ARTICLE IN PRESS

Applied Radiation and Isotopes 67 (2009) 287–295

Contents lists available at ScienceDirect

Applied Radiation and Isotopes

0969-80

doi:10.1

Abbre

HME, H

Multi-fo

tramine

diffracti

journal homepage: www.elsevier.com/locate/apradiso

Conference

X-ray diffraction imaging—A multi-generational perspective

G. Harding

GE Security Germany GmbH, Heselstuecken 3, 22453 Hamburg, Germany

a r t i c l e i n f o

Article history:

Received 3 July 2008

Accepted 5 August 2008

Keywords:

X-ray diffraction imaging

Explosives detection

Narcotics detection

System generations

Throughput optimization

Parallelization

43/$ - see front matter

016/j.apradiso.2008.08.006

viations: CT, Computed tomography; EDS, E

ome-made explosive; HMX, Cyclotetramethy

cus X-ray source; MP, Massively-parallel; RD

; SNM, Special nuclear material; TATP, Tri-ace

on imaging; XRD, X-ray diffraction

a b s t r a c t

A brief description is given of some applications of X-ray diffraction imaging (XDI) in security screening,

including detection of narcotics and a wide range of explosives: organic (plastic) explosives, liquids,

home-made explosives (HMEs) and special nuclear materials (SNMs). A Bayesian formulation of the

‘‘rare event scenario’’ is presented, allowing the probability to be quantified that an unlikely threat is

indeed present when an uncertain detection system raises an alarm.

Granted the utility of X-ray diffraction (XRD) as a significant screening modality for false-alarm

resolution, the topic of its technological feasibility is addressed. It is shown that, in analogy to computed

tomography, XDI permits a significant reduction to be achieved in measurement time per object volume

element (voxel) compared with that of a classical X-ray diffractometer. This reduction can be

accomplished by designing the XDI system to record energy-dispersive XRD profiles from many volume

elements (object voxels) in parallel.

A general scheme for designing ‘‘massively-parallel’’ (MP) XDI systems is presented. XDI

configurations of the first generation (1 voxel s�1), second generation (100 voxels s�1) and third

generation (104 voxels s�1) are presented and discussed. Three alternative 3rd Generation XDI

geometries, namely: direct fan-beam; parallel (waterfall) beam; and inverse fan-beam are compared

with respect to technological realization. Directions for future development of XDI in screening

applications are outlined.

1. Introduction

X-ray diffraction imaging (XDI) is a novel modality thatsynthesizes two important characteristics of X-rays: namely theirability to form images (radiography) and their capacity to analyzematerial via the technique of X-ray diffraction (XRD) (Harding andHarding, 2007). The main application of XDI up to now is thematerial-specific screening of air passenger luggage for explosivesand narcotics. XDI is establishing itself for baggage inspection,combining high detection rate with low-false-alarm rate.

A commercial XDI device for security screening and narcoticsdetection, the GE XRD 3500TM, is illustrated in Fig. 1. It measuresdiffraction profiles of the material in many volume elements(voxels) of the object under investigation. Examples of thediffraction profiles for various substances of interest will be givenin Section 2 and the principle of operation will be described inSection 4.

First impressions are important and this device is impressiveon account of its sheer bulk. It is based on a design originating in

xplosives detection system;

lenetetranitramine; MFXS,

X, Cyclotrimethylenetrini-

tone tri-peroxide; XDI, X-ray

the late 1980s. Moreover the time taken to measure a completesuitcase is on the order of several tens of seconds. This articleconcerns the ‘‘parallelization potential’’ of XDI; meaning theextent to which it is possible to increase scan speed and reducebulk of the scanner by increasing the number of voxels whose XRDprofiles are measured in parallel. In this respect XDI is followingthe development of computed tomography (CT), for which it iscustomary to talk of first generation, second generation equip-ment, etc. The ultimate goal is the 4th Generation, correspondingto the current development status of CT, in which a full 3-Dvolume is simultaneously imaged.

2. Representative XDI results

2.1. Measurement conditions

The results presented in this section were obtained using theXDI device depicted in Fig. 1. It implements energy-dispersivedirect tomographic XRD as discussed in Section 4. The diffractionprofiles are plotted as a function of momentum transfer, x, asdefined in atomic units by the following equation:

x ¼sin ðy=2Þ

l(1)

ARTICLE IN PRESS

Fig. 1. Direct tomographic, energy-dispersive XDI system. Suitcase enters device at

right of figure where spatial landmarks for registration purposes are measured by

pre-scanner. In main housing centre-left of figure a primary cone-beam executes a

meander scan, either of a region-of-interest or suitcase in its entirety. Illustration

courtesy of GE Security GmbH, Germany.

