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Simulation Study of X-Ray Backscatter Imaging of Pressure-Plate

Improvised Explosive Devices

Johan van den Heuvel and Franco Fiore

NATO C3 Agency, Oude Waalsdorperweg 61, 2597 AK The Hague, The Netherlands

ABSTRACT

Improvised Explosive Devices (IEDs) triggered by pressure-plates are a serious threat in current theatres of operation.X-ray backscatter imaging (XBI) is a potential method for detecting buried pressure-plates. Monte-Carlo simulation codewas developed in-house and has been used to study the potential of XBI for pressure-plate detection. It is shown that

pressure-plates can be detected at depths up to 7 cm with high photon energies of 350 keV with reasonable speeds of 1 to10 km/h. However, spatial resolution is relatively low due to multiple scattering.

Keywords: CIED, pressure-plate, X-ray, Monte-Carlo, detection

1.

INTRODUCTION

Improvised explosive devices (IEDs) are the insurgent’s weapons of choice in Iraq and Afghanistan. IEDs are being usedto target NATO and national forces at the strategic, operational and tactical levels in theatres of operation. There have

been successes in countering these devices and the networks associated with them. However, IEDs are still a major threatand a major cause of casualties in coalition forces.

There are many types of IEDs and they can be used in various ways. A pressure-plate IED is generally placed in theroad, usually buried to hide the IED. Note that the trigger mechanism can be separated from the explosive charge. Forthe IED emplacer this gives flexibility to place the trigger mechanism (pressure plate) at its optimum position, e.g. in thewheel tracks, while the explosive charge can be placed between the tracks or at the road side for maximum damage.

In this paper the detection of buried pressure-plates is addressed. Detection of buried pressure-plates has manysimilarities with the issue of landmine detection. In section 2 a brief overview of the research in detection technologiesfor humanitarian demining is given.

Section 3 presents the results of the simulation study of x-ray backscatter imaging of pressure-plate IEDs.

2. HUMANITARIAN DEMINING AND CHANGE DETECTION

There was a large international research activity on the landmine detection problem or humanitarian demining in the1990s which culminated in the Nobel Peace prize being awarded in 1997 to two NGOs. Unfortunately, this researcheffort was only partly successful and funding for humanitarian demining research has decreased considerably.[1] However, many of the technologies that were tried in humanitarian demining can also be applied for IED detection.

The RAND report gives an excellent overview of the problem of humanitarian demining with the traditional detectionand clearance methods and the innovative technologies that were pursued at the time. [1] Around the end of the 20th

century the US was spending $100 million annually in mine clearance. In the EU there was a similar activity.

[2]

The major problem in humanitarian demining is the high false alarm rate. Currently, electromagnetic induction is the

best and the preferred technology for mine detection, but this technology suffers from a high false alarm rate due to smallmetal parts in the soil. For low-metal landmines, the detection threshold has to be set very low, which results in a verylarge false alarm rate.

There are many similarities between landmine detection and IED detection. Not the least is that the same detectiontechnologies are used or are being investigated. For instance, buried IEDs are also detected by electromagnetic induction

Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XVII,edited by J. Thomas Broach, John H. Holloway Jr., Proc. of SPIE Vol. 8357, 835716

© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.918547

Proc. of SPIE Vol. 8357 835716-1

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using vehicles or dismounted soldier equipped with ‘mine’ detectors.[3] In Table 1 technologies are listed that have beentried in humanitarian demining and are discussed in the RAND report.

