Ke Chen and David CastañónECE Department, Boston University   {ck, dac}@bu.edu

X-ray Diffraction Tomographic Imaging and Reconstruction

Material discrimination based on conventionalor dual energy X‐ray computed tomography (CT)imaging can be ambiguous. X‐ray diffractionimaging (XDI) can be used to construct

MethodologiesAbstract Experiment and Results

detectors

XDI Imaging Modality

imaging (XDI) can be used to constructdiffraction profiles of objects, providing newmolecular signature information that can beused to characterize the presence of specificmaterials. Combining X‐ray CT and diffractionimaging can lead to enhanced detection andidentification of explosives in luggage screening.In this work we are investigating techniques for

A phantom with size 105×105 mm consisting of 5materials and air as background was centered at theorigin. A mono‐energetic X‐ray parallel beam of 60KeVwas used to probe the phantom. Given form factor

Phantom and synthetic diffraction profile priorsSingle‐energy source at λ

object

source

G

Schematic drawing of XDT system: left x-y plane, right y-z plane.

D

joint reconstruction of CT absorption and X‐raydiffraction profile images of objects to achieveimproved image quality and enhanced materialclassification. The initial results have beenvalidated via simulation of X‐ray absorption andcoherent scattering in 2 dimensions.

priors, diffraction patterns were simulated on adetector of size 100(height)×151(width) mm placed620 mm away from the origin. 90 projections werecollected for reconstruction.Filtered backprojection reconstructions weregenerated for different levels of additive noise undervarious Gaussian noise. Every pixel in thereconstructed fields was assigned to the class that

FBP reconstruction of diffraction profile at SNR=20dB.

Truth, q=0.5nm‐1                                            Noiseless, ∆=4.929e‐2

Filtered Backprojection (FBP) reconstruction

: incident x‐ray intensity;: attenuation along the incoming ray;: attenuation along the scattered ray;: form factor at                                               ;

geometrical efficiency factor. 

Measurement:

Backgroundreconstructed fields was assigned to the class thatminimizes the Euclidean distance from thereconstructed diffraction profile to the priors.

Simulated diffraction patterns at 45o

viewing angle.FBP R t ti t 0 5 1 t i i l l

SNR=30dB, ∆=6.093e‐2                       SNR=20dB,  ∆=1.274e‐1

X‐ray Diffraction ImagingX‐ray scattering types: coherent and incoherentXDI makes use of coherently scattered X‐ray to 

reconstruct the coherent‐scatter form factorXDI identifies material based on their molecular 

composition

Filtered Backprojection (FBP) reconstruction[2]

Assumption: • Collimator blades are used to restrict measurements to scattering perpendicular to excitation plane

• Attenuation along the path of scattered radiation isindependent of the scattering angle  

where

Algorithm:

Where                                                                ,         is a ramp filter     

• Develop fast algebraic reconstruction algorithm• Apply robust joint multi‐frequency inversion.techniques developed in [4] to XDT for 

d d

Future WorkDiscussion

FBP Reconstruction at q=0.5nm-1 at various noise level.composition   Form factor |F(q)|2

• expressed in transferred momentum  q that causes the deviation of photon of wavelength λby angle θ : q = λ‐1sin(θ/2) • reveal Bragg peaks for material discrimination The initial results are encouraging, but are limited

by the fidelity of the simulation model, which issimilar to the model used in the reconstructionXDI State‐of‐the‐Art[1]

improved reconstruction and recognition.• Extend the work for polychromatic X‐ray radiation with limited‐angles.

ReferencesAlgebraic reconstruction[3]

where y of size m is a stack of intensity measurements,  x is a stack of q‐images to be estimated, and A denotes the forward operator.

Algorithm: for the k‐th iteration updates with the

[1] G. Harding and et al., “Radiation source considerations relevant tonext‐generation x‐ray diffraction imaging for security screeningapplications”, Proc. SPIE, Vol. 7450, 2009.[2] U St d l d t l “A t ti l ith f h t

algorithm. We are exploring integration of higherfidelity X‐ray models based on Monte Carlotechniques. We also want to explore algorithmsthat avoid the independence assumption of thescattering paths, requiring algebraic inversion, andperform joint reconstruction and recognition.The resulting algorithms can lead to newgenerations of X‐ray diffraction imaging sensors that

• Direct imaging rather thantomographic

• Probe with polychromaticX‐ray radiation

• Measure coherent scattering with energy‐resolving detectors

• Require line collimators to localize scattering

Morpho XRD 3500TM

Algorithm:  for the k th iteration, updates with the relaxation parameter ρk as following

where ai denotes the i‐th row of A.      

[2] U. Stevandaal and et al., “A reconstruction algorithm for coherentscatter computed tomography based on filtered back‐projection”,Med.Phys., 30(9), pp. 2465—2474, 2003.[3] S. Schneider and et al., “Coherent Scatter Computed TomographyApplying a Fan‐Beam Geometry”, Proc. SPIE, Vol. 4320, pp. 754—763,2001.[4] K. Chen, D. Castañón, “Robust Multifrequency Inversion in TerahertzDiffraction Tomography”, to appear in SPIE Defense, Security, andSensing, April 2011.

generations of X‐ray diffraction imaging sensors thathave higher photon counts than current systems bycapturing additional scattering directions. Theapproach can be combined with multi‐energyillumination and photon counting detectors, as wellas advanced inversion techniques.

This material is based upon work supported by the U.S. Department of Homeland Security under Award Number 2008-ST-061-ED0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied of the U.S. Department of Homeland Security.

location under investigation• Often used as confirmation sensor for ambiguousregions in CT

• Can be slow