Applied Radiation and Isotopes 82 (2013) 293–299
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Depth discrimination method based on a multirow linear array detector for push-broom Compton scatter imaging Yantao Liu a,b, Zhiming Zhang a,b, Daowu Li a,b, ChuangXin Ma a,b, Cunfeng Wei a,b, Meiling Zhu a,b, Lei Shuai a,b, Tingting Hu a,b, Baotong Feng a,b, Pei Chai a,b, Xianchao Huang a,b, Haohui Tang a,b, Ting Li a,b, Kai Zhuang a,b, Xiaopan Jiang a,b, Yingjie Wang a,b, Yiwen Zhang a,b, Wei Zhou a,b, Shifeng Sun a,b, Long Wei a,b,n a b
Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Beijing Engineering Research Center of Radiographic Techniques and Equipment, Beijing 100049, China
H I G H L I G H T S
We devise a depth discrimination method for push-broom Compton scatter imaging. Depth of sample is indicated by comparing signal proportions of different modules. The depth discrimination is linked to different measurement geometries. A multirow linear array detector based on XP1452 and LYSO was developed. Simulation model is built using GEANT4 to support the method well.
art ic l e i nf o
a b s t r a c t
Article history: Received 11 June 2013 Received in revised form 12 August 2013 Accepted 2 September 2013 Available online 21 September 2013
A depth discrimination method is devised based on a multirow linear array detector for push-broom Compton scatter imaging. Two or more rows of detector modules are placed at different positions towards a sample. An improved parallel-hole collimator is fixed in front of the modules to restrict their fields of view. The depth information could be indicated by comparing the signal differences. In addition, an available detector and several related simulations using GEANT4 are given to support the method well. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Depth discrimination Compton scatter imaging GEANT4 Detector Collimator
1. Introduction Compton scatter imaging (CSI) is a noninvasive imaging technique based on the Compton scattering effect, which was discovered by Compton in 1923. It was first described in the medical field by Lale (1959) and then applied in many nondestructive testing fields, such as corrosion detection in aircraft (Dunn and Yacout 2000), food checks (McFarlane et al., 2003), buried landmine detection (Yuka et al., 2006), security inspection (Vogel 2007a,b), and historical exploration (Harding and Harding 2010). n Corresponding author at: Chinese Academy of Sciences, Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy Physics, Beijing 100049, China. Tel.: þ86 10 88236347; fax: þ 86 10 88236413. E-mail addresses: [email protected] (Y. Liu), [email protected] (L. Wei).
0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.09.001
Unlike transmission imaging, CSI allows a flexible choice of measurement geometries. Its radiation source and detectors can be arranged in any direction, especially on the same side of a sample. Therefore, CSI is applicable in detecting the sample underground or in walls where transmission imaging fails. It is also suitable for a surface measurement of large, thick, bulky objects. Moreover, CSI is highly sensitive to light-element materials such as hydrogen, carbon, nitrogen, and oxygen. Therefore, it could provide a high-contrast image of organic contraband such as petrol, drugs, explosives, etc. Finally, scatter voxels could be directly located using the intersection points of primary photons and scattered photons. However, CSI is inferior compared to transmission imaging in its signal-to-noise ratio (SNR). The quantity of photons backscattered (scatter angle beyond 901) to a detector is less than 0.8% of those
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transmitted, in theory, to its counterpart detector (Park et al., 2006). These scattered photons would be further limited by the locating devices in front of the detector. The scatter energies of photons are less than the primary energy; therefore, they are more susceptible to noises from the radiation source and the detector. To improve the SNR, it usually increases the intensity of primary photons, expands effective areas of the detector, and/or prolongs sampling time in CSI systems. To realize positioning and imaging, an appropriate scheme is required to scan the sample. One main scan scheme in present CSI systems is called flying spot (Towe and Jacobs 1981a,b; Herr et al., 1994). It uses a pencil beam of X-rays to scan the sample in a point-by-point method. In this way, it can provide a highresolution three-dimensional (3D) image of the sample, but has a low utilization efficiency of the radiation source and a long sampling time. The other scan scheme is called push-broom (Yuka et al., 2006; Park et al., 2006; Guangzhi Sun et al., 2008) and uses a fan beam of X-rays and linear array detectors directly. This scheme enhances the utilization efficiency of the radiation source and reduces the sampling time. However, it only provides a superposed two-dimensional (2D) projection without depth information in existing systems. More details of the scan schemes are compared in Section 3. In this work, a method was devised to achieve a primary depth discrimination based on a multirow linear array detector for pushbroom CSI. The detector was composed of two or more rows of modules, an improved parallel-hole collimator, and the corresponding data acquisition system (DAQ). The modules were placed in different directions towards a sample to receive scattered signals independently. The collimator was fixed in front of the modules to restrict their fields of view (FOVs). When Compton scattering occurred at different depths, scattered photons would be distributed into the adjacent modules in different proportions. The proportions indicated depth information using a special algorithm. In addition, an available detector was presented and several related simulations using GEANT4 (Miceli et al., 2007; Sullivan et al., 2008; Harkness et al., 2009; Trinci et al., 2010; Cirrone et al., 2010; Rossi et al., 2011) were given that supported the method well.
2. Characteristics of Compton scattering Compton scattering and photoemission are two main competitive interactions when photon energy is below 1 MeV. In addition, Compton scattering dominates the reaction cross section from 100 keV to 1 MeV in aluminum (a representative of the low and moderate atomic number Z materials) (Harding and Harding 2010). The scatter energy and the angular distribution of the Compton scatter for stationary, free electrons are calculated by the two formulas below: EðθÞ ¼ ½1=E0 þ ð1 cos θÞ=me c2 1
ð1Þ
ds=dΩ ¼ ðr 2e =2Þη2 ðη þ η 1 sin θÞ
ð2Þ
2
In Eqs. (1) and (2), θ is the scatter angle; ds/dΩ is the Klein– Nishina cross section; E0 and E(θ) are the primary energy and the scatter energy of photons, respectively; η is defined as the ratio of E(θ) to E0 (E(θ)/E0); mec2 is the rest mass energy of electron (511 keV); and re is the classical electron radius (2.82 fm). If photons were emitted from an X-ray tube of 450 kVp, their average primary energy would be approximately 150 keV, using the theory of bremsstrahlung. When the scatter angle θ was equal to 1351, and the primary energies E0 ranged from 50 to 450 keV, the corresponding scatter energies E(θ) and the linear attenuation
Table. 1 The scatter energies and the linear attenuation coefficients of scintillator Lu2SiO5 in different primary energies (θ¼ 1351, ρ¼ 7.3 g/cm3). Primary energy (keV)
Scatter energy (keV)
Linear attenuation coefficient (cm 1) a
50 100 150 200 300 450
42.8 74.9 99.9 119.8 149.7 179.6
44.2 47.6 22.6 14.3 8.2 5.3
a Data were employed in linear interpolation on the original data from the National Institute of Standards and Technology (http://physics.nist.gov/PhysRefData/FFast/html/ form.html).
Table 2 The scatter energies and the Klein–Nishina cross sections at different scatter angles (E0 ¼ 150 keV, ρ ¼7.3 g/cm3). Scatter angle (1)
Scatter energy (keV)
Klein–Nishina cross section (mb)
90 105 120 135 150 165 180
116.0 109.5 104.1 99.9 96.9 95.1 94.5
25.3 24.7 26.5 29.4 32.2 34.3 35.0
coefficients μ of Lu2SiO5 are listed in Table 1. It was found that the average scatter energy was approximately 99.9 keV and the corresponding linear attenuation coefficient was approximately 22.6 cm 1. Therefore, in this case, a Lu2SiO5 scintillator of 3 mm depth could provide enough stopping power for scattered photons. When the primary energy E0 equaled to 150 keV, and the scatter angles θ ranged from 901 to 1801, the corresponding scatter energies E(θ) and the Klein–Nishina cross sections ds/dΩ were listed in Table 2. The scatter energies and the cross sections varied to a small extent. This variation could be corrected or even overlooked, especially for a detector of a limit solid angle. The angular distribution of Compton scatter could be assumed to be an isotropic distribution in the below calculations and simulations. When considered in materials, electrons were not free but were bound by nuclei. Therefore, an incoherent atomic scatter function S(q, Z) (Sharaf 2001; Hubbell et al., 1975; Böke 2013; Massaro and Matt 1986), which accounted for electron binding energy effects with the photon momentum transfer q, should be considered in the actual scattering cross section. Its value was tabulated for all elements by Hubbell et al. (1975). For low Z materials, S(q, Z) was considered equal to Z because the electron binding energy was small. Therefore, the intensity of scattered photons was directly proportion to the electron density of materials. For high Z materials, S(q, Z) did not trend to Z but instead rapidly decreased. The intensity of scattered photons was small.