Table 1 Landmine detection technologies.[1]

Technology Operating Principle

Electromagnetic induction Induces electric currents in metal components of mine

Ground-penetrating radar Reflects radio waves off mine/soil interface

Electrical impedance tomography Determines electrical conductivity distribution

X-ray backscatter Images buried objects with x rays

Infrared/hyperspectral Assesses temperature, light reflectance differences

Acoustic/Seismic Reflects sound or seismic waves off mines

Biological (dogs, bees, bacteria) Living organisms detect explosive vapours

Fluorescent Measures changes in polymer fluorescence in presence of explosive vapours

Electrochemical Measures changes in polymer electrical resistance upon exposure to explosivevapours

Piezoelectric Measures shift in resonant frequency of various materials upon exposure toexplosive vapours

Spectroscopic Analyzes spectral response of sample

Nuclear quadrupole resonance Induces radio frequency pulse that causes the chemical bonds in explosives toresonate

Neutron Induces radiation emissions from the atomic nuclei in explosives

Advanced Prodders/ Probes Provide feedback about nature of probed object and amount of force applied by probe

Technologies that were investigated for landmine detection are now being considered for IED detection. Of particularinterest for this paper is the technology of X-ray backscatter imaging. Previous results from humanitarian demining givea good indication of the ground penetration and system aspects of the technique.

The X-ray backscatter imaging technology was chosen for further analysis since it has been successful in scanningvehicles for IEDs and is a technology that has not been extensively investigated for detection of buried objects. In thenext section previous results from humanitarian demining will be discussed and analysis and simulation results will be

presented to assess the potential of X-ray backscatter imaging.

It must be stressed that there is the potential of change detection in IED detection which is not present (or less valuable)in humanitarian demining. Change detection is a sensor-data processing technique in which sensor data taken at differenttimes are being compared. Time differences are typically hours, days or weeks. Detection of IEDs is based on difference

between sensor data at the location where the IED is buried (or placed). For some technologies, the clutter that causes ahigh false alarm rate has not changed during the observation period and will not show up in change detection. Note thatthis false alarm rate has been a limiting factor for many detection technologies.

The attractive technique of change detection is less feasible in humanitarian landmine detection since this is done longafter the placement of the mine. Change-detection is currently investigated for camera systems mounted on roadvehicles. A similar technique could be used for the X-ray backscatter imaging that is studied in this paper. However, thiswill not be presented here since it is outside the scope of this paper. This is based on the fact that clutter reduction due tochange-detection is not easily studied through simulation, because the clutter properties are not very well known.



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3. X-RAY BACKSCATTER IMAGING

3.1 Principle of X-ray backscatter imaging (XBI)

X-ray backscatter imaging has been used in the inspection of sea containers, vehicles, luggage and sometimes people.[4] Backscatter imaging compared to the more traditional x-ray transmission imaging offers the advantage of having bothsource and detection devices on one side of the target object. This is of course invaluable in the detection of buried IEDs.

Figure 1 shows the principle of X-ray imaging. An image is formed by scanning an X-ray beam in two directions, just asin a cathode-ray tube for television. In most implementations, one scanning direction is based on a rotating chopperwheel while the other scanning direction is due to the perpendicular movement of the object with respect to the scanner.Size of the backscatter detector will be as large as possible, to collect as many scattered photons as possible. Note that

backscattered photons travel in all directions. The size of the transmission detector determines the field of view.

Figure 1 Principle of X-ray backscatter and transmission imaging.[4] Image is courtesy of AS&E.

For the imaging of containers, vehicles and luggage, the XBI technique gives satisfactory results. Figure 2 shows anillustrative XBI image of a vehicle that shows suspect parcels in the vehicle. A favorable property of XBI is thatsubstances with a low atomic number show up very clearly while the metal container having a high atomic number has alower backscatter. This means that XBI is an excellent technique for inspecting vehicles that may have hiddencontraband or IEDs. For NATO operations in Afghanistan, a number of XBI systems have been installed for this

purpose.



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Figure 2 Illustrative X-ray backscatter image.[4]

3.2

Use of XBI in landmine detection

In the Rand report on landmine detection,[1] there are two papers on XBI. The first paper (appendix L) of L. Grodzinsfrom the company AS&E deals mostly with potential approaches to address the specific problems in detection of buriedlandmines. It is more or less a research proposal for a technology demonstrator. The second paper (appendix M) ofA. Jacobs and E. Dugan from the University of Florida deals almost exclusively with research from the University ofFlorida during the period 1996-2002. An interesting reference is to a 1975 US Army report on the theory of X-ray

backscatter for landmine detection.[5] Clearly, XBI has been seen as a potential solution for a long time.

