Simulation of X-ray fluorescence computed tomography imaging scanner based on gaseous detectors

Abstract

Gaseous detectors offer an attractive alternative to commonly used semiconductor detectors in X-ray Fluorescence Computed Tomography (XFCT) systems, mainly due to their potential for large active areas and lower cost. In this work, a novel concept of XFCT imaging was investigated through Monte Carlo simulations using the GATE software. The simulated system integrates a collimation-based optical system and a position and energy-sensitive gaseous detector, filled with krypton gas, for fluorescence photon detection. Three phantoms with different geometries, sizes, elemental compositions, and attenuation conditions were simulated to evaluate the system’s capability. The results demonstrate the ability of the system to discriminate multiple elements and to reconstruct cross-sectional and three-dimensional elemental images, confirming the feasibility of XFCT imaging based on gaseous detectors. These findings highlight the potential of this approach as an alternative to semiconductor-based XFCT systems, supporting further optimization and experimental validation.

1 Introduction

The X-ray Fluorescence (XRF) technique is based on detecting the characteristic X-rays emitted by the atoms in a sample when exposed to ionising radiation. The energy of the radiation emitted is specific to each element, allowing it to be identified. This technique features several advantages, including the simultaneous identification of multiple elements, its non-destructive nature, and minimal sample preparation requirements (Shackley, 2018).

Computed Tomography (CT) imaging technique is based on acquiring X-ray projections of a sample from multiple angles, which are then reconstructed mathematically to form a 3D image providing spatial information about the density and structure of the sample. It is widely used in medical imaging, e.g., CT scans, but is also applied in industrial areas (Bartscher et al., 2007).

X-ray Fluorescence Computed Tomography (XFCT) is the combination of the two aforementioned techniques. It is a non-invasive and non-destructive imaging modality that can map the three-dimensional (3D) elemental distributions inside a sample. It can be employed in biomedical imaging, for example, to detect trace elements in tissues and map nanoparticles, but also in material science, among other fields (Li et al., 2017; Jones et al., 2012; Yu et al., 2001).

Most systems rely on monoenergetic X-ray beams using synchrotron radiation, which are unsuitable for routine biomedical imaging due to their limited accessibility and high radiation dose rates. To overcome these limitations, laboratory-based systems have been developed, leveraging advances in X-ray instrumentation for 2D/3D XRF imaging, with various geometries and detection approaches. These systems often use micro-XRF technology with X-ray polycapillary optics (Cherepennikov et al., 2018) or use X-ray pixel detectors and collimating apertures (Dunning and Bazalova-Carter, 2020) (Deng et al., 2015), similar to methods used in single-photon emission tomography.

Jones et al. (2012) reported a benchtop cone-beam XFCT system designed to determine the spatial distribution and concentration of gold nanoparticles (GNPs) in small-animal-sized objects. The system used a microfocus X-ray source to irradiate the sample and a cadmium telluride (CdTe) detector to detect the gold fluorescence photons. Li et al. (2017) presented a full-field fan-beam XFCT system employing an X-ray tube, a tungsten pinhole, and a CZT linear photon counting array. The system’s performance was evaluated using a PMMA phantom with gadolinium (Gd) inserts placed on a motion stage. Moktan et al.(2020) investigated the impact of different X-ray detection setups on the sensitivity and resolution of benchtop XFCT systems. Using a Geant4-based Monte Carlo simulation, they modelled photon detection from phantoms containing GNPs, optimising XFCT setups through factors such as detection efficiency and the quality of reconstructed images.

However, the XFCT systems based on semiconductor detectors have limitations, such as their complexity, lack of sustainability due to high costs, and current semiconductor shortage (Manohar et al., 2018; Mohammad et al., 2022). Gaseous detectors represent an excellent alternative: they can be fabricated at significantly lower cost and scaled to large active areas; their filling gas composition can be modified to optimize detection efficiency; and position- and energy-sensitive gaseous detectors can fulfil the detection requirements of XFCT imaging.

Gaseous detectors are widely used in experiments of high-energy physics and have also attracted strong interest in areas beyond this field, ranging from cultural heritage studies to medical/biomedical imaging (Silva et al., 2015; Sauli, 2020).

