穿透式X光顯微鏡中的相位影像

國

立

交

通

大

學

光電工程研究所

博

士

論

文

穿透式 X 光顯微鏡中的相位影像

Phase Imaging in Transmission X-ray Microscope

研 究 生：殷廣鈐

指導教授：謝漢萍 教授

陳福榮 教授

穿透式 X 光顯微鏡中的相位影像

Phase Imaging in Transmission X-ray Microscope

研 究 生：殷廣鈐

Student：Gung-Chian Yin

指導教授：謝漢萍

Advisors：Han-Ping D. Shieh

陳福榮

Fu-Rong Chen

國立交通大學 電機學院

光電工程研究所

博士論文

Submitted in partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy in

The Institute of Electro-Optical Engineering

College of Electrical Engineering and Computer Engineering National Chiao Tung University

in Jan 2008

Hsinchu, Taiwan, R.O.C

i

穿透式 X 光顯微鏡中的相位影像

學生：殷廣鈐

指導教授：謝漢萍教授

陳福榮教授

國立交通大學光電工程所博士班

摘

要

X 光影像在生物以及醫療應用上有著非常重要的角色。而相位對比在高解析

度的 X 光影像是一個很重要的工具，因為相位的對比較傳統的吸收造成的對比

要能提高個二至三個數量級，並且非常有效的減少 X 光影像帶來的輻射劑量。

相位對比在於我們目前注重的高解析度的細胞影像，以及其他軟物質有非常重要

的貢獻。

這篇論文，最主要的目的是要在穿透式 X 光顯位鏡中發展相位對比的方法。

利用同步輻射所提供的光源，我們所使用的穿透式 X 光顯微鏡(TXM)在吸收的對

比下能夠達到具有數十奈米的解析度。對相位對比，我們使用發展出兩種不同的

方式來觀察相位。第一種是利用光波傳遞的方式紀錄不同位置的繞射的條紋，第

二種是利用 Zernike 的相位方法來觀察干涉的相位圖樣。第一種方法我們利用合

併以往兩種分別使用在高解析度電子顯微鏡(TEM)的迭代方法(SCWP)，以及以往

利用在低解析度 X 光影像的(TIE)方法來解出 X 光顯微鏡中的相位。第二種方法

我們使用一個疊代的方式解 Zernike 的相位方法，並且可以只用一張影像解出相

位的資訊。這個方法將可以應用在立體的相位對比斷層掃描(phase tomography)

上。理論方法和實驗的結果都呈現在論文之內。此兩種方法，都可以應用在 X

光顯微鏡之內，並且有效的回覆相位資訊。此項技術將對三維高解析度的生物醫

學影像帶來很大的貢獻。

ii

Phase Imaging

in

Transmission X-ray Microscope

Student：Gung-Chian Yin

Advisors： Han-Ping D. Shieh

Fu-Rong Chen

The Institute of Electro-Optical Engineering

National Chiao Tung University

ABSTRACT

The phase imaging in X-ray is a powerful tool for non-destructive investigation at nanometer

scale. The phase image enhances the contrast for 2 to 3 orders of magnitude higher then the

absorption contrast at the hard x-ray region. Furthermore, with the high penetration deep, the phase

imaging in hard x-ray is good for the soft material like a cell or bio-medical tissue.

This thesis describes the development of the x-ray phase imaging technique using transmission

X-ray microscope (TXM) at a synchrotron source National Synchrotron Radiation Research Center

(NSRRC). The TXM has the spatial resolution of several tens of nanometer by using absorption

contrast. For phase contrast imaging, the combination method of transport of intensity equation (TIE)

and self-consistent wave propagation (SCWP) is applied to retrieve the pure phase information and a

resolution of tens of nanometer resolution at hard x-ray region is demonstrated experimentally. To

realize the phase tomography, an iterative method (iterative phase retrieval for common path

interferometer, IPR-CPI) to calculate the phase image from the Zernike phase contrast method is

proposed. It is realized that by using only one x-ray image and a known structure of Zernike phase

plate, the phase image can be retrieved and the new methodology was verified by both computer

simulation and TXM experiment.

iii

Acknowledgements

This work is done by a group of people. First I thank Prof. Keng Liang (梁耕三老師), the director of

NSRRC, who organized, initiated and fully supported the transmission X-ray microscope project and

is also the advisor of my Ph.D. thesis. I thank Prof. Fu-Rong Chen (陳福榮老師) who introduced me

into the phase problem in the field of microscopy. My special thanks are due to Prof. Hang-Ping

Shieh (謝漢萍老師), who instructed me the effective way of presentation and guided me through the

course of my Ph.D. research.

The installation of TXM was a joint development for Xradia and NSRRC. I thank Dr. Fred

Duewer, Dr. Michael Feser, Mr. Shashi Kamath and Dr. Andrei Tkachuk for sharing knowledge and

experience during my visit in Xradia and the time for commissioning this machine at NSRRC.