In Europe there was a large research activity on Humanitarian Demining involving many national and EU projects. Therewas a considerable effort in Germany by the YXLON and Philips consortium that resulted in an XBI demonstrator.[7] EUDEM was one of the EU projects that collected information on the sensor technologies in a database.[2] This activityhas continued after the final report in 1999, but has now virtually stopped. In the EUDEM final report,[6] XBI is

mentioned on page 13:

“Backscattered radiation is detected during active illumination of the ground with X-rays, and basicallydetermines whether or not an object is made up predominantly of light chemical elements (i.e. low atomicnumber Z). The technique is intended for real-time detection of AT mines. The system is said to be able(Thomson-CSF Detexis in France) to produce a 2D image with a resolution of some cm. Potential

problems come from shallow penetration, system complexity, sensitivity to soil topography, sensor heightvariation, and safety aspects due to the use of ionising radiation. Outside Europe, research on the subjecthas been carried out during the last decade in particular by the University of Florida, mostly for defenceapplications. X-ray backscatter techniques are also used in geological studies.”

Activity on XBI has dropped considerably as far as this can be monitored from the number of research papers. There arestill some recent papers that deal with landmine and IED detection. Some recent articles are from Canada, [8] South-Korea,[9] USA,[10] and New Zealand[11].

The problem with XBI for landmine detection (or buried IEDs) were well summarized in the EUDEM final report:“Potential problems come from shallow penetration, system complexity, sensitivity to soil topography, sensor heightvariation, and safety aspects due to the use of ionizing radiation”. Results of the University of Florida in ref. [1] and [12]illustrate these problems quite well. Ref. [12] shows XBI images for a buried anti-personnel mine at a depth of 1 inch.However, the paper shows no results at greater depths than 2 inch. This is due to the attenuation of the X-ray beam in thesoil, which is the most fundamental problem of the technique. In the next section the theory of XBI will be treated withemphasis on understanding the penetration depth and potential solutions.



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3.3 Theory of XBI

The theory of x-ray scattering is well established. A website with the theory and an up-to-date database of scattering properties is maintained by NIST.[13] There are a number of scattering processes. The total cross section for all scattering processes can be written as the sum over contributions from the principal photon interactions:

where σ pe is the atomic photoeffect cross section, σ coh and σ incoh are the coherent (Rayleigh) and the incoherent (Compton)scattering cross sections, respectively, σ pair and σ trip are the cross sections for electron-positron production in the fields ofthe nucleus and of the atomic electrons, respectively, and σ ph.n. is the photonuclear cross section.

In order to obtain a good X-ray backscatter image of a buried object, the incoherent (Compton) scattering has todominate and the attenuation should be sufficiently low. The attenuation coefficient is simply proportional to scatteringcross section σ. Now it is possible to calculate the attenuation of soil. Fortunately, the attenuation only depends on theweight fractions of the elements not on the chemical compounds. It is only necessary to know the elemental compositionof the soil to determine the X-ray attenuation. Since the soil is mostly composed of SiO2, Al2O3, and FeO3,

[14] a weight percentage of the chemical elements can be established, see Table 2.

Table 2 General chemical composition of soil.

Chemical element O Si Al Fe H Mg Ca Na K

Weight fraction (%) 46.8 27.0 8.1 5.0 0.1 4.1 4.8 2.2 1.9

With the chemical composition of the soil, the X-ray attenuation coefficients for the various photon scattering processesin soil can be calculated using the NIST tabulated coefficients for the elements. Figure 3 shows the attenuationcoefficients as a function of photon energy. Please note that the incoherent scattering, which is the scattering used inXBI, is dominant for photon energies between 60 keV and 15 MeV.

