X-ray transmittance and backscatter imaging are important methods for detecting drugs and plastic explosives in the security-inspection field. In this study, we developed an analytical model based on Geant4 toolkit and verified it by measuring the energy spectrum and backscatter images. According to the model, we analyzed the imaging contrasts to detect concealed contrabands. The results show that the backscatter contrasts are significantly better than those of the transmission, especially in thinner organic materials. However, for shelters with strong absorption and scattering, the gaps become smaller. In addition, the variations in the contrasts with thickness appear to linearly increase in the transmittance imaging and nonlinearly grow until saturation in the backscatter imaging. Compared with traditional methods, our model, which is more accurate and complete, employs energetically distributed X-rays, instead of monochromatic X-rays, and involves multiple scattering effects. By using this method, we cannot only calculate and analyze the image characteristics of large amounts of contrabands in various system structures but also design and optimize instruments specially used to detect drugs and explosives.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
X-ray imaging is importantly applied in the fields of medicine [1–3], nondestructive testing [4,5], and security inspection [6–8] owing to the strong penetrability of X-rays. In particular, in the security-inspection field, X-ray transmission imaging (XTI) is also the main method of inspecting dangerous goods such as guns, knives, explosives, drugs, and so on. This technique is effective for detecting metal objects but suffers from a relative difficulty in detecting organics such as drugs and plastic explosives because the attenuation coefficient of most organic matters to X-ray radiation is very low, and the material appears to be transparent. To solve this problem, the X-ray backscattering imaging (XBI) technique has been proposed, which is based on the Compton scattering principle and reconstructs the image by detecting the backscattering signal of an object. In recent years, several inspection technologies based on XBI have been developed, such as the “Flying Spot”  scanner, coded aperture imaging , lobster-eye objective [6,7], and so on. At present, an imaging system that integrates XTI and XBI becomes the main inspection method. Unfortunately however, in terms of the two inspection technologies, the detection accuracy remains very low (<10%) and depends to a large extent on the operator experience, which limits its use in security inspection.
In the above-mentioned methods, the image brightness and contrast of objects are the most important features used to determine the type of objects. However, for most organic contrabands, the chemical compositions and physical properties are similar to those of general commodities whose main elements are C, H, O, and N, such as food, sugar, drugs, and plastic explosives. Thus, the image brightness and contrast are nearly similar to one another, which make distinguishing the objects difficult. In addition, contrabands are often manufactured into thin sheets and blocked by complex backgrounds. The radiation intensity is dramatically attenuated (two times the attenuation in backscattering), which further reduces the image brightness and contrast and increases detection difficulty. Therefore, we need to quantitatively study the correlation between the image features and chemical elements and the physical parameters of the contrabands under different shelters. Traditionally, experiments are the most effective methods of studying the above-mentioned problems, but the implementations are often limited. Completely acquiring the image feature information is also difficult because most drugs and explosives are artificially synthesized in large varieties, and the various components exhibit different image features. In addition, a problem that cannot be ignored is that the equipment is expensive, and carrying out experimental research using multiple systems of various structures is unrealistic.
However, to solve the aforementioned problems, we can quantitatively study XTI and XBI by constructing a simulation model. Several publications have reported these models based on Beer–Lambert Law and Klein–Nishina (K–N) equation and studied the two imaging methods using developed models [10–12]. Meanwhile, the interactions of X-rays and matters are a complex physical process, which mainly include photoelectric effects, Rayleigh scattering, Compton scattering, etc. Both imaging methods obtain the result of the integrated physical effects. Furthermore, these simulation models suffer from some limitations such as the consideration of a mono-energetic source or employment of only a single scattering with collimation. However, the most realistic generator is energetically distributed, such as an X-ray tube with a tungsten target, and incident photons are scattered many times and re-emitted from the objects, which also contribute to the total intensity of the X-rays and signal-to-noise ratio, as shown in Fig. 1. In general, the above-mentioned models are yet incomplete and inaccurate for quantitative investigation of the transmission and backscattering imaging; thus, other approaches are required to accurately determine the image feature parameters of the two imaging modes and to provide useful reference data for system design and application.