Silva et al. (2013) developed a benchtop Energy Dispersive X-ray Fluorescence (EDXRF) imaging system based on a 2D-Micro Hole and Strip Plate for analysis of human teeth treated with dental amalgam, emphasizing its potential for EDXRF imaging applications. Later, Leite et al. (2022) used a Full-Field Energy Dispersive X-ray Fluorescence (FF-XRF) imaging system, based on the 2D-THCOBRA micropattern gas detector, to monitor heavy metal accumulation in zebrafish during a water-borne exposure bioassay. In 2025, Łach et al. (2025) presented an imaging system based on Gas Electron Multiplier (GEM) detector technology designed to analyze the elemental composition of complex 3D cultural heritage objects without physically sampling or damaging them. This system expands Macro-XRF applications beyond flat paintings to geometrically complex objects, representing a significant advancement in non-invasive cultural heritage imaging.

These results highlight the potential of gas-detector-based XRF imaging systems for elemental mapping applications in different areas.

The present work explores the use of a gaseous detector-based imaging system for XFCT, investigating its capability for three-dimensional elemental imaging through Monte Carlo simulations performed using GATE software. Simulations were recognised as a crucial tool for system design and optimization, enabling the evaluation of acquisition parameters, data analysis procedures, and image reconstruction methods before experimental implementation, reducing development time and guiding experimental choices. The simulated system’s capability was assessed using phantoms of distinct geometries, sizes, elemental compositions, and attenuation conditions, to evaluate elemental discrimination and three-dimensional image reconstruction.

2 Materials and methods

2.1 XFCT imaging concept

The proposed XFCT system consists of an X-ray tube for sample excitation, a collimation-based optical system–a multi-hole collimator–for image formation, and a position- and energy-sensitive gaseous detector for detecting the fluorescence radiation emitted by the sample. As illustrated in Figure 1, the sample is positioned at the centre of the system and rotated over a full angular range of 0–360°. During acquisition, the X-ray beam irradiates the sample, inducing the emission of characteristic fluorescence photons. Those photons that successfully pass through the collimation aperture are recorded by the gaseous detector, which registers both their energy and interaction position.

FIGURE 1

The collected data are processed and organized into a sinogram, which represents the set of projections acquired at different rotation angles. This sinogram serves as input for the reconstruction algorithms to produce cross-sectional images, which can subsequently be combined to generate a three-dimensional representation of the elemental distribution within the sample.

The single-photon counting capability of the detector allows for the acquisition of spectral images, correlating event locations with their corresponding energies. This capability allows for the generation of individual 3D elemental maps, representing the spatial distribution of specific elements within the sample. As illustrated on the right in Figure 1, the detector records information for each detected photon, generating a complete energy spectrum. By selecting regions of interest (ROI) within this spectrum, specific energy windows corresponding to different elements can be isolated. For each selected energy range, the projection data are organized into a sinogram, which serves as the basis for image reconstruction. The reconstructed images of individual elements are then combined to produce a 3D elemental distribution of the sample.

2.2 GATE simulation

Simulations were performed using GATE (Geant4 Application for Tomographic Emission), an advanced open-source software dedicated to numerical simulations in medical imaging (Sarrut et al., 2021). In this study, GATE version 9.2, using Geant4 version 11.0.4, was used. All simulations were performed on a computer equipped with an AMD Ryzen 9 7950X 16-Core Processor, 5.8 GHz each one, 62 GB RAM, running Ubuntu. The modeled system consisted of a phantom, an optical system, and a detector, as illustrated in Figure 2. Electromagnetic interactions were simulated using the Livermore low-energy physics list, which provides accurate modelling of photon and electron interactions at low energies. Simulation outputs were collected using GATE’s built-in ROOT output module. The Singles digitizer chain processed the hits registered in the sensitive detector, producing event-by-event data including deposited energy and spatial coordinates of each detected photon.

FIGURE 2

The simulation geometry consisted of a krypton gas detector modelled as a box with dimensions 4 × 4 × 1 cm³. Krypton was selected as the detection medium due to its higher atomic number compared to lighter noble gases such as argon or neon, which increases the photoelectric absorption probability for X-ray photons in the energy range of interest, thereby improving the detection efficiency.