Special thanks are due to Dr. Wenbing Yun (雲文兵博士) who always encourages me to explore the

new thinking in TXM.

Understandably, this TXM can not operate without a beamline. I thank for NSRRC beamline

group for building the beamline 01, which is leaded by Dr. King-Long Tseng (曾金榮博士) who

was passed away in 2006. I am grateful to Dr. Mau-Tsu Tang (湯茂竹博士) and Dr. Yang-Feng

Song (宋艷芳博士) for their kind helps in the beginning stage of the project. I give special thanks to

Mr. Te-Hui Lee (李德輝先生) who taught me the knowledge of programming and electronic control

for over 4 years. I also thanks to Mr. Tang-Er Dann (但唐諤先生), who was also the helped to

promote this project.

Thanks are also due to my colleague in the laboratory. I thank for Mr. Yi-Ming Chen (陳一銘)

and Mr. Jian-Hua Chen (陳建樺) who shared my experimental work while I was writing my thesis. I

thank Mr. Roman Dronyak for the discussion on the algorithm of phase retrieval and Mr. Bau-Yueh

Shiaw (蕭寶岳) who did a good sample preparation for TXM. I also thank Mr. Ying-So Tseng (曾英

碩), Mr. Shi-Yu (林信余), Ms. Fanny Chuang (莊惠芳), Ms. Ling Li (黃麗玲) and Mr. Ping-Chen

Tseng (曾斌誠) for making me a pleasant laboratory life in last stage of my Ph.D. research.

Finally, I thank for my parents for unconditional support and countless generosities.

iv

Table of contents

Abstract in Chinese……..……….………..……. i

Abstract in English….………..……. ii

Acknowledgements…….………..……. iii

Table of Contents…….………..……. iv

List of Tables………..………. vi

List of Figures…….………..……….. vii

Chapter 1: Introduction………..……. 1

1.1 Matter, Light and their Interactions……….………… 3

1.1.1 The complex reflection index of X-rays ………..……… 3

1.1.2 The absorption and phase shift……….……… 6

1.1.3 The free space wave equation……… 7

1.2 The X-ray Phase Imaging – a literature survey……… 8

1.3 The Progress of X-ray Microscope……….……… 9

1.4 Current Issue- towards living cell tomography……… 11

Chapter 2: Transmission X-ray Microscope (TXM) at NSRRC………..…. 14

2.1 NSRRC Storage Ring and Superconducting Wavelength Shifter………..………..…

14

2.2 NSRRC’s TXM…..………

16

2.3 Absorption Contrast Image……….……….. 24

2.4 Third Order Image……….……….…..

26

2.5 Dark Field Image……….……….……….. 35

2.6 Tomography………...

42

2.6.1 The principle of x-ray tomography……….…

42

2.6.1.1 Projections……….…...

42

2.6.1.2 Fourier Slice Theorem……….…… 44

2.6.1.3 The Filtered Back Projection Algorithm……….….. 45

2.6.2 Nano Tomography………..…....

48

2.6.2.1 Synchrotron Radiation (SR)-based micro tomography……….... 48

2.6.2.2 Nano-Tomography by TXM………..……... 49

2.7 Summary………. 54

Chapter 3:

Phase Retrieval of Wave Propagation in TXM………..……….

55

3.1 Transport of Intensity Equation (TIE)………..

57

v

3.3 Combination of TIE and SCWP for Phase Retrieval………

62

3.3.1 The different response of TIE and SCWP……….

62

3.3.2 The Applicable range of TIE and SCWP………..

66

3.3.3 Phase retrieval by combination of TIE and SCWP…….……….

68

3.4 The Quantitative Phase Retrieval in Transmission X-ray Microscope………...

69

3.4.1 Applying phase retrieval in TXM………...

69

3.4.2 Experimental result and analysis……… 71

3.5 Summary ………...

76

Chapter 4:

Zernike’s Phase Imaging and Phase Tomography………..…. 77

4.1 Zernike’s Phase Contrast ……….. 78

4.2 Iterative Phase Retrieval for Common Path Interferometry (IPR-CPI)……….

81

4.2.1 The process of common path interferometer (CPI)………

81

4.2.2 The iterative way of phase retrieval from CPI………

85

4.2.3 Analysis of IPR-CPI……… 87

4.2.4 The experimental result……….. 95

4.2.5 Summary for IPR-CPI………...

100

4.3 The Phase Tomography……….. 101

4.3.1 Phase tomography by Zernike’s phase contrast………..

101

4.3.2 Phase tomography by combined method of TIE and SCWP……….

105

4.3.3 Phase tomography by IPR-CPI………. 106

4.4 Summary………

110

Chapter 5:

Conclusions…………..………. 111

vi

Table Index

Table 1-1 The simulated parameter(for biology sample) ...11 Table 2-1 Specification of the three zone plates in NSRRC-TXM ...24

vii

Figure Index

Figure 1-1 The schematic view of (a) TXM and (b) STXM ...10

Figure 1-2 The simulation of the projection of the cell in the micro tube ...12

Figure 1-3 Radiation dose calculated for minimal exposure imaging...13

Figure 2-1 The optical layout of BL01B...15

Figure 2-2 The measured flux for BL01B...15

Figure 2-3 The schematic drawing of the TXM ...16

Figure 2-4 The images of TXM in BL01B hutch...17

Figure 2-5 The reflectivity versus incident grazing angle for the glass (SiO2)capillary for photon energy of 8 keV ...19

Figure 2-6 The optical layout of the condenser ...19

Figure 2-7 The capillary condenser use to focus X-ray ...20

Figure 2-8 The zone plate image by SEM...22

Figure 2-9 (a) The CCD .(b) the schematic of the internal design of the microscope...

