design, fabrication and characterization of an x-ray multi-mirror array suitable for photon phase

230 Pages·2013·6.67 MB·English

DESIGN, FABRICATION AND CHARACTERIZATION
OF AN X-RAY MULTI-MIRROR ARRAY
SUITABLE FOR PHOTON PHASE SPACE OF
SYNCHROTRON RADIATION

REN YAPING

NATIONAL UNIVERSITY OF SINGAPORE

2013
DESIGN, FABRICATION AND CHARACTERIZATION
OF AN X-RAY MULTI-MIRROR ARRAY
SUITABLE FOR PHOTON PHASE SPACE OF
SYNCHROTRON RADIATION

REN YAPING
(M.Sc. LOUISIANA STATE UNIVERSITY, USA)
(M.Sc. THE CHINESE ACADEMY OF SCIENCE, CHINA)
(B. Eng., XIAN INSTITUTE OF TECHNOLOGY, CHINA)

A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE

2013

Acknowledgements

Acknowledgements

First and foremost I would like to extend my sincere gratitude to Prof. Herbert Oskar
Moser for his erudite knowledge, expert guidance and invaluable suggestions. Alongside
Prof. Herbert Oskar Moser, my special thanks go to Prof. Francis Tay Eng Hock and Prof.
Thomas Osipowicz for their continuous support within the project and specifically during
the regular project review.

I would like to thank Dr. Yang Ping, Dr. Yu Xiaojiang, Dr. Jian Linke, Dr. Li Zhiwang, Dr.
Sascha Pierre Heussler, Dr. Krzysztof Banas, Dr. Diao Caozheng, Mr. Miao Hua, Mr.
Chew Eh Piew, Prof. Mark B H Breese and other staff members in Singapore
Synchrotron Light Source (SSLS) for their selfless help and assistance as well as the
generous sharing of their knowledge and expertise.

I would also like to thank deep heartedly Dr. Yue Weisheng and Prof. Jeroen Anton van
Kan from Centre for Ion Beam Applications (CIBA) of National University of Singapore
for extending their fullest support in my research work.

In addition, I would like to thank all my friends in Singapore, China, United States and
Germany, for their supports and encouragements.

II
Acknowledgements

Finally, the love, support and encouragements from my daughter Jenny, my son John, and
my parents have inspired me continuously to march forward in the research study.

Many thanks to you all,

Ren Yaping
NUS, Singapore 2013

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Table of Contents

Table of Contents

Declaration I
Acknowledgements II
Table of Contents IV
Summary VIII
List of Tables XII
List of Figures XIII
List of Symbols XXIII

Chapter 1 Introduction 1
1.1 Background of the project 1
1.2 Objectives of this thesis 5
1.3 Organization of this thesis 7

Chapter 2 Literature Review of X-ray Focusing Optics in 9
Synchrotron Beamlines
2.1 Introduction 9
2.2 Overview of general x-ray focusing optics 9
2.3 Total external reflection mirrors in synchrotron beamlines 16
2.4 Microstructured x-ray focusing devices 24
2.5 Summary 28

Chapter 3 Representation of Synchrotron Radiation Source in 29
Phase Space
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Table of Contents

3.1 Introduction 29
3.2 Synchrotron radiation source 29
3.2.1 Synchrotron radiation source 30
3.2.2 Properties of synchrotron radiation 32
3.3 The distribution of synchrotron radiation in phase space 34
3.3.1 Concept of phase space method 34
3.3.2 Distribution of synchrotron radiation in phase space 36
3.3.3 Phase space representation of a synchrotron radiation source 48
3.3.3.1 Definition of the coordinate systems 48
3.3.3.2 Derivation of the projection equations 50
3.3.3.3 Phase space representation of a synchrotron radiation source 52
3.4 Transformation of the synchrotron radiation beam 64
3.4.1 Liouville’s theorem 64
3.4.2 Transformation of phase space ellipse 64
3.4.3 Transformation of synchrotron radiation source 69
3.5 Summary 71