In front of the detector, a lead (Pb) multi-hole collimator was implemented with overall dimensions of 4 × 4 × 1.5 cm³ and an active area of 3 × 3 × 1.5 cm³. The collimator septa thickness was 0.3 mm, and the holes had a hexagonal geometry with diameters of 1 mm, with an additional configuration using 0.5 mm diameter holes. As reported by Carvalho et al. (Carvalho et al., 2023) for similar MPGD-based XRF systems, reducing the collimator hole diameter improves spatial resolution at the cost of detection sensitivity. This fundamental trade-off motivates future optimisation of the collimator geometry for specific imaging tasks.

A phantom of smaller dimensions was positioned in front of the collimator, with its centre of rotation aligned with the centre of the detector, and the phantom was rotated about its own axis.

All components were defined within a world volume filled with air, represented by a box with dimensions 40 × 40 × 40 cm³.

Three phantoms, with different elemental objects and dimensions, were used in simulations, represented in Figure 3.

FIGURE 3

The three phantoms were designed with increasing levels of complexity to evaluate different aspects of the system performance. Phantom 1 represents a simple configuration used for basic validation of elemental detection and spatial resolution. Phantom 2 introduces a more realistic scenario, with multiple elements embedded in a PMMA matrix, allowing the assessment of attenuation effects and multi-element discrimination. Phantom 3 represents a more complex geometry, combining different shapes, sizes, and orientations, in order to evaluate the system performance under more challenging conditions, including object overlap and spatial resolution limitations.

The phantom materials were selected based on their characteristic fluorescence emission energies. Specifically, the K-shell lines of Fe (Kα ≈ 6.40 keV) and Cu (Kα ≈ 8.05 keV), and the L-shell line of Au (Lα ≈ 9.71 keV) fall within the optimal detection efficiency range of the krypton gaseous detector, where the absorption cross-section is significantly higher than at the elevated energies of the Au K-shell lines (Kα ≈ 68.8 keV, Kβ ≈ 77.9 keV). This energy range is also compatible with low-voltage X-ray tubes, making the system both technically feasible and cost-effective.

To reduce computational resources, the fluorescence process was modelled by defining each object as a radioactive source emitting photons at the characteristic energies of the corresponding elements, with emission restricted to the surface of each object. This approximation is supported by transmission versus energy calculations performed for the material thickness considered, which confirmed that photons emitted from the interior of the objects undergo significant attenuation before reaching the detector, making their contribution to the detected signal negligible. The detector was defined with an energy resolution of 18% at 5.9 keV, reproducing the expected performance of the experimental setup. This value was based on results reported by R. Nunes (Nunes, 2021), who characterized the energy resolution of a gaseous detector using krypton.

2.3 Image reconstruction and analysis

The simulation output provides information on the interaction position of each detected photon, namely, the x and y coordinates in the detector plane, as well as the photon energy. This information is organised according to the rotation angle of the phantom, allowing the detected photons to be associated with their corresponding acquisition angle.

Using these data, the projections were generated using a 256 × 256 pixel matrix, where each pixel corresponds to 40/256 ≈ 0.156 mm, matching the physical dimensions of the detector (40 × 40 mm). In addition, an energy window can be applied to select photons within a specific energy range corresponding to the characteristic X-ray emission of a given element in the phantom. This enables the generation of element-specific projection images.

The resulting projections are then arranged into a sinogram, which serves as the input for the image reconstruction process.

Cross-sectional images are reconstructed using the Filtered Back Projection (FBP) algorithm via the iradon function from the Matlab image processing toolbox (MathWorks I. MATLAB, 2023). For 3D reconstruction, multi-slice reconstruction divides projection images into user-defined slices, stacking the corresponding cross-sectional images into a 3D representation. Regarding slice thickness, each reconstructed slice corresponds to one detector row, representing a thickness of 1 pixel.

The reconstructed CT images were analysed to evaluate the spatial response of the imaging system for the different elemental components in the phantom. Normalized intensity profiles were extracted along both the tangential and radial directions. These profiles were fitted using Gaussian functions, enabling the determination of the full width at half maximum (FWHM), which was used as a quantitative metric to assess the spatial resolution of the system.