0

400

800

1200

43210

Momentum transfer nm-1

Am

plitu

de

Fig. 2. X-ray diffraction (XRD) profile of TNT obtained from XDI device depicted in

Fig. 1.

0

1000

2000

3000

4000

0

Momentum nm-1

Am

plitu

de

1 2 3 4

Fig. 3. XRD profile of representative HME obtained from XDI device depicted in

Fig. 1.

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295288

The angle of scatter is y in the numerator and l is the photonwavelength. There are two fundamentally analogous ways ofprobing a crystal lattice by varying the momentum transfer. In thefirst (classical) case the photon wavelength, l, is held constant andthe angle of scatter, y, is varied (angular-dispersive). Alternativelyit is possible to hold y constant and to allow l to vary (energy-dispersive).

It transpires that, when measurement speed is a criticalrequirement, energy-dispersive XRD is the technique of choice.This conclusion is drawn both from the relative faintness ofmonochromatic relative to polychromatic (bremsstrahlung) X-raysources and also the high bandwidth of large-area, pixellatedenergy-sensitive detectors. The bandwidth is a measure of thecounting efficiency of the system and is defined as the product ofthe number of pixels into which the detector is segmented and thenumber of independent energy channels through which data canbe simultaneously acquired.

There are in principle four types of data processing correctionthat are applied to the raw data delivered by the detector (Hardingand Harding, 2007). First, scatter angle and photon energy arecombined using Eq. (1) to derive the momentum transfer. Second,an attenuation correction is performed, bearing in mind the lowangle of scatter, y�0.4 rad, to account for self-attenuation of theprimary and scattered X-ray beams by the object responsible forX-ray scattering. Third, a multiple scatter component is invariablypresent, owing to scattered photons that undergo successiveinteractions; and its magnitude is estimated and accounted for, ifnecessary. Finally, the XRD profiles are acquired under extremetime pressure and are consequently degraded by photon noise‘‘photon starvation’’. Thus some form of filtering (e.g. Wiener–Hopf) is applied to optimally extract the desired signal from thenoisy background. These corrections are described in more detailelsewhere (Harding and Harding, 2007).

Material identification of crystalline species is mainly per-formed from the knowledge of the peak positions in the XRDprofile. Bragg’s equation relates the momentum position, xp, atwhich X-rays constructively interfere to the interference order, n,and the lattice spacing, d

xp ¼n

2d(2)

The examples of XDI in security screening given in the nextsections are unashamedly curt; and their purpose is merely toconvey an impression of the breadth of applications in which XDIis establishing itself.

2.2. Organic explosives

The XRD profile of TNT, representative of many organicexplosives, such as Semtex, cyclotetramethylenetetranitramine(HMX), PETN etc. is shown in Fig. 2.

As indicated in Eq. (2) the Bragg peak positions are ofparticular significance for explosives detection as they are relatedto lattice spacings in the microcrystallites of which the substanceis composed. It is recalled that the momentum resolution, dx/x, ofthe XDI device used to make these measurements has the modestvalue of only a few percent. This value is a compromise among theconflicting factors of high scan speed and high resolution. Hencethe XRD peaks observed in Fig. 2 are in reality the superposition ofmany individual lines that are too close to be separately resolved.

2.3. Home-made explosives (HMEs)

In addition to the military and commercially-available ex-plosives that can be legitimately procured by authorized entities,there are several HMEs that are more or less easy to manufactureusing domestic facilities. These range from the ‘‘weed-killer andsugar’’ variety to the highly-explosive triacetone triperoxide(TATP) http://www.globalsecurity.org/military/systems/munitions/tatp.htm. The representative energy-dispersive XRD profile of aninfamous HME is shown in Fig. 3.

ARTICLE IN PRESS

Acetone

0

5

10

15

0.25

Momentum nm-1

Mo

lecu

lar

inte

rfere

nce f

un

cti

on

Position

Amplitude

Width

Gaussian fit

0.5 0.75 1 1.25 1.5 1.75 2 2.25

Fig. 4. Relative interference function of acetone. This function is derived by

normalizing the XRD profile against that of a calibration substance of known

composition and using the HETRA method Harding and Delfs (2007) to determine

effective atomic number. Physical parameters of use for identification purposes are

the peak position, shape, width and amplitude.

