recent advances in x-ray microtomography applied to...

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Recent advances in X-ray microtomographyapplied to materials

S. R. Stock*

This review highlights recent advances in X-ray microcomputed tomography (microCT) as

applied to materials, specifically advances made since the first materials microCT review

appeared in International Materials Reviews.1 Improvements in instrumentation are covered, and

one focus is microCT using phase (as opposed to absorption) contrast. Instead of grouping

studies by disciplines, the reviewed reports are organised by type of application, specifically the

study of the spatial distribution of phases, of cellular solids (including static and temporally

evolving structures, fibrous network solids, mineralised tissues and biomedical applications), of

channel structures, of deformation, fatigue and fracture, of processing and of corrosion and

environmental interactions. Metrology applications are covered briefly, and several applications

where microCT is combined with position resolved X-ray scattering are described in more detail.

The accuracy of microCT reconstructions is discussed before data handling challenges are

outlined. The review closes with speculations on the future directions of materials microCT.

Keywords: Microtomography, X-ray imaging, Synchrotron radiation

IntroductionLess than a decade ago, microcomputed tomography ormicrotomography (microCT) of materials was reviewedin this journal by this author.1 A reader might ask why asecond review is needed so soon after the first. One findsan answer to such a reasonable question by consideringthe very rapid development of instrumentation and theconcomitant increase in accessibility (and in publicationrate) that have occurred since the mid 1990s.

Dedicated microCT instruments at the third genera-tion synchrotron X-radiation sources (e.g. APS, ESRFand SPring-8) and at other storage rings have multipliedopportunities for three-dimensional (3D) imaging at thehighest spatial resolution and contrast sensitivity, butdaily access is not an option. Multiple manufacturersnow offer affordable, turnkey microCT systems forroutine, day to day laboratory characterisation byscanning electron microscopy (SEM). Recently, com-mercial nanoCT systems (claimed spatial resolutionssubstantially below 1 mm) and in vivo microCT systems(for small animals) began to appear in researchlaboratories.

The increase in microCT papers since the firstInternational Materials Reviews (IMR) review1 amountsto an explosion. Quantifying the rate of increase inpublication of microCT papers is problematic becauseof artificial issues such as the division betweenmicroCT and conventional tomography (here the author

arbitrarily takes the same definition as in the first review,namely that microCT describes tomographic imagingwith y50 mm voxels, which is volume elements).Nonetheless, a feel for the increase can be gained byconsidering the SPIE conference series Developments inX-ray Tomography (1997, 1999, 2001, 2004 and 2006); itspans biology to engineering and its proceedings hasgrown from 266 to 340 to 374 to 802 to 682 pagesrespectively, which represents a saturation of thisparticular forum (limited to the papers that can bepresented in a 3 day symposium). The slight decrease inpages from 2004 to 2006 probably represents a decreasein frequency (3 year gap preceding 2004 and 2 year gappreceding 2006).

Some authors of microCT studies use synonyms(including microCT, X-ray tomographic microscopy,computerised microtomography, the recent nanoCT andeven just tomography) in describing their studies, andthis complicates the search for relevant papers. Further,the same class of structure, requiring similar analysistools, can occur in disciplines spanning the life sciencesto art conservation to the physical sciences and engineer-ing, and reports appear in a wide dispersion of journalsand conference proceedings. One example is cellularsolids with trabecular or spongy bone and bone growthscaffolds found in the biomedical literature and withmetal foams in engineering publications. These twofactors combine to hinder newcomers finding pre-vious paradigms on which to base their analyses andto produce examples of unneeded (except perhaps inan existential sense) sweat expenditure via wheelreinvention.

Considering the following experiment in locatingmicroCT papers relating to foams, a class of cellular

Department of Molecular Pharmacology and Biological Chemistry,Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

*Corresponding author, email [email protected]

� 2008 Institute of Materials, Minerals and Mining and ASM InternationalPublished by Maney for the Institute and ASM InternationalDOI 10.1179/174328008X277803 International Materials Reviews 2008 VOL 53 NO 3 129

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solids described in more detail below. Over the pastseveral years, the author desultorily collected ninepapers on microCT of cellular solids (excluding thoseon trabecular bone) without any particularly purposebeyond the possibility of writing this review. A literaturesearch in Compendex, a database for engineeringpapers, on ‘microCT and foam’, revealed one paper(one of the nine); on ‘microtomography and foam’produced 30 hits (three more of the nine) and on‘tomography and foam’ resulted in 139 hits (six of thenine). Separate searches on ‘cellular solid and tomo-graphy’ or ‘wood and tomography’ or ‘scaffolds andtomography’ would be required to reveal the other threepapers of the nine; note that the middle search yields 204hits most of which are irrelevant to microCT.

This review examines developments since the firstreview appeared in this journal1 and except whereneeded for understanding the more recent developments,this earlier material will not be described again. To agreat extent, organisation of the papers in differenttopical areas is arbitrary. Further, many papers could bediscussed in more than one subsection. The readerfamiliar with some of the literature, might, therefore, besurprised at where a given paper appears. One hopesthat this reader will not be surprised by significantomissions in the literature reviewed.

Developments in instrumentation will be covered firstbecause these dictate what has been possible in theapplications that follow. The subsections of the instru-mentation section are listed at the start of that section.

MicroCT of the distribution of phases is the firstsubsection of the materials applications section. Cellularsolids such as foams and trabecular bone are coveredsecond because the analysis techniques extend thoseillustrated in the previous section. Channel structures,essentially the converse structure of foams (minorityphase being open space instead of solid like in foams),are considered after cellular solids. Cracks are often animportant feature in fatigue, deformation and fractureapplications, and, because measurement of quantitiessuch as the 3D spatial distribution of crack openings isnot dissimilar to what is required with channel struc-tures, these applications are summarised next. Defor-mation and crack opening/closing studies often requirerepeated imaging of the same specimen, and this threadis continued in subsections on processing and oncorrosion and other environmental interactions.

MicroCT’s use in metrology is covered in a separatesection following the materials applications section.Multimode studies (microCT plus another modalitysuch as X-ray microbeam diffraction mapping) arecovered in the next section. Accuracies of microCTreconstructions and of various measured quantities anddata handling challenges are discussed in separatesections. A prognosis for the future of microCT imagingof materials concludes the review.

InstrumentationThis section covers laboratory (absorption) microCTfirst with the primary emphasis on available commercialsystems and on promising new developments that have,for whatever reason, not appeared on the market. Thesecond subsection reviews synchrotron (absorption)microCT. Spatial resolutions substantially below 1 mmare the province of nanoCT, and, as the instrumentation

needed differs from that in the first two subsections,nanoCT is discussed in a separate, somewhat shortersubsection. Phase microCT, mainly performed withsynchrotron radiation, is the subject of the ratherlengthy (fourth) subsection. Fluorescence microCT andmicroCT employing X-ray scattering (small angle X-rayscattering, SAXS, and wide angle X-ray scattering,WAXS, or diffraction) are the subjects of the fifthsubsection; these two modalities are treated separatelybecause they require translate-rotate data collection anddifferent detector configurations. Alternative approachesto tomography are discussed next, and the section endswith a discussion of reconstruction improvements.

Before developments embodied in the current genera-tion of laboratory and synchrotron systems are dis-cussed, it is useful to reiterate the interplay between fieldof view (FOV), the number of detector elements and theminimum corresponding voxel (volume element) size(Fig. 1). Exact reconstruction requires the specimen toremain in the FOV for all rotations (i.e. FOV equals orexceeds the specimen diameter as in Fig. 1e); otherwise,difficult to predict errors will result from parts of thespecimen rotating into and out of the FOV (i.e. thesituation in Fig. 1a and b for points A and B). Ifthe specimen diameter is fov and the detector has Nelements, then the minimum voxel size containingphysical information is vox5fov/N (note that one canalways reconstruct with smaller voxels, but this is strictlya mathematical exercise). For a 5 mm diameter speci-men and a 1 K detector, reconstruction can be with5 mm voxels; recent literature reports increasing use of2 K detectors which would result in 2?5 mm voxels of thesame specimen. At least one manufacturer of a com-mercial, tube based system offers a 4 K62 K detectorand capability to produce (8 K)2 voxel reconstructions.As a very rough estimate, spatial resolution is somewhatworse than twice the voxel size, but metrics such as themodulation transfer function are required for moreprecise discussion of resolution. Effects like penumbralblurring (finite X-ray source size) or optical andmechanical imperfections may degrade spatial resolutionbeyond what is expected from the voxel size.