23

Figure 2-10 The calculated magnification versus energy from 8-11 keV ...

25

Figure 2-11

Image is taken at 8.4 keV (a) and 9.5 keV (b) ...26

Figure 2-12 The cross-section profile of the outmost zone of the zoneplate ...28

Figure 2-13 The setup of third order image ...29

Figure 2-14 The spoke pattern are imaged under different image mode ...33

Figure 2-15 The modulation transfer functions for third order and first order image...34

Figure 2-16 Two methods implement the dark field in TXM ...36

Figure 2-17 The frequency response for the dark field and bright field ...37

Figure 2-18 The image of a siemen’s star in (a) bright field and (b) dark-field...38

Figure 2-19 A Siemens star in (a) Bright field and (b) Dark-field after 2D Fourier transform ...39

Figure 2-20 The dark field of used zone plate in (a) Bright field and (b) Dark-field...40

Figure 2-21 The dark field image of a tungsten plug in the memory chip...41

Figure 2-22 The schematic of projections of the object...43

Figure 2-23 The projections of a half-zone plate model ...43

Figure 2-24 The reconstructed slice of tomography ...47

Figure 2-25 The setup for SR-based tomography...48

Figure 2-26 The projection images from IC before process ...50

Figure 2-27 The projection images from after align and reference processes...50

Figure 2-28 3D rendering of tungsten plug with “key hole” ...50

Figure 2-29 The 3D rendering of tungsten plug is plotted with higher threshold ...51

Figure 2-30 The top-view and side view of the tungsten plug displayed in voxel mode (top) and iso-surface (bottom) mode ...52

viii

Figure 3-1 The scheme of the SCWP ...61

Figure 3-2 The intensity simulation of a wave concentric phase retardation with propagation different position ...64

Figure 3-3 The retrieved phase by TIE for a zone-plate-like pattern ...65

Figure 3-4 The retrieved phase by TIE (blue), SCWP (red), and Combine (green) method...66

Figure 3-5 The applicable range for TIE and SCWP. For SCWP ...68

Figure 3-6 The optical system of a single lens system...70

Figure 3-7 A plastic zone plate is used as the sample for testing ...72

Figure 3-8The experimental and simulated images of TXM ...73

Figure 3-9 The results of three phase retrieval methods...74

Figure 4-1 The schematic drawing of Zernike’s phase contrast in TXM ...79

Figure 4-2 The out look of the phase ring...80

Figure 4-3 The biology images under Zernike’s phase contrast...81

Figure 4-4 The common path interferometer in the microscope...83

Figure 4-5 The modulation of the phase ring in the back focal plane (BFP) ...85

Figure 4-6 The scheme of the iterative phase retrieval form Zernike’s Phase contrast...86

Figure 4-7 The derivation of normalized intensity of the CPI...88

Figure 4-8 The initial condition of IPR-CPI...91

Figure 4-9 The phase is retrieved with different width of phase ring ...92

Figure 4-10 The phase is retrieved with different thickness of phase ring ...93

Figure 4-11 The error value in the iteration in IPR-CPI ...94

Figure 4-12 The cross-section plot of the retrieved phase with initial phase of zero value ...95

Figure 4-13 Plastic zone plate measured by Zernike’s phase contrast ...96

Figure 4-14 The Zernike’s phase contrast image and its simulation image ...

97

Figure 4-15 The Zernike’s phase contrast image and its retrieved phase image ...99

Figure 4-16 The plastic zoneplate for verifying the IPR-CPI method for smaller line width...100

Figure 4-17 The reconstructed slice of tomography from the object shown in the left ...103

Figure 4-18 The phase tomography by the FBP and Zernike’s Phase contrast of the filter material with Os stained ...104

Figure 4-19 The phase retrieved by SCWP and TIE method………. .105

Figure 4-20 The reconstructed slice from Zernike’s Phase contrast and IPR-CPI……… ...106

Figure 4-21 The image of Zernike’s phase contrast of the AGS cell (a) and its retrieved phase (b)....108

Figure 4-22 The rendering of the phase tomography of the outer shell of the stained AGS cell...109

Figure 5-1 The phase image of the biology cell in the capillary...112

Figure 5-2 (a) the 3d rendering of the original cell in the capillary (b) the 3d rendering of the reconstruct phase tomography of cell in the capillary ...113