Chapter 4 Design Optimization of X-ray Multi-Mirror Array 73
4.1 Introductions 73
4.2 Scheme of a multi-mirror focusing system in synchrotron beamlines 73
4.2.1 X-ray beam condensation in synchrotron radiation beamline 74
4.2.2 Scheme of a multi-mirror focusing array 77
4.3 Design of a multi-mirror array 81
4.3.1 Principle and property of a basic multi-mirror focusing array 81
4.3.2 Design of the basic multi-mirror focusing array 85
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Table of Contents

4.3.2.1 Position of the mirrors 85
4.3.2.2 Inclination of the mirrors 90
4.3.2.3 Curvature of the mirrors 93
4.3.3 Advanced design of a multi-mirror focusing array 96
4.3.3.1 Phase space representation of x-ray beam in synchrotron 97
beamline
4.3.3.2 Preliminary analytical calculation of approximate position of 100
the mirrors
4.3.3.3 Advanced design of a multi-mirror focusing array 101
4.3.3.3.1 Position of the mirrors 101
4.3.3.3.2 Inclination of the mirrors 104
4.3.3.3.3 Curvature of the mirrors 105
4.3.4 Determination of geometric shape and dimension of the mirrors 110
4.3.4.1 Geometric shape and dimension of the mirrors 110
4.3.4.2 Size of a multi-mirror array 113
4.4 Summary 113

Chapter 5 Fabrication of Multi-Mirror Structures 115
5.1 Introduction 115
5.2 Fabrication procedures and materials of multi-mirror structures 115
5.3 Mask fabrication 120
5.3.1 Graphite x-ray mask 120
5.3.2 Proton beam writing x-ray mask 124
5.3.3 Discussion 127
5.4 Fabrication of multi-mirror structures 128
5.4.1 Fabrication of lamellar mirrors via DXRL by using graphite x-ray 130
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Table of Contents

mask
5.4.2 Fabrication of triangular mirrors via DXRL by using PBW x-ray 132
mask
5.4.3 Fabrication of curved mirrors via optical lithography by using 134
optical mask
5.5 Reflection layer coating 137
5.6 Roughness measurement 140
5.7 Summary 147

Chapter 6 Characterization of Multi-Mirror System 148
6.1 Introduction 149
6.2 Ray tracing 149
6.3 Focusing performance of multi-mirror array in synchrotron beamline 155
6.4 Summary 164

Chapter 7 Conclusion 165

Bibliography 169
Publications 181
Appendices 183
Appendix 1 X-ray Total External Reflection 183
Appendix 2 Helios 2 and Beamlines Layout at SSLS 185
Appendix 3 Characteristics of Synchrotron Radiation 187
Appendix 4 Fabrication of the Cr Optical Mask 193
Appendix 5 Thin Glass Multi-Mirror Device 195

VII
Summary

Summary

X-ray synchrotron radiation is a very powerful tool for basic science and industry
research as its shorter wavelength can result in a higher spatial resolution, longer focal
length and larger penetration depth in matter. In practical applications, the fan-like x-ray
photon beam emitted from a storage ring of synchrotron source needs to be firstly
collected and focused or collimated before directing onto samples to achieve high spatial
resolution and high photon throughput. X-ray optical elements to gather and effectively
transport large percentage or all of the radiation to the sample is highly desired.

Micro optics with high acceptance angles to collect and focus x-rays with higher flux
throughput has been attracting great interest due to its advantages such as flexible optical
configuration, minimal structure size, and cost efficiency in fabrication. The development
of a multi-mirror system intended to be based on advanced microfabrication technologies
to effectively focus x-rays in synchrotron radiation beamlines has great potential. This
multi-mirror system should be able to intercept all radiated x-rays from a synchrotron
source and focus them with high flux throughput.

This dissertation presents the design concept of a novel multi-mirror focusing scheme to
condense synchrotron radiation beam. The design of the x-ray focusing optic is based on
advanced microfabrication techniques and studying the distribution of synchrotron
radiations in phase space.

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