Figure 3 Soil attenuation coefficients for the various photon scattering processes. The incoherent (Compton) scattering isindicated by an arrow. This scattering is dominant for photon energies between 100 keV and 10 MeV.

10-3

10-2

10-1

100

101

102

10-8

10-6

10-4

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100

102

104

Photon energy (MeV)

M a s s a t t e n u a t i o n c o e f f i c i e n t ( c m 2 / g )

Soil

Coherent Scatter

Incoher. Scatter

Photoel. Absorb.

Nuclear Pr. Prd.

Electron Pr. Prd.

Tot. w/ Coherent

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For the calculation of the penetration depth, the density of the soil is required. This density can vary due to the varyingwater content and particle size of the soil. In general soil density is between 1.1 and 1.6 g/cm3, which is between1.0 g/cm3 of water and 2.65 g/cm3 of solid quartz.[15] For the photon energy, the information in the paper of ref. [12] isused. Herein, an X-ray tube voltage of 160 kVp is used, which gives a maximum photon energy of 160 keV. However,an X-ray tube gives a continuous spectrum and it is more realistic to use an effective value of 100 keV for the photonenergy.[16] Using the mass attenuation coefficient of 0.18 cm2/g, which is given by Figure 3 at 100 keV with the soil

density of 1.5 g/cm3

, an attenuation of 0.27 cm-1

is obtained. Thus, the penetration depth, which is the reciprocal of theattenuation, is 3.7 cm. This is in agreement with the results of,[12] which show mine detections up to 5 cm (2 inches).

In order to increase the penetration depth, the photon energy can be increased. For instance, at a photon energy of400 keV, the attenuation coefficient is decreased by a factor two, thus increasing the penetration depth by the samefactor. However, the backward scattered energy is considerably reduced at high photon energies. According to the Klein-

Nishina function, the relative amount of backward scattered energy falls off with increasing photon energy.[17] TheKlein-Nishina function gives the differential cross section of X-ray incoherent scattering:

where E γ is the incident photon of energy, α is the fine structure constant, θ is the scattering angle, r c is the Comptonradius of the electron, and P ( E γ ,θ ) is the ratio of photon energy after and before the collision:

Figure 4 shows this effect by plotting the differential scattering cross section as a function of scattering angle in a radial plot (the left side is the back side). The cross section for backward scattering is much lower than for forward scatteringand this effect is more pronounced at 400 keV than at 100 keV.

Figure 4 Klein-Nishima scattering function for 100 keV (solid blue) and 400 keV (dashed red).

2e-030

4e-030

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was developed in-house. As in the section above, about 10000 photons are used in the simulation per pixel. These photons are scattered with a probability given by the scatter coefficient under an angle given by the Klein-Nishinafunction. A random generator is used to decide whether a photon is scattered and under which angle.

First, we simulate the XBI of soil without any buried object for the same conditions that were treated in the previoussection, i.e. a photon energy of 100 keV and a soil density of 1.5 g/cm3. Figure 6 shows the scattered photons as points intwo projections of the 3D-geometry. The x-ray beam was aimed at an angle of 45 deg. With a detector size of0.5 x 1.0 m, about 160 photons are detected by the detector with some variation due to the random nature of thescattering. Note that this is about 1.6% of the incident photons. Without the collimator, which is along the entire width ofdetector and extends from 20 cm to 10 cm above ground level, the number of detected photons is 420.

Figure 6 Scattered photons at 100 keV. Blue, green, and red dots show propagating, detected, and absorbed photons,respectively.

Figure 7 shows how deep the detected photons have penetrated the soil. It is clear that most photons come from shallowdepths. The penetration depth is about 5 cm in correspondence with the previous calculation of the attenuationcoefficient. In order to achieve a higher penetration depth we will use a higher photon energy.

Figure 7 Depth of scattering at a photon energy of 100 keV.

