X-ray beam shaping

Initial X-ray beams were generated using an empirical model (i.e., TASMIP code), and then filter materials were combinations with the initial X-ray beams. The simulation tool for spectrum measurement and quantitative evaluation used a Geant4 Application for Tomographic Emission (GATE) Monte Carlo platform to model X-ray beam through filter and object. GATE is well validated, with highly realistic simulations [29]. The geometry of simulation was illustrated for monochromatic X-ray beam design as shown in figure 3.1. The initial beam in accordance with alternations of tube potentials is exposed to the detector through the filter. Detected X-ray beams are sorted by number of photons and the photon energy in GATE. Therefore, we obtained the filtered X-ray spectrum for each tube potential and filter material.

Figure 3.1 Illustration of geometry to acquire spectrum of designed X-ray beam with initial X-ray source, filter, and a-Se detector.

We simulated the monochromatic X-ray beam by increasing filter thickness at each tube potential. The filter thickness was increased from 2 to 8 HVL for observing the reduction in photon number by filtering. The number of photons in filtered beam is reduced to 128 times compared to the number of photons of initial beam at 7 HVL. The mean energy of each filtered beam was distributed by tube potential at the filter thickness of 7 HVL. Since tube loading can reduce the quantity of filtered beam to 128 times, the 7 HVL filter thickness was used to shape the X-ray beam. If 8 HVL is used as filter thickness, it is insufficient because the photon quantity of the filtered beam is reduced to 256 times. The plots of energy spectra in accordance with filter thickness for absolute and relative numbers of photons are illustrated in figures 3.2 and 3.3, respectively. Since maximum K-edge energy of a filter was about 70 keV, tube potential of more than 100 kV is not sufficient for spectral shaping. Therefore, we selected tube potential ranging from 40 to 90 kV. The relationship between the number of photons and X-ray beam shaping by Ba filter was indicated as having a high-energy range and narrow beam shaping, with increasing HVL at 50 kV, in figure 3.2. The quantity of the initial X-ray beam of 50 kV is reduced to 128 times, but tube loading can be controlled by increasing number of photons (i.e., mAs). The relative spectra by using 2, 7, and 8 HVL Ba filter at 50 kV are shown in figure 3.3. The spectral quality exhibits a complex distribution with higher tube potential (≥ 80 kV), where filtering has a greater effect on controlling mean energy change. Filtered X-ray beam is more narrow than the unfiltered X-ray beam. The mean energy of the narrow beam is expected to be close to the mean energy of K-edge energy of a filter. From figure 3.3, it

can be seen that there is significant beam hardening for the unfiltered case, regardless of tube potential.

Figure 3.2 The relationship between the number of photons and X-ray beam shaping was simulated by using a Ba filter with increasing filter thickness at 50 kV.

Figure 3.3 The alternation of relative X-ray beam shaping with increasing filter

The mean energy of filtered X-ray spectrum is not dependent on the number of photons; it is only affected by distribution of X-ray spectrum. A plot of the mean of the filtered energy spectra for Ba at various filter thicknesses is shown in figure 3.4. The K-edge energy of Ba is 37.44 keV, while with an unfiltered spectrum, mean energy increases with increasing tube potential. Increasing filter thickness results in an increase in the mean energy due to more efficient pre-hardening of the spectra and, as a result, a qualitatively more quasi-monochromatic beam. When using 2 HVL thicknesses, the trend of mean energy increases similarly to that of an unfiltered beam.

The trend of mean energy is similar between 7 and 8 HVL thicknesses at all tube potentials. Mean energy is rapidly more increased over the 70 kV with 7 and 8 HVL thicknesses than with the K-edge energy of Ba. Thus, K-edge peak of Ba does not contribute to the spectrum due to the existence of high energy with high tube potential.

A plot of the mean of the filtered energy spectra for various filter materials at 7 HVL indicates relatively invariant mean energies within some tube potential operating range with K-edge energy materials, as shown in figure 3.5. Mean energies of Al and Cu filters increased corresponding to the increasing tube potential. Higher Z corresponds to a higher mean energy within the range of 40 to 60 kV. The order of increasing invariant mean energies corresponds to the increasing K-edge energies of each material up to approximately 60 kV. However, the tungsten K-characteristic X-rays bias the spectrum more than the filter’s K-edge at tube potentials greater than 60 kV and, hence, shift the mean energy of the spectrum, leading to an inversion of the rank order of mean energies with increasing Z. Overall, mean energy is increasing

because the X-ray spectra is shifted to the high energy by filter. This means that the shapes of spectra were broad to narrow.

Figure 3.4 Mean energy with respect to tube potential using Ba filter at 2, 7, and 8 HVL thicknesses and mean energy of K-edge, and without filtration.

Figure 3.5 Mean energy using various filter materials corresponds to the increasing tube potential at 7 HVL.