本論文利用國家同步輻射中心(National Synchrotron Radiation Research Center, NSRRC)台灣光子源(Taiwan Photon Source, TPS)的X光奈米探測(XNP)光束站(23A)進行了第一組使用Nested Montel Mirror的反射聚焦鏡作為光源的硬X光掃描式同調光繞射影像(X-ray Ptychography)之實驗技術研發。
Nested Montel Mirrors優化了傳統Kirkpatrick-Baez Mirrors，提供了5500電子伏特的奈米同調性聚焦光源。透過了Extension Ptychography Iteration Engine (ePIE) 演算法，我們成功地在金製的輪狀標準樣品上完成了具有50nm解析度的重建影像。
本論文將詳細介紹X光相位問題、X光同調影像的原理與最近發展、Nested Montel Mirrors 聚焦原理、實驗設置、數值模擬、實驗影像重建過程及其結果、結論與展望、參考資料。

We investigate the first nested Montel mirrors based hard x-ray ptychography at the x-ray nanoprobe beamline at Taiwan Photon Source. The nested Montel mirrors, a variant of Kirkpatrick-Baez optics, provide diffraction-limited nano-focusing and coherent x-rays at 5.5 KeV. With extended ptychographical iterative engine (ePIE) algorithm, we have successfully demonstrated the reconstructed images of a gold spoke pattern with pixel resolution about 50nm. In this article, we will present the X-ray phase problem, the principle of coherent diffractive image and the up-to-date reconstruction algorithms, the experimental setup at TPS, the simulation based on ePIE, the reconstruction results, future prospects and references.

目錄
1 緒論…………………………………………....................………………...…….6
1.1 X光光源…………………………………………...………………..……..6
1.1.1 X光的發現……………………………………………………….…...6
1.1.2 同步輻射……………………………………………………….……...7
1.2 同步輻射發展………………………………………………………….......9
1.2.1 偏彎磁鐵…………………………………………………………..…..9
1.2.2 插件磁鐵……………………………………………………..….…...10
1.2.3 聚頻磁鐵………………………………………………………....…..11
1.3 同調性……………………………………………………………..….…..14
1.3.1 時間同調性………………………………………….……….…..…..16
1.3.2 空間同調性………………………………………….……….…..…..17
2 實驗技術與原理………………………………………………..…………..…...19
2.1 繞射與傅立葉轉換……………………………………..………...……....19
2.1.1 惠根斯-菲涅耳公式………………………………..………....……...19
2.1.2 遠場近軸繞射………………………………..………………..……..20
2.2 X光相位問題(X-ray Phase Problem) ………..…………………..…..…..21
2.3 同調X光繞射影像顯微技術(Coherent diffraction image ,CDI) .……....23
2.3.1 實驗架設……………………………………..……………….……...24
2.3.2 數據處理……………………………………..……………….….…..25
2.4 解析度……………………………………..……………….………….….26
2.4.1 布拉格繞射…………………………..………….…….………….….26
2.4.2 像素解析度…………………………..………….…….………….….27
2.4.3 Phase Retrieval Transfer Function (PRTF) …….…….………..….….28
2.5 過採樣(Oversampling) …………………..………….…….……….…......29
2.6 演算法…………………..………….…….……….…................................32
2.6.1 Hybrid input output, HIO…….…….……….…..................................32
2.6.2 模擬數據以及HIO的缺陷.…….……….…......................................33
2.6.3 Guided Hybird Input Output (GHIO) …….….....................................34
2.7 Ptychography...............................................…............................................35
2.7.1 Convolution .......................................…..............................................35
2.7.2 The extension Ptychography iteration engine (ePIE) ..........................36
2.7.3 座標修正(pcPIE) ..................…...........................................................38
2.7.4 多重模態(Muti-mode) ......…...............................................................42
3 實驗樣品與實驗儀器...........................................................................................44
3.1 TPS實驗站23A實驗架設 ......................................................................44
3.1.1 實驗站..................................................................................................46
3.1.2 樣品......................................................................................................47
3.1.3 偵檢器..................................................................................................48
3.1.4 真空實驗系統......................................................................................49
3.1.5 細孔......................................................................................................50
3.2 聚焦元件.....................................................................................................51
3.2.1 放大率..................................................................................................51
3.2.2 全反射與X光反射鏡.........................................................................51
3.2.3 Nested Montel Mirror...........................................................................53
3.3 實驗步驟.....................................................................................................56
3.3.1 校正光源、聚焦..................................................................................56
3.3.2 放置樣品..............................................................................................57
3.3.3 設定程式與數據讀取..........................................................................58
4 實驗結果與分析...................................................................................................61
4.1 模擬結果.....................................................................................................61
4.1.1 HIO(hybrid input output) .....................................................................61
4.1.2 網格式掃描之ePIE .............................................................................63
4.1.3 Fermat Spiral掃描...............................................................................65
4.1.4 pcPIE....................................................................................................67
4.2 實驗數據.....................................................................................................69
4.2.1 2018年9月- Mesh Grid式掃描.........................................................69
4.2.2 2019年2月-Fermat Spiral式掃描.....................................................71
5 結論.......................................................................................................................73
6 參考資料...............................................................................................................74

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功能概要