Measured low-energy x-ray spectra of interest in diagnostic radiology and mammography

We used a planar high-purity germanium low-energy detector ORTEC model GLP-25300/13-PL-S for high-count-rates (1000 counts s⁻¹), serial number 57-D626. The active volume is a Ge crystal of 25 mm in diameter and 13 mm in length plus an inactive Ge layer of 0.3 μm. The detector also has an absorbing beryllium window of 0.254 mm in thickness. The detector is associated with a preamplifier model A232N serial number 17139954. The operating bias voltage is negative 2000 V. Due to the relatively high current (2 mA) of the x-ray tube, all the measurements were performed at 1770 mm distance from the source to reduce the count rates, thereafter corrected due to attenuation and air density to 1000 mm. A collimator of 3 mm diameter was used for the output of the beam. Additional filters of high purity aluminium foils (99.999%), rhodium (99.99%), molybdenum (99.99%) and silver (99.99%) were used. The minimum thickness foil used was 0.0254 mm which has been measured using Scanning Electron Microscope installed in the central microscope laboratory at our Institute. The uncertainties in the thicknesses are less than 0.4%. Tables 1 and 2 show the different beam qualities studied in this work.

The spectrometry measurements were carried out at the x-ray Irradiation Room. This laboratory is used for basic research and mammography studies. Figure 1 displays the experimental setup of the spectrometry measurements.

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The x-ray tube is an YXLON Y.SMART 160E/1.5 with tungsten (W) anode and an inherent filtration of 1 mm beryllium. The tube which has a 3.0 mm focal spot operates from 10 to 160 kV in steps of 1 kV. The effective anode angle is 30°. The minimum current generates by the x-ray tube is 2 mA and this value was used during all the measurements.

When doing spectrometry, the number of photons that the detector is capable to read with respect to the number of photons emitted by the radiation source is fundamental. Thus, the efficiency of the detector must be evaluated since not all the incident photons are detected and if they are detected, not all the energy is deposited into the detector crystal. The efficiency can be obtained experimentally or through simulation. In this work the efficiency of the detector was measured using three radioactive sources of ¹³³Ba, ¹³⁷Cs and ⁵⁵Fe calibrated at the National Institute of Nuclear Research. First, each radioactive source was collocated individually at 1 cm from the detector and the gamma spectrum was obtained during 600 s. To perform these measurements, the detector and the radioactive source were both collocated within the steel cylinder without the entry lead collimator in the front part as shown in figure 1 so that the radioactive source could be very close to the detector at 1 cm. The 1 cm distance was choosing due to the low activity of the radioactive sources. We analyzed the gamma spectra through a deconvolution process. Using the deconvolution results, the efficiency, $\varepsilon ,$ was evaluated as:

$$\begin{eqnarray}&&\varepsilon =\displaystyle \frac{N}{A\rho t},\end{eqnarray} \tag{ 1 }$$

where N is the net area under each gamma peak (total counting), A (Bq) is the activity reported in the calibration certificate, ρ is the γ-ray emission probability for this peak according to the nuclear data center (NuDat 2.8 2022) and t the collection time. Figure 2. shows the efficiency of the detector measured as a function of the photon energy.

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After, we made a second measurement by collocating the 3 radioactive sources simultaneously at 1 cm from the detector and obtained a wide spectrum that includes many gamma-ray peaks. The collection time was 600 s. Figure 3 depicts the deconvoluted spectrum.

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Using the net area under each gamma peak and the results for the efficiency shown in figure 2, the activity for each source was obtained and compared with the reference value reported in the calibration certificate. Good agreement was observed with differences of 0.5% (70842.2 Bq reference versus 71198.6 Bq measured) for the ¹³³Ba source, 0.05% (222382.1 Bq reference versus 222495.7 Bq measured) for the ¹³⁷Cs source and 0.03% (288978.6 Bq reference versus 288877.0 Bq measured) for the ⁵⁵Fe source. So, the corrected x-ray spectrum was obtained as the ratio of the measured spectrum divided by the efficiency.

The spectra were collected using a DSPEC Jr 2.0 ^TM digital signal processing module serial number 17219224 from ORTEC and the MAESTRO-32 MCA software version 7.01. After an optimisation test, we used a rise time of 1.2 μs and a flat top width of 0.3 μs. The raw spectra were collected within 512 channels. The channels were calibrated in terms of energy using the same gamma sources mentioned above. Tables 3 and 4 display the count rates, the total counts collected and the dead time for each x-ray beam measured. A background spectrum was collected for 48 h and after subtracted from each x-ray spectrum measured.