Table 1Crystal structures for all elements of the Periodic Table having density greater than

104 kg m�3

Metal Z Symbol Density kg m�3 Crystal structure

Molybdenum 42 Mo 10,280 Cubic (bcc)

Silver 47 Ag 10,490 Cubic (ccp)

Tantalum 73 Ta 16,650 Cubic (bcc)

Tungsten 74 W 19,250 Cubic (bcc)

Iridium 77 Ir 22,650 Cubic (ccp)

Platinum 78 Pt 21,090 Cubic (ccp)

Gold 79 Au 19,300 Cubic (ccp)

Lead 82 Pb 11,340 Cubic (ccp)

Uranium 92 U 19,050 Orthorhombic

Plutonium 94 Pu 19,816 Monoclinic

XRD-SNM at 1 MeV

0

3

6

9

12

9.006.003.000.00

Angle (mr)

Lin

e n

um

ber

uranium

lead (fcc)

Fig. 5. Angular positions in mr of first 12 Bragg peaks for uranium (circles) and

lead (trapezoids) at a photon energy of 1 MeV. The forbidden band around 3 mr, in

which lead (fcc) XRD lines are absent, is marked by a dashed rectangle.

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295 289

2.4. Liquids

It may come as some surprise to learn that XRD, conventionallyapplied to crystal structure determinations, also yields usefulinformation with which liquids may be characterized. The radialdistribution function, g(r), generally forms the starting point foranalysis of liquid structure. This describes the probability per unitvolume of finding a particle at distance r given a first particle atthe origin and is a statistical average over all the molecules ofwhich the liquid is composed. The function g(r) is zero at smallseparations, where Coulomb repulsion prevents particles closelyapproaching one another: each molecule excludes others from thespace it itself occupies. There is a radius, r, from the origin atwhich the probability of finding a neighboring atom is greatest,leading to a first peak in g(r). The radial distribution function ischaracterized at larger radii by exponentially-dampened oscilla-tions, before it asymptotically approaches a value of unity, whennormalized to the mean density.

As discussed by Hukins (1981), there is a Fourier transformrelationship between and g(r) and s(x), the molecular interferencefunction. This function can be derived from XRD liquid profiles;and the Fourier transform relationship between s(x) and g(r) maybe exploited to extract the latter from which, hopefully, meanmolecular separations, intermolecular potentials and the like maybe derived.

The relative interference function of acetone is depicted inFig. 4, which also indicates parameters of use for liquididentification.

2.5. Special nuclear material (SNM) lattice structures

Uranium and plutonium belong to the class of SNM, defined asthose that can undergo an uncontrolled fission reaction whenexposed to their own neutron flux. Significant amounts ofenriched uranium go missing from time to time; and this couldput a nuclear device or the components from which one could bemanufactured into unauthorized hands (Cameron, 1999).

Table 1 reproduces the densities and crystal structures of allelements of the Periodic Table whose density exceeds 104 kg m�3.The table is exclusively populated with metals; and the SNMs Uand Pu are listed in the final two rows. It is evident that thephysical densities of SNMs overlap with those of non-threatmetals; hence density is not a good feature for SNM detection. It

may possibly be surprising to discover from Table 1 that thecrystal structures of all non-threat elements are cubic.

The (10 0), (0 10) and (0 0 1) planes, which have identicallattice spacings, d, in cubic structures, have different spacings fororthorhombic and monoclinic crystals. Hence from Eq. (2) theirBragg peaks fall at non-equal x values i.e. they can be separatelyresolved.

2.5.1. Allowed SNM XRD lines

There are several conditions regarding the Miller indices, h, k

and l, that must be satisfied for constructive interference to occur.For face-centred cubic (fcc) this relation is that the h, k and l

values of a plane are either all even or all odd, but not mixed.Hence, for example, the allowed Miller indices for lead are: (111),(2 0 0), (2 2 0) etc. For a body-centred cubic structure such astungsten, the sum of h, k and l must be even leading to (110),(2 0 0) reflections etc. There are wide gaps in the XRD profiles ofcubic lattices that are devoid of allowed lines.

By contrast, the non-cubic structures of uranium and pluto-nium mean that their XRD profiles are much more denselypopulated with peaks than their cubic neighbors in the PeriodicTable, whether fcc (e.g. lead) or body-centred cubic (e.g. tungsten).

By way of example, Fig. 5 compares the angular positions of thefirst 12 XRD lines of lead with those of uranium for a photonenergy of 1 MeV (Harding, 2008). Granted the unquestioned

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G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295290

technical challenges of performing XRD at 1 MeV, it is apparentthat the broad momentum bands, from which XRD lines for cubiclattices are absent, do not exist for uranium and plutonium. Forthis reason XRD suggests itself as an active photon interrogationtechnique for SNMs.

2.5.2. Atomic form factors

The XRD line amplitudes of elemental, crystalline species aremodulated by the atomic form factor, F(x, Z); and their intensitiesare thus modulated by F2(x, Z). The atomic form factor at zeroabscissa, F(0, Z), is equal to the atomic number, Z. Hence, the XRDpatterns of SNMs, scaling approximately as Z2, are the mostintense of all elements of the Periodic Table. This scaling lawprovides a further reason for applying XRD to SNM detection:SNMs yield the strongest XRD signals of all the elements.