Angular sampling is another important variable. TheNyquist limit2 defines the rotation increment consistentwith a given spatial sampling, i.e. voxel size. In (1 K)2

synchrotron microCT reconstructions, the authoremploys 0?25u angular steps over 180u (somewhat morethan 700 projections), and this appears adequate toproduce sharp reconstructions. When the size of thereconstruction is doubled to (2 K)2, the angular incre-ment is decreased to 0?125u. Sample geometry has animportant effect on the acceptable level of angularundersampling. For example, long, straight edges willcause worse streaking in the case of angular under-sampling than they would under conditions of adequatesampling.

The dynamic range within the projections is extremelyimportant in dictating the levels of contrast that can beretrieved reliably from reconstructions. The X-rayintensity flux through the specimen and the exposuretime determine the total number of X-ray photonsincident per image pixel and hence dictate the levels ofcontrast that will exist in a reconstructed slice providedthe detector is not saturated by light photons; thecondition for optimum contrast was discussed in the first

Stock Recent advances in X-ray microtomography applied to materials

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IMR review1 and is not repeated here. Not only dospecimen characteristics affect contrast sensitivity, butseveral instrument characteristics also have a role. Thenumber of light photons produced per transmitted X-ray photon (i.e. the fraction of X-ray photons absorbedby the scintillator and the output of light photons perabsorbed X-ray photon) is an important variable,especially given that detectors have limits to themaximum number of photons that can be collectedbefore saturation. Dynamic range in the projections(range of intensities from positions where the beammisses the sample to where the beam is most attenuatedby the specimen) also is constrained by the bit depth ofthe area detector used (a 12 bit detector allowsdifferentiation of 4096 levels; a 14 bit detector increasethis four times). Noise in reconstructions decreases(more precisely, the signal to noise ratio increases) withincreasing average counts in the projections, so use ofthe entire dynamic range of a 14 bit detector willimprove contrast (roughly) by a factor of 2 comparedto a 12 bit detector.2 Decreased noise in reconstructionscan be achieved by frame averaging if the incident beamis reasonably stable: one expects four frame averageswith a 12 bit detector to provide comparable signal tonoise ratios as are obtained with a 14 bit detector.Because reconstructions are invalid if the beam saturates

the detector at any position, incident beam inhomogene-ities produce decreased contrast in slices from thedimmer areas of the beam. It should be emphasisedthat noise is X-ray count limited and for the veryinefficient optical coupling, noise is at best limited by thedetector’s full well capacity (which in turn has fewercontrast levels than one thinks because of the largelyunexamined interplay between number of light photonsproduced per absorbed X-ray photon and the smallfraction of light photons collected by the optics).

There are some tricks that can be used to preservethe required voxel size for larger than ideal samplediameters. A rotation axis placed to one side of the FOVand 360u specimen rotation doubles the specimendiameter possible for a given voxel size (Fig. 1c and d);the author has used this successfully with synchrotronmicroCT, and some manufacturers use this in their fanbeam instruments. Local or region of interest (ROI)tomography is another approach (Fig. 1f), but discus-sion of these (to a greater or lesser extent) approximatereconstruction methods is postponed until the subsec-tion on alternative tomographic methods.

Laboratory (absorption) microCT systemsTurnkey systems with presets for voxel size can beobtained from a number of vendors. Table 1 is a recent

1 Field of view (FOV) and specimen diameter. The X-ray beam illuminates area shaded grey. a and b Points A and B

rotate into and out of FOV. c and d Illustration of how placing centre of rotation to one side of FOV and rotating

through 360u provides data missing in a and b. e Entire specimen diameter is within FOV, but smallest voxel size islimited by number of detector elements. Points C–E remain in FOV. f Local or region of interest tomography where

FOV is much smaller, points C and D remain in FOV while E moves in and out and only region within dotted line is

reconstructed. Here the voxel size (region diameter divided by number of detector elements) can be much smaller

than in e


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Table 1 Commercial laboratory (absorption) microCT systems with manufacturer’s listed voxel and reconstruction sizesas well as notes on specimen sizes: adapted from table compiled and copyrighted by Steven Cool, RadiationMonitoring Devices (used with permission) and supplemented by additional entries

Manufacturer Model (application) Reconstruction size, voxel Notes

BIR (BioImaging Research) MicroCT (specimens) ,50 mm; 10242 [a]Bioscan NanoSPECT/CT (in vivo animal) ,200 mm [b]Biospace c IMAGER-S-CT (small animal) 250 mm [c]Gamma Medica-Ideas X-O (small animal) To 43 mm; 5123–20483 [d]GE [e] EXplore Vista PET/CT (small animal) … …

EXplore Locus MicroCT (in vivo) 27, 45 or 90 mm isotropic [f]EXplore Locus SP MicroCT (specimen) To 8 mm isotropic … [g]EXplore Locus Ultra CT … [h]

Nittetsu Elex Ele Scan (specimen) … [i]Ele Scan Mini (specimen) … [j]

Phoenix X-ray Nanotom To 0.5 mm [k]v|tome|x| 240 To 4 mm [l]

Scanco Medical XtremeCT (human peripheral in vivo) 41–256 mm; 5123–30723 [m]vivaCT 40 (in vivo animal) 10–72 mm isotropic; to 20482 [n]MicroCT 80 (specimens) 10–74 mm isotropic; to 20482 [o]MicroCT 40 (specimens) 6–72 mm isotropic; to 20482 [p]MicroCT 20 (specimens) 8–34 mm isotropic; to 10242 [q]

Shimadzu SMX-225CT-SV3 (specimens) To 40962. [r]Siemens [q] Inveon Multimodality To 15 mm [s]

MicroCAT To 15 mm; to 40962 [t]Skyscan 1074 (portable) 22 mm; 5122 [u]

1076 (in vivo) ,9 mm isotropic, ,15 mm [v]1078 (ultrafast in vivo) 47 mm, 94 mm; (48 mm)3 [w]1172 (specimens) ,1 mm, 2 mm, 5 or 8 mm [x]1178 (high throughput, in vivo) 80, 160 mm; 10243 [y]2011 (nanotomography) 150, 250, 400 nm [z]

VAMP TomoScope 30 s (rapid examination) 80 mm [aa]Xradia MicroXCT 1–6 mm; 10242 [bb]

NanoXCT 50–70 nm; 10242 [cc]NanoXFi , 8 nm [dd]

XRT X-AMIN PCX … [ee]XuM ,100 nm [ff]

X-tek Benchtop CT 5 mm [gg]HMX(ST) CT Feature detection to 1 mm [hh]Venlo CT … [ii]

[a] Specimen diameter up to 25 mm, length up to 55 mm.[b] One, two or four SPECT detectors.[c] Maximum object size: 100 mm length, 90 mm diameter.[d] Maximum object size: 97 mm length, 93 mm diameter.[e] General Electric, previously enhanced vision systems.[f] Specimen diameter up to 85 mm.[g] Specimen diameter up to 40 mm. Cone beam system.[h] Diameter up to 140 mm, long axis up to 100 mm/rotation.[i] Examples of operating parameters given in user reports.340

[j] Diameter up to 45 mm, length to 50 mm.[k] Diameter up to 125 mm, length to 150 mm.[l] Diameter up to 500 mm, length to 600 mm. Other variants of this industrial system are available.[m] Diameter up to 125 mm, scan length up to 150 mm.[o] Diameters from 20 to 38 mm, scan length up to 145 mm.[p] Diameter up to 75?8 mm, scan length up to 120 mm. Cone beam system.[q] Diameter up to 36?9 mm, scan length up to 80 mm. Stacked (40) fan beam system.[r] Diameter up to 17?4 mm, scan length up to 50 mm. Fan beam system.[s] Diameter up to 140 mm.[t] Previously CTI and Imtek.[u] PET, SPECT, CT. Diameter to 100 mm.[v] Cone beam. SPECT option.[w] Diameter up to 68 mm, scan length up to 200 mm. Cone beam.[x] Diameter up to 16 mm. Cone beam.[y] Diameter up to 48 mm, scan length up to 140 mm. Cone beam.[z] Diameters 20/37 mm or 35/68 depending on version.[aa] Diameter up to 82 mm, scan length up to 210 mm.[bb] 0?5–1 mm for maximum resolution, 11 mm maximum diameter (9 mm voxels). Cone beam.[cc] Diameter up to 40 mm, axial length up to 37 mm. Cone beam.[dd] Diameters 0?5–12 mm; 16 slices.[ee] Phase imaging.[ff] SEM based instrument, phase and absorption imaging.[gg] Field of view (20 mm)2.[hh] Diameter up to 50 mm.[ii] Few details available online.