3 Results

3.1 Phantom 1

The Phantom 1 emitted 1 × 10¹¹ photons per second in all directions being detected approximately 2.3 × 10⁶ photons in total. (Figures 4a,b) shows the generated spectrum and sinogram, respectively, of the phantom. The two elements present in the sample are well discriminated in the energy spectrum and can be clearly identified in the sinogram.

FIGURE 4

In the spectrum shown in (Figure 4a), three distinct peaks can be observed. The first peak corresponds to the characteristic energy of argon (Ar) as a result of the interaction of the photons with the air defined in the simulation world volume. The other two peaks correspond to the characteristic fluorescence energies of the elements present in the sample (Fe and Cu) and were used as reference energies for defining the energy windows employed in the elemental reconstruction.

The sinogram shown in (Figure 4b) represents the projections of the phantom acquired over a full rotation. The two sinusoidal curves correspond to the projections of Cu and Fe elements, represented in blue and red, respectively.

It can also be observed that, for rotation angles close to 90°, the signal is absent in the Fe curve, while the Cu curve remains visible. This occurs because, at this angular position, the Cu cylinder is located between the Fe cylinder and the detector, leading to attenuation of the fluorescence photons emitted by Fe, which therefore are not detected.

The width of the sinusoidal traces in the sinogram is proportional to the size of the corresponding objects. As expected, the trace associated with Cu appears wider than that of Fe, indicating the larger dimensions of the Cu cylinder. These sinogram data were subsequently used to reconstruct the cross-sectional images of the sample, as shown in (Figure 4c).

Figure 5 presents the radial and tangential profiles for each element of Phantom 1. In the Cu reconstruction, a decrease in intensity is observed at the centre of the object, which is consistent with the simulation approach adopted: fluorescence photon emission was defined only at the surface of the cylindrical inserts, since photons emitted from the interior would be largely absorbed by the surrounding material before reaching the detector. This approximation was intentionally applied to reduce computational time, as the contribution of interior-emitted photons to the detected signal is negligible due to self-attenuation effects. The values of FWHM were extracted and summarized in Table 1, to be compared with the theoretical ones (defined in the GATE simulation).

FIGURE 5

The reconstructed image for the iron cylinder had a diameter of 1.76 ± 0.03 mm and 2.03 ± 0.02 mm in the radial and tangential directions, respectively. For the copper cylinder, the diameter in the radial direction was 3.61 ± 0.31 mm, and in the tangential direction was 4.43 ± 0.20 mm. These values exceed the nominal diameters of 1 mm for iron and 3 mm for copper, which is primarily due to the limited spatial resolution of the imaging system. The system resolution is constrained by the collimator aperture size, as the holes determine the angular acceptance of photons, and is further affected by blurring introduced during the image reconstruction process. Consequently, smaller objects appear slightly enlarged in the reconstructed images.

In the tangential direction, the absolute difference increases with cylinder diameter, as observed when comparing the Fe and Cu rods; the opposite tendency is observed in the radial direction, where a smaller absolute difference is obtained for the larger rod.

In this phantom, the distance between the two rods was measured, obtaining the value of approximately 10.2 ± 0.1 mm. This result is in good agreement with the distance defined in the simulation, which was 10 mm.

For the creation of the 3D images of this phantom, the cross-sectional images were combined. Initially, each elemental material was processed separately due to the energy selection capability. A specific range of values representative of its surface was defined for visualisation, and the corresponding iso-surface for each material was then displayed. Finally, the individual 3D representations of each energy selection were combined, resulting in the final 3D image with all the elements of the phantom, as shown in Figure 6.

FIGURE 6

Some artifacts are visible in the 3D representation, slightly distorting the cylindrical shapes of the phantom objects. These artifacts arise from noise present in the projection images, which propagates through the reconstruction process and becomes more apparent in the 3D visualization. The appearance of these artifacts highlights the impact of noise and limited spatial resolution on the 3D reconstruction quality.