Each x-ray spectrum presented here is normalized to the standard reference conditions of air density $\rho {\,}_{0}$ = 1.1974 × 10⁻³ g.cm⁻³, pressure P₀ = 101.3 kPa, temperature T₀ = 20 °C and distance of 1000 mm from the detector to the x-ray focal spot. To convert each x-ray spectrum measured under the environmental conditions of pressure P, temperature T and humidity r in our lab to that under standard reference conditions, the exponential attenuation function was used considering the Drake and Böhm equation for air density ρ (Drake and Böhm 1990):

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{E}\left(E\right)={{\rm{\Phi }}}_{E,m}\left(E\right)\exp \left[-\left(\mu \left(E\right)/{\rho }_{0}\right)d\left({\rho }_{0}-\rho \right)\right],\end{eqnarray} \tag{ 2 }$$

with

$$\begin{eqnarray}&&\rho ={\rho }_{0}\left[\displaystyle \frac{P}{101.3}-\displaystyle \frac{r}{114.2}{\left(\displaystyle \frac{T}{293.15}\right)}^{17.97}\right]\displaystyle \frac{293.15}{T},\end{eqnarray} \tag{ 3 }$$

where Φ_E and Φ_{E, m} are the photon fluence at the standard reference conditions (SRC) and the laboratory conditions (LC), respectively. $\mu \left(E\right)$ are the mass attenuation coefficients (Hubbell and Seltzer 2004) and were adjusted to double logarithmic function for a better interpolation, d is the distance between the Ge spectrometer and the x-ray tube focal spot. In our lab, P, T and r were monitored simultaneously with each x-ray spectrum using high precision thermometer Fluke 1523, barometer Druk DPI, and hygrometer EasyLog EL-USB-2-LCD. To normalize the x-ray spectra from 1770 to 1000 mm, the measured spectra were corrected by inverse square law plus air attenuation.

The half value layer (HVL) was evaluated using the x-ray spectra and measured with a reference ionization chamber from Standard Imaging model A12. To determine the HVL using the spectra, first the air kerma was calculated as

$$\begin{eqnarray}&&{K}_{air}=\displaystyle {\int }_{{E}_{0}}^{{E}_{\max }}\varphi \left(E\right)\displaystyle \frac{{\mu }_{tr}\left(E\right)}{\rho }dE,\end{eqnarray} \tag{ 4 }$$

where $\varphi \left(E\right)$ is the photon fluence, $E$ the energy and $\tfrac{{\mu }_{tr}\left(E\right)}{\rho }$ is the mass energy transfer coefficient for air. As the mass energy transfer coefficient and the mass absorption coefficient are the same at this energy range, we used the mass absorption coefficients published by Hubbell and Seltzer (2004).

Thus, using the exponential attenuation law, the HVL was calculated as

$$\begin{eqnarray}&&{K}_{air,att}={K}_{air}{e}^{\left[-\displaystyle \frac{\mu \left(E\right)}{\rho }\right]\rho x},\end{eqnarray} \tag{ 5 }$$

where, ${K}_{air,att}$ is the air kerma after crossing the filter material (aluminium), $\tfrac{\mu \left(E\right)}{\rho }$ is the mass attenuation coefficient for aluminium, $\rho$ is the density of the filter material.

The mean photon energy was calculated as:

$$\begin{eqnarray}&&{\bar{E}}_{ph}=\,\displaystyle \frac{\displaystyle {\int }_{{E}_{0}}^{{E}_{\max }}\varphi \left(E\right)EdE}{\displaystyle {\int }_{{E}_{0}}^{{E}_{\max }}\varphi \left(E\right)dE}.\end{eqnarray} \tag{ 6 }$$

The several mammography x-ray spectra measured in this work are displayed in figures 4(a)–(c) for the additional filtration of molybdenum, rhodium and silver, respectively. Table 5 presents the HVL from the spectra and the average energies.