2.6. Narcotics

The term ‘‘narcoterrorism’’ is being increasingly used todecribe the engagement of terrorist organizations in drugtrafficking activity as a means of funding their operations. Forthis and other reasons the detection of narcotics in air passengerluggage is an important challenge. Fig. 6, of cocaine hydrochloride,illustrates the utility of XRD for narcotics screening.

Extensive trials of XDI for narcotics detection have beenconducted and have proved very successful, yielding a highdetection rate with low-false-alarm rate. As a consequence the GEXRD 3500 is now being deployed by a national customs authorityat a major international airport.

Cocaine

0

100

200

300

400

500

600

0.5

momentum (nm-1)

Am

plitu

de

1.5 2.5 3.5

Fig. 6. XRD profile of cocaine hydrochloride obtained from XDI device depicted in

Fig. 1.

Fig. 7. Graphical depiction of threat status. Left: initial (prior) neutral threat status. Cen

(2006).

3. False-alarm resolution and the ‘‘rare-event’’ scenario

At the heart of every explosives detection system (EDS) there isa ‘‘threat probability meter’’, registering the likelihood that a pieceof luggage actually contains threat material (Skatter, 2006). This isshown pictorially in Fig. 7: when the threat probability meterexceeds a threshold value (centre) an alarm is raised. Otherwisethe bag is cleared as innocuous.

Naturally, nobody is perfect and there is a finite probability, Pfa,that a ‘‘false alarm’’ is raised although in reality no threat ispresent. Similarly, the probability of detection, Pd, that a threatwhen present is detected, is less than unity. These two conditionalprobabilities can be written as

Pd ¼ PðAjTÞ; Pfa ¼ PðAjTÞ (3)

T and its negative represent the conditions that a threat ispresent and absent, respectively. Bayes’ equation can be used toreverse the order of the conditionalities and thus to answer thequestion: what is the probability, P(T|A), that a threat is actuallypresent when an alarm has been raised. It is

PðTjAÞ ¼PðAjTÞ � PðTÞ

PðAjTÞ � PðTÞ þ PðAjTÞ � PðTÞ(4)

P(T) is the likelihood that a threat will occur and is assessed, forexample, from previous experience. P(T̄)is simply unity minus P(T).

It is noteworthy that P(T) is generally very small in baggageinspection for explosives detection and it is common to refer tothis occurrence as a ‘‘rare-event scenario’’. An order of magnitudeassessment of P(T|A) can be derived from Eq. (4) when P(T)5P(T̄)and P(A|T)�1

PðTjAÞ �PðTÞ

PðAjTÞ(5)

Consider a (fictitious) situation in which P(T) ¼ 10�5 andPfa ¼ P(A|T) ¼ 10�1. Inserting for illustrative purposes these valuesinto Eq. (5) leads to the interesting conclusion that such an EDSwould incorrectly raise the alarm in 9999 times out of 10,000.

3.1. Economics of false-alarm resolution

The sobering conclusion of the previous section is that, in the‘‘rare-event scenario’’, an alarm situation is most likely much adoabout nothing. Unfortunately the alarm has nevertheless to betreated seriously. In the final instance and as a last resort a humaninspector will be called upon to open a suitcase in the so-called‘‘bomb room’’ and manually resolve the alarm. It has to bestressed that this is a very inconvenient, occasionally hazardousand above all costly procedure.

Calculations of false-alarm resolution in air passenger baggageinspection suggest that each percentage point reduction in the

tre: threat status in alarming range. Right: threat status in innocuous range Skatter

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G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295 291

false-alarm rate saves $25 million for the United States alone(Zarur, 2007).

The false-alarm rate is thus a very critical parameter indescribing an EDS. XDI plays a significant role in reducing thecost of false alarms, either in its use to resolve alarms raised byother types of sensors (e.g., CT) or on account of its inherentlylow-false-alarm rate, which is a product of its intrinsic, material-specific identification capability.

4. Massively-parallel XDI

The history of CT is interesting as it illustrates how a simpleprinciple, that of parallelization of the measurement data stream,can yield enormous gains. Whereas the prototype EMI CT scannerdallied around for over 5 min to perform a single-slice brain scan,its contemporaries can image 256 slices of the brain in less than asecond. Parallelization brings two benefits: it measures signalssimultaneously rather than sequentially; and it reduces or evenobviates the need for time-consuming mechanical movements.The degree of parallelization can thus be assessed either bycounting the number of data streams that are measuredsimultaneously; or by evaluating how many independent move-ment dimensions are required to perform a 3-D volume scan. It isthe latter measure that will be used in this article to compare thevarious generations of XDI.