3.2 Phantom 2

Phantom 2 presents a higher level of complexity compared to Phantom 1, as the elemental inserts are now embedded in a PMMA cylinder, where the emitted photons undergo attenuation before reaching the detector. In the simulation, the phantom was defined to emit fluorescence photons isotropically at a rate of 6 × 10⁹ photons per second and in the end were detected approximately 6.7 × 10⁶ events.

The cumulative energy spectrum, representing the photon interaction in the gas detector medium, and the corresponding sinogram are presented in Figures 7a,b, respectively. The energy spectrum shows the characteristic fluorescence energies of the three elements (Fe, Cu, and Au) constituting the phantom, preceded by a peak corresponding to the Ar energy. The separation of these peaks allows the definition of element-specific energy windows, enabling the reconstruction of individual elemental distributions.

FIGURE 7

The sinogram enables the identification of three distinct objects, corresponding to the elemental cylinders within the phantom. The elemental cross-sectional images were reconstructed from the sinogram data using the FBP algorithm, and the axial views are presented in (Figure 7c). The slightly flattened shape of the cylinders is visible in the reconstructed images of all elements, being most evident in the iron cylinder. This occurs because, at certain rotation angles, the cylinders block one another, preventing the fluorescence signal from those positions from reaching the detector. The resulting gaps in the sinogram data affect the accurate reconstruction of the phantom’s geometric shape.

Table 2 summarises the cylinder diameter analysis obtained from the elemental cross-sectional images of Phantom 2. The cylinder diameters were estimated using FWHM measurements in the radial and tangential directions. The measured values were compared with the corresponding theoretical diameters.

The results presented in Table 2 show that, for all materials, the FWHM values obtained from the reconstructed images are larger than the corresponding theoretical diameters. A directional dependence is observed, with larger deviations generally occurring in the radial direction compared to the tangential direction for this phantom. In contrast to the behaviour observed for Phantom 1, the tangential FWHM values show smaller deviations from theoretical diameters, suggesting a more accurate reconstruction in this direction. Additionally, no clear dependence on the material type or cylinder diameter is observed, indicating that the observed broadening is mainly related to the intrinsic spatial resolution of the system and reconstruction effects rather than the elemental composition of the cylinders.

Table 3 presents the analysis of the distances between the centres of the objects identified in Phantom 2. The centre-to-centre distances obtained from the reconstructed images were compared with the corresponding theoretical values defined in the simulation.

The results in Table 3 show that the distances between the centres of the objects measured in the reconstructed images are consistently larger than the corresponding theoretical values. Despite these differences, the relative spatial arrangement of the objects is preserved, as the measured distances remain consistent with the expected geometry of Phantom 2.

The three-dimensional image of Phantom 2 was generated using the cross-sectional images obtained by dividing the image according to the number of pixels used to visualize the projection. As for Phantom 1, each elemental material was processed independently based on energy selection, and a specific range of values representative of its surface was defined for visualisation. Finally, the individual 3D representations of the three elemental objects were combined into a single 3D image, as shown in Figure 8.

FIGURE 8

3.3 Phantom 3

Phantom 3 was defined to emit 1.5 × 10⁹ photons per second for each object, 6 × 10⁹ photons in total per angle. Were detected approximately 1.4 × 10⁶ photons in total. In this configuration, the phantom contained four objects: two cylinders and two spheres. This phantom was designed to understand the capability of the system to differentiate between different shapes (cylinders and spheres), and also study the ability of splitting elements composed of the same material (two spheres of Fe).

Following the same methodology adopted for Phantoms 1 and 2, the simulation results are presented in Figure 9.

FIGURE 9

The energy spectrum shown in (Figure 9a) exhibits three peaks corresponding to the characteristic fluorescence photons emitted by the objects, as well as a preceding peak associated with Ar.

The sinogram of the phantom after energy window selection is shown in (Figure 9b), clearly representing the different elemental objects. The iron spheres, aligned along the y-direction, appear as a single sinusoidal trace because the sinogram is generated by integrating the signal along the vertical direction, which combines the contributions from both spheres and results in the dominance of the larger one. As expected, the sinusoidal curves corresponding to the different elements are well separated, enabling clear identification of the individual objects.

