7.3 Fan-Beam and Volumetric Imaging Modes
XFCT and XLCT allow more imaging modes than optical imaging and standard CT
due to freedom in detector placement and due to the much lower absorption and
scatter probability of X-rays compared to optical photons. As energetic X-rays
mainly transverse the imaging medium on a linear path with exponential attenuation,
the possible lines of response (LORs) can be either annotated by the source beam
geometry or the detector collimation. Besides the pencil beam and Compton camera
XFCT geometries described above, it is possible to use different detector collimation
designs and combine them with different X-ray source collimation geometries.
Basically, six different combinations of X-ray source and detector collimation are
possible. Dual collimation of the source, the detector, or both yields LORs along
which projective measurements can be performed. These LORs result from the
intersection of two planes, wherein each plane is defined either by an excitation or
detection collimator. Using this principle, a pencil-beam geometry is achieved by
collimating the source in two orthogonal directions; a fan-beam geometry by
collimating the beam and the detectors each once orthogonally; and the cone-beam
geometry by collimating the detectors in two orthogonal dimensions. Each geometry
offers a different trade-off in terms of spatial resolution, sensitivity, imaging time,
and imaging dose. On top of these three basic collimation concepts, it is possible to
directly measure elemental concentrations at “points of response” (PORs) with the
use of three orthogonal collimation planes. This can either be achieved by a
combination of a pencil-beam collimation and a strip collimator orthogonal to
each other or by a fan-beam excitation perpendicular to a parallel hole collimator.
In these designs, no ill-posed inverse problem must be solved for image reconstruction and quantitative images can be obtained with a direct attenuation correction on
the measured data. This scheme offers the attractive possibility of directly probing
the PORs of interest and also removes the noise amplification inherent to the image
reconstruction process.
Last, pinhole collimators can be used in place of parallel hole collimators with
cone-beam excitation. With the pinhole collimators, it is possible to achieve higher
spatial resolutions than restricted by the dimensions of an exciting pencil beam. As
pinhole collimation may reduce the sensitivity, the following approximation should
motivate the approach: The goal is to achieve around 1 mm spatial resolution in
molecular information extraction. We consider a 1 mm
3 volume element, filled with
10 μg/ml of AuNPs, irradiated with X-rays (10 cGy total dose, 81 keV) (similar to
the dose used in microCT). This corresponds to an energy transfer of 100 μJ, or 7.7
billion photons. Out of those photons, about 0.05% interact with gold, while the
remainder interacts with water (this is based on the higher density and attenuation
cross-section of gold compared to water). Out of the 3.85 millions of photons that
interact with gold, 99% do so via the photoelectric absorption, and 80% of these with
the K-shell. Based on the fluorescence yield of gold (95%), roughly 3.66 million
fluorescent X-rays are emitted. Assuming a 10% photon sensitivity (pencil beam, no
detector collimator), 366,000 photons can be detected that emanate from a single
140
D. Vernekohl and L. Xing
XFCT and XLCT allow more imaging modes than optical imaging and standard CT
due to freedom in detector placement and due to the much lower absorption and
scatter probability of X-rays compared to optical photons. As energetic X-rays
mainly transverse the imaging medium on a linear path with exponential attenuation,
the possible lines of response (LORs) can be either annotated by the source beam
geometry or the detector collimation. Besides the pencil beam and Compton camera
XFCT geometries described above, it is possible to use different detector collimation
designs and combine them with different X-ray source collimation geometries.
Basically, six different combinations of X-ray source and detector collimation are
possible. Dual collimation of the source, the detector, or both yields LORs along
which projective measurements can be performed. These LORs result from the
intersection of two planes, wherein each plane is defined either by an excitation or
detection collimator. Using this principle, a pencil-beam geometry is achieved by
collimating the source in two orthogonal directions; a fan-beam geometry by
collimating the beam and the detectors each once orthogonally; and the cone-beam
geometry by collimating the detectors in two orthogonal dimensions. Each geometry
offers a different trade-off in terms of spatial resolution, sensitivity, imaging time,
and imaging dose. On top of these three basic collimation concepts, it is possible to
directly measure elemental concentrations at “points of response” (PORs) with the
use of three orthogonal collimation planes. This can either be achieved by a
combination of a pencil-beam collimation and a strip collimator orthogonal to
each other or by a fan-beam excitation perpendicular to a parallel hole collimator.
In these designs, no ill-posed inverse problem must be solved for image reconstruction and quantitative images can be obtained with a direct attenuation correction on
the measured data. This scheme offers the attractive possibility of directly probing
the PORs of interest and also removes the noise amplification inherent to the image
reconstruction process.
Last, pinhole collimators can be used in place of parallel hole collimators with
cone-beam excitation. With the pinhole collimators, it is possible to achieve higher
spatial resolutions than restricted by the dimensions of an exciting pencil beam. As
pinhole collimation may reduce the sensitivity, the following approximation should
motivate the approach: The goal is to achieve around 1 mm spatial resolution in
molecular information extraction. We consider a 1 mm
3 volume element, filled with
10 μg/ml of AuNPs, irradiated with X-rays (10 cGy total dose, 81 keV) (similar to
the dose used in microCT). This corresponds to an energy transfer of 100 μJ, or 7.7
billion photons. Out of those photons, about 0.05% interact with gold, while the
remainder interacts with water (this is based on the higher density and attenuation
cross-section of gold compared to water). Out of the 3.85 millions of photons that
interact with gold, 99% do so via the photoelectric absorption, and 80% of these with
the K-shell. Based on the fluorescence yield of gold (95%), roughly 3.66 million
fluorescent X-rays are emitted. Assuming a 10% photon sensitivity (pencil beam, no
detector collimator), 366,000 photons can be detected that emanate from a single
140
D. Vernekohl and L. Xing