3. Scan schemes of Compton scattering imaging 3.1. Point-by-point scan scheme The first CSI system developed by Lale (1959) adopted a simple point-by-point scan scheme. A narrow pencil beam was collimated by beam collimators directly to hit a sample, while a single
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photomultiplier was set to receive the corresponding scattering signal. After one sampling, the whole system was moved a constant distance to detect the next point. This scan scheme made poor use of primary photons and resulted in a long sampling time that spanned several hours (Lale 1959). Then, an improved point-by-point scan scheme called flying spot was introduced into CSI systems. A pencil beam, which was shaped from a fan or cone beam by a mechanically rotating device, periodically swept a sample from one side to another side. Meanwhile, the sample was moved relatively perpendicular to the sweep direction. Since the sweep rate was faster than the move speed, its total sampling time could be reduced to several minutes. For example, the American Science & Engineering Incorporation (AS&E) used this scan scheme in their CSI systems to present a 2D projection of the sample (Vogel 2007a,b). It was very easy to distinguish suspicious organic objects from their complex surroundings because organic objects and light metallic materials were highlighted in the projection and heavy metallic materials were darkened. However, it was hard to discriminate their relative depth from only the projection. The ComScan system (Harding and Harding 2010) was another commercially available CSI system that used the flying spot scheme. It is different from AS&E systems, in that two arrays of 11 scintillator Bi4Ge3O12 (BGO) strips were arranged on two sides of a pencil beam to detect depth information simultaneously. In this way, a line of 22 voxels of different depths was obtained in one sampling, then a 2D section was obtained along the sweep direction, and finally a 3D image was obtained along the move direction. Because ComScan is equipped with two single-slit collimators, which allowed a variable spatial resolution, and sensitivity depended on detect distances, the flying spot scheme is preferred for a small FOV and high-resolution imaging. 3.2. Line-by-line scan scheme Recently, a direct line-by-line scan scheme called push-broom has been developed for CSI (Yuka et al., 2006; Park et al., 2006; Guangzhi Sun et al., 2008). In this scheme, a fan beam of X-rays scanned the sample directly and a linear array detector detected a line of scatter voxels in parallel. A parallel-hole collimator was fixed in front of the detector to restrict scattered photons. The push-broom scheme could enhance the utilization efficiency of X-rays and when implemented, it further reduced the sampling time. It allowed a moderate image resolution and an approximate constant sensitivity, making it the preferred choice for a large FOV and high-speed imaging of large objects. Currently, imaging performances of the push-broom scheme are similar to AS&E systems. However, the problem of superposed 2D projection has not been resolved yet.
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4. Principles of depth discrimination For simplicity, the principles of depth discrimination and the measurement geometries were illustrated in Fig. 1 based on a double-row linear array detector as the representative of multirow ones. A radiation source was placed over a moving sample. Two linear array detector modules were placed towards different zones of the sample at a given obliquity of α to the horizontal. Each module was made up of several detector elements of l (length) by w (width) in parallel. An improved parallel-hole collimator was fixed in front of the modules. The collimator included two arrays of slices and an adjustable extrusive board of heavy metal. The slices were arranged to separate detector elements (not necessarily one-to-one). Their lengths, thicknesses, and intervals would affect the collimator's performance in the transverse direction. The extrusive board was arranged to separate the two modules, as it should be thick enough to stop photons from passing through. When a collimated beam of photons from the radiation source entered the sample along a primary track, part of the photons were scattered at a relative depth of Δd and then left along a scattered track at a scatter angle of θ. The intensity of these scattered photons I(Δd, θ) should be expressed as a function of Δd and θ. Here, Δd equaled zero, while Compton scattering occurred at the intersection O of the primary track and the extension line of the extrusive board. Each detector element's signal S was an integral of I(Δd, θ) in its FOV. The FOV was limited by measurement geometries of the module and the collimator such as the elements length l, the module obliquity α, the detect distance D, and the extrusive board length L. Further, the upper module and the lower module faced toward different depths of the sample and there was an intermediate zone, owing to the overlap of two FOVs. While Compton scattering occurred on the superficial zone A, scattered photons could only be received by the upper module because of the restriction of the extrusive board. In addition, while Compton scattering occurred on the deep zone C, it presented opposite results compared to those gathered from the superficial zone A. While Compton scattering occurred on the intermediate zone B, scattered photons would be distributed into the two modules in a proportion. The proportion was related to the relative depth of scatter voxel in this zone. Therefore, depth information could be indicated from the proportion using a special algorithm. 5. Design of detector In our work, a scintillator linear array detector was designed for a large FOV, high-speed imaging. The detector was composed of
3.3. Plane-by-plane scan scheme A potential method to solve the problem of superposed 2D projection is to use a panel detector instead of a linear array detector for push-broom CSI. It could detect transverse and depth information simultaneously. However, the panel detector was not in current favor for the following reasons. First, it was no more sensitive than its linear counterpart, in spite of the large detector area. Moreover, there was no possibility of discriminating with mechanical collimation against multiple scatter radiation. Finally, it currently is more expensive than its linear counterpart is. An alternative method was to use two or more linear array detector modules that could detect transverse information from different angles and then resolve depth information from signal differences of the two modules.
Fig. 1. The principles of depth discrimination and the measurement geometries based on a double-row linear array detector.
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two rows of modules, an improved parallel-hole collimator, and the corresponding DAQ (Fig. 2). Photonis XP1452, a four-channel photomultiplier, was chosen due to its large effective area (32 mm 32 mm), fast response time (29 ns), compact structure, and moderate cost. The XP1452 obtained the position as follows: X ¼ ðS1 þ S2 S3 S4 Þ=ðS1 þ S2 þ S3 þ S4 Þ
Fig. 2. The photograph of the scintillator linear array detector.
ð3Þ
Y ¼ ðS1 S2 S3 þ S4 Þ=ðS1 þ S2 þ S3 þ S4 Þ
ð4Þ
In Eqs. (3) and (4), S1, S2, S3, S4 are the signals of four quadrants of the XP1452. The gains of the four quadrants could be adjusted individually by a high-voltage divider circuit. The X-direction was adopted to locate the transverse position of scattered photons, and the Y-direction was adjusted symmetric to balance the gains of the four quadrants. Scintillator LYSO, similar to Lu2SiO5, was chosen due to its large stopping power (ρ¼7.1 g/cm3), high light output (32,000 photons/ MeV) and fast decay time (41 ns). The emission wavelength of the LYSO (420 nm) matched the spectral range of the XP1452 well. Each scintillator strip was 40 mm 5.5 mm 3 mm to provide moderate resolution (5.5 mm) and a large effective area. Seven strips were combined to create a block of 40 mm 40 mm 3 mm and the gaps of 0.2-mm-wide were filled with a reflective material to reduce the light crosstalk. A special light-guide was designed to distribute the scintillation photons. The light-guide was made of a 10-mm-thick optical glass. It was processed into a prismoid with an upper surface of 40 mm 40 mm and a lower surface of 32 mm 32 mm to fit the scintillator block and the XP1452, respectively. Several slits in the light-guide were filled with the reflective material to change the light distribution (Kim et al., 2010). The scintillator block of seven strips together with the light-guide, was experimented upon using a radioactive source 137Cs (Fig. 3). The scatter diagram and the projection of X-direction showed that the seven strips were clearly differentiated and the peak-to-valley ratio was more
Fig. 3. The experiment results of the scintillator block of seven strips with the prismoid light-guide: energy spectrum (upper left), projection of X-direction (lower left), and scatter diagram (right).