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compilation of vendors and their systems, a listing thatis almost certainly incomplete. Instruments range fromsingle fan beam to stacked fan beam to cone beamsystems,3–9 and manufacturers’ websites should beconsulted for specifics of their systems. Commerciallab microCT systems designed for studying specimenswith diameters y10 mm can be expected to producehighest resolutions with voxels between 1 and 10 mm insize. It is not uncommon for specimen diameters greaterthan 20 mm to be accommodated, although a moment’sreflection should make it clear that not all 20 mmdiameter specimens can be studied (e.g. beam penetra-tion is a problem for Ti samples). It is very difficult todiscuss data collection rates without going into con-siderable detail as data collection rates and reconstruc-tion times can vary widely for a single instrumentdepending on chosen operating conditions. Collection ofdata for 40 slices in 25 min is a reasonable order ofmagnitude figure for the highest sensitivity sampling (i.e.smallest voxel size with the largest integration time).Generally, reconstruction times for the highest resolu-tion/highest sensitivity settings are longer than the timerequired for data collection, but this depends onvariables such as computer architecture and number ofprocessors, and the resulting lag builds up considerablyfor large numbers of slices. Intermediate resolutions andsensitivities, therefore, are often used for large datasetsin order to increase throughput and also to decrease thehard drive space required to store the data.

In vivo microCT systems for imaging small animalshave been available commercially for several years,5,10

and the radiation doses received by the tissue beingimaged are surprisingly low. Other descriptions of invivo systems have also appeared.11–16 Somewhat lowerresolution clinical systems designed for imaging thehuman periphery (appendages), and hence constrainedby required dose limitation, are also to be found and aretermed peripheral quantitative CT (pQCT) systems.

The interplay of the different components of microCTsystems has been carefully considered by Davis andElliott.17–19 Cone beam systems are susceptible tocertain classes of artefacts, and Davis suggested thatimprove reconstructions would result by combining data(for the same specimen) collected with short and longsource specimen separations.20 Other systems’ develop-ment has also been described.21 A dedicated cryomicroCT system has been reported,22 and at least onemanufacturer’s system has been used in a subzero (C)environment. Because tube based microCT systemsoperate under conditions of photon starvation, there isconsiderable impetus to use X-ray optics to increaseX-ray intensity. One lab microCT system has beendeveloped that employs polycapillary X-ray focusingoptics to increase the flux passing through the specimenwithout increasing penumbral blurring.10,23 Gurkeret al.24 describe a system using bent multilayer opticsfor focusing; although the reported system is a pinholedesign (single channel detector in the translate rotategeometry), the authors indicate that the system can alsobe used in a fan beam geometry.

Before an experiment using lab microCT is designed,it is important to appreciate the interplay between thedifferent possible instrument settings and the micro-structure of interest. Turnkey systems might have presetsfor voxel sizes based on the specimen holder diameters

and for different sampling resolutions based on thenumber of projections collected. One instrument withwhich the author is familiar offers five diameterholders and three ‘resolution’ settings. An exampleof thorough characterisation of the dependence ofmorphometric indices (see cellular materials subsectionbelow) on scan parameters in one commercial systemappears elsewhere.25

Because lab microCT employs polychromatic radia-tion, one expects it to provide lower contrast thansynchrotron microCT with monochromatic radiation,and a simple example suffices to illustrate the magnitudeof the effect. Suppose X-rays with photon energiesbetween 15 and 20 keV comprise the beam used to studya specimen containing multiple (spatially resolvable)phases including Al. Because the mass attenuationcoefficients m/r of Al for this ranges of energies spans7?96–3?44 cm2 g21 respectively,26 this significant smear-ing of absorptivity makes it very difficult to distinguishdifferent phases, particularly in the presence of partialvolumes, i.e. voxels partially occupied by two or morephases. Some quantitative comparisons are possible ifone computes the effective energy of beam and com-pares the experimental linear attenuation coefficient(s)with the value(s) calculated for the phase(s) at theeffective X-ray energy (see Ref. 27 for an illustration).Another example is calibration for calcified tissue,described in Ref. 28.

Low contrast may be improved by infiltrating contrastagents into specimens (e.g. brominated silane in wood,29

iodine based solutions in microcracks in a polymericmatrix composite,30 and lead chromate based polymer inblood vessels31). Dual energy microCT has been appliedto analysis of several ZrO2/Al MMCP specimens, andthis approach enhanced the detectability of the particlesenough that quantitative analyses of void clustering, ofparticle clustering and of particle-void association infractured specimens could be performed.32

For someone new to microCT, it is a daunting task todecide which microCT system to purchase (the otheroption of build it yourself is inadvisable unlessmanufacturers do not provide the required capabilitiesoff the shelf and the builder has considerable experiencewith X-ray imaging and with instrumentation andsoftware development}. The recent paper by Schenaet al.33 discusses design considerations for a custom builtsystem, and Davis and Elliott34 discuss a new, custombuilt low noise, high definition system. As Table 1demonstrates, there are quite a number of choices, and itis unreasonable to expect any one instrument to be ableto do everything imaginable. The author would ask (andanswer) the following questions: what are the ranges ofsample diameters that it is essential to scan? What arethe elemental compositions of the specimens of interest,and will the X-ray beam penetrate the specimen? Whatare the minimum dimensions of the features that are tobe studied and what is their contrast? What specimenthroughput is required, and what analysis software isneeded? What computer platform is used? How doesdata archiving work? Once possible solutions areidentified from websites and literature, the best answersto the above questions will be found by contacting themanufacturer expressing interest in a specific system andarranging for them to scan several specimens embodyingthe applications for which the system is intended. A



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second important step is to use a candidate system inperson, either by visiting the manufacturer or the lab ofsomeone with the instrument being considered. Thismay be the only way to verify considerations such aswhether there is adequate space within the apparatus forin situ stages of various sorts. Friendliness of thesoftware is particularly important if multiple users willuse the apparatus.

Synchrotron (absorption) microCTReviews of microCT at a given synchrotron radiationsource appear periodically and typically update newcapabilities.35–62 Because the components required toperform microCT are readily available, many experi-mental stations occasionally perform microCT inresponse to their users’ requests. Results in the literatureincreasingly come from dedicated imaging/microCTbeamlines, not just because they award many moreshifts for microCT but also because the productionfacilities tailored to a small range of activities are muchmore efficient.

Synchrotron microCT (without lenses) is typicallyperformed with voxel sizes between 1 and 10 mm,although routine operation with voxels sizes below0?5 mm is possible at certain facilities and larger voxelsizes are used upon occasion at most facilities whenlarger specimen diameters dictate it. Design of microCTsystems is driven by the portfolio of specimen types thatare expected and the features within that need to beresolved. Available resources inevitably play a role insystem characteristics, and constant upgrade of cap-abilities is the rule at active synchrotron microCTfacilities. The systems of which the author is aware arehighly modular, and this allows incremental instrumen-tal improvements.

The typical synchrotron (absorption) microCT system(that uses the parallel beam directly without focusingoptics) is pretty much the same as was described in thefirst IMR review.1 The essentials are: specimen rotator,X-ray phosphor (single crystal or manufactured), opticallens and CCD detector. The available components haveimproved in capability and affordability, and it iscertainly worth a brief discussion of what has beenaccomplished.