The next simulation is with a photon energy of 350 keV in the expectation to reach a higher penetration depth. Figure 8shows the scattered photons as points in two projections of the 3D-geometry. Note that at the end of the simulation, thereare still propagating photons in the soil. This is due to the low photo-electric absorption at 350 keV. At this photon

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energy, there is almost only incoherent scattering. This causes a deeper penetration of the soil. Figure 9 show themaximum depth the photons have reached after being scattered back to the detector. The penetration depth is now almost20 cm. There are also detected photons that have reached depths beyond 30 cm. It is also noteworthy that the number ofdetected photons have increased to about 460 compared to the 160 at 100 keV.

Figure 8 Scattered photons at 350 keV. Blue, green, and red dots show propagating, detected, and absorbed photons,respectively.

Figure 9 Depth of scattering at a photon energy of 350 keV.

It has been mentioned in the literature[1] that multiple scattering increases and becomes dominant at higher photonenergies. Figure 10 shows the number of scatter events that detected photons have experienced before being detected. Inthe histogram for a photon energy of 100 keV the single scatter event is still the most likely event (70 photons), though

multiple scattering amounts to half of the events. For a photon energy of 350 keV, multiple scattering is even moreimportant and the number scatter events has increased considerably. The complication of multiple scattering is that thedetected photon does not have to come directly from the material in the beam. The photon can be scattered outside the

beam and have a second (or more) scatter event before being detected. The horizontal resolution will suffer considerablydue to this effect.

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propagating

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Figure 10 Multiply scattering at 100 keV (left) and at 350 keV (right).

Since the increase of photon energy from 100 keV to 350 keV showed a considerably increase in penetration depth, it isworthwhile to consider an even larger photon energy. Figure 11 shows the simulation results for a photon energy of

1 MeV. The results are similar to those at 350 MeV. The number of detected photons is a little higher at around 600.Unfortunately, the penetration depth is only slightly higher for 1 MeV. An explanation for this small increase is thereduction of the photon energy by backward scattering. As was expressed by the Klein-Nishina function, the scattered

photon looses energy that depends on the scattering angle. Figure 12 shows that the photon energy at the detector is predominantly much lower that the initial photon energy of 1 MeV. This means that the advantage of a high initial photon energy is diminished in the multi-scatter situation that we have here.

Figure 11 Simulation results for a photon energy of 1 MeV.

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80Multiple scattering of detected photons

Number of scatter events per photon

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H e i g h t a b o v e

g r o u n d ( m )

propagating

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Figure 12 Photon energy at detector showing the loss of energy due to scattering.

Since the effect of a 1 MeV photon energy is very low, the following simulations will deal with a photon energy of350 keV. Note that 1 MeV sources are much harder technologically as well. In practice, the initial photon energies willfollow an energy distribution instead of a single value. However, this will be not be taken into account here.

3.5 Pressure-plate Simulation

For the pressure-plate simulation, a pressure plate will be simulated by a cavity. Since the pressure plate is of low densitymaterial (mostly wood) with an air gap this is a good approximation. This cavity will be in the form of a single layer with5 cm thickness or the cavity will have a size of 20 x 20 x 5 cm, with a thickness of 5 cm.

Table 3 shows the number of detected photons as a function of the cavity-layer depth in the columns on the left. Photonenergies are 350 keV for all simulations. Note that in this simulation a whole layer is used to simulate the pressure plate.In another simulation the finite size of the plate was taken into account. This is shown in the table by the columns on theright with a light grey background. All values were obtained by running the simulation 20 times with 10000 photons per

run. In this way the mean and the standard deviation of the number of detected photons was found. The table shows thatthe number of detected photons increases with shallower depth of the cavity. However, it will be hard to detect pressure-

plates buried deeper than 10 cm, since the number of detected photons is almost the same as without a cavity.

Table 3 Mean number and standard deviation of detected photons versus depth of cavity layer.