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than 7:1. Then these 10 blocks were combined to create a module of 400-mm-wide. An improved parallel-hole collimator (Fig. 4a) was composed of two parallel arrays of tungsten alloy slices and an adjustable extrusive lead board of an aluminum covering. The slices were 40-mm-wide and the distance between two slices was 1.9 mm. Every 3 slices fit 1 scintillator strip (5.5 mm þ 0.2 mm) and every 21 slices fit 1 scintillator block (40 mm) well. The length and
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thickness of the slices were simulated by Monte Carlo software GEANT4. In Fig. 4b and c, the x-axis references the distance (1 channel ¼ 1.9 mm) from the center and the y-axis references the counts in a given channel. The full width at half maximum (FWHM) of the counts shows the collimate performance. Fig. 4b showed the FWHM was inversely proportional to the length approximately and Fig. 4c showed the FWHM would reduce along with the increase of the thickness of slices. When the length was 10 mm and the thickness was 0.3 mm, the FWHM was 3.48 channels (6.6 mm). A readout circuit was designed included four channels of current sensitive preamplifiers and a channel of timer to fit the XP1452. The four signals recorded by the XP1452 were picked up from anodes, amplified, and then shaped with the integral time of 300 ns by the readout circuit. Another signal was picked up from the last dynode as a timing signal. All these analog signals of different blocks were counted and processed by a high speed DAQ in parallel to obtain the position and energy information. They then were displayed line-by-line.
6. Simulations and experiments A simulation was completed by GEANT4 to validate the principles of depth discrimination. The arrangements of the simulation referred to Fig. 1. The primary photons entered the sample along a vertical direction. Two detector modules were placed at an obliquity of 451 with an interval of 1 cm. Each detector element was 40-mm-long 5.5-mm-wide 3-mm-thick. The detect distance D from the intersection O to the surface of detector modules was 50 cm vertically. The lead extrusive board was initially 2 mm thick and 25 cm long. For simplicity, the scatter energy was fixed as 100 keV and the ds/dΩ was assumed isotropic. The simulation results for a single-point scatter are shown in Fig. 5. As was expected, the proportion of two modules’ counts was related to the relative depth of scatter voxel. P was defined as the proportion of the minor counts to the major counts of two modules. While Compton scattering occurred around the intersection O ( 0.5 cm oΔd o0.5 cm), P was close to 100% because the measurement geometries could be deemed symmetrical in this case. So the detector was “blind” to discriminate the relative depth in this case. While Compton scattering occurred above the intersection O ( 5 cmo Δdo 0.5 cm), P, as the proportion of the lower counts to the upper counts, decreased linearly by a rate v of 20.3%/cm because some scattered photons towards the lower
Fig. 4. (a) The structure of the improved parallel-hole collimator, (b) the effects of the length of slices on collimate performance, and (c) the effects of the thickness of slices on collimate performance.
Fig. 5. The simulation result for depth discrimination of single-point scatter. (l ¼ 4 cm, α ¼ 451, D¼ 50 cm, and L ¼25 cm).
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module were stopped by the extrusive board. While Compton scattering occurred below the intersection O (0.5 cmo Δdo 7 cm), P, as the proportion of the upper counts to the lower counts, decrease linearly by a different rate v þ of 13.8%/cm. The two variation rates, v and v þ , depend on measurement geometries and can be obtained beforehand through a simulation or experiment. So the relative depth could be calculated easily from the proportion in this zone. Besides, it was found that the major counts of two modules reduced linearly with the relative depth increasing. It was because the fact that the actual detect distances of two modules changed when scatter voxels deviated from the intersection O. However, as the relative depth was varied from the proportion of two modules it is expected that the distance effect would be taken care of by this process of analysis. The relative depth was derived from the proportion of two modules. So the distance effect would be counteracted mostly. Then, an experiment was completed based on the scintillator linear array detector mentioned previously. The measurement geometries were the same with above simulation. A plastic board was tested at different relative depths. All experiment results were summed up in Fig. 6. In the ideal case, the image should be homogeneous. But it would be affected by many factors, for example, the uniformity of detection efficiency of 70 strips, the absorption of the plastic board and its supporter, the “direct through” X-rays (without scattered) and so on. So it is a semiquantitative method and need more corrections. In this work, only the mean counts in selected areas were chosen to calculate the relative depth. When the actual relative depth was 0 cm (Fig. 6c and h), the mean counts of the upper module and the lower module were 625 and 669, respectively. The proportion P equaled 93.4%, so according to above simulation, v þ ¼13.8%/cm, the calculated relative depth was about 0.98 cm. If the uniformity of the image (especially the center of upper module) was corrected, the mean counts of two modules would be more or less identical. Similarly when the actual relative depth was 4 cm (Fig. 6a and f), the mean counts of two modules reduced to 312 and 584, respectively. So the calculated relative depth was about 3.88 cm. When the actual relative depth was 4 cm (Fig. 6e and j), the mean counts of the upper module increased to 755 and the lower one reduced to 294. In this case, v ¼20.3%/cm, the calculated relative depth was about 3.51 cm. More comparisons were listed in Table 3. All these calculated relative depth matched the actual values well. Several similar simulations were completed in different measurement geometries and the corresponding variation rates are listed in Table 4. The results showed that the proportion P varied more quickly in measurement geometries than the longer board length L, the shorter detect distance D, the smaller module obliquity α, and the shorter elements length l. A larger variation rate represented a better contrast in a smaller FOV. Usually the element length l was fixed once the detector module was produced. Therefore, an appropriate depth
discrimination could be achieved by changing the module obliquity α, the detect distance D, and the board length L. It was also found that the sensitivity of the module had little relation with the module obliquity α and the extrusive board length L.
7. Further discussions Though devised from the single-point scatter, the preceding method also could be applied to find the average depth of scatter voxels along the primary track in actual imaging. However, it did not provide in-depth details of the voxels. To achieve further detail, an analytic algorithm was considered. Supposed the primary track was separated to N voxels and each voxel was deemed to homogeneous, the signal S was simplified to a sum of products Table 3 The comparisons of simulation and experiment of single-point scatter. No. Actual Upper module depth (cm) mean counts
Lower module mean counts
Calculated depth (cm)
1
4
312
584
2
2
449
637
3
0
625
669
4
2
701
513
5
4
755
294
(584 312)/ (584 13.8%)þ 0.5 ¼ 3.88 (637 449)/ (637 13.8%) þ 0.5 ¼ 2.64 (669 625)/ (669 13.8%) þ 0.5 ¼ 0.98 (513 701)/ (701 20.3%) 0.5 ¼ 1.82 (294 755)/ (755 20.3%) 0.5 ¼ 3.51
Table 4 The simulation results for depth discrimination of single-point scatter in different measurement geometries. No. Elements length (cm)
Module obliquity (1)
Detect distance (cm)
Board v vþ length (cm) (%/cm) (%/cm)
1 2 3 4 5 6 7 8 9
45 45 45 45 45 30 60 45 45
50 50 50 40 60 50 50 50 50
25 20 30 25 25 25 25 25 25
4 4 4 4 4 4 4 3 5
20.3 13.7 29.9 33.5 14.4 23.2 15.8 26.1 16.9
Fig. 6. The experiment results for a plastic board at different relative depths, 4 cm, 2 cm, 0 cm, 2 cm, and 4 cm, respectively (from left to right).