4.1. Zeroth generation: classical X-ray diffractometer

The discussion of generationality starts with an evaluation ofthe classical X-ray diffractometer, illustrated in Fig. 8. X-ray sourceand detector are both mounted on arms, which rotate around thesystem axis on which the sample is located. Radiation from anelectron-impact X-ray source (often incorporating a Cu anode) ismonochromatized to allow only the Ka characteristic radiation(at 8 keV for Cu) to irradiate the sample. As discussed inconnection with Eq. (1) the momentum response of a crystallinespecies can be probed by allowing the angle of scatter to vary atconstant wavelength: the classical diffractometer thus imple-ments angular-dispersive XRD.

Fig. 8. Powder X-ray diffractometer of the y�2y type, showing sample holder

(centre), X-ray source mounted on rotatable arm (left) and radiation detector, also

mounted on rotatable arm (right). Image courtesy of GE Enterprise Solutions,

Ahrensburg, Germany.

The overall momentum resolution can be derived fromEq. (1) as

Dx

x¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidyy

� �2

þdll

� �2s

(6)

The second term in Eq. (6) is much smaller than the first,angular uncertainty term. The momentum resolution of the X-raydiffractometer displayed in Fig. 8 is typically 10�3 and the scantime for a complete XRD profile is typically 1000 s.

4.2. First generation: single-point tomographic XRD

A marked reduction in measurement time can be achievedwith the energy-dispersive XRD arrangement depicted in Fig. 9.

Polychromatic radiation from a conventional bremsstrahlungX-ray source at the left of the figure is collimated by mechanicalapertures to form a ‘‘pencil’’ beam of X-rays. An energy-resolvingdetector is arranged to record radiation deflected by the angle, y,from the primary beam. This detector is equipped with acollimator so that it only sees radiation scattered from a localizedvolume element (voxel) of the object under investigation. HenceXDI yields direct tomographic information without the need toreconstruct from projections. Energy analysis of the polychro-matic radiation at constant scatter angle incident on the scatterdetector yields an XRD profile (cf. Eq. (1)). Corrections forattenuation and the non-uniform X-ray source emission can beperformed by simultaneously measuring the transmitted beamthrough the object. A 2-D ‘‘image’’ of the XRD properties of thevoxels of which the object is composed can be acquired byscanning the object relative to the measurement system in themanner indicated by the scan pattern at the top of the figure.

The system illustrated in Fig. 9 reduces the mechanicalcomplexity of Fig. 8 by eliminating the need for source anddetector rotation (cf. Section 4.1). An alternative description isthat it realizes 1 dimension of parallelization, as the XRD profileis measured for many momentum values simultaneously. It iscapable of acquiring an XRD profile from a single voxel in �1 s.The momentum resolution is typically however a factor of 10poorer than that of the classical diffractometer.

4.3. Second generation: line-parallel XDI

A further increase in parallelization can be achieved with thesystem illustrated in Fig. 10.

The single scatter detector of Fig. 9 has been replaced by anarray of many detector elements, which record XRD profiles froma multiplicity of object voxels along the primary beam pathsimultaneously. It is no longer necessary to perform a 2-D rasterscan movement to obtain a 2-D image; a simple linear translationsuffices. For this reason the arrangement displayed in Fig. 10 isconsidered to belong to the 2nd generation. It is possible with thisconfiguration to measure XRD profiles from �100 voxels persecond.

radiation source

primary collimator transmission detector

scatter detector

raster scan movement

θ

sensitive voxel

Fig. 9. Schematic illustration of ‘‘single-point’’ tomographic energy-dispersive

XRD imager.

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radiation source

primary collimator transmission detector

scatter collimator

θ

linear scan movement

detector array

sensitive voxel

Fig. 10. Schematic illustration of ‘‘line-parallel’’ tomographic energy-dispersive XRD imager.

radiationsource

primary collimator

transmissiondetector row

scatter collimator

object

φ

h scatter detector array

zx

yP1 P2

Rd

Fig. 11. Illustration of 3rd generation, direct fan-beam XDI. Radiation emitted by

source located at origin of Cartesian coordinate system is formed into thin fan-

beam by primary collimator. Detector pixels have vertical coordinate (column) of h

and horizontal coordinate (row) of f. Radiation transmitted through object is

recorded in lowest row (h ¼ 0) of detector. For a primary ray of coordinate f,

scatter collimator passes only scatter rays with angular coordinates f and yrelative to XY scan plane.

vertex, O

cone angle, α

separation, Sx

x-ray sourcelets

φ max

symmetry axis

Fig. 12. Geometrical scheme for constructing energy-dispersive 3rd Generation

XDI systems.

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295292

The XDI system illustrated in Fig. 1 is in fact a member of the2nd Generation family and requires two orthogonal translationsto analyze a 3-D object. It may be thus be made simpler and fasterwhen a 3rd Generation design is adopted as detailed in the nextsection.

