Imaging with parabolic refractive x-ray lenses [Elektronische Ressource] / vorgelegt von Boris Benner

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• Physik

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2005
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 19 Mo

Extrait

Imaging with Parabolic Refractive X-Ray Lenses
Von der Fakult¨ at fur¨ Mathematik, Informatik und Naturwissenschaften
der Rheinisch-Westf¨ alischen Technischen Hochschule Aachen zur
Erlangung des akademischen Grades eines Doktors der
Naturwissenschaften genehmigte Dissertation
vorgelegt von
Diplom-Physiker Boris Benner
aus K¨oln-Lindenthal
Berichter:
Universit¨ atsprofessor Dr. rer. nat. Bruno Lengeler
Universit¨ Dr. rer. nat. Hans Luth¨
Tag der mundlic¨ hen Prufung:¨
09. Juni 2005
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfugbar.¨Contents
1 Introduction 1
2 X-Ray Sources 3
2.1 X-RayTube................................... 3
2.1.1 Bremstrahlung............................. 4
2.1.2 Characteristic Emission and Fluorescence Radiation . . . . . . . . . 7
2.1.3 TypicalCharacteristicsofX-RayTubes................ 9
2.2 SynchrotronRadiation 12
2.2.1 BendingMagnet ............................ 15
2.2.2 InsertionDevices 17
2.2.3 DevelopmentofX-RaySources .................... 20
3 Overview of X-Ray Optics 23
3.1 InteractionofX-RayswithMater....................... 23
3.1.1 TheComplexIndexofRefraction................... 24
3.1.2 Refraction................................ 25
3.1.3 Absorption ............................... 26
3.1.4 Reflection. 26
3.1.5 Bragscatering ............................ 30
3.2 Monochromators. 30
3.3 Mirrors and Capillaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Multilayer.................................... 34
3.5 FresnelZonePlates............................... 35
3.6 OtherX-RayOptics .............................. 37
3.7 TypicalBeamlineLayoutforSRSources................... 37
4 Parabolic Refractive X-Ray Lenses 41
4.1 Geometry of Parabolic Refractive X-Ray Lenses (PRXL) . . . . . . . . . . 41
4.2 GeometricalOptics............................... 42
4.2.1 InfluenceofDiffraction......................... 46
4.3 Properties of Parabolic Refractive X-Ray Lenses . . . . . . . . . . . . . . . 46
4.3.1 Focal Length of a Single Parabolic Refractive X-Ray Lens . . . . . 46
iii CONTENTS
4.3.2 Focal Length of Compound Parabolic Refractive X-Ray Lenses
(cPRXL)................................. 48
4.3.3 Transmission and Gain of Refractive Lenses . . . . . . . . . . . . . 49
4.3.4 Lateral Resolution and Effective Aperture . . . . . . . . . . . . . . 52
4.3.5 Depth of Field, Depth of Focus, and Field of View . . . . . . . . . . 53
4.3.6 ChromaticAberation......................... 5
4.3.7 SurfaceRoughnes........................... 57
4.4 LensMaterialRequirements. 58
4.5 HousingandHolderforLenses 6
5 Imaging with PRXL 69
5.1 AbsorptionandPhaseContrast........................ 69
5.2 CoherenceLengths............................... 72
5.2.1 Thelongitudinalcoherencelength................... 72
5.2.2 Thetransversalcoherencelengths 73
5.2.3 CoherenceLengthsatID2 ...................... 73
5.3 Diffuser..................................... 75
5.3.1 TechnicalDetails............................ 76
5.3.2 ChoiceoftheDiffuserMaterial .................... 76
5.4 X-RayMicroscope ............................... 81
5.4.1 Lateralresolution 81
5.4.2 FieldofView.............................. 84
5.4.3 CondenserLens............................. 87
5.5 X-RayLithography 89
5.6 Microfocus.................................... 91
6 Tomography 93
6.1 TheReconstructionofAbsorptionTomograms................ 95
6.1.1 Discrete Number of Projections and Rotations . . . . . . . . . . . . 101
6.2 FluorescenceMicro-Tomography........................102
6.3 MagnifyingTomography............................105
7 Summary 111
List of Figures 115
List of Symbols and Abbreviations 121
List of Publications 126
Bibliography 127Chapter 1
Introduction
There is an increasing need for 3-dimensional imaging in many areas of technology, basic
science, and medicine. Hard x-rays are one of the probes which are used for that purpose.
X-ray tomography is a wide spread tool in medical diagnosis. Other areas need a higher
lateral resolution as, for instance, material science, geophysics, plant physiology, analysis
of art objects, and also medical research. X-rays have two major advantages. Firstly, the
relatively large penetration depth of hard x-rays allows for the analysis of opaque media
with sample sizes in the millimeters to centimeters range. Secondly, the short wavelength
˚ ˚¨ ¨of x-rays in the Angstrom and sub-Angstrom range allows for a lateral resolution
far below 1 micrometer. The availability of synchrotron radiation sources of the third