Consider first the mechanical components and thephysical stability that is required for high qualityreconstructions. Voxel sizes down to 1–2 mm can beachieved with (relatively) affordable positioning andoptical components. Reconstructions with voxel sizesdown to 0?5 mm are not uncommon (and capabilitiesapparently exist for voxel sizes down to 0?3 mm), butrequired stability increases system cost considerably.The specimen rotator is the single mechanical motionduring data collection with the typical rotate onlysynchrotron microCT system. A rotator without wobble(unintended in plane and out of plane translations fromperfect circular paths) would be ideal, but measuring therotator’s imperfections and correcting for themimproves reconstruction quality considerably45,61 (seethe section on ‘Reconstruction improvements’).

X-ray detector systems in most synchrotron microCTinstruments consist of commercially available modules:thin single crystal phosphors, microscope objectivelenses and CCD or other area detectors for opticalwavelengths. Cadmium tungstate single crystal phos-phors precut and polished to the desired thickness are

widely used and are relatively inexpensive. These crystalsprovide light wavelengths with acceptable efficienciesfor CCD detectors; phosphor development continuesincluding materials formed through thin film processingroutes.50,63 Radiation damage dictates periodic replace-ment of phosphor crystals (and optical lenses if theyare in line with the direct beam or prisms if the opticallenses are placed off the beam axis). Most instrumentscan switch between several optical lenses for differentFOV and voxel sizes (Station 2BM of APS routinelyuses 61?25, 62?5, 64 and 65 objectives providingFOV of 5?4, 2?7, 1?7 and 1?36 mm respectively, whenused with a 1 K detector and twice these values whenused with a 2 K camera43); switches require adjustmentof lens focus and can be completed in a few minutes.Most area detectors are (1 K)2 or (2 K)2 scientific gradeCCDs with depths of 12 bits64; the specialised FReLoNdetector developed at ESRF provides (2 K)2 elementswith 14 bit depth51.

Significant advances in beam delivery optics includewide band pass monochromator systems based on multi-layers; these produce surprisingly uniform beams andincrease throughput dramatically compared to singlecrystal optics.65–67 The system with which the author isfamiliar is based on a pair of multilayer optics with areasof different layer spacings; tuning to different energies iscarried out by simple translation to the appropriatepositions on both optical elements.65 At ID 19 of ESRF,for example, multilayer optics provide DE/E,1022 andcorresponding increases in intensity compared to DE/E,1024 for an Si(111) double crystal monochromator.67

Decreased voxel sizes in synchrotron microCT aretypically achieved by increasing the magnification of theoptical lens coupling phosphor to area detector, butthere is a limit to what optical magnifications can beused. If the beam passing through the specimen is spreadbefore the phosphor, much smaller voxel sizes can result(at the cost of decreased FOV and increased datacollection times for a given brightness incident beam).Placing a perfect crystal in the beam transmittedthrough the specimen, orienting the crystal to diffractfrom a Bragg plane inclined with respect to the surface(angle of incidence less than the Bragg angle and exitangle greater than the Bragg angle) and using thisdiffracted beam for the reconstruction allows smallervoxel sizes for a given lens area detector combination.This magnification is only along one direction, and useof a second orthogonally oriented crystal is required tomagnify along the second direction. Asymmetric Braggmagnifiers have long been used in X-ray diffractiontopography (imaging of nearly perfect crystals usingdiffraction contrast),68 and Bragg magnifiers have beenused between specimen and phosphor in microCT.69,70

There has recently been renewed interest in thisapproach at the third generation synchrotron radiationsources,71–76 and some of these results are describedbelow in the section on nanoCT.

Various synchrotron microCT facilities emphasisedifferent scientific missions, time domains or spatialdomains. The author’s impressions of some of thesedifferences follow (with apologies for its incomplete,subjective nature). At DESY, the emphasis appears tobe on high energy microCT and interferometer basedphase imaging.48 The various facilities at ESRF appearto emphasise high spatial resolution, high temporal



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resolution and phase imaging with the propagationmethod: for example, polychromatic radiation from awiggler source can be used from near real time microCT,down to 10 s per set of projections for one reconstruc-tion.77 At SLS grating based phase imaging has receivedconsiderable emphasis. Reports from SPring-8 that havecome to the author’s attention are centred around highspatial resolution and on phase imaging with inter-ferometry. At APS, GSE-CARS focuses on geologicalapplications including measurements at high pressure;78

station 2BM at APS emphasises rapid throughput (rapidreconstruction via a large dedicated computer cluster,robotic sample changer, facilities for remote access);time resolved microCT of evolution of fuel spray (5?1 mstemporal and 150 mm spatial resolution) has beenachieved using the pulsed nature of the storage ring.79

Absorption edge difference imaging can increasesensitivity to small concentrations of the element ofinterest and is absolutely straightforward at mostsynchrotron imaging beam lines. Applications includetransport in low porosity materials80 and in sands;81

mapping of flame retardants (Br and Sb) in polymers;82

mapping Cs adsorption on iron oxide hydroxideparticles;83 mapping new bone formation throughadministration of Pb or Sr labels.84 Tetrachloroethanewith 8 vol.-% iodobenzene was used in model studies oforganic, water immiscible phase distribution in porouswater filled materials.85,86 Multienergy data collectionand reconstruction algorithms have also received atten-tion for materials where there are no convenientabsorption edges.87

Sensitivity limits to contrast agents have beeninvestigated. Sensitivity to a fixed concentration of KIin water was clearly much better in a coarse sand (meanparticle diameter d5050?58 mm in a 6 mm diametersample) than in a fine sand (d5050?17 mm in a 1?5 mmdiameter sample) because the larger photon flux in theformer produces a much higher signal to noise ratio;81

this example is particularly compelling because thespecimens are self-similar, that is, the relative sizes ofpore and particle do not vary.

Synchrotron microCT data from sources such as APS,ESRF, SLS and SPring-8 seem to invariably have astrong component of phase contrast in the reconstruc-tions. Sometimes this can lead to anomalously largevalues of the linear attenuation coefficient in positionswithin a specimen that are not easily recognisable asbeing near surfaces. In one study,88 such unexpectedcontrast (Fig. 2) was not recognised until later.89 Thiseffect may or may not be responsible for contrastinterpreted as solute segregation (e.g. high local Znconcentration in an Al engineering alloy90). Con-siderable care must be taken, therefore, in the inter-pretation of voxel values in synchrotron microCT. Insituations like those mentioned above, viewing a moviepaging through a stack of slices can be very helpful.

NanoCTCommercial nanoCT systems are listed in Table 1;commercial desktop systems have been described inliterature.91,92 Manufacturers report voxel sizes to100 nm and perhaps smaller; concomitantly smallerspecimen diameters than in microCT are required.Scanning electron microscopes (SEMs) possesses manyof the attributes required for nanoCT of small speci-mens, and several groups have modified SEMs for this

purpose.93–95 They produce very small diameter electronbeams, i.e. a very tiny X-ray source, essential forminimising penumbral blurring and for high spatialcoherence for phase imaging.

Synchrotron nanoCT reconstructions have beenreported using optics to provide submicrometre resolu-tion (parabolic X-ray focusing lenses, asymmetric crystalmagnifiers and Fresnel zone plates). The nanoCT systemproduced by X-radia employs Fresnel zone plates, forexample, as well as image registration software tocorrect for wobble and displacement during specimenrotation. A recent study by Bay96 illustrates use ofFresnel zone plate optics to approach 100 nm spatialresolution. Nanoplates of c-Ag2Al with different {111}habit planes were clearly resolved in the age hardeningAl–Ag alloy. The reader interested in more details isdirected elsewhere.37,72,74,75,97–107

Phase contrast microCTThe first IMR review1 mentioned microCT using phasecontrast as a future prospect, and considerable progresshas resulted during the intervening years. As theemphasis of this review is materials applications, neitherthe fundamentals of phase contrast nor the esoterica ofthe different phase imaging approaches are coveredexcept as needed to illustrate the applications. Technicaldevelopments have centred in Europe (Cloetens and co-workers at ESRF ID-19, workers at the Swiss Light

2 Anomalous values of linear attenuation coefficient

seen at internal interfaces in synchrotron microCT

reconstructions. (Top) Slice through tooth of sea

urchin Lytechinus variegatus. 14 keV, 1 K61 K recon-struction with 1?7 mm voxels. (Bottom) Histogram of

linear attenuation coefficients from area shown in box

in the slice. Values greater than 40 cm21 result from

phase contrast effects, in particular from surfaces just

above or just below slice. Reproduced from Ref. 89.

