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are absorbed by the surrounding material. Photoelectric absorption is the
dominant process in tissue for photons with energy below approximately
30 keV.
11.4.4 Implications for Medical Imaging
Compton scattering and photoelectric absorption dominate the interaction
of diagnostic X-rays with organic matter such as soft tissue. The probabili-
ties for these effects to occur depend on the incident X-ray energy and the
atomic number Z of the penetrated material. To be able to distinguish differ-
ent materials, the attenuation of the incident X-ray beam needs to be signifi-
cantly different for different materials. If the X-ray energy is too high, most
of the Compton-scattered photons traverse the body almost unchanged,
leading to images with low contrast. Lower-energetic X-rays may not pen-
etrate dense material, like bones, or thick materials, but they are suitable
for imaging thin, soft tissues. Here, one can take advantage of the fact that
absorption due to the photoelectric effect shows a sharp increase at energies
around the element-specific energy level of the innermost electron orbit (i.e.,
K-edge imaging). Furthermore, the absorption probability for the photoelec-
tric effect increases with the cube of the atomic number Z , so that small
differences in tissue composition are amplified in the attenuation. The low-
energy part of the X-ray spectrum is not useful for medical imaging since
it is completely absorbed by the patient's body. To avoid this unnecessary
radiation dose, a filter is placed between the X-ray tube and the patient. For
planar or C-arm systems, the filter consists of a thin layer of copper or alu-
minum. For diagnostic CT systems (discussed in the section 11.6 on X-ray
CT), a bow-tie-shaped filter is used.
11.4.5 Attenuation Coefficients
The attenuation of the intensity that an X-ray beam encounters when travel-
ing through a uniform material depends exponentially on the thickness of
the material:
α γ
E x
I x
( ) =
I e
0
where I 0 is the incident intensity, x is the path length of the X-rays through
the object, and α E is the linear attenuation coefficient . The attenuation coeffi-
cient is specific for a material and depends on the photon energy as indicated
by the subscript E γ . Consequently, the transmitted X-ray spectrum contains
information about both the material composition and the thickness of the
structures inside the object. The linear attenuation coefficient of a material is
determined by its specific interaction with X-rays as described. Therefore, it
can be written as follows:
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