Element specific X-ray fluorescence microtomography [Elektronische Ressource] / vorgelegt von Til Florian Günzler

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• Physik

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• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2003
• Nombre de lectures: 59
• Poids de l'ouvrage: 2 Mo

Extrait

Element-speci c X-ray Fluorescence
Microtomography
Von der Fakult t f r Mathematik, Informatik und Naturwissenschaften
der Rheinisch-Westf lisc hen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines Doktors der
Naturwissenschaften genehmigte Dissertation
vorgelegt von
Diplom-Physiker Til Florian G nzler
aus Nordhorn
Berichter: Universit tsprofessor Dr. B. Lengeler
Univ Dr. U. Klemradt
Tag der m ndlic hen Pr fung: 21.11.2003
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verf gbar.Contents
1 Introduction 1
2 Interactions of X Rays with Matter 5
2.1 Photoabsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Fluorescence Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Auger Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Rayleigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Refractive Decrement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Detectors 19
3.1 Measurement of X-ray Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Ionization Chamber and Proportional Counter . . . . . . . . . . . . . 19
3.1.2 Semiconductor Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Energy Dispersive Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 X-ray Optic: Refractive Lens 31
4.1 Parabolice Lens (PRL) . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 Transmission T of the Lens . . . . . . . . . . . . . . . . . . . . . . 33PRL
4.2.2 E ectiv e Aperture D . . . . . . . . . . . . . . . . . . . . . . . . . . . 34e
4.3 Microbeam Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Numerical Aperture N:A: . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.2 Focal Spot Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.3 Gain g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Nanofocusing Lens (NFL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Primary Beam Properties 43
5.1 Monochromatic Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Polyc Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6 Fluorescence Tomography 55
6.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Analysis of the spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
iCONTENTS
6.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.5 Improvements and Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 Experiments 77
7.1 Geology/Astrophysics Investigation: Micrometeorite . . . . . . . . . . . . . . 77
7.2 Ion Transport in Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2.1 Spruce Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.2.2 Trichomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8 Feasibility of a Laboratory Setup 91
9 Conclusion and Outlook 95
A Filtered Backprojection Technique (FBT) I
A.1 Fourier Slice Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
A.2 Filtered Backprojection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
B Correcting Sinograms VII
C Calculating the Focal Spot Size IX
Bibliography XI
List of Figures XX
iiChapter 1
Introduction
Since the discovery of x rays by W. C. R n tgen in 1895 [R n95 ] they have become a powerful
tool in various elds of science. Max v. Laue [vL13] and later the Braggs [Bra13] employed
x rays to investigate the crystal structure of matter. They made use of x-ray di raction that
is nowadays a common technique to analyze crystalline samples. Nearly every laboratory
around the world that works in the eld of material science owns an x-ray di ractometer to
analyze crystalline samples.
Other techniques and experimental setups using x rays have been conceived over the
years by scientists working in various scienti c elds. Many of these techniques allow one to
measure physical properties of samples with unique precision or made it possible for the rst
time to access these properties by an experiment. This is especially true for the interatomic
con guration and distances in crystalline matter determined by x-ray di raction.
X-ray absorption spectroscopy (XAS), for instance, provides information about the oxida-
tion state of atoms [Sch03a, St 96 ] in condensed matter. Also the corresponding coordination
number and the interatomic distances of atoms to their nearest neighbor atoms can be ob-
tained from x-ray absorption spectra.
Measuring the re ectivit y of x ray under grazing incidence is another powerful technique
to investigate samples with x rays. The re ectivit y of x rays strongly depends on the density
of the re ecting matter. Therefore, this method is an ideal probe to measure the density of
thin layers with unique precision. In addition, the thickness of layers in multilayer stacks as
well as the roughness of the re ecting surface can be obtained by measuring the re ectivit y.
Interfaces are also accessible by this method because the high penetration depth of x rays
allows them to deeply enter into matter.
X-ray uorescence analysis is a wide spread microanalytic technique. It can be used
to detect and quantify low concentrations of chemical elements in samples. The chemical
elements can be identi ed because uorescence radiation emitted by an atom is characteristic
for the chemical species. In the hard x-ray range (E>2keV) the uorescence radiation again
bene ts from the high penetration depth of x rays. X-ray uorescence can give information
about the occurrence of chemical elements inside of a sample. This determination is not
only very sensitive it is also very precise in terms of quantitative analysis. Thus, it can be
used to quantitatively measure concentrations of chemical element in samples (cf. [dB90]).
Moreover, x-ray uorescence analysis has been foreseen as a method for certi cation in the
1CHAPTER 1. INTRODUCTION
eld of microanalysis [Ada98].
However, the greatest impact as already mentioned x rays have had due to their
property of penetrating matter. R n tgen himself used this to image the inside of objects. A
very well known radiograph (see gure 1.1) taken by R n tgen is the hand of Geheimrath von
K llik er. Projecting the inside of objects is still used for several applications of modern life.
From material inspection in several elds of industries to the inspection of luggage at airports
to the medical applications of x rays in hospitals projecting the interior of an object by x rays
is very useful. However, the features of an object overlay in a projection and an object is hard
to recognize from a single projection. This drawback led to the development of laminography
where a few projection under di eren t angles are taken. With the upcoming of fast improving
computer technology x-ray tomography was introduced and has since developed into a very
common tool, especially, for physicians but also in other elds of science.
Figure 1.1: The rst radiograph publicly taken by R n tgen is the hand of Geheimrath von K llik er.
He was the chairman of the session in W rzburg where R n tgen presented his discovery
for the rst time.
High resolution projections taken by x rays demand high resolution detectors or lms.
Today the physical limitation in resolution for such projections appears to be reached. It
amounts to one micrometer. In order to further improve the resolution of projections a mag-
nifying x-ray optic comparable to glass lenses for visible light is needed. Since 1996 parabolic
refractive lenses (PRL) have been developed at the II. Physikalisches Institut B of Aachen
University. These newly developed x-ray lenses work similarly to glass lenses for visible light.
They make it possible to image an object without spherical aberration. This allows to op-
tically magnify the image of samples and to improve the resolution of projections obtained
by this imaging technique. Besides this, they also can serve to demagnify the image of an
x-ray source and to produce a microbeam with an extent in the range of micrometers. The
microbeam can be used to scan a sample stepwise and get local information about the sample.
This information depends on the applied technique which can vary from x-ray absorption spec-
troscopy [Sch03a] to re ectivit y measurements to di raction [Sch03b] of x rays to uorescence
spectroscopy [Sim01] and other methods.
Within this work, uorescence spectroscopy is used to obtain the local distribution of
2CHAPTER 1. INTRODUCTION
chemical elements in a sample. In order to access this distribution tomography is employed.
Scanning uorescence tomography gives the opportunity to measure the chemical element
distribution of samples semi-quantitatively on a virtual slice through the sample without
the need of sectioning the sample. Semi-quantitative mea