In this paper, we describe an analytical and accurate approach for studying XTI and XBI used for security inspection and for analyzing the feature parameters determined from the samples and system. The simulated model was based on Geant4 toolkit, which involves the main physics of the interaction of the photoelectric effect, Rayleigh and Compton scattering (single and multiple scattering), and so on . In this model, energetically distributed X-rays were generated via the interaction between electrons and tungsten (W) target. To verify our model, we performed experiments using nonprohibited materials such as polymethyl methacrylate (PMMA) and found excellent agreement between the computational feature parameters and experimental data. Using this model, the image features of drugs and explosives under two imaging modes were also calculated. The results show that the contrasts of the backscatter were significantly better than those of the transmission without a shelter, and backscatter could relatively easily distinguish between dangerous materials and flour. In addition, when shelters with strong absorption and scattering were used, the difference in the contrasts became weak, but for thinner sample, the backscatter (<10 mm) mode was better. By using this method, we cannot only calculate and analyze the image characteristics of large amounts of contraband in various system structures and enrich the reference data of image features but also design and optimize the instruments specially used for detecting drugs and explosives.
2. Simulation model
Compton scattering refers to the inelastic scattering of a photon by a charged particle, usually an electron. It results in a decrease in the photon energy (X-rays or gamma photons), which is called the Compton effect. The energy of Compton scattered X-rays is uniquely related to the incident energy (E) and scattering angle (θ) and is expressed as 15].11].
Theoretically, the number of scattered photons detected at the detector is calculated by the integral of Eq. (2) and Eq. (3) for each differential volume considered for the radiation and its interaction with the material. This model can be widely used for rough analysis of scattering and transmission imaging, but it suffers from two disadvantages. First, the model can only deal with single scattering; however, multiple scattering phenomena occur in the material, which not only change the energy of the X-rays but also affect the total number of photons that are eventually detected. Second, studying the scattering effect of mono-energetic rays is feasible; however, simulating the interaction between matters and polychromatic X-rays (PXRs) is difficult. In fact, in many fields, the main X-ray generator is the X-ray tube, which generates PXRs with continuous and characteristic spectra. Therefore, the simple integral of Eq. (2) and Eq. (3) is yet incomplete and inaccurate, but this simulation can be performed using the Monte Carlo algorithm to manage the multiple scattering interactions and polychromatic radiation to quantitatively investigate the transmission and backscattering imaging.
Geant4 is an object-oriented toolkit for full and fast Monte Carlo simulations of the passage of particles through matter, which is intended for a wide range of applications [16,17]. Geant4 offers an ample set of complementary and alternative physics models (electromagnetic (EM), hadronic, and optical) to describe the interaction of particles with matter over a wide range of energy based either on theory, experimental data, or parameterization . In the present study, the interactions of photons and electrons were simulated using the Geant4 implementation of the physics models developed for low-energy EM code, which has been specifically developed for gamma and electron transport in materials, and great care was afforded to the description of the low-energy physics processes, including the photoelectric effect, Compton scattering, Rayleigh effect, ionization, and bremsstrahlung. The latter two are the main code that describes the X-ray product due to the interactions between the high-speed incident electrons and atom of the target such as Cu, Mo, and W. The Geant4 multiple scattering code simulates the multiple scattering of particles in material. It simulates the scattering of the particle after a given step, computes the mean path length correction and the mean lateral displacement. It can simulate the collisions, interactions and transportations experienced by the particles .
For the interactions, the main physical processes include: ionization, bremsstrahlung, photoelectric effect, Compton scattering, and Rayleigh effect. The total cross section can be expressed as:
The cross sections of bremsstrahlung, photoelectric effect, Compton scattering, and Rayleigh effect for an element were derived from the evaluated photon data library tables (EPDL97) for all the processes considered . These data include electron binding effects averaged over all atomic electron states, and are valid from ~250 eV to 100 GeV. For compound materials, a weighted average of the elemental component cross sections was used, based on the relative number of electrons for each component element. For each process, the total cross section at given energy E was obtained by interpolating the available data according to the following equation :Eq. (5). Then, the corresponding total cross section was obtained by summing the partial cross sections over all the shells.