Copyright Elsevier Inc., 2003



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Source and others), in the USA (Chapman andco-workers among others), in Japan (Momose andco-workers and others), in Australia (Wilkinsand co-workers and others) and elsewhere.

X-rays are ever so slightly refracted when passingthrough solids (indices of refraction differ from one by afew parts per million), enough so that X-ray wavefrontsdistort when passing through regions of differentelectron density (see Ref. 108 for an introduction).With a suitable X-ray source, i.e. one with adequatespatial coherence, it is possible to detect changes inphase related contrast resulting from X-rays traversingvolumes with different electron densities. Most fre-quently, phase imaging is performed at a synchrotronradiation source such as the Advanced Photon Source(APS); imaging can also be performed with X-ray tubesources.109

Figure 3110 illustrates four methods where phaseeffects are used to produce contrast in X-ray images.In the propagation method (Fig. 3a), the detector isplaced much farther away from the sample than isnormal for X-ray imaging (y1 m v. y1 cm); refractedX-rays ‘r’ diverge and interfere with other X-rays at thedetector plane producing detectable fringes in the imageat external and internal boundaries between materialswith different electron densities. Here contrast isprovided by differences in the second derivative of theX-ray phase.111–117 Images acquired at four or morespecimen detector separations (typically from 5 mm to1 m or more) are required to extract the phase infor-mation,118 and this method can be described as ananalogue of the focus variation method in transmissionelectron microscopy.114 In diffraction enhanced imaging(DEI, Fig. 3b), an analyser crystal is placed in the X-raybeam after the sample; images recorded with differentsettings of the analyser isolate changes in the phase angleand this method produces image contrast based onchanges in the first derivative of the X-ray phase.119,120

Essentially, the analyser selects only a small angularfraction of the refracted radiation. The grating enhancedimaging method (Fig. 3c) is analogous to DEI except

that contrast from changes in the first derivative ofphase is provided by translation of one analyser gratingrelative to a second instead of by rotation of the analysercrystal and its periodic array (the crystal lattice).53,121–125

Interferometry for phase imaging is illustrated in Fig. 3d(and in the first IMR review1). In the Bonse–Hartgeometry, a beam splitter ‘S’ produces a reference beamand an imaging beam, the mirror ‘M’ redirects thebeams together, the object is placed in one of the beamsexiting the mirror and the analyser ‘A’ recombines thereference and object modified beams.62,126–129 An alter-native is the shearing interferometer.130,131 Recently, thelimited FOV of interferometers from monolithic blocksof Si has recently been improved.132–134 Interferometersallow changes in the X-ray phase to be measureddirectly, not merely its derivatives.

At this point in the development of X-ray phaseimaging, relatively little comparison of the differentmodalities has appeared in literature. Kiss and co-workers135 discuss image contrast numerically forabsorption v. diffraction enhanced radiography. Pagotet al.136 compared radiography for phase propagationand diffraction enhanced imaging, but it is not clearhow their conclusions translate to microCT. Wernicket al.137–139 and Paganin et al.140 discuss differentrepresentations of phase imaging data, but notmicroCT data; and Mayo et al.141 examine theserepresentations in microCT reconstructions.

Grating based phase imaging provides an illuminatingillustration of how phase microCT techniques work.Consider first the situation where no specimen is presentand the spatially coherent X-ray beam passes throughphase grating G1, the lines of which show negligibleabsorption but substantial phase shift (Fig. 3c). Notethat grating G0 is typically present only with imagingwith an X-ray tube with large source size. Grating G1acts as a beam splitter, producing the two diffractedbeams used for image formation. Because the wave-length of the illuminating X-rays (y10210 m) is muchsmaller than the grating period (y1026 m), the anglebetween the two beams is so small that the beams

3 Methods of X-ray phase imaging. a Propagation method. Images with detector near sample are dominated by absorp-

tion contrast, but placing detector far from specimens allows refracted X-rays ‘r’ to interfere with transmitted X-rays

and to produce edge contrast. b Diffraction enhanced imaging (DEI). c Grating enhanced imaging. Grating G0 is not

required with synchrotron X-radiation but is needed to provide series of small virtual sources X-ray tube based ima-

ging. d Bonse–Hart interferometer for imaging. S, M and A are crystal beam splitters, mirror and analyser respec-

tively. Reproduced from Ref. 110



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overlap almost completely as they propagate away fromG1 and interfere. The interference pattern generatedcould be imaged directly with an X-ray detector placedan appropriate distance dg from G1 (see Refs. 121 and123 for the relationship of dg to X-ray wavelength l,periodicity and other characteristics of the grating), butlack of spatial resolution of the detector systems has ledto an alternative solution, use of an absorption gratingG2 positioned dg away from G1. The analyser grating G2acts as a transmission mask for the detector placedimmediately behind it and transforms the local inter-ference fringe position into signal intensity variation.Note that the gratings must be parallel.

Placing a specimen upstream of G1 produces localwavefront distortions W(x,y) and alters the interferencepattern. Phase imaging is performed by translating theanalyser grating G2 by small increments xg of the fringeperiodicity g and recording a radiograph at each posi-tion. Figure 4 shows images of polystyrene spheres fordifferent xg.

123 The signal intensity I(x,y) at each pixel(x,y) in the detector plane oscillates as a function of xg,and the phases Q(x,y) of the intensity oscillations in eachpixel are related to W(x,y) via

Q~(ldg=g2)LW=Lx

where g2 is the period of the absorption grating.123 The

phase profile of the object can be retrieved from Q(x,y)by simple one-dimensional integration (Fig. 4g). Radio-graphs at as few as three positions xg are needed toextract Q if one knows a priori that the intensity oscil-lation is sinusoidal, but the reconstructions123 wereobtained using eight phase steps per projection. Once theset of phase radiographs are obtained at different view-ing angles, a pure phase reconstruction can be computedusing the normal methods.

Synchrotron radiation is not essential for phasemicroCT.108 The X-ray source size provided by theelectron beam in an SEM provides adequate spatialcoherence for phase microCT,94 and modifying anSEM can be an effective way of studying small speci-mens. The fringe formation underlying the gratingmethod described in the previous paragraph is indepen-dent of X-ray wavelength, and, provided a grating G0 isused before the specimen (Fig. 4c) to provide a smallvirtual source size (more precisely, a set of independentsmall sources), a relatively high power X-ray tube andgratings can be used for phase microCT.109

In specimens such as foams where the majority ofvolume is air, the total phase shift across the speci-men varies relatively little, and holotomographic

4 Principle of phase stepping. a–d Interferograms of polystyrene spheres (100 and 200 mm diameter), taken at different

relative positions xg5x1, …, x4 of two interferometer gratings. e Intensity oscillation in two different detector pixels

i51, 2 as function of xg. For each pixel, oscillation phase Qi and average intensity ai over one grating period can be

determined. f Image of oscillation phase Q for all pixels. g Wavefront phase W retrieved from Q by integration. h

Image of averaged intensity a for all pixels, equivalent to non-interferometric image. Length of scale bar is 50 mm.

Reproduced with permission from Ref. 123



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reconstruction can utilise the absolute values of thephase. In solid cylindrical Al–Si specimens such as thatused by Cloetens et al. (y1?5 mm diameter), phaseshifts will vary over 200 radians at 18 keV,111 and thisdictates that the reconstructions employ the phasevariations with respect to the phase introduced by thehomogeneous matrix (i.e. the X-ray phase relative tothat of the matrix).

Cloetens et al.111 provide a clear illustration of dif-ferences in absorption and phase enhanced tomographyreconstructions produced with the propagation method.Figure 5 compares the same slice from an Al–Si speci-men (grains of Al embedded in a matrix of very fine Al–Si eutectic) obtained under three different imagingconditions. The radiographs for the first reconstructionwere absorption dominated (i.e. they were recorded witha very small specimen detector separation DS); theradiographs for the second with a single, large DS (edgeenhanced interface contrast) and the radiographs at fourDS were combined via the holotomography algorithm(see above) for the third. In Fig. 5a, absorption contrastdoes not allow one to distinguish the Al grains and Al–Si eutectic matrix. Edge enhancement allows the twophases to be seen clearly (Fig. 5b), but because theFresnel fringe intensity varies from position to position,segmentation of the grain and eutectic phases ischallenging. The reconstruction with variation in refrac-tive index decrement (Fig. 5c) clearly shows the differentmetallurgical phases whose difference in density is on theorder of 0?05 g cm23,111 and segmentation is quitestraightforward.