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Note that the effect of the different material used as additional filtration is slightly reflected on the shape of the spectra shown in figure 4 where the maximum intensity of the molybdenum filtration is narrower than the others. The spectra with additional filtration of molybdenum are narrower than those with additional filtration of rhodium and silver. With respect to the HVL for the mammography beams shown in table 5, the results are within the interval expected since the HVL generally reported for mammography beams are in the interval between 0.27 mm and 0.67 mm Al (IAEA 2021). Figure 4(d) shows the mammography x-ray spectra for tungsten anode with additional filtration of 50 μm molybdenum obtained in this work compared to mathematically filtered beam from Ketelhut et al 2021. As can be seen there is good agreement between the two spectra. The HVL calculated for the spectrum from Ketelhut is 0.325 mm Al versus 0.276 mm Al from ours which represents a difference of 15%. However, besides the remarkable discrepancy on the HVL, the average energies obtained in both studies are similar with a difference of 1.2% (17.41 keV from Ketelhut et al versus 17.19 keV from this work).

The x-ray spectra measured under standard reference (SRC) and laboratory conditions (LC) for the M30, M40, M80, M100 and M120 are presented in figures 5, 6(a)–(c), respectively. For all the spectra, the counts were divided by the product of the current of the x-ray tube, the measuring time, and the area of the collimator aperture.Thereafter, the M80, M100 and M120 beams are normalised by the maximum fluence for comparison with calculations or with data reported in the literature. A slight difference can be observed between the spectra under LC and SRC for the M30 and M40, whereas for the M80, M100 and M120, such a difference vanishes. This suggests that the effect of the air density in Mexico City affects slightly the x-ray spectra below 50 kV, mainly if the spectra are filtrated.

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Table 6 displays the HVL obtained through the spectra and measured with ionization chamber as well as the average energy for the radiological beams. As can be observed in table 6, within measurement uncertainties, there is good agreement between the HVL from the spectra and those measured with ionization chambers. The differences observed are around 0.2% and 13% which are smaller than the uncertainties on the measurements with ionization chamber. Comparing the HVL obtained from the spectra with the data published by NIST for the M-series beams, the maximum difference is about 10%. Even though in some case, it was not possible to reproduce the same additional filtration due to the limitation of the aluminum foil thickness available in our Lab.

SpekCalc is an executable for calculating x-ray emission spectra from tungsten anode x-ray tubes in the energy range between 40 to 300 kV and anode angles between 6° and 30° (Poludniowski et al 2009). It is based on Monte Carlo methods for electron penetration and an analytic approach for the x-ray emission, using theoretical bremsstrahlung cross sections (Poludniowski 2007). The x-ray spectra are generated through a user interface where the characteristics of an x-ray tube can be reproduced by selecting the distance from the focal spot, the anode angle, and the inherent and additional filtrations. X-ray spectra generated through SpekCalc, have been used by several research groups for dosimetry or biomedical studies (Tedgren et al 2011, Friedland et al 2019, Massillon-JL et al 2019). In this work, X-ray spectra from SpekCalc were also generated for x-ray beams of 80 kV, 100 kV and 120 kV considering the characteristics of our x-ray tube and the additional filtration for the M-series beams. Thus, also displayed in figures 6(a)–(c) are the x-ray spectra calculated with SpekCalc for M80, M100 and M120 beams. As observed, the SpekCalc reproduces qualitatively the experimental spectra, but not quantitatively, mainly for M100 and M120 beams. Nonetheless, the differences on the HVL are 4.4% (2.63 mm Al from SpekCalc versus 2.75 mm Al this work), 2.3% (4.69 mm Al from SpekCalc versus 4.8 mm Al this work) and 1.4% (6.44 mm Al from SpekCalc versus 6.53 mm Al this work) for the M80, M100 and M120 beams, respectively. With respect to the average energies, the discrepancies are 0.8% (42.7 keV from SpekCalc versus 43.04 keV this work), 1.0% (52.7 keV from SpekCalc versus 53.24 keV this work) and 2.24% (60.2 keV from SpekCalc versus 61.58 keV this work) for the M80, M100 and M120 beams, respectively. Such a result suggests that having a good agreement between the HVL of a beam from two different methods does not mean the x-ray spectra are the same. Besides, we compared the M80 spectrum with a mathematically filtered beam measured at PTB by Ankerhold. The result is depicted in figure 6(a). Both spectra agree quite well with a difference of 0.7% in the average energy (43.36 keV from Ankerhold versus 43.04 keV this work).

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