The angular and energy distribution of the incoherently scattered photon is given by the product of the Klein-Nishina formula Φ(ε) and the scattering function F(q) which are calculated from the values available in the EPDL97 data library [13,19].
The setup used for the simulation consisted of the PXR source, collimator, backscatter, and transmission configuration, as shown in Fig. 2. PXR was generated when high-energy electrons collided with the tungsten target positioned at z = 0 and by the main physics processes of ionization and bremsstrahlung. The entire PXR source was surrounded with a lead layer, except for the window through which X-rays passed. To prevent scattered electrons and low-energy rays, a composite filter with 0.8-mm Be and 0.1-mm Al was selected. A lead collimator was placed at a 15-cm distance from the tungsten target, which was used to shape a pencil beam. The pencil PXR radiated the sample at z = 37.5 cm. The shape of the sample was defined as a square with an area of 50 × 50 mm2 and different thicknesses from 5 to 30 mm. The materials of the samples included caffeine, cocaine, HMX -octogen, PMMA, and flour. The details of these materials are listed in Table 1. The suitcase and container materials are well known to be aluminum alloy and steel, respectively. Thus, for real-like simulation, we chose a 1-mm-thick Al or Fe sheet to shield the samples, and the simulations were carried out with or without a shelter. The imaging contrast was defined as follows:
Photon detection was achieved using two scintillator detectors. The sizes of these detectors were the same, i.e., 40 × 20 × 5 cm3 in the x–y–z direction. The large thickness was aimed to sufficiently absorb the photons. In terms of the transmittance mode, we utilized one detector at z = 70 cm to collect the photons attenuated by the sample and a lead sheet to block the forward scattered photons. However, for the backscattering mode, two sensors were used to collect sufficient backscattered photons from the sample to enhance the signal intensity. The backscatter detectors were installed 21.5 cm from the sample, which resulted in a larger solid angle of approximately 1.9 sr for the photons scattered at the surface of the sample.
3. Experimental details
The experimental configuration was coincident with the geometry of the simulation, as shown in Section 2.2 and Fig. 2. The difference was that a real X-ray tube (Varian, NDI-225-22) was employed to generate polychromatic radiations, as shown in Fig. 3. The maximum acceleration voltage and power were 225 kV and 3 kW, respectively. Two plastic scintillator detectors were used to convert the incident X-rays into optical light. The base material of the detector was polystyrene ((C8H8)n) with high transmittance for optical light, and p-terphenyls was added as scintillating material. The main peak of scintillator emission spectrum was at the wavelength of 423 nm. The luminescence efficiency of the plastic scintillator was about 50% of anthracene crystal (C14H10). The sizes of these detectors were the same, i.e., 40 × 20 × 5 cm3 in the x–y–z direction. The large thickness was aimed to sufficiently absorb the photons. To adequately collect the optical light produced by the X-ray photons and eliminate the influence of diffused light in the laboratory, a highly reflective film (Teflon) was firmly attached to the scintillator surface. In addition, a lead layer was also applied to shelter the X-rays from the background, except for the surface that faced the sample. The optical light produced by scintillator was collected by 50-mm-diameter photomultiplier tubes (Hamamatsu, CR135) and transformed into pulse signals. The spectral response range of the photomultiplier tube was 300 nm~650 nm, and the wavelength corresponding to the highest quantum efficiency was 420 nm. The digital pulses were then obtained using an analog-to-digital converter after amplification and shaping. Therefore, the digital pulses were proportional to the intensity of the incident photons in the experiments. The radiation spectrum of the X-ray tube was calculated based on our model when electrons with 160-keV energy interacted with the W target, as shown in Fig. 4. The experimental spectrum was measured using a cadmium telluride (AMPTEK, XR-100T-CdTe) detector with an area of 25 mm2 and energy resolution of 1% at 59.5 keV (241Am). When the spectrum was measured, the samples were removed. The measured spectrum was the radiation spectrum emitted from the X-ray tube. The consistent results indicate that the model can be adapted for calculating the radiation spectrum of X-ray tubes and can be employed to simulate X-ray imaging.