In interferometer based phase microCT, the spatialdistribution of polystyrene (PS) and poly(methyl metha-crylate) (PMMA) in a y50 vol.-% mixture wereimaged.142 The polymers are immiscible (althoughanalyses of the values of the refraction indices of bothphases suggest that immiscibility is not total) and form aphase separated system. The achieved contrast resolu-tion was, in terms of density resolution, ,4 mg cm23,clearly beyond what is obtainable with absorption basedmicroCT.

Phase based microCT has been used in a wide varietyof studies, descriptions of which are folded into thevarious subsections of materials applications. A fewexamples are mentioned here in closing the subsection,including damage in composites143,144 and structures in

biological specimens.126,145 Real time phase radio-graphy of insect respiration produced interesting newinsights,130 and phase microCT, providing the thirddimension, will undoubtedly prove very valuable.

X-ray microCT using signals other thanabsorption or phaseSignal variations other than changes in transmittedintensity can be used as the basis for microCT. Theprimary and secondary topics of this section arefluorescence microCT and SAXS microCT, and, as thesignals utilised might be unfamiliar to some readers, abrief introduction is provided before experimentalgeometries are discussed and examples of studies areapplied.

Several interactions can occur between a beam of X-rays and the atoms in the specimen through which thebeam passes. If the X-ray photon energy is high enough,atoms can fluoresce, emitting photons with energiescharacteristic of the electronic shell transition thatproduced the emitted photons. These characteristic X-rays have well defined energies, an energy sensitivedetector can measure the intensity of each characteristicpeak and this intensity can be converted to theconcentration of these atoms within the irradiatedvolume. Detection limits (atomic concentration) for X-ray fluorescence are much, much lower than for X-rayabsorption, and the elemental specificity is much, muchhigher for the former; these advantages continue to drivedevelopment of fluorescence microCT for applicationswhere small concentrations of elements need to bemapped.

X-rays can also be scattered by structures withelectron densities differing from their surroundings.Scattering from periodic arrays of atoms reinforcesintensity along certain directions in the wide angle X-rayscattering regime, and scattering from fibrils, particles,etc., can produce peaks in scattered intensity or othercharacteristic scattering profiles in the small angleregime. The larger the size or spacing of the scatterers,the smaller angle of the scattered intensity.

X-ray fluorescence occurs in all directions, and thetypical experimental set-up positions an energy sensitiveX-ray detector to one side of the specimen in order tocount the photons emitted from the irradiated volume(in the direction of the detector). Neither an area nor a

5 Matching slices of Al–Si alloy quenched from semisolid state using a absorption contrast (sample detector separation

DS57 mm), b phase (propagation) contrast (DS50?6 m) and c phase contrast (holotomography) with DS50?07, 0?2,

0?6 and 0?9 m. Horizontal field of view was y0?9 mm, and data were collected with 18 keV X-ray photons and recon-structed with effective voxel size of 1?9 mm. Reproduced from Ref. 111 with permission of Lavoisier



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ribbon like X-ray beam appears to be practical for use influorescence microCT due to the confounding cross-firefrom different ray paths through the specimen. Oneconsequence of sampling along only a single ray (i.e. ofusing a pencil beam) is that data collection rates arequite low. Quantification requires correction for absorp-tion of the emitted characteristic X-rays along the pathto the detector, and the reader is directed elsewhere formore details.146,147

An interesting option is to use a polycapillaryfocusing optic to localise fluorescence from a singleposition along the beam path. This appears to be aviable option for 3D mapping, an option that does notrequire sample rotation to provide a complete map ofelemental distribution in a slice.148

Reports combining fluorescence and phase microCTin biomedical applications (organs labelled with iodinecontaining contrast agents) have appeared.149–151 Otherreports of element distributions in organs includeRef. 152. Elemental maps in slices of specimens of rootshave been published: K, Fe, Rb and Cl in maho-gany153,154 and K, Fe and Zn in tomato.35 Mapping insmall particles has been of interest, both for those ofterrestrial origin (fly ash particles,153 sediment parti-cles,155 and diatoms156) and extraterrestrial origin (Si,Ca, Fe and Cr maps in a microfragment of theTatahouine meteriorite;153,157 S, Ca, Cr, Mn, Fe, Ni,Cu and Zn maps in a cosmic dust particle;158 Fe and Nimaps in micrometeriorites159,160). Other studies includeFe nanocatalyst spatial distribution,161 trace elements ina SiC shell of a nuclear fuel particle,162 metal elementalmaps within inclusions in diamond and quartz148 andlight elements in biological specimen.148 Spectroscopyrelated to absorption edges has been used in chemicaltomographic mapping.163–166

Small angle X-ray scattering (SAXS) microCT is anideal approach for studying polymer texture: absorptionmicroCT shows no contrast but differences in SAXSwith position can be pronounced.167,168 The completeSAXS pattern must be recorded for a single ray throughthe specimen; there would be too much overlap betweenpatterns of adjacent rays if, for example, a ribbon beamwere used. In a y5 mm rod of warm drawn poly-ethylene (PE), different layers could be resolved withSAXS microCT (see the processing subsection for moredetails). Tomographic reconstructions of idealised speci-mens using diffracted intensity from different hkl (anddifferent phases) have also been reported.64,168

Alternative tomographic methodsRegion of interest (ROI) or local tomography is anapproach where portions of the specimen pass out of theFOV during rotation (Fig. 1f). The effect of the missingmass can be corrected by stitching together lowerresolution data for the missing areas of the project orusing known sample composition and geometry andcalculating corrected views.169,170 Uncorrected localtomography reconstructions are necessarily approxi-mate, but the extent to which their fidelity is degraded(geometry, linear attenuation coefficient values) dependson many factors. Errors will become more important asmore mass remains longer out of the FOV, and oneexpects a priori that specimens with anisotropic cross-sections will provide the greatest problems. In generalterms, the internal geometries in local reconstructionswill be reproduced with good fidelity, but if there is

significant mass outside of the FOV, dynamic range maybe suppressed and/or linear attenuation coefficientsaffected. For specimens with complex, highly anisotro-pic cross-sections or with high frequency, anisotropicinternal structure, it is essential to ascertain the extent ofartefacts.171

A number of groups/facilities routinely use localtomography. In a custom built lab microCT system,local tomographic reconstruction compared well withreconstruction with the complete FOV.9 Local tomo-graphy is routinely used at ESRF, so much so that it issometimes only mentioned in passing.172 Local tomo-graphy is particularly effective in specimens withrelatively low absorption such as foams; it has beenapplied to good effect to study deformation of an Alfoam.90

Partial view reconstruction, where an angular range ofprojections is unavailable, is related to local tomographyin the sense that information is missing. Interpolation ofthe missing views from the existing data seems toproduce tolerable reconstructions,173 but this sort ofapproximation should be avoided if at all possible. Ifonly one or two adjacent projections are interpolatedwithin an otherwise complete set of views spaced 0?25uapart, one will not normally be able to see an effect inthe reconstruction.

Laminography, also termed tomosynthesis, is analternative approach mentioned briefly in the firstIMR review,1 a method that is particularly valuablefor specimens whose aspect ratios are impractical forconventional microCT (e.g. plate like specimens).Recent digital methods have been reviewed,174 althoughfrom a clinical and not a microimaging perspective, andFig. 6 illustrates one method of determining 3D posi-tions from a series of views limited to one side of thespecimen. There is a cost in terms of degraded contrastby methods such as the shift and add algorithmillustrated in Fig. 6. Tomosynthesis has been appliedto microscopic imaging in recent studies of perfusion,175

of integrated circuits176 and of non-destructive evalua-tion (NDE) of long objects.177 In situations wheredisplacement of well defined features can be followedversus rotation, the relative translations of eachresolvable point can be converted in depth from one ofthe specimen surfaces. In this approach termed stereo-metry, use of 8–10 views allows a feature’s depth to bedetermined to higher precision than in simple two viewtriangulation; the 3D fatigue crack surface positionsdetermined with stereometry were in excellent agreementwith conventional microCT.178,179

Reconstruction improvementsReconstruction software must cope with various non-idealities intrinsic in the experimental apparatus and inthe X-ray sources and return the highest fidelityreconstructions practical. An ideal microCT apparatuswould have positioning component errors that arealways much smaller than the smallest informationcontaining voxel size specified in the system design. Thisideal system would employ a bright, highly stable X-raysource amenable to flat field correction. It is best tocollect the highest quality data consistent with the goalsof the imaging experiment and any practical constraintsdering the problem at hand. Software sometimes canameliorate the effects of instrument non-idealities and



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from less than optimum sampling dictated by experi-mental requirements.