Single cavity layer Cavity of 20x20x5 cm

Layer depth (cm) Mean number

detected photons

Standard deviation Mean number

detected photons

Standard deviation

None 461 20

20 456 19 466 23

15 460 20 461 23

12 470 22 475 26

10 470 22 474 237 502 23 508 29

5 562 20 534 18

3 634 22 596 30

2 712 21 646 22

1 777 23 704 27

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

300

350Photon energy of detected photons

Photon energy (MeV)

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Figure 13 shows simulated X-ray images for various pressure-plate depths. The color scale is the same for all images andis chosen to see the noise in the image as well. Note that the signal is saturated for a shallow buried pressure plate (leftimage). These images correspond to a system with a scanning X-ray beam mounted on a driving vehicle. The X-ray

beam is scanned in one direction while the vehicle drives in the other direction. It can be noticed from the figure that it isvery hard to distinguish a pressure-plate buried at 10 cm depth from the background. Another striking feature is thatthere is not a strict cut-off at the edges of the pressure-plate. This is due to the multi-scatter problem at these high photon

energies. On the other hand this also means that the sampling can be coarse, which will result in a higher detection speedor driving speed.

Figure 13 Simulated X-ray backscatter images of a scanning beam mounted on a moving platform. Images have a pressure plate in the centre buried at depths of 1, 2, 3, 5, 7, and 10 cm.

The trajectories of the detected photons from impact at the origin to detection at the detector surface are shown in Figure14. This simulation was done without a cavity to show the inherent scattering of the soil. Scatter events are indicated bya dot on the trajectory. It is clear from the trajectories that the photons have a wide distribution in the soil which results

in a reduced imaging resolution.

Figure 14 Photon trajectories showing multiple scattering with a spiral indicating the origin and surface. Left figure showsthe histogram of scatter events of the 48 detected photons.

Width (m)

D i s t a n c e ( m )

Depth 1 cm

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3.6

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Table 4 Differences in the simulations of AS&E and NC3A.

AS&E simulation NC3A simulation

photoelectric absorption, Compton scatter, Rayleigh scatter, pair production

photoelectric absorption, Compton scatter

6mm x 6mm image pixels pencil beam, sampling 5 cmX-ray Bremstrahlung spectra generated with Be window

tubes at 225 and 350kV end-point energies

Monochromatic photons of 350 keV

25.000 or 100.000 photons in incident beam per image pixel 10.000 photons in incident beam per image pixel

The agreement of the AS&E and the NC3A simulations using different computer models and done independently giveconfidence that the simulated results will agree with actual performance in the field. The biggest drawback of thetechnique seems to be the limited penetration depth, which will restrict its detection potential to shallow buried pressure-

plates. Maximum detection depth of the pressure-plate seems to be around 5 cm.

4. CONCLUSIONS

A Monte Carlo simulation study was performed on the problem of pressure-plate detection with X-ray backscatter

imaging. The model was validated using results from previous landmine detection trials. Though only a superficialcomparison could be made with the experiments, the model is believed to be accurate enough. Here, it has to be realizedthat X-ray scattering has a well established theory which is also relatively simple with accurate physical parameters.

Simulated results of X-ray backscatter images from a buried pressure plate show that there is enough contrast fordetection at 5 cm but not at 10 cm depth. The resolution of these images is quite low due to the multiple scattering at350 keV. For pressure-plate detection, this is not a big drawback since these devices are relatively large. It also meansthat the scanning can be quite fast since the resolution doesn’t have to be very high. Increasing the photon energy doesnot improve the soil penetration due to the reduction of photon energy after scattering.

X-ray backscatter imaging seems to be a viable technique for detection of pressure-plates that are not buried too deep,i.e. around 5 cm. Scanning speeds will be in the wide range of 1 to 10 km/h mentioned in ref. [4]. Note that somewhathigher speeds may be achieved here since the intrinsic resolution is lower due to multiple scattering.

ACKNOWLEDGEMENTS

The authors had great benefit of the discussions with Joe Callerame and Peter Rothschild of American Science andEngineering (AS&E) and acknowledge the use of images from them. In addition, the authors thank AS&E for thefollow-on experiments that cannot be reported here due to classification reasons.