4.4. Third generation: area-parallel XDI

3rd Generation XDI is defined by the ability to analyzesimultaneously the local diffraction properties of a 2-D array ofvoxels without the need for mechanical movements.

4.4.1. Direct fan-beam

An example of a 3rd Generation XDI arrangement, in whichvoxels lying on a planar 2-D surface of the object are simulta-neously analyzed by a 2-D pixellated, energy-resolving detector ispresented in Fig. 11. The primary collimator forms from the X-raysource emission a well-collimated fan-beam in the XY plane. Thesecondary collimator has two sets of interlocking lamella. The firstset is oriented at the constant angle, y, to the XY plane. The secondset of lamella is vertical and they converge at the source focus. Thevertical lamella ensure that a certain detector column (constantf) is only able to ‘‘see’’ object voxels lying in a narrow strip ofangular width df around f. Referring again to Fig. 11, a primaryray at a certain f value is drawn through two points, P1 and P2.The scatter collimator ensures that only rays from these andinterposed voxels at constant angle may reach the detector. If theradius of the detector array referred to the source is denoted Rd,the XY coordinates of a voxel that scatters into a detector pixel

having coordinates (h, f) is

x ¼ Rd �h

tan y

� �� cos f;

y ¼ Rd �h

tan y

� �� sin f (7)

Although the arrangement illustrated in Fig. 11 is intuitivelysimple it is technologically very challenging. In particular thescatter collimator is an awesome construction when it is recalledthat its width in the Y dimension is necessarily over 1.5 m in orderto allow suitcases of 1 m width to be completely analyzed.Moreover the scatter detector is a major undertaking as it iscomposed of many hundreds of energy-resolving pixels formingan assembly of over 1.5 m width.

It transpires that innumerable variants for 3rd Generationenergy-dispersive XDI can be conceived (Harding, 2005). Briefly,they can be constructed (see Fig. 12) by taking an arbitrarysymmetry axis and locating a vertex point somewhere on it.A conical surface with origin at the vertex is created by rotating aline at some value of the semicone angle, a, around the symmetryaxis. Lines are drawn on the conical surface passing through thevertex and equally-spaced in azimuth around the cone. Theselines will eventually be elemental primary X-ray beam paths.Finally, the 2-D arrangement of Fig. 10 is replicated on each ofthese lines, with the plane of that drawing being normal to thesurface of the cone.

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Table 3Comparison of three variant 3rd Generation XDI geometries

Parameter Direct fan-beam Parallel beam Inverse fan-beam

Separation, Sx 0 N Rd

Angle, a 901 901 901

Multiplicity, M 102 102 10

Relative photon throughput per unit source power 102 1 10

Comments Highest degree of parallelity.

Technological challenge of large

secondary collimator and

detector array

Requires both extended

pixellated detector and also

large pixellated X-ray source

Requires large, pixellated X-ray

source. Can be combined with

multiple detector systems.

Table 2Illustration of 3 alternative area-parallel geometries

Direct fan-beam Parallel beam (‘‘waterfall’’) Inverse fan-beam

These analyze simultaneously the local diffraction properties of a 2-D array of voxels without the need for mechanical movements

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295 293

The 3rd Generation energy-dispersive XDI configurations socreated are characterized by three arbitrarily-chosen geometricalvariables: a cone angle, a, between the primary X-ray beam anda symmetry axis (the Z axis in Fig. 11); a separation, Sx,(not necessarily zero) of the X-ray source from the cone vertex;and an azimuthal range, fmax, around the base circumferencewithin which primary X-ray paths are permitted. If eachelemental primary beam is taken to have an azimuthal width,df, the increase in photon throughput of the 3rd Generation XDIarrangement in Fig. 12 relative to the ‘‘pencil beam’’ 2ndGeneration scheme shown in Fig. 10 is fmax/df. This ratio willbe termed the multiplicity factor, M, here.

Three variant 3rd Generation XDI configurations; namely theDirect fan-beam, the Parallel (waterfall) beam and the Inverse fan-beam are illustrated in Table 2.

It is conceptually trivial to increase photon throughput byincreasing the source power. In the Direct fan-beam arrangementeach elemental primary beam shares the same X-ray source. Thisis no longer true for the Parallel beam and Inverse fan-beamvariants, in which the multiplicity of sourcelets is bought at thecost of reducing the power of each one, when the total sourcepower is to be maintained constant.

4.4.2. Parallel beam XDI

The X-ray source is of pixellated design (see Section 4.4.3) in anelongated housing along the Y axis and comprises many individual

foci that can be switched on and off. The primary collimatorcomprises many parallel plates in the vertical (Z) direction. Thescatter collimator is of similar design to the Direct fan-beam,containing lamella angled at y to the XY plane, interlocked withlamella of identical pitch to the primary collimator and lying inparallel XZ planes.