In current generations of microCT systems (employ-ing ribbon or area beams), the only required specimenmotion is rotation (translation along the rotation axis inorder to enlarge the scanned volume does not affect thequality of reconstructions). Specimen wobble, describedin the following paragraph, and rotation axis misalign-ment, can be significant sources of error in reconstruc-tions. Reconstruction software typically uses each rowof detector pixels to reconstruct a single slice (note thatthis is not true of cone beam reconstruction). Tilt of therotation axis from perpendicular to detector rows bringsmaterial from adjacent slices into and out of the beamfor specific ranges of angles; this degrades the fidelity ofthe reconstruction. Such tilts are best avoided by verycareful alignment (note tilts of even 0?03u over 2 Kpixels can shift projected data to an adjacent row), butthis can be corrected by post-collection rotation of theprojection (and resampling of the pixels) to align therows precisely perpendicular to the actual rotation axis.Automatic routines for this geometric correction aredescribed elsewhere.180

Accurate reconstruction requires that the centre ofrotation be known very precisely, to within a fraction ofa voxel of that in the intended reconstruction. Brunettiand De Carlo181 reported on a recentring algorithm thatseems to work quite well. The approach is based on theform of artefacts from centring errors: tails of (apparent)mass extending from features like the corners of thespecimen. These tails increase the numbers of voxelswith non-zero values, and iterating through differenttrial centres for a representative slice of the volumeallows one to select the ‘best’ centre for reconstructingthe rest of the volume, even in the presence of beamfluctuations, noise and low contrast. Donath et al.182

developed metrics for optimisation of centre of rotationcorrections. The centre of rotation can also be refined byeye, but this is impractical when more than a fewspecimens are being imaged.

Ring artefacts, existing even when careful flat fieldrenormalisation has been performed, often pose pro-blems for accurate segmentation. Correction with a

median filter often does not work particularly well, anduse of a purpose built filter taking advantage of theconcentric nature of the rings seems to work well tominimise the rings.183 Ring reduction using 21 ptsmooth to the average of all rows of the sinogram (2Dplot showing transmitted intensity in the radiograph, forone slice, i.e. one row of the radiograph, as a function ofrotation angle) offers substantial improvement overuncorrected reconstructions:61 the actual high frequencycontent of the slices do not appear to be affected, onlythe rings. Sinogram correction algorithms for ringreduction have also been investigated for lab microCTdata.184 Ring artefacts can also be reduced by smalldisplacements of the detector during data collection.These and other artefacts in lab microCT reconstruc-tions have been recently discussed by Davis andElliott185 and in synchrotron microCT by Vidal et al.186

Sasov187 used data from narrow cone beam systemand compared slices reconstructed with a fan beamalgorithm, a cone beam algorithm and a spiral scanalgorithm. The quality of slices at the ends of the stackwas compared to that at the centre, and this studyshould be considered by those interested in differentstrategies for rapid data collection.

Materials applicationsMaterials applications continue to be quite varied, andmany of the studies reported below could be organizedinto a different collection of subsections. Most of theresults presented below were obtained with absorptionmicroCT, but results of phase microCT or othermodalities will be incorporated where they fit into thecoverage of different materials applications. Severalmaterials microCT reviews and perspectives haveappeared elsewhere,47,188–191 and these tend to havespecific geographic foci, by design, in addition tocovering a range of examples. Reviews of more interestto the biologist/bioengineer include Refs. 192–196.

The first subsection below is concerned with thespatial distribution of phases within specimens. Cellularsolids comprise the second topic reviewed; this ratherlong subsection includes engineering as well as biological

6 Illustration of tomosynthesis via add and shift method for parallel rays. (Left) Image positions of features (on planes

A and B) on detector plane are shown for source positions 1, 2 and 3 relative to object. (Right) Images shifted to

reinforce objects in plane A (star) or to reinforce those in plane B (circle). Features out of plane of interest are

smeared out across detector, and sharp images occur only for focal plane. In this illustration, amount of shift

depends on experimental quantities such as separation between specimen plane and detector and angle of incidence

of X-ray beam



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cellular materials and provides some background intoanalysis techniques. Channel structures are the thirdarea reviewed; these structures are complements ofcellular materials. In this and the second subsection,the materials scientist/engineer can learn much from thebiomedical microCT literature. In all fairness; biologistsalso have a lot to learn from the rigorous (quantitative)microstructural characterisation practiced by manymaterials scientists and engineers. Deformation, fractureand fatigue studies are covered in the fourth subsection.Materials processing is reviewed in the fifth subsection,and environmental interaction of materials is the subjectof the final subsection.

Distribution of phasesNote that this use of the word ‘phase’ does not describeX-ray phases employed in imaging but rather refers tohomogenous regions of matter bounded by a surfacemechanically separating it from other phases. Arelatively new application of lab microCT is evaluationof the spatial distribution of phases in pharmaceuticalmanufactured materials, that is, in solid dosage forms(tablets and soft gelatin capsules).197 Thicknesses andinterface character in multilayer tablets, microstructureof rapidly dissolving tablets produced by lyophilisation(ice crystallisation followed by drying) and particle sizeswithin controlled release osmotic tablets are importantcharacteristics directly measurable via microCT. Non-destructive microCT comparison of genuine and coun-terfeit tablets has the additional advantage of preservingthe evidence in patent litigation or other legal proceed-ings. Pores in pharmaceutical granules have also beenstudied with lab microCT.198 Magnetic particles arebeing investigated for controlled drug delivery, forexample, to tumours, and microCT has been used tomeasure these particles’ distribution in tissue of animalmodels.199

In one synchrotron microCT study, quartz, magnetiteand sanidine size distributions were measured in pumiceclasts (isolated crystals surrounded by a low densitymatrix);200 this investigation was undertaken to addresspossible limitations of earlier work on the same material.Previous characterisation used a crushingzsievingzwinnowing procedure to quantify the size distribu-tions,201 avoiding stereology’s well known limitationsin transforming 2D data into true measures of the 3Darrangements in the solid. Such processing, however,tends to cause significant loss of small crystals andfrequently fragments larger crystals. This latter artefactis especially significant in that it obscures characterisa-tion of fragmentation generated in magmatic processes.As the steps involved in the analysis of the microCT dataare characteristic of those often encountered in microCTstudies, they are described here in some detail.

In phase quantification studies, the first imageanalysis step (after reconstruction) is image classifica-tion, that is, assigning each voxel in the 3D volume to agiven phase. The second step is identifying individualgrains, i.e. clusters of voxels belonging to a single phaseparticle. In the study cited in the previous paragraph,200

contrast sensitivity (256 grey levels) was adequate toquantify the volumes and size distributions for particlesgreater than 5 voxels diameter in the Bishop Tuff pumiceclast; noise limited the investigators’ ability to reliablyidentify smaller particles. Nonetheless, Gualda andRivers200 found that the combination of contrast and

spatial information allowed distinction between quartzand sanidine, despite the fact that the distribution oflinear attenuation coefficients of the minority phase(sanidine) formed an indistinct shoulder of the quartzpeak. The microCT results agreed with earlier resultsfrom destructive analysis,201 namely, the distribution ofquartz particle sizes indicated action of magmatic frag-mentation processes but that of magnetite was largelyunaffected by the fragmentation process recorded byquartz. The trade-off between spatial resolution andcontrast sensitivity is clearly explained in Ref. 200 as itaffects these results, but the authors do not providedetails of the number of X-ray counts recorded in the262 binned detector pixels, and one is unable to assessthe numerical extent to which contrast for a given phaseis the spread because of counting statistics. It wouldhave been interesting if the investigators had investi-gated frame averaging for improving contrast sensitivityand increasing the small particle detection limit. Offurther interest in this carefully done study200 is thedocumentation of exceptional volumes that divergequite markedly from the rest of the sample: this simpleresult should serve as a caution to all investigators usingmicroCT of small sections derived from larger objects.