generation with their outstanding brilliance has promoted the technical development in
this direction, despite the small number of these installations, as compared to laboratory
x-ray sources. X-rays may also have a major disadvantage for tomography, in particular for
biological samples and in medical applications. This is the radiation damage, which must be
minimized for biological tissue with a very low level of tolerance, in particular for humans.
For animals and plants the level of radiation must be at least that low that the object of
investigation is not destroyed during the exposure. In general, this requirement in x-ray
tomography is not easy to fulfill in biological systems, whereas radiation damage is of no
major concern for anorganic materials. An important development in x-ray tomography
which took place in the last 10 years is the combination of 3-dimensional imaging and
spectroscopy. Here, x-ray fluorescence is the most appropriate technique. In that way it is
possible to link the geometrical structure of an object with its local chemical composition.
Plant physiology, in particular, has profited from this development. X-ray tomography with
high lateral resolution requires a sophisticated experimental set-up. Besides a high brilliant
x-ray source, made available to the public by the synchrotron radiation facilities, like e.g.
the European Synchrotron Radiation Facility (ESRF), there is need for a sophisticated
x-ray optic, for a sample environment with many translational and rotational degrees of
6freedom and for a 2-dimensional detector with a high resolution (>10 pixels with 10-
20 micrometers in size). In this thesis the emphasis is on x-ray optics.
Compared to optics for visible light, all x-ray optical components suffer from the weak
refraction of x-rays in matter and from the relatively strong absorption, as compared to that
12 CHAPTER 1. INTRODUCTION
of visible light in glass. Indeed, the index of refraction for x-rays in matter can be written
−6as n=1− δ + iβ . The refractive decrement δ is only of the order of 10 ,comparedtoa
refractive increment of 0.5 for visible light in glass. As a consequence, x-ray mirrors based
◦on total external reflection can only operate at glancing angles, typically below 0.2 .For
the same reason, refractive x-ray lenses have long been considered as non feasible. However,
in 1996 it could be shown that refractive x-ray lenses can be made, if a few conditions are
met [Snigirev96]. Firstly, the lens material must have a low atomic number Z in order to
reduce the x-ray absorption, and it must show weak small angle x-ray scattering, as small
angle x-ray scattering generates a blur of the image. Secondly, the radius of curvature of
the lenses must be small (typically 200 micrometers), in order to increase the refractive
power. Thirdly, many lenses must be stacked in a row (up to a few hundred), also in
order to increase the refraction power and to bring the focal length in the meter range and
below. At the II. Physikalisches Institut B of RWTH Aachen University the technology for
the manufacturing of these lenses has been developed. A breakthrough for imaging with
x-rays was achieved in Aachen by shaping the lenses as biconcave paraboloids of rotation.
This allows for imaging without spherical aberration and without any other distortions.
Parabolic refractive x-ray lenses have another advantage compared to spherical lenses.
The geometrical aperture and the radius of curvature at the apices of the parabolas can
be chosen independently of one another. Our lenses have typically a radius of curvature
of 200 micrometers and a geometric aperture of 1 millimeter. Therefore, these lenses
match very well the beam size of undulator radiation at third generation synchrotron
radiation sources. The main focus of this thesis is on the technical details which have to
be specified in order to optimize the fabrication of parabolic refractive x-ray lenses and on
their applications in typical scientific problems.
The thesis includes the following chapters. Chapter 2 gives an overview of x-ray sources:
x-ray tubes and synchrotron radiation sources. Chapter 3 reviews the most important
optical devices used at present for monochromatizing and focusing x-ray beams. Chapter 4
describes in detail the parameters which have to be considered in the process of fabricating
parabolic refractive x-ray lenses. This includes the choice of the lens material concerning
x-ray absorption, small angle x-ray scattering, stability in the beam, and stacking of the
lenses in a row. A large number of possible lens materials have been investigated. The
results are presented in this thesis. The transmission and the gain, the e