductor hetero-interface stress analysis, semiconductor materials structural analysis and so on, and in non-destructive way to provide high-resolution strain field and defect information, so this technique make non-periodic structure can be analyzed and bring many of possibilities for studying crystal structures. In recent years, various forms of coherent X-ray diffraction imaging have been extended for studying the challenges of different areas.

This thesis demonstrates how to use coherent X-ray diffraction for imaging of Fe3O4 nanoparticles, which includes algorithms, simulations, instrumentation, and measurement results to provide experience with coherent X-ray diffraction imaging measurement method.

第一章 緒論 1
1.1 前言 1
1.2 同調性光源特性 1
1.2.1 空間同調性： 3
1.2.2 時間同調性： 4
1.2.3 夫朗和斐繞射 (Fraunhofer diffraction)： 5
1.3 X光與物質的交互作用 8
1.3.1 原子結構因子： 9

第二章 實驗技術與方法 12
2.1 同調性X光繞射 12
2.1.1掃描式X光同調性繞射成像(Ptychography): 13
2.2 樣品備製 14
2.3 實驗儀器 17
2.3.1 光學顯微鏡： 17
2.3.2 掃描式電子顯微鏡: 18
2.3.3 X光同調性繞射成像的實驗儀器： 19

第三章 實驗數據分析方法 22
3.1弗里德爾定律 (Friedel's law) 22
3.2 超取樣 (Oversampling) 25
3.2.1 超取樣率(Oversampling ratio)： 27
3.3 相位恢復演算法 36
3.3.1 誤差減少演算法(Error Reduction Algorithm)： 37
3.3.2 混合輸入輸出演算法(Hybrid Input Output Algorithm)： 38

第四章 實驗數據分析與結果 40

第五章 結論 58

參考文獻 59

附錄 62
A. 掃描式X光同調性繞射成像(Ptychography)數據： 62
B. 布拉格式X光同調性繞射成像(Bragg CDI)數據： 64
C. 相位恢復演算法程式碼 (MATLAB)： 66

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