Bubble (vesicle) characteristics in basalts provideinsight into various processes in magma before, duringand after eruption; a distribution of bubble sizes, forexample, can be due to multiple or continuous nuclea-tion processes or differences in growth rates.Synchrotron microCT of five basalts from differentlocations showed bubbles were spheroidal, comprised45 vol.-% lavas to 80 vol.-% scoria and were at least90 vol.-% interconnected.202

The distribution of Cr particles in alumina, deter-mined via synchrotron microCT, was used as the inputfor a finite element calculation of residual stresses arisingduring cooling from the processing temperature(1450uC).203 Hydrostatic stresses were found in thealumina near the Cr particles. In a separate paper, theauthors compared calculations with actual residualstress measurements.204 Such residual stress measure-ments are readily performed with high energy synchro-tron X-radiation.205 Similar input was used for finiteelement modelling (FEM) of dynamic response ofporous (and epoxy infiltrated) shape memory alloyspecimens.206

Calculations of macroscopic properties have beenperformed using actual particle spatial and orientationdistributions were measured in an Al–20 vol.-%Al2O3composite. Finite element modelling (FEM) and meanfield and multiscale modelling were used to computevarious elastic properties, good agreement with experi-mental moduli measurements were obtained 207–209 andsomewhat larger fraction of particles fractured in theinterior of the specimen compared to a zone 2–3 particlediameters from the surface. Sanchez et al.210 quantifiedgraphite volume fraction in Al matrix composites andused the microCT determined spatial distribution ofgraphite to calculate flow of Al into the graphitepreform and to simulate the spatial distribution ofstrains from deformation of the solid composite. AsHeggli et al.211 discuss in conjunction with theirmicroCT data on a graphite/Al composite, accuratemodels depend on employing representative volumeelements that are sufficiently large to be representative



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of the material on a macroscopic scale (but are smallenough to be tractable numerically); and these authorsconcluded that reasonably accurate predictions ofresistivity could be obtained using ensemble averagingover a sufficient number of small models.

Radio-opaque polymers are desirable for dentalapplications; Anderson and co-workers212 employedlab microCT to show that barium methacrylate mono-mer did not blend well when diluted in methacrylate,whereas inhomogeneities could not be detected when tinmethacrylate was used. Microdiamond content and sizedistribution in kimberlite are important indicators ofthe likelihood of finding coarser valuable diamonds;microCT has been applied to the problem of quantifyingdiamond content of drill hole cores, as discussed in areport of tomography research at De Beers.213 Voiddistribution determination in HY-100 steel is one of thefew synchrotron microCT studies of very highlyattenuating material.214 Catalytic conversion of naturalgas to (clean) liquid fuels via Fe nanoparticles is ofinterest for lessening internal combustion related pollu-tion, and the spatial distribution of these nanoparticleshas been studied with fluorescence microCT.161

The distribution of different carbon based phases in acomposite was studied with phase microCT.215 Therefractive index decrements of resin, carbon fibres anddeposited carbon were clearly different and allowedclear segmentation of the different phases. Absorptioncontrast would have revealed only porosity.

Different biological tissue types can be regarded asphases in the materials sense, and the number of studiesemploying microCT of tissue specimens, scaffolds forimplants, etc., dwarfs those of engineering materials;needless to say, the budgets are correspondingly asym-metric. Mineralised tissues such as bone (apatite,calcium phosphate, plus collagen) or echinodermossicles (calcite and calcium carbonate) can take theform of a cellular solid (i.e. plates and struts surroundedby soft tissue). These studies, therefore, are reviewed inthe subsection of cellular solids. Likewise, studies ofblood vessel and airway networks are covered in thechannel structure subsection. MicroCT studies of densemineralised tissues (cortical bone and sea urchin teeth)are distributed within other subsections, but pathologi-cal calcifications have also been studied.178,216 Quanti-tative comparisons based on microCT data have shownstatistically significant differences between control anddisease affected tissue.217

MicroCT of soft tissue is mostly carried out withphase contrast in order to differentiate between differentsoft tissue types, although as recent data on braintissue218 and on fixed lung sections219 showed, this is notalways necessary for certain tissue types. Tumour tissuehas been well differentiated from healthy tissue,126,220–222

and different normal tissue structures (e.g. mammaryducts) can also be made out.223 An example where invivo absorption microCT was used to study soft tissuefeatures (lung tumours in a mouse model) is typical ofsuch studies: a priori information was necessary todifferentiate tumours from other features (large bloodvessels).224 Respiratory gating was used in this study ofthe accuracy of microCT characterisation, and furtherdetails are covered in the section on accuracy. Injectionof contrast agents that concentrate in the soft tissue typeof interest has been used to good effect to image murine

liver tumours, but success depends on adequate contrastenhancement,225 a process that may be difficult tocontrol.

Not all medical X-ray applications require full 3Dinformation, and considerations of dose limitation and/or specimen geometry often indictate that simple radio-graphy is required. It is worth a brief mention of the fewphase radiographic imaging studies, then, because thismodality may become more important clinically in thefuture. Digital phase mammography has received atten-tion because sensitivity per unit dose to tumour cells ortumour precursors such as microcalcifications is muchgreater than with conventional mammography.226–228

Diffraction enhanced radiography of cartilage in dis-articulated as well as in intact joints is quite promis-ing,229–232 although the technical challenges of coveringthe FOV for human joints such as the ankle areconsiderable.

Cellular solidsFollowing the definition of Gibson and Ashby,233 acellular solid consists of an interconnected network ofsolid struts (rods) or plates which form the edges andfaces of cells respectively. In other words, faces separatetwo cells, and edges, are common to three or moresubvolumes (cells) of the larger structure. The cells in thepresent context are, of course, different from the cellsone normally encounters in microbiology. In 3D, thecells are polyhedra filling space and such materials areoften termed foams. If the cells connect through openfaces (the only material being struts at the cells’ edges),the material is termed an open cell foam; if the faces aresolid, sealing off adjacent cells, it is a closed cell foam.Many cellular materials are produced by plants andanimals, including wood, cork and bone. Engineered (byhumans) cellular solids employ all classes of materialsincluding composites and are used for: thermal insula-tion, packaging (energy absorption), structures (for highspecific strengths), buoyancy (marine) and scaffoldingfor cell growth. The microstructural characteristics ofcellular solids are difficult to quantify except with non-invasive, 3D methods such as microCT. In what follows,for purposes of simplicity, the solid phase will bediscussed as if it occupies a relatively small fraction ofthe total volume.

As noted by Maire et al.,234 cellular solids are oftenvery challenging to analyse with tomographic techni-ques, particularly with respect to the different levelswithin the hierarchy of structural scales influencing thematerials performance, specifically the scale of theconstitutive material and the scale of cellular micro-structure. The interplay among voxel size, contrastsensitivity and FOV is particularly prominent inmaterials such as foams. If, on the one hand, thedistribution of cell sizes is important, then large voxelsizes may be required for the FOV to span the halfdozen or more cells required to represent the structureadequately, and an instrument optimised for theseparameters (perhaps an industrial or medical peripheralCT system) might prove more efficient than a microCTsystem. If, on the other hand, features within the cellwalls are of central importance, then microCT or evennanoCT on small sections of the material is required.Both scales sometimes can be studied productivelyon the same instrument, and several investigationshave employed either two extreme resolution/FOV



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combinations on a single instrument,235 two or moresystems236,237 or local tomography techniques.

A structure like a cellular solid, i.e. a complex mixtureof empty space and solid, requires several parameters inorder to describe its microstructure, specifically, howmuch material is present and how the material isdistributed spatially. These microstructural characteris-tics have largely been defined in studies of cancellousbone, and unbiased methods of measuring thesequantities are products of these studies.238 The amountof material is given by the volume fraction of solid VV;in bone quantification software bundled with commer-cial software systems and in some literature, this iswritten BV