The relative photon throughput of Parallel beam XDI in Table 3is seen to be unity: it exhibits no flux advantage over a 2ndGeneration system, as it makes no difference whether many faintsources are used or one bright one. It may nevertheless have aspeed advantage over 2nd Generation XDI owing to its avoidanceof a mechanical scan movement.

4.4.3. Inverse fan-beam configuration

The Inverse fan-beam arrangement locates the detector at thecone vertex (cf. Fig. 12) with the consequence that the detector ismuch more compact than in the Direct fan-beam and Parallelbeam configurations. As the X-ray source is large and the detectorsmall, in contrast to conventional direct X-ray imaging, thisgeometry is often referred to as inverse X-ray imaging. The X-raysource is of linear-segmented design, as demonstrated forexample in Fig. 13, and comprises many individually-addressableX-ray foci http://www.xinraysystems.com. This type of X-raysource will for convenience by termed a multi-focus X-ray source(MFXS) in this contribution.

ARTICLE IN PRESS

Fig. 13. Illustration of linearly-segmented multi-focus X-ray source (MFXS) http://

www.xinraysystems.com. Total length is approximately 500 mm and pitch of foci

is �10 mm. Each focus is individually activated by grid control voltages, which

either inhibit or allow electron beams from a multiplicity of cathodes, one per

focus, to reach the common anode, comprising an elongated block of tungsten.

1500

Secondarycollimator

Baggage tunnel

Primary collimator

MFXS XinRay

Conveyor belt

XY plane

Discrete x-rcoherent detector pos

650

Transmission detector array

Fig. 14. Schematic illustrations of checkpoint advanced diffraction imager. Left: proje

primary collimator simultaneously three focus points at the top of figure. System is supe

foci provides full coverage of object in baggage tunnel. Right: coherent X-ray scatter de

lamella. Secondary collimator is common to all scatter detectors. A transmission dete

projection directions from each active focus.

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295294

A 2-D XDI scan of an XY section through the object proceeds bysequentially activating foci along the length of the anode. Theprimary collimator transmits from each focus a narrow X-raybeam converging at the point, O. There is no mechanicalmovement involved as the X-ray sources are activated throughelectrical signals delivered to grids positioned in front of thecathodes.

The Inverse fan-beam approach is unique among thosediscussed here in avoiding the need to collimate the detector inthe f sense. This brings several advantages: it drastically reducesthe complexity of the secondary collimator; it increases thedetector solid angle relative to the Parallel beam design; and itenables multiple detector schemes, in which each X-ray beaminduces scatter into several detector systems in parallel.

For this reason the photon throughput per unit total X-raysource power, while not as high as that of the Direct fan-beam, isnevertheless an order of magnitude greater than the Parallel beamdesign. An additional technological reason favoring Inverse fan-beam relative to Direct fan-beam XDI is the increased DC powercapability of a 1-D MFXS, which distributes power over a largerstationary-anode area than is possible in a conventional singlefocus X-ray tube.

4.4.4. Design study for checkpoint advanced diffraction

imaging (ADI)

The considerations of the previous sections will be illustratedby a design study for a checkpoint XDI scanner based on theInverse fan-beam approach and illustrated in Fig. 14. This has thefollowing characteristics: it is compact, having overall dimensions

ay

n.

1500

500

Secondarycollimator

Baggage tunnel

Primary collimator

MFXS anode

Conveyorbelt

XZ plane

Coherent x-ray

detector

Transmission detector array

ction on XY plane; Right: XZ projection. Left: a linear MFXS irradiates through a

rposition of 3 Inverse fan-beam XDI configurations. Sequential activation of source

tector monitors radiation through secondary collimator comprising many parallel

ctor array uses a second beam line from MFXS to obtain transmission data from

ARTICLE IN PRESS

radiationsource

transmissiondetector row

scatter collimator

φ

zx

y

primary collimator

scatter detectorarray P

Fig. 15. Parallel multi-direct fan beam XDI. The point source of Fig. 11 is replaced

with a MFXS. Object movement in the Z direction of P, the pitch is required for

complete object coverage.

G. Harding / Applied Radiation and Isotopes 67 (2009) 287–295 295

of 750 mm (wide)�700 mm (deep)�1750 mm high. It is in-tended to permit a wide range of drugs and explosives to bedetected, including organics, HMEs and liquids, while at the sametime giving a visual image of threat items such as guns and knivesto the operator.