4. Results and discussion
For both imaging modes, the effective signals are the transmitted and backscattered photons, but the physical processes in which X-rays interact with the substance are identical. Therefore, to verify the simulated model, backscatter experiments were carried out using PMMA as scatterers because the density of PMMA is similar to several drugs, and this material is not prohibited. In addition, in order to further verify the model, we selected the flour with low density as scatterers and carried out the experiments. The experimental details and simulated configurations are shown in Fig. 2 and Fig. 3. Here K is the contrast between the samples and shelters that are present in the backscatter images. Because the X-ray intensity affects the accuracy of the measured contrasts, for each sample thickness, experiments were performed using the same acceleration voltage of 160 kV and three currents of 2.5, 5, and 7.5 mA. Figures 5(a)-5(d) show the backscatter contrasts between the samples (PMMA and flour) and shelters when covered by 1-mm-thick Al and Fe sheets, respectively. The error bars represent the standard deviations measured using 160 kV and three different current (2.5, 5, and 7.5 mA) of the X-ray tube.
The results in Fig. 5(a) show that the imaging contrast was 0.63 with a PMMA thickness of 5 mm. As the sample thickness increased, the contrast significantly improved and could reach 0.86 when the thickness was 30 mm. We observed that the simulation results were consistent with the experimental results, and the maximum deviation was approximately 0.01. For the Fe shelter, the imaging contrasts obviously deteriorated, and the deviation between the simulations and experiments was slightly larger than that of the Al shelter, as shown in Fig. 5(b). The results in Figs. 5(c) and 5(d) were the imaging contrasts of the flour samples. For the Al shelter, the imaging contrast was 0.41 with a flour thickness of 5 mm. As the sample thickness increased, the contrast improved and could reach 0.73 when the thickness was 30 mm. However, for the Fe shelter, the imaging contrasts were very low even when the sample thickness was 30 mm. The maximum deviation between the simulations and experiments was about 0.05. According to Figs. 5(a)-5(d), the maximum error occurred when the sample thickness was 5 mm, and the main reason for the results was that because of the lower scattering of thin samples and stronger attenuation of Fe, the collected photons were so weak that the background noise significantly contributed to the measured value. However, in general, the simulation results agreed with the experimental ones shown in Fig. 5, and the method can be used to quantitatively study X-ray imaging.
According to our model, we first studied the imaging contrasts of drugs and explosives relative to the daily commodities such as flour without any shelter in the transmittance and backscatter imaging modes. Second, to meet the actual security inspection requirement, the contrasts relative to the shelters and flour were calculated using a thin Al or Fe sheet as a shelter because most suitcases, cars, and carriages are made of these materials. Figure 6 shows the calculated contrasts of caffeine, cocaine, and HMX relative to the flour for the transmittance and backscatter imaging where no shelter was used. For the transmittance imaging, the contrasts obviously improved as the samples thickened, which can be easily explained by Eq. (3) with respect to given μ and ρ. As the thickness changed, the photon intensities increased; thus, the differences also increased. However, when the samples were thin such as 5 mm, the contrasts were approximately 0.05 and 0.1 for the drugs and explosives, respectively, which means that these contrabands are almost the same and cannot be distinguished. By comparison, in the backscatter imaging mode, the contrasts could reach approximately 0.3–0.4 for most thickness, and the variations were very small. In particular, they were even better with thinner samples such as 5-mm HMX. This phenomenon may have been caused by the attenuation, scattering inside the materials, and multiple scattering. Because of the attenuation, photons that were scattered at a specific depth were nonlinearly reduced and eventually tended to saturate as the depth increased and could be detected. In fact, the main contributor to the contrast was the scattered photons from the surface and shallow layers of the materials, and the photons scattered in the deep layers have greater probability to undergo multiple scattering. These photons have weaker influence on the contrasts and could even deteriorate them. However, in general, compared with the transmittance mode, the backscatter imaging mode appeared to be more effective in distinguishing between contrabands and daily commodities, especially for thinner materials.