The three elements present in the simulation were successfully identified, and their corresponding cross-sectional images reconstructed, as shown in (Figure 9c). However, as this representation corresponds to the sum of all projections, it does not allow the two Fe spheres present in the phantom to be differentiated. This limitation is overcome in the three-dimensional reconstruction: as illustrated in Figure 10, the two spheres are clearly resolved and spatially separated in the 3D elemental map.

FIGURE 10

In this phantom, the objects are clearly separated from one another, which can be readily observed in the three-dimensional reconstruction. A certain level of noise is also present in the three elements, being more evident in the Fe spheres. Despite this, the reconstruction process successfully reproduces the correct geometry and spatial distribution of the objects, demonstrating the capability of the reconstruction process to accurately recover the structural features of the phantom.

3.4 Detector point spread function characterisation

To isolate the detector response from the combined effects of collimation and reconstruction, a dedicated simulation was performed to characterise the intrinsic Point Spread Function (PSF) of the krypton gaseous detector. A perpendicular pencil beam of monoenergetic photons (10⁵ photons per energy) was simulated incident at the detector centre, positioned at the same phantom-to-detector distance used in the imaging geometry, without a collimator or phantom present.

PSF was evaluated at seven energies spanning the range 3–20 keV, including the three characteristic fluorescence energies used in this work. For each energy, the spatial distribution of detected events was recorded and fitted with a two-dimensional Gaussian function to extract the FWHM in both the X and Y directions. The results are summarised in Table 4.

The intrinsic detector FWHM increases from approximately 0.02 mm at 3 keV to 0.51 mm at 15 keV, with values of 0.12 mm, 0.20 mm, and 0.31 mm at the three working energies (6.4, 8.0, and 9.7 keV), respectively. This energy-dependent broadening is attributed to the increasing photon range in krypton gas and charge diffusion effects at higher deposited energies. These values are in good agreement with those reported by Azevedo et al. (Azevedo et al., 2015).

Essentially, these measurements demonstrate that the intrinsic detector response is not the limiting factor in system spatial resolution. Instead, the collimator aperture (1 mm or 0.5 mm hole diameter) is the dominant spatial resolution constraint.

4 Conclusion

In this work, GATE simulations were performed to understand the XFCT imaging concept based on gaseous detectors. Three cylindrical phantoms containing cylindrical inserts of distinct elemental compositions were studied to assess the feasibility of three-dimensional elemental imaging with these systems.

The simulation results demonstrate that the system is capable of identifying and spatially resolving multiple elements under different geometric and attenuation conditions. Elemental discrimination was achieved through energy selection of characteristic fluorescence regions, enabling the reconstruction of both cross-sectional and three-dimensional elemental maps. The FWHM analysis revealed that reconstructed dimensions are systematically larger than theoretical values. This overestimation arises from a combination of three factors: the finite collimator hole size (1 mm or 0.5 mm), which is the dominant factor for system spatial resolution degradation in the simulation; the FBP reconstruction algorithm that introduces blurring artifacts at objects edges; and the intrinsic detector spatial response presented in Section 3.4, which contributes negligibly to the overall system resolution. The dedicated PSF characterisation has isolated and quantified each contribution, demonstrating that the detector itself performs excellently and is not responsible for the observed dimensional errors. Despite these resolution limitations, the relative spatial arrangement of the elements was consistently preserved across all phantoms, confirming the system’s capability to recover the overall geometry of the samples.

These results establish the feasibility of XFCT imaging using gaseous detectors and highlight their potential as a cost-effective and scalable possible alternative to semiconductor-based systems. However, several aspects require further investigation before experimental implementation. The spatial resolution of the system is currently constrained by the collimator hole size, as demonstrated by the PSF characterization. Optimisation of the collimator geometry is expected to yield significant improvements. Additionally, the use of more advanced reconstruction algorithms, such as iterative methods, may reduce the observed dimensional overestimation and improve image quality.

Future work will focus on experimental validation of the proposed concept using the gaseous detector system currently under development, as well as on the optimisation of both the system geometry and the image reconstruction process. Also, a rigorous quantitative comparison between gaseous detectors and semiconductor photo-counting detectors could be carried out as future research.

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