REFERENCES

[1] Macdonald, J., and Lockwood, J.R., “Alternatives for landmine detection”, 2003, Rand Corporation, USA.[2] EUDEM: The EU in humanitarian DEMining, http://www.eudem.vub.ac.be.[3] Center for Army Lessons Learned (CALL), “Handbook Route Clearance: Tactics, Techniques, and

Procedures”, Ft. Leavenworth, USA, April 2008. US Unclassified.[4]

Callerame, J., “X-ray backscatter imaging: photography through barriers”, Powder Diffraction, vol. 21,issue 2, p. 132.

[5] Roder, F.L., and Van Konyenburg, R.A., “Theory and application of X-ray and gamma-ray backscatter tolandmine detection”, Fort Belvoir, Va.: U.S. Army Mobility Equipment Research and Development Center,Report 2134, 1975.

[6] EUDEM: The EU in humanitarian DEMining, “Study on the State of the Art in the EU related to humanitariandemining technology, products and practice”, Final Report, 1999.

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[7] Niemann, W., Olesinski, S., Thiele, T., “Detection of buried landmines with X-ray backscatter technology”,Paper presented at the 8th ECNDT, Barcelona, June 2002. http://www.ndt.net/article/ecndt02/96/96.htm

[8] Faust, A.A., Rothschild, A.R., Leblanc, P., McFee , J., “Development of a coded aperture X-ray BackscatterImager for Explosive Device Detection”, IEEE Transactions on nuclear science, vol X, no X, 2005

[9] Yuk, S., Kim, K.H., Yi, Y., “Detection of buried landmine with X-ray backscatter technique”, 10th EuropeanSymposium on Semiconductor Detectors, 30 November 2006; Nuclear Instruments and Methods in Physics

Research, Volume 568, Issue 1[10] Gertsenshteyn, M, “Roadside Explosive Device X-Ray (REX)“, http://www.onr.navy.mil/en/Science-Technology/Departments

[11] Bartle, C.M., Kroger, C., Stephenson, W., and West, J.G., “ Advances of Industrial Dual Beam X-rayScanners and Improved Methods for Detection of Explosives and Humanitarian De-mining”, http://www-naweb.iaea.org/napc/physics/meetings/TM29225/prcdngs/papers/C-01.pdf

[12] Dugan, E., Jacobs, A., Su, Z., Houssay, L., and Ekdahl, D., “Detection of Land Mines Using Lateral MigrationX-ray Radiography”, Proceedings of SPIE 48th Annual Meeting, Symposium on Optical Science andTechnology, Penetrating Radiation Systems and Applications V, Vol. 5199, pp 1-11, San Diego, August, 2003

[13] Hubbell, J. H., and Seltzer, S. M., “Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances ofDosimetric Interest Ionizing Radiation Division”, Physics Laboratory, NIST, 2010,http://www.nist.gov/pml/data/xraycoef/index.cfm

[14]

Texas A&M University, http://organiclifestyles.tamu.edu/soil/index.html[15]

Hillel, D. (1982). “Introduction to soil physics” Academic Press, Inc. San Diego, California. See alsohttp://web.ead.anl.gov/resrad/datacoll/soildens.htm

[16] Boone, J.M. and Seibert, J.A., “An accurate method for computer-generating tungsten anode x-ray spectrafrom 30 to 140 kV”, Med. Phys. 24 (11), November 1997

[17] Klein, O and Nishina, Y, “Über die Streuung von Strahlung durch freie Elektronen nach der neuenrelativistischen Quantendynamik von Dirac”, Z. F. Phys. 52, 853 and 869, 1929.

[18] Su, Z., “Fundamental Analysis and Algorithms for Development of a Mobile Fast-Scan Lateral MigrationRadiography System”, Ph.D. dissertation, University of Florida, 2001.

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