CSEM Scientific and Technical Report 2008

Element Sensitive X-ray Imaging – a Roentgen Progress
J. Nüesch, P. Seitz
X-ray absorption spectroscopy allows detecting the elemental composition of an investigated object.
For the last hundred years x-ray absorption images gave only
the density of the scanned sample. There is the possibility to
use the fluorescent radiation of a sample surface to determine
its composition. But the volumetric information gets lost with
this approach as the fluorescent radiation is emitted in 4 π and
it only works for the surface
Figure 1: A sample setup to image an object with this technique.
From right to left: source, object, and spectrometer.
The element sensitive detection is possible due to an effect in
the photoabsorption. In general the x-ray absorption is
described by the Beer-Lambert-Law
66
���� �� � � ��·� � � � � ��·�·�
�
The loss of intensity I loss is dependent on the thickness x,
the density ρ, and the mass-absorption coefficient � � �.
In the
x-ray domain up to about 60 keV the photoabsorption is the
dominate effect. The simplified formula for the
photoabsorption is
� ��
�
� �� In most models the exponents a and b are considered to be
constants. But these exponents are dependent on the energy
(E) respective to the atomic number (Z). This crossdependency
permits the calculation of the elemental
composition.
Figure 2: The part of the periodic system with the elements
detectable in the range of 10 – 20 keV. All these elements are in this
domain completely in photoabsorption without an edge.
In the photoabsorption there is an additional effect not
included in this equation. At the energy of each electron shell
the function � �� ��� has a step, called edge. This limits in a
first step the detection to the elements highlighted in Figure 2.
The absolute density of the object cannot be measured by one
measurement. This limit only calculates a density length
product
���·�
If some kind of tomography is used or if x is known for the
geometry all densities can be calculated.
Counts [s -1 ]
40
35
30
25
20
15
10
5
0
0 7.8 15.6 23.4 31.2 39 46.8 54.6
Energy [keV]
Figure 3: The outputs of an Amptek semiconductor spectrometer with
different elements in a beam at 40 kVp acceleration voltage. The
three pure plates have a thickness of 500 µm.
For the calculation the equation of the photoabsorption can be
rewritten as
���� � ��� � ·� ��
This equation can be solved in linear algebra
�� ���� ·���� ����������
The matrix B can be calculated with reference data.
Afterwards the areal density is directly calculated from the
measurements.
The X-ray spectrometer from Amptek (Figure 1) used at the
moment has a resolution up to 149 eV @ 5.9 keV. Besides the
spectral resolution the number of the maximal counts per
second is important (Figure 3). This limits the maximal
intensity of the beam. Overshooting this limit will increase the
error of the signal as double impact cannot be detected in all
cases and some measures must be discarded.
�
Al
Si
Ti