In reality, contrabands are often hidden in luggage, cars, and containers, which may cause different results because of the intensive attenuation and scattering from these materials. Figure 7 and Fig. 8 show the simulated contrasts of the samples sheltered by a 1-mm-thick Al sheet for the transmittance and backscatter imaging, respectively. Figures 7(a) and 8(a) show the contrasts among four samples and the Al sheet. Imax in Eq. (9) represents the X-ray intensities contributed by not only the samples but also the Al plate, and Imin represents that just dominated by the Al sheet. Figures 7(b) and 8(b) show the contrasts among caffeine, cocaine, and HMX relative to the flour. Figure 7(a) shows that the contrasts at 5 mm were small, which were 0.04, 0.07, 0.08, and 0.11 for the flour, cocaine, caffeine, and HMX, respectively. The contrasts approximately linearly increased with the thickening of the samples, which is similar to those shown in Fig. 6(a). The main reason for this result was that mass attenuation coefficient μ and density ρ of these materials were small at high X-ray energy, and only the first two terms significantly contributed to the attenuation during the Taylor expansion of the exponential term in Eq. (3). Moreover, the growth rates were higher for the drugs and explosive than for the flour because of higher μ and ρ, indicating that the thicker the samples are, the greater is the contrast difference. Figure 7(b) also shows the approximate linear relationship between the contrasts and thickness. The simulated results in Fig. 7 show that the contrasts displayed a linear trend with respect to the thickness regardless of the contrasts between the samples and Al plate. Those between the contrabands and flour were relatively low, especially for thinner samples.
For comparison, we simulated the contrasts of the samples sheltered by an Al sheet similar to that shown in Fig. 7 for backscatter imaging. Figure 8(a) shows that, in terms of the backscatter imaging, the contrasts of the 5 -mm thick samples with respect to the 1-mm thick Al plate could reach 0.45, 0.63, 0.67, and 0.68 for the flour, cocaine, caffeine, and HMX, respectively, and 0.75, 0.88, 0.89 and 0.90 for the 30-mm-thick samples, which were significantly better than those of the transmission mode. In contrast to the transmission imaging, the contrasts changes were not linear, and they tended to saturate as the thickness increased, which were caused by the “surface scattering” phenomenon, i.e., scattering mainly occurred at the surface of the materials, and the effectively scattered photons of each voxel decreased as the depth in the materials increased. Figure 8(b) shows the contrasts of caffeine, cocaine, and HMX relative to the flour. Obviously, the contrasts in the backscatter imaging were better than those of the transmittance for thinner samples, but the differences decreased as the thickness increased. We can speculate that for thicker samples such as 50 mm or thicker, the transmittance contrasts will exceed those of the backscatter imaging.
Figure 9 and Fig. 10 show the simulated contrasts of the samples sheltered by a 1-mm-thick Fe sheet for the transmittance and backscatter imaging, respectively. Because Fe has larger mass attenuation coefficient μ and density ρ, large amounts of photons with low energy (<40 keV) were filtered out, as shown in Fig. 11, in which the transmittance of Fe was obtained based on the National Institute of Standards and Technology data . The attenuated energy spectrum was calculated using our model. Therefore, the radiation on the samples has been dominated by X-rays with higher energy, which resulted in deterioration in the contrast of the transmission imaging according to Eq. (3) because μ further decreased at higher energy levels. These effects are shown in Figs. 9(a) and 9(b). For thinner samples (5 mm), the contrasts were even less than 0.1, i.e., only 0.07, 0.06, 0.02, and 0.01 for HMX, caffeine, cocaine and flour, respectively, which indicate that these samples appear to be transparent and difficult to detect. However, for the backscatter imaging, the influence of the Fe shelter was much more serious. By comparing Figs. 8(a) and 10(a), we can see that the contrasts between the four samples and Fe sheet decreased by six and three times for the 5- and 30-mm-thick samples, respectively. The contrasts of caffeine, cocaine, and HMX with respect to the flour also dramatically deteriorated, as shown in Fig. 10(b). The phenomenon can be explained according to the K–N formula [Eq. (2)] and Beer–Lambert Law [Eq. (3)]. According to the K–N formula, the low-energy photons have stronger scattering properties than the high-energy photons. The full-spectrum photons were scattered by the Fe sheet, but only the high-energy photons underwent scattering at the surface and inside the samples because of the Fe attenuation, which greatly reduced the effectively scattered photons of the samples. As a result, the contrasts significantly decreased when the samples were sheltered by the Fe sheet.
According to the above-mentioned results, the characteristics of the two imaging methods were summarized as follows. First, when no shelter is employed or the mass attenuation coefficient and density of the shelter are small, the contrasts of the backscatter imaging are better than those of the transmittance imaging, especially for thinner samples, but the advantages diminish as the thickness increases. Second, the contrasts display a linear trend with respect to the thickness in the transmittance imaging, but in the backscatter imaging, “surface scattering” dominates and is a major contributor to the contrasts. Thus, the contrasts nonlinearly change and tend to saturate with the increase in the sample thickness. Third, when contrabands are concealed behind materials with high attenuation, such as Fe, the contrasts of the two imaging modes are both low, and the effects on the backscattering are more dramatic. However, for thinner samples, the backscatter imaging performs slightly better. In other words, backscatter is more appropriate for inspecting thinner contrabands or scanning the surface of objects such as slices of drugs and plastic explosives concealed in luggage or under the clothes of a human body, but this detection is comparatively difficult in the transmittance mode. However, no obvious advantage is present in inspecting large-volume samples in the backscatter imaging, such as bulk contrabands in containers. For this type of inspection, another backscattering feature is utilized, namely, an X-ray source and a detector are installed at the same side, and for this type of inspection, combination of the transmission and backscattering modes is required.
In this study, we have constructed an analytical model based on Geant4 toolkit and analyzed the imaging contrasts determined by the material types, thickness of samples, and shelters for the two imaging methods of XTI and XBI used in the field of security inspection. In this model, energetically distributed X-rays are generated via the interaction between electrons and the tungsten target. From the experiments, the model was verified based on the energy-spectrum measurement and backscatter imaging using PMMA and flour, and the simulated radiation spectrum and backscatter signals were consistent with the experimental data. Based on this model, the image features of drugs and explosives under different shelters were also calculated using the two imaging modes. The results show that the contrast of the backscatter imaging was significantly better than that of the transmission imaging without a shelter or using a shelter composed of low-atomic-number substance, and the backscatter imaging could relatively easily distinguish dangerous materials from the flour. However, when the shelters have strong absorption and scattering, the difference in the contrasts became weak. Nevertheless, for thinner samples (<10 mm), the backscatter mode was still better. In addition, the variations in the contrasts displayed two different trends: linear increase in the transmittance imaging and nonlinear growth until saturation in the backscatter mode. From this method, we cannot only calculate and analyze the image characteristics of a large number of contrabands in various system structures and enrich the reference data of the image features but also design and optimize the instruments specially used to inspect drugs and explosives.
National Key R&D Program of China (2016YFC0800904-Z03); Fundamental Research Funds for the Central Universities (22120180135).
1. A. Sarapata, M. Willner, M. Walter, T. Duttenhofer, K. Kaiser, P. Meyer, C. Braun, A. Fingerle, P. B. Noël, F. Pfeiffer, and J. Herzen, “Quantitative imaging using high-energy X-ray phase-contrast CT with a 70 kVp polychromatic X-ray spectrum,” Opt. Express 23(1), 523–535 (2015). [CrossRef] [PubMed]
2. V. S. K. Yokhana, B. D. Arhatari, T. E. Gureyev, and B. Abbey, “Soft-tissue differentiation and bone densitometry via energy-discriminating X-ray microCT,” Opt. Express 25(23), 29328–29341 (2017). [CrossRef]
4. D. Shedlock, T. Edwards, and C. Toh, “X-ray backscatter imaging for aerospace applications,” in AIP Conference Proceedings, Vol. 1335. (American Institute of Physics, 2011), pp: 509–516.