4.5. Fourth generation: volume-parallel XDI

Concepts for volume-parallel, 4th Generation XDI based on acone-beam X-ray geometry have so far faced an insurmountableobstacle: that it is not possible to design a detection scheme thatcan separate low-angle coherent scatter from the primary X-raysincident on the same detector. The best that can be done at themoment is the 3.5th Generation realized using a multiple surface-beam approach. An example of a parallel multi-direct fan-beamXDI system is shown in Fig. 15. All of the 3rd Generation variantscan be combined with one another to derive the 3.5th Generation.For a single X-ray source focus the results is a diverging multi-direct fan-beam. A linear-segmented MFXS allows parallel multi-direct fan-beams and diverging multi-direct fan-beams. A 2-Dpixellated MFXS opens up new possibilities, such as parallelmulti-parallel beams, parallel multi-inverse fan-beams etc.

The decisive advantage of 3.5th Generation XDI is thereduction in object translation required to achieve completecoverage in three spatial dimensions.

There is a legitimate question as to whether 3.5th GenerationXDI is economically worthwhile. Except in the case of thediverging multi-direct fan-beam the added parallelity is boughtat the cost of a proportional increase in X-ray tube power loading.There seems no gain in power loading to be achieved by a 2-Dpixellated to a 1-D MFXS. Hence it seems to make more economicsense at the present time to emphasize 3rd Generation XDI at hightube powers rather than invest in development of 3.5rd Genera-tion XDI.

5. Conclusions

X-ray diffraction imaging (XDI) is an exceptionally promisingtechnique for material-specific false-alarm resolution in rare-event

screening scenarios; permitting organic explosives, liquids, HMEs,SNMs and narcotics to be identified with high detection rate andlow-false-alarm rate Strecker et al. (1993). Contemporary 2ndGeneration (line-parallel) XDI screeners are however extremelybulky and suffer from long measurement times.

XDI is amenable to a large improvement in scan speed withconcomitant reduction in bulk by parallelizing the measurementprocess; in which data streams from many object voxels aresimultaneously measured. Parallelization also reduces the needfor mechanical scanning movements, thus reducing bulk and cost.Area-parallel 3rd Generation (Next generation) XDI, in which thelocal diffraction properties of a 2-D array of voxels are measuredwithout the need for mechanical movements, is a naturaldevelopment from contemporary 2nd Generation XDI. The Inversefan-beam geometry described here is technologically-feasible andcan be implemented using commercially-available detectors and a1inearly-segmented MFXS X-ray source.

In addition to the parallelization approach espoused here,future development of XDI will doubtless progress along twoparallel paths: on the one hand, further improvements to systemcomponents (sources, collimators and detectors) will be made toimprove XRD signal quality (SNR and momentum resolution); onthe other hand data processing procedures will continue to evolveto optimize detection rate and minimize false-alarm rate.

References

Cameron, Gavin, 1999. Nuclear Terrorism: A Threat Assessment for the 21stCentury. St. Martin’s Press, New York.

Harding, G., 2005. The design of direct tomographic, energy-dispersive X-raydiffraction imaging (XDI) systems. In: Proc SPIE 59230R.

Harding, G., 2008. Potential of x-ray diffraction for detecting Special NuclearMaterials (SNMs). accepted for publication. In: Larry A. Franks, Arnold Burger,Ralph B. James, H. Bradford Barber, F. Patrick Doty, Hans Roehrig (Eds.),Proceedings of the SPIE 7080, Hard X-Ray and Gamma-Ray Detector Physicsand Penetrating Radiation Systems IX.

Harding, G., Delfs, J., 2007. Liquids identification by X-ray diffraction. In: PatrickDoty, F., Bradford Barber, H., Hans Roehrig, (Eds.), Proceedings of the SPIE Vol.6707, Penetrating Radiation Systems and Applications VIII.

Harding, G., Harding, A., 2007. X-ray diffraction imaging. In: Yinon, J. (Ed.),Counterterrorist Detection Techniques of Explosives. Elsevier, London,pp. 119–235.

http://www.globalsecurity.org/military/systems/munitions/tatp.htm.The XinRay source is described on the website /www.xinraysystems.comS.Hukins, D.L., 1981. X-ray Diffraction from Ordered and Disordered Systems.

Pergamon, London.Skatter, S., 2006. Cooperating detection systems: a protocol for distributed sensor

fusion. In: Proceedings of the fourth International Aviation Security Technol-ogy Symposium. Washington: USA.

Strecker, H., Harding, G., Bomsdorf, H., Kanzenbach, J., Linde, R., Martens, G., 1993.Detection of explosives in airport baggage using coherent X-ray scatter. In:Harding, Lanza, Myers, Young, (Eds.), Proceedings of the SPIE 2092.pp. 399–410.

Zarur, G., 2007. Science and Technology Directorate of US Department of HomelandSecurity, private communication.

G. HardingGE Security Germany GmbH, Heselstuecken 3, 22453 Hamburg,

Germany

E-mail address: Geoffrey.Harding@ge.com