13.8 8.5 20.7 23.6 10.0 18.6 8.8 19.3 10.7
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of the electron densities ne(Δd) and the corresponding weights w(Δd) as shown below: S¼C
N i
∑
Δd ¼ i
ne ðΔdÞ wðΔdÞ
ð5Þ
In Eq. (5), i was the number of scatter voxels above the intersection O and C was the coefficient. When the measurement geometries were fixed, w(Δd) and C could be calibrated from the results of the single-point scatter beforehand, leaving only ne(Δd) unknown. In the theory of linear equations, the N independent equations were required to solve the N unknown electron densities. These equations could be obtained by two available methods. The first method adds more modules to achieve S directly, as with the panel detector, but greatly increased the cost. The second method changes the weights w(Δd) using different measurement geometries. For example, it was convenient to change the extrusive board length L and keep other measurement geometries stable. The complexity of this method depended on the number of voxels N, which meant the depth resolution could be resolved by numerical calculations such as the Gauss–Jordan elimination, Doolittle decomposition, Courant decomposition, Jacobi iteration, etc. Once the inverse of the coefficient matrix was defined, the electron densities could be directly reconstructed from the signals. Previous discussions ignored the effect of attenuation. To compensate for attenuation, there were several physical and algorithmic correction methods developed by predecessors such as dual energy techniques (Huddleston and Weaver 1983; Harding and Tischler 1986) and reconstruction algorithms (Battista et al., 1977). In this work, a predictor–corrector iterative algorithm was considered to correct these effects (Evans et al., 2002). The total procedure can be described briefly as follows: S¼C
N i
∑
Δd ¼ i
ne ðΔdÞ wðΔdÞ f I f s
ð6Þ
In Eq. (6), fI and fS were the attenuation factors of the primary track and the scattered track, respectively. First, two attenuation factors were set as one to calculate ne(Δd). If ne(Δd) was in proportion to the linear attenuation coefficient, the two attenuation factors could be calculated using this sampling. Then, ne(Δd) was recalculated by the updated attenuation factors. The criterion ε is defined below: 2 N i ne ðΔdÞnew ε¼ ∑ 1 =N ð7Þ ne ðΔdÞold Δd ¼ i The iteration was stopped until ε was below the default value. The convergence rate depended on the number of voxels N and the criterion ε. 8. Conclusions A depth discrimination method has been devised based on linear array detector modules for push-broom CSI. This method is applicable for both semiconductor detectors and scintillator detectors. In our work, an available scintillator detector was designed based on XP1452. Its spatial resolution was 5.5 mm and could be improved using narrow scintillator strips and an appropriate lightguide. An improved parallel-hole collimator was adopted to change the measurement geometries. For the single-point scatter, the correlation of the depth and the signal proportion has been validated using both simulations and experiments. Because the
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correlation depends on the measurement geometries, and could be obtained beforehand, the average depth of scatter voxels could easily be calculated by the signal proportion. More details of depth require more equations about the unknown electron densities. These equations could be achieved by adding modules or changing measurement geometries. The correction for attenuation has been described briefly using a predictor–corrector iterative algorithm. The solutions of linear equations and the iterative algorithm are mature in numerical calculations. The complexity lies on the number of voxels N. These questions should be considered and carefully improved to achieve better results in future works. References Battista, J.J, et al., 1977. Compton scatter imaging of transverse section: corrections for multiple scattering and attenuation, Phys. Med. Biol. 22, 229–244. Böke, Aysun, 2013. The total incoherent scattering cross sections for low-Z elements, Radiat. Phys. Chem. 83, 34–41. Cirrone, G.A.P., et al., 2010. A new variable parallel holes collimator for scintigraphic device with validation method based on Monte Carlo simulations, Nucl. Instrum. Methods Phys. Res., Sect. A 618, 315–322. Dunn, William L., Yacout, Abdelfatah M., 2000. Corrosion detection in aircraft by Xray backscatter methods, Appl. Radiat. Isot. 53, 625–632. Evans, Brian L., et al., 2002. Demonstration of energy-coded Compton scatter tomography with fan beams for one-sided inspection, Nucl. Instrum. Methods Phys. Res., Sect. A 480, 797–806. Guangzhi Sun, et al., 2008. Development of a type of a one-dimensional positionsensitive scintillator-fiber detector for X-ray Backscatter imaging, Nucl. Instrum. Methods Phys. Res., Sect. A 594, 61–65. Harding, G., Harding, E., 2010. Compton scatter imaging A tool for historical exploration, Appl. Radiat. Isot. 68, 993–1005. Harding, G., Tischler, R, 1986. Dual energy Compton scatter tomography, Phys. Med. Biol. 31, 477–489. Harkness, L.J., et al., 2009. Optimisation of a dual head semiconductor Compton camera using Geant4, Nucl. Instrum. Methods Phys. Res., Sect. A 604, 351–354. Herr, Michael D., McInerney, Joseph J., Lamser, Dennis G., Copenhaver, Gary L., 1994. A flying spot x-ray system for Compton backscatter imaging, IEEE Trans. Med. Imaging 13 (3), 461–469. Hubbell, J.H., et al., 1975. Atomic form factors, incoherent scattering functions, and photon, J. Phys. Chem. Ref. Data 4, 471–538. Huddleston, A.L., Weaver, J.B., 1983. Dual-energy Compton-scatter densitometry, Int. J. Appl. Radiat. Isot. 34, 997–1002. Kim, C.L., Ivan, A., Ganin. A., 2010. A Compact SPECT Detector based on a Quad PMT. In: IEEE Nuclear Science Symposium Conference Record (NSS/MIC). Lale, P.G., 1959. The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography, Phys. Med. Biol. 4, 159–166. Massaro, Enrico, Matt, Giorgio, 1986. A simple approximate formula for the incoherent scattering cross section of X and γ-rays, Nucl. Instrum. Methods Phys. Res., Sect. A 251, 545–549. McFarlane, N.J.B., Speller, R.D., Bull, C.R., Tillett, R.D., 2003. Detection of bone fragments in chicken meat using X-ray backscatter, Biosystems Eng. 85 (2), 185–199. Miceli, A., et al., 2007. 450kVp Comparison of simulated and measured spectra of an industrial 450 kV X-ray tube, Nucl. Instrum. Methods Phys. Res., Sect. A 580, 123–126. Park, Shin-Woong, et al., 2006. Development of the body scan system with backscattered X-rays, Nucl. Instrum. Methods Phys. Res., Sect. A 568, 369–374. 〈http://physics.nist.gov/PhysRefData/FFast/html/form.html2011-4-24〉 2011-4-24. Rossi, P., et al., 2011. Design and performance tests of the calorimetric tract of a Compton Camera for small-animals imaging, Nucl. Instrum. Methods Phys. Res., Sect. A 628, 430–433. Sharaf, J.M., 2001. Practical aspects of Compton scatter densitometry, Appl. Radiat. Isot. 54, 801–809. Sullivan, John P., Tornga, Shawn R., Rawool-Sullivan, Mohini W., 2008. Extended radiation source imaging with a prototype Compton imager, Appl. Radiat. Isot. 67, 617–624. Towe, Bruce C., Jacobs, Alan M., 1981a. X-ray backscatter imaging, IEEE Trans. Biomed. Eng. 28 (9), 646–654. Towe, Bruce C., Jacobs, Alan M., 1981b. X-Ray Compton Scatter Imaging Using a High Speed, IEEE Trans. Biomed. Eng. 28 (10), 717–721. Trinci, G., et al., 2010. Validation of the Geant4 electromagnetic photon crosssections for elements and compounds, Nucl. Instrum. Methods Phys. Res., Sect. A 621, 406–412. Vogel, H., 2007a. Search for persons, Eur. J. Radiol. 63, 227–236. Vogel, H., 2007b. Search by X-rays applied technology, Eur. J. Radiol. 63, 220–226. Yuka, Sunwoo, Hyun Kimb, Kwang, Yi, Yun, 2006. Detection of buried landmine with X-ray backscatter technique, Nucl. Instrum. Methods Phys. Res., Sect. A 568, 388–392.
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Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Depth discrimination method based on a multirow linear array detector for push-broom Compton scatter imaging Yantao Liu a,b, Zhiming Zhang a,b, Daowu Li a,b, ChuangXin Ma a,b, Cunfeng Wei a,b, Meiling Zhu a,b, Lei Shuai a,b, Tingting Hu a,b, Baotong Feng a,b, Pei Chai a,b, Xianchao Huang a,b, Haohui Tang a,b, Ting Li a,b, Kai Zhuang a,b, Xiaopan Jiang a,b, Yingjie Wang a,b, Yiwen Zhang a,b, Wei Zhou a,b, Shifeng Sun a,b, Long Wei a,b,n a b
Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Beijing Engineering Research Center of Radiographic Techniques and Equipment, Beijing 100049, China
H I G H L I G H T S
We devise a depth discrimination method for push-broom Compton scatter imaging. Depth of sample is indicated by comparing signal proportions of different modules. The depth discrimination is linked to different measurement geometries. A multirow linear array detector based on XP1452 and LYSO was developed. Simulation model is built using GEANT4 to support the method well.
art ic l e i nf o
a b s t r a c t
Article history: Received 11 June 2013 Received in revised form 12 August 2013 Accepted 2 September 2013 Available online 21 September 2013
A depth discrimination method is devised based on a multirow linear array detector for push-broom Compton scatter imaging. Two or more rows of detector modules are placed at different positions towards a sample. An improved parallel-hole collimator is fixed in front of the modules to restrict their fields of view. The depth information could be indicated by comparing the signal differences. In addition, an available detector and several related simulations using GEANT4 are given to support the method well. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Depth discrimination Compton scatter imaging GEANT4 Detector Collimator
1. Introduction Compton scatter imaging (CSI) is a noninvasive imaging technique based on the Compton scattering effect, which was discovered by Compton in 1923. It was first described in the medical field by Lale (1959) and then applied in many nondestructive testing fields, such as corrosion detection in aircraft (Dunn and Yacout 2000), food checks (McFarlane et al., 2003), buried landmine detection (Yuka et al., 2006), security inspection (Vogel 2007a,b), and historical exploration (Harding and Harding 2010). n Corresponding author at: Chinese Academy of Sciences, Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy Physics, Beijing 100049, China. Tel.: þ86 10 88236347; fax: þ 86 10 88236413. E-mail addresses: [email protected] (Y. Liu), [email protected] (L. Wei).
0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.09.001
Unlike transmission imaging, CSI allows a flexible choice of measurement geometries. Its radiation source and detectors can be arranged in any direction, especially on the same side of a sample. Therefore, CSI is applicable in detecting the sample underground or in walls where transmission imaging fails. It is also suitable for a surface measurement of large, thick, bulky objects. Moreover, CSI is highly sensitive to light-element materials such as hydrogen, carbon, nitrogen, and oxygen. Therefore, it could provide a high-contrast image of organic contraband such as petrol, drugs, explosives, etc. Finally, scatter voxels could be directly located using the intersection points of primary photons and scattered photons. However, CSI is inferior compared to transmission imaging in its signal-to-noise ratio (SNR). The quantity of photons backscattered (scatter angle beyond 901) to a detector is less than 0.8% of those
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transmitted, in theory, to its counterpart detector (Park et al., 2006). These scattered photons would be further limited by the locating devices in front of the detector. The scatter energies of photons are less than the primary energy; therefore, they are more susceptible to noises from the radiation source and the detector. To improve the SNR, it usually increases the intensity of primary photons, expands effective areas of the detector, and/or prolongs sampling time in CSI systems. To realize positioning and imaging, an appropriate scheme is required to scan the sample. One main scan scheme in present CSI systems is called flying spot (Towe and Jacobs 1981a,b; Herr et al., 1994). It uses a pencil beam of X-rays to scan the sample in a point-by-point method. In this way, it can provide a highresolution three-dimensional (3D) image of the sample, but has a low utilization efficiency of the radiation source and a long sampling time. The other scan scheme is called push-broom (Yuka et al., 2006; Park et al., 2006; Guangzhi Sun et al., 2008) and uses a fan beam of X-rays and linear array detectors directly. This scheme enhances the utilization efficiency of the radiation source and reduces the sampling time. However, it only provides a superposed two-dimensional (2D) projection without depth information in existing systems. More details of the scan schemes are compared in Section 3. In this work, a method was devised to achieve a primary depth discrimination based on a multirow linear array detector for pushbroom CSI. The detector was composed of two or more rows of modules, an improved parallel-hole collimator, and the corresponding data acquisition system (DAQ). The modules were placed in different directions towards a sample to receive scattered signals independently. The collimator was fixed in front of the modules to restrict their fields of view (FOVs). When Compton scattering occurred at different depths, scattered photons would be distributed into the adjacent modules in different proportions. The proportions indicated depth information using a special algorithm. In addition, an available detector was presented and several related simulations using GEANT4 (Miceli et al., 2007; Sullivan et al., 2008; Harkness et al., 2009; Trinci et al., 2010; Cirrone et al., 2010; Rossi et al., 2011) were given that supported the method well.
2. Characteristics of Compton scattering Compton scattering and photoemission are two main competitive interactions when photon energy is below 1 MeV. In addition, Compton scattering dominates the reaction cross section from 100 keV to 1 MeV in aluminum (a representative of the low and moderate atomic number Z materials) (Harding and Harding 2010). The scatter energy and the angular distribution of the Compton scatter for stationary, free electrons are calculated by the two formulas below: EðθÞ ¼ ½1=E0 þ ð1 cos θÞ=me c2 1
ð1Þ
ds=dΩ ¼ ðr 2e =2Þη2 ðη þ η 1 sin θÞ
ð2Þ
2
In Eqs. (1) and (2), θ is the scatter angle; ds/dΩ is the Klein– Nishina cross section; E0 and E(θ) are the primary energy and the scatter energy of photons, respectively; η is defined as the ratio of E(θ) to E0 (E(θ)/E0); mec2 is the rest mass energy of electron (511 keV); and re is the classical electron radius (2.82 fm). If photons were emitted from an X-ray tube of 450 kVp, their average primary energy would be approximately 150 keV, using the theory of bremsstrahlung. When the scatter angle θ was equal to 1351, and the primary energies E0 ranged from 50 to 450 keV, the corresponding scatter energies E(θ) and the linear attenuation
Table. 1 The scatter energies and the linear attenuation coefficients of scintillator Lu2SiO5 in different primary energies (θ¼ 1351, ρ¼ 7.3 g/cm3). Primary energy (keV)
Scatter energy (keV)
Linear attenuation coefficient (cm 1) a
50 100 150 200 300 450
42.8 74.9 99.9 119.8 149.7 179.6
44.2 47.6 22.6 14.3 8.2 5.3
a Data were employed in linear interpolation on the original data from the National Institute of Standards and Technology (http://physics.nist.gov/PhysRefData/FFast/html/ form.html).
Table 2 The scatter energies and the Klein–Nishina cross sections at different scatter angles (E0 ¼ 150 keV, ρ ¼7.3 g/cm3). Scatter angle (1)
Scatter energy (keV)
Klein–Nishina cross section (mb)
90 105 120 135 150 165 180
116.0 109.5 104.1 99.9 96.9 95.1 94.5
25.3 24.7 26.5 29.4 32.2 34.3 35.0
coefficients μ of Lu2SiO5 are listed in Table 1. It was found that the average scatter energy was approximately 99.9 keV and the corresponding linear attenuation coefficient was approximately 22.6 cm 1. Therefore, in this case, a Lu2SiO5 scintillator of 3 mm depth could provide enough stopping power for scattered photons. When the primary energy E0 equaled to 150 keV, and the scatter angles θ ranged from 901 to 1801, the corresponding scatter energies E(θ) and the Klein–Nishina cross sections ds/dΩ were listed in Table 2. The scatter energies and the cross sections varied to a small extent. This variation could be corrected or even overlooked, especially for a detector of a limit solid angle. The angular distribution of Compton scatter could be assumed to be an isotropic distribution in the below calculations and simulations. When considered in materials, electrons were not free but were bound by nuclei. Therefore, an incoherent atomic scatter function S(q, Z) (Sharaf 2001; Hubbell et al., 1975; Böke 2013; Massaro and Matt 1986), which accounted for electron binding energy effects with the photon momentum transfer q, should be considered in the actual scattering cross section. Its value was tabulated for all elements by Hubbell et al. (1975). For low Z materials, S(q, Z) was considered equal to Z because the electron binding energy was small. Therefore, the intensity of scattered photons was directly proportion to the electron density of materials. For high Z materials, S(q, Z) did not trend to Z but instead rapidly decreased. The intensity of scattered photons was small.
3. Scan schemes of Compton scattering imaging 3.1. Point-by-point scan scheme The first CSI system developed by Lale (1959) adopted a simple point-by-point scan scheme. A narrow pencil beam was collimated by beam collimators directly to hit a sample, while a single
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photomultiplier was set to receive the corresponding scattering signal. After one sampling, the whole system was moved a constant distance to detect the next point. This scan scheme made poor use of primary photons and resulted in a long sampling time that spanned several hours (Lale 1959). Then, an improved point-by-point scan scheme called flying spot was introduced into CSI systems. A pencil beam, which was shaped from a fan or cone beam by a mechanically rotating device, periodically swept a sample from one side to another side. Meanwhile, the sample was moved relatively perpendicular to the sweep direction. Since the sweep rate was faster than the move speed, its total sampling time could be reduced to several minutes. For example, the American Science & Engineering Incorporation (AS&E) used this scan scheme in their CSI systems to present a 2D projection of the sample (Vogel 2007a,b). It was very easy to distinguish suspicious organic objects from their complex surroundings because organic objects and light metallic materials were highlighted in the projection and heavy metallic materials were darkened. However, it was hard to discriminate their relative depth from only the projection. The ComScan system (Harding and Harding 2010) was another commercially available CSI system that used the flying spot scheme. It is different from AS&E systems, in that two arrays of 11 scintillator Bi4Ge3O12 (BGO) strips were arranged on two sides of a pencil beam to detect depth information simultaneously. In this way, a line of 22 voxels of different depths was obtained in one sampling, then a 2D section was obtained along the sweep direction, and finally a 3D image was obtained along the move direction. Because ComScan is equipped with two single-slit collimators, which allowed a variable spatial resolution, and sensitivity depended on detect distances, the flying spot scheme is preferred for a small FOV and high-resolution imaging. 3.2. Line-by-line scan scheme Recently, a direct line-by-line scan scheme called push-broom has been developed for CSI (Yuka et al., 2006; Park et al., 2006; Guangzhi Sun et al., 2008). In this scheme, a fan beam of X-rays scanned the sample directly and a linear array detector detected a line of scatter voxels in parallel. A parallel-hole collimator was fixed in front of the detector to restrict scattered photons. The push-broom scheme could enhance the utilization efficiency of X-rays and when implemented, it further reduced the sampling time. It allowed a moderate image resolution and an approximate constant sensitivity, making it the preferred choice for a large FOV and high-speed imaging of large objects. Currently, imaging performances of the push-broom scheme are similar to AS&E systems. However, the problem of superposed 2D projection has not been resolved yet.
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4. Principles of depth discrimination For simplicity, the principles of depth discrimination and the measurement geometries were illustrated in Fig. 1 based on a double-row linear array detector as the representative of multirow ones. A radiation source was placed over a moving sample. Two linear array detector modules were placed towards different zones of the sample at a given obliquity of α to the horizontal. Each module was made up of several detector elements of l (length) by w (width) in parallel. An improved parallel-hole collimator was fixed in front of the modules. The collimator included two arrays of slices and an adjustable extrusive board of heavy metal. The slices were arranged to separate detector elements (not necessarily one-to-one). Their lengths, thicknesses, and intervals would affect the collimator's performance in the transverse direction. The extrusive board was arranged to separate the two modules, as it should be thick enough to stop photons from passing through. When a collimated beam of photons from the radiation source entered the sample along a primary track, part of the photons were scattered at a relative depth of Δd and then left along a scattered track at a scatter angle of θ. The intensity of these scattered photons I(Δd, θ) should be expressed as a function of Δd and θ. Here, Δd equaled zero, while Compton scattering occurred at the intersection O of the primary track and the extension line of the extrusive board. Each detector element's signal S was an integral of I(Δd, θ) in its FOV. The FOV was limited by measurement geometries of the module and the collimator such as the elements length l, the module obliquity α, the detect distance D, and the extrusive board length L. Further, the upper module and the lower module faced toward different depths of the sample and there was an intermediate zone, owing to the overlap of two FOVs. While Compton scattering occurred on the superficial zone A, scattered photons could only be received by the upper module because of the restriction of the extrusive board. In addition, while Compton scattering occurred on the deep zone C, it presented opposite results compared to those gathered from the superficial zone A. While Compton scattering occurred on the intermediate zone B, scattered photons would be distributed into the two modules in a proportion. The proportion was related to the relative depth of scatter voxel in this zone. Therefore, depth information could be indicated from the proportion using a special algorithm. 5. Design of detector In our work, a scintillator linear array detector was designed for a large FOV, high-speed imaging. The detector was composed of
3.3. Plane-by-plane scan scheme A potential method to solve the problem of superposed 2D projection is to use a panel detector instead of a linear array detector for push-broom CSI. It could detect transverse and depth information simultaneously. However, the panel detector was not in current favor for the following reasons. First, it was no more sensitive than its linear counterpart, in spite of the large detector area. Moreover, there was no possibility of discriminating with mechanical collimation against multiple scatter radiation. Finally, it currently is more expensive than its linear counterpart is. An alternative method was to use two or more linear array detector modules that could detect transverse information from different angles and then resolve depth information from signal differences of the two modules.
Fig. 1. The principles of depth discrimination and the measurement geometries based on a double-row linear array detector.
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two rows of modules, an improved parallel-hole collimator, and the corresponding DAQ (Fig. 2). Photonis XP1452, a four-channel photomultiplier, was chosen due to its large effective area (32 mm 32 mm), fast response time (29 ns), compact structure, and moderate cost. The XP1452 obtained the position as follows: X ¼ ðS1 þ S2 S3 S4 Þ=ðS1 þ S2 þ S3 þ S4 Þ
Fig. 2. The photograph of the scintillator linear array detector.
ð3Þ
Y ¼ ðS1 S2 S3 þ S4 Þ=ðS1 þ S2 þ S3 þ S4 Þ
ð4Þ
In Eqs. (3) and (4), S1, S2, S3, S4 are the signals of four quadrants of the XP1452. The gains of the four quadrants could be adjusted individually by a high-voltage divider circuit. The X-direction was adopted to locate the transverse position of scattered photons, and the Y-direction was adjusted symmetric to balance the gains of the four quadrants. Scintillator LYSO, similar to Lu2SiO5, was chosen due to its large stopping power (ρ¼7.1 g/cm3), high light output (32,000 photons/ MeV) and fast decay time (41 ns). The emission wavelength of the LYSO (420 nm) matched the spectral range of the XP1452 well. Each scintillator strip was 40 mm 5.5 mm 3 mm to provide moderate resolution (5.5 mm) and a large effective area. Seven strips were combined to create a block of 40 mm 40 mm 3 mm and the gaps of 0.2-mm-wide were filled with a reflective material to reduce the light crosstalk. A special light-guide was designed to distribute the scintillation photons. The light-guide was made of a 10-mm-thick optical glass. It was processed into a prismoid with an upper surface of 40 mm 40 mm and a lower surface of 32 mm 32 mm to fit the scintillator block and the XP1452, respectively. Several slits in the light-guide were filled with the reflective material to change the light distribution (Kim et al., 2010). The scintillator block of seven strips together with the light-guide, was experimented upon using a radioactive source 137Cs (Fig. 3). The scatter diagram and the projection of X-direction showed that the seven strips were clearly differentiated and the peak-to-valley ratio was more
Fig. 3. The experiment results of the scintillator block of seven strips with the prismoid light-guide: energy spectrum (upper left), projection of X-direction (lower left), and scatter diagram (right).
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than 7:1. Then these 10 blocks were combined to create a module of 400-mm-wide. An improved parallel-hole collimator (Fig. 4a) was composed of two parallel arrays of tungsten alloy slices and an adjustable extrusive lead board of an aluminum covering. The slices were 40-mm-wide and the distance between two slices was 1.9 mm. Every 3 slices fit 1 scintillator strip (5.5 mm þ 0.2 mm) and every 21 slices fit 1 scintillator block (40 mm) well. The length and
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thickness of the slices were simulated by Monte Carlo software GEANT4. In Fig. 4b and c, the x-axis references the distance (1 channel ¼ 1.9 mm) from the center and the y-axis references the counts in a given channel. The full width at half maximum (FWHM) of the counts shows the collimate performance. Fig. 4b showed the FWHM was inversely proportional to the length approximately and Fig. 4c showed the FWHM would reduce along with the increase of the thickness of slices. When the length was 10 mm and the thickness was 0.3 mm, the FWHM was 3.48 channels (6.6 mm). A readout circuit was designed included four channels of current sensitive preamplifiers and a channel of timer to fit the XP1452. The four signals recorded by the XP1452 were picked up from anodes, amplified, and then shaped with the integral time of 300 ns by the readout circuit. Another signal was picked up from the last dynode as a timing signal. All these analog signals of different blocks were counted and processed by a high speed DAQ in parallel to obtain the position and energy information. They then were displayed line-by-line.
6. Simulations and experiments A simulation was completed by GEANT4 to validate the principles of depth discrimination. The arrangements of the simulation referred to Fig. 1. The primary photons entered the sample along a vertical direction. Two detector modules were placed at an obliquity of 451 with an interval of 1 cm. Each detector element was 40-mm-long 5.5-mm-wide 3-mm-thick. The detect distance D from the intersection O to the surface of detector modules was 50 cm vertically. The lead extrusive board was initially 2 mm thick and 25 cm long. For simplicity, the scatter energy was fixed as 100 keV and the ds/dΩ was assumed isotropic. The simulation results for a single-point scatter are shown in Fig. 5. As was expected, the proportion of two modules’ counts was related to the relative depth of scatter voxel. P was defined as the proportion of the minor counts to the major counts of two modules. While Compton scattering occurred around the intersection O ( 0.5 cm oΔd o0.5 cm), P was close to 100% because the measurement geometries could be deemed symmetrical in this case. So the detector was “blind” to discriminate the relative depth in this case. While Compton scattering occurred above the intersection O ( 5 cmo Δdo 0.5 cm), P, as the proportion of the lower counts to the upper counts, decreased linearly by a rate v of 20.3%/cm because some scattered photons towards the lower
Fig. 4. (a) The structure of the improved parallel-hole collimator, (b) the effects of the length of slices on collimate performance, and (c) the effects of the thickness of slices on collimate performance.
Fig. 5. The simulation result for depth discrimination of single-point scatter. (l ¼ 4 cm, α ¼ 451, D¼ 50 cm, and L ¼25 cm).
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module were stopped by the extrusive board. While Compton scattering occurred below the intersection O (0.5 cmo Δdo 7 cm), P, as the proportion of the upper counts to the lower counts, decrease linearly by a different rate v þ of 13.8%/cm. The two variation rates, v and v þ , depend on measurement geometries and can be obtained beforehand through a simulation or experiment. So the relative depth could be calculated easily from the proportion in this zone. Besides, it was found that the major counts of two modules reduced linearly with the relative depth increasing. It was because the fact that the actual detect distances of two modules changed when scatter voxels deviated from the intersection O. However, as the relative depth was varied from the proportion of two modules it is expected that the distance effect would be taken care of by this process of analysis. The relative depth was derived from the proportion of two modules. So the distance effect would be counteracted mostly. Then, an experiment was completed based on the scintillator linear array detector mentioned previously. The measurement geometries were the same with above simulation. A plastic board was tested at different relative depths. All experiment results were summed up in Fig. 6. In the ideal case, the image should be homogeneous. But it would be affected by many factors, for example, the uniformity of detection efficiency of 70 strips, the absorption of the plastic board and its supporter, the “direct through” X-rays (without scattered) and so on. So it is a semiquantitative method and need more corrections. In this work, only the mean counts in selected areas were chosen to calculate the relative depth. When the actual relative depth was 0 cm (Fig. 6c and h), the mean counts of the upper module and the lower module were 625 and 669, respectively. The proportion P equaled 93.4%, so according to above simulation, v þ ¼13.8%/cm, the calculated relative depth was about 0.98 cm. If the uniformity of the image (especially the center of upper module) was corrected, the mean counts of two modules would be more or less identical. Similarly when the actual relative depth was 4 cm (Fig. 6a and f), the mean counts of two modules reduced to 312 and 584, respectively. So the calculated relative depth was about 3.88 cm. When the actual relative depth was 4 cm (Fig. 6e and j), the mean counts of the upper module increased to 755 and the lower one reduced to 294. In this case, v ¼20.3%/cm, the calculated relative depth was about 3.51 cm. More comparisons were listed in Table 3. All these calculated relative depth matched the actual values well. Several similar simulations were completed in different measurement geometries and the corresponding variation rates are listed in Table 4. The results showed that the proportion P varied more quickly in measurement geometries than the longer board length L, the shorter detect distance D, the smaller module obliquity α, and the shorter elements length l. A larger variation rate represented a better contrast in a smaller FOV. Usually the element length l was fixed once the detector module was produced. Therefore, an appropriate depth
discrimination could be achieved by changing the module obliquity α, the detect distance D, and the board length L. It was also found that the sensitivity of the module had little relation with the module obliquity α and the extrusive board length L.
7. Further discussions Though devised from the single-point scatter, the preceding method also could be applied to find the average depth of scatter voxels along the primary track in actual imaging. However, it did not provide in-depth details of the voxels. To achieve further detail, an analytic algorithm was considered. Supposed the primary track was separated to N voxels and each voxel was deemed to homogeneous, the signal S was simplified to a sum of products Table 3 The comparisons of simulation and experiment of single-point scatter. No. Actual Upper module depth (cm) mean counts
Lower module mean counts
Calculated depth (cm)
1
4
312
584
2
2
449
637
3
0
625
669
4
2
701
513
5
4
755
294
(584 312)/ (584 13.8%)þ 0.5 ¼ 3.88 (637 449)/ (637 13.8%) þ 0.5 ¼ 2.64 (669 625)/ (669 13.8%) þ 0.5 ¼ 0.98 (513 701)/ (701 20.3%) 0.5 ¼ 1.82 (294 755)/ (755 20.3%) 0.5 ¼ 3.51
Table 4 The simulation results for depth discrimination of single-point scatter in different measurement geometries. No. Elements length (cm)
Module obliquity (1)
Detect distance (cm)
Board v vþ length (cm) (%/cm) (%/cm)
1 2 3 4 5 6 7 8 9
45 45 45 45 45 30 60 45 45
50 50 50 40 60 50 50 50 50
25 20 30 25 25 25 25 25 25
4 4 4 4 4 4 4 3 5
20.3 13.7 29.9 33.5 14.4 23.2 15.8 26.1 16.9
Fig. 6. The experiment results for a plastic board at different relative depths, 4 cm, 2 cm, 0 cm, 2 cm, and 4 cm, respectively (from left to right).
13.8 8.5 20.7 23.6 10.0 18.6 8.8 19.3 10.7
Y. Liu et al. / Applied Radiation and Isotopes 82 (2013) 293–299
of the electron densities ne(Δd) and the corresponding weights w(Δd) as shown below: S¼C
N i
∑
Δd ¼ i
ne ðΔdÞ wðΔdÞ
ð5Þ
In Eq. (5), i was the number of scatter voxels above the intersection O and C was the coefficient. When the measurement geometries were fixed, w(Δd) and C could be calibrated from the results of the single-point scatter beforehand, leaving only ne(Δd) unknown. In the theory of linear equations, the N independent equations were required to solve the N unknown electron densities. These equations could be obtained by two available methods. The first method adds more modules to achieve S directly, as with the panel detector, but greatly increased the cost. The second method changes the weights w(Δd) using different measurement geometries. For example, it was convenient to change the extrusive board length L and keep other measurement geometries stable. The complexity of this method depended on the number of voxels N, which meant the depth resolution could be resolved by numerical calculations such as the Gauss–Jordan elimination, Doolittle decomposition, Courant decomposition, Jacobi iteration, etc. Once the inverse of the coefficient matrix was defined, the electron densities could be directly reconstructed from the signals. Previous discussions ignored the effect of attenuation. To compensate for attenuation, there were several physical and algorithmic correction methods developed by predecessors such as dual energy techniques (Huddleston and Weaver 1983; Harding and Tischler 1986) and reconstruction algorithms (Battista et al., 1977). In this work, a predictor–corrector iterative algorithm was considered to correct these effects (Evans et al., 2002). The total procedure can be described briefly as follows: S¼C
N i
∑
Δd ¼ i
ne ðΔdÞ wðΔdÞ f I f s
ð6Þ
In Eq. (6), fI and fS were the attenuation factors of the primary track and the scattered track, respectively. First, two attenuation factors were set as one to calculate ne(Δd). If ne(Δd) was in proportion to the linear attenuation coefficient, the two attenuation factors could be calculated using this sampling. Then, ne(Δd) was recalculated by the updated attenuation factors. The criterion ε is defined below: 2 N i ne ðΔdÞnew ε¼ ∑ 1 =N ð7Þ ne ðΔdÞold Δd ¼ i The iteration was stopped until ε was below the default value. The convergence rate depended on the number of voxels N and the criterion ε. 8. Conclusions A depth discrimination method has been devised based on linear array detector modules for push-broom CSI. This method is applicable for both semiconductor detectors and scintillator detectors. In our work, an available scintillator detector was designed based on XP1452. Its spatial resolution was 5.5 mm and could be improved using narrow scintillator strips and an appropriate lightguide. An improved parallel-hole collimator was adopted to change the measurement geometries. For the single-point scatter, the correlation of the depth and the signal proportion has been validated using both simulations and experiments. Because the
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correlation depends on the measurement geometries, and could be obtained beforehand, the average depth of scatter voxels could easily be calculated by the signal proportion. More details of depth require more equations about the unknown electron densities. These equations could be achieved by adding modules or changing measurement geometries. The correction for attenuation has been described briefly using a predictor–corrector iterative algorithm. The solutions of linear equations and the iterative algorithm are mature in numerical calculations. The complexity lies on the number of voxels N. These questions should be considered and carefully improved to achieve better results in future works. References Battista, J.J, et al., 1977. Compton scatter imaging of transverse section: corrections for multiple scattering and attenuation, Phys. Med. Biol. 22, 229–244. Böke, Aysun, 2013. The total incoherent scattering cross sections for low-Z elements, Radiat. Phys. Chem. 83, 34–41. Cirrone, G.A.P., et al., 2010. A new variable parallel holes collimator for scintigraphic device with validation method based on Monte Carlo simulations, Nucl. Instrum. Methods Phys. Res., Sect. A 618, 315–322. Dunn, William L., Yacout, Abdelfatah M., 2000. Corrosion detection in aircraft by Xray backscatter methods, Appl. Radiat. Isot. 53, 625–632. Evans, Brian L., et al., 2002. Demonstration of energy-coded Compton scatter tomography with fan beams for one-sided inspection, Nucl. Instrum. Methods Phys. Res., Sect. A 480, 797–806. Guangzhi Sun, et al., 2008. Development of a type of a one-dimensional positionsensitive scintillator-fiber detector for X-ray Backscatter imaging, Nucl. Instrum. Methods Phys. Res., Sect. A 594, 61–65. Harding, G., Harding, E., 2010. Compton scatter imaging A tool for historical exploration, Appl. Radiat. Isot. 68, 993–1005. Harding, G., Tischler, R, 1986. Dual energy Compton scatter tomography, Phys. Med. Biol. 31, 477–489. Harkness, L.J., et al., 2009. Optimisation of a dual head semiconductor Compton camera using Geant4, Nucl. Instrum. Methods Phys. Res., Sect. A 604, 351–354. Herr, Michael D., McInerney, Joseph J., Lamser, Dennis G., Copenhaver, Gary L., 1994. A flying spot x-ray system for Compton backscatter imaging, IEEE Trans. Med. Imaging 13 (3), 461–469. Hubbell, J.H., et al., 1975. Atomic form factors, incoherent scattering functions, and photon, J. Phys. Chem. Ref. Data 4, 471–538. Huddleston, A.L., Weaver, J.B., 1983. Dual-energy Compton-scatter densitometry, Int. J. Appl. Radiat. Isot. 34, 997–1002. Kim, C.L., Ivan, A., Ganin. A., 2010. A Compact SPECT Detector based on a Quad PMT. In: IEEE Nuclear Science Symposium Conference Record (NSS/MIC). Lale, P.G., 1959. The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography, Phys. Med. Biol. 4, 159–166. Massaro, Enrico, Matt, Giorgio, 1986. A simple approximate formula for the incoherent scattering cross section of X and γ-rays, Nucl. Instrum. Methods Phys. Res., Sect. A 251, 545–549. McFarlane, N.J.B., Speller, R.D., Bull, C.R., Tillett, R.D., 2003. Detection of bone fragments in chicken meat using X-ray backscatter, Biosystems Eng. 85 (2), 185–199. Miceli, A., et al., 2007. 450kVp Comparison of simulated and measured spectra of an industrial 450 kV X-ray tube, Nucl. Instrum. Methods Phys. Res., Sect. A 580, 123–126. Park, Shin-Woong, et al., 2006. Development of the body scan system with backscattered X-rays, Nucl. Instrum. Methods Phys. Res., Sect. A 568, 369–374. 〈http://physics.nist.gov/PhysRefData/FFast/html/form.html2011-4-24〉 2011-4-24. Rossi, P., et al., 2011. Design and performance tests of the calorimetric tract of a Compton Camera for small-animals imaging, Nucl. Instrum. Methods Phys. Res., Sect. A 628, 430–433. Sharaf, J.M., 2001. Practical aspects of Compton scatter densitometry, Appl. Radiat. Isot. 54, 801–809. Sullivan, John P., Tornga, Shawn R., Rawool-Sullivan, Mohini W., 2008. Extended radiation source imaging with a prototype Compton imager, Appl. Radiat. Isot. 67, 617–624. Towe, Bruce C., Jacobs, Alan M., 1981a. X-ray backscatter imaging, IEEE Trans. Biomed. Eng. 28 (9), 646–654. Towe, Bruce C., Jacobs, Alan M., 1981b. X-Ray Compton Scatter Imaging Using a High Speed, IEEE Trans. Biomed. Eng. 28 (10), 717–721. Trinci, G., et al., 2010. Validation of the Geant4 electromagnetic photon crosssections for elements and compounds, Nucl. Instrum. Methods Phys. Res., Sect. A 621, 406–412. Vogel, H., 2007a. Search for persons, Eur. J. Radiol. 63, 227–236. Vogel, H., 2007b. Search by X-rays applied technology, Eur. J. Radiol. 63, 220–226. Yuka, Sunwoo, Hyun Kimb, Kwang, Yi, Yun, 2006. Detection of buried landmine with X-ray backscatter technique, Nucl. Instrum. Methods Phys. Res., Sect. A 568, 388–392.