5. C. N. Boyer, G. E. Holland, and J. F. Seely, “Portable hard X-ray source for nondestructive testing and medical imaging,” Rev. Sci. Instrum. 69(6), 2524–2530 (1998). [CrossRef]
6. J. Xu, X. Wang, Q. Zhan, S. L. Huang, Y. F. Chen, and B. Z. Mu, “A novel lobster-eye imaging system based on Schmidt-type objective for X-ray backscattering inspection,” Rev. Sci. Instrum. 87(7), 073103 (2016). [CrossRef] [PubMed]
7. V. Grubsky, M. Gertsenshteyn, T. Jannson, and G. Savant, “Non-scanning X-ray backscattering inspection systems based on X-ray focusing,” Proc. SPIE 6540, 65401N (2007). [CrossRef]
8. A. S. Lalleman, G. Ferrand, B. Rosse, I. Thfoin, R. Wrobel, J. Tabary, N. B. Pierron, F. Mougel, C. Paulus, and L. Verger, “A dual X-ray backscatter system for detecting explosives: image and discrimination of a suspicious content,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2011), pp. 299–304. [CrossRef]
9. A. Chalmers, “Applications of backscatter X-ray imaging sensors for homeland defense,” Proc. SPIE 5071, 388–396 (2003). [CrossRef]
10. A. Sharma, B. S. Sandhu, and B. Singh, “Incoherent scattering of gamma photons for non-destructive tomographic inspection of pipeline,” Appl. Radiat. Isot. 68(12), 2181–2188 (2010). [CrossRef] [PubMed]
11. J. L. Glover and L. T. Hudson, “A method for organic/inorganic differentiation using an X-ray forward/ backscatter personnel scanner,” XRay Spectrom. 42(6), 531–536 (2013). [CrossRef]
12. J. van den Heuvel and F. Fiore, “Simulation study of X-ray backscatter imaging of pressure-plate improvised explosive devices,” Proc. SPIE 8357, 835716 (2012). [CrossRef]
13. Geant4 Collaboration, Physics reference manual, release 10.4 (European Organization for Nuclear Research, 2017), Chap. 5–8.
14. A. H. Compton, “A quantum theory of the scattering of X-rays by light elements,” Phys. Rev. 21(5), 483–502 (1923). [CrossRef]
15. J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” J. Phys. Chem. Ref. Data 4(3), 471–538 (1975). [CrossRef]
16. A. Lechner, V. N. Ivanchenko, and J. Knobloch, “Validation of recent Geant4 physics models for application in carbon ion therapy,” Nucl. Instrum. Methods Phys. Res. B 268(14), 2343–2354 (2010). [CrossRef]
17. R. M. Kippen, “The Geant low energy Compton scattering (GLECS) package for use in simulating advanced Compton telescopes,” New Astron. Rev. 48(1-4), 221–225 (2004). [CrossRef]
18. G. A. P. Cirrone, G. Cuttone, F. Di Rosa, L. Pandola, F. Romano, and Q. Zhang, “Validation of the Geant4 electromagnetic photon cross-sections for elements and compounds,” Nucl. Instrum. Methods Phys. Res. A 618(1-3), 315–322 (2010). [CrossRef]
19. D. E. Cullen, J. H. Hubbell, and L. Kissel, “Epdl97: the evaluated photon data library, 97 version,” Tech. rep., Lawrence Livermore National Lab., CA (United States) (1997).
20. NIST, Physical Measurement Laboratory, “X-ray form factor, attenuation, and scattering tables,” https://physics.nist.gov/PhysRefData/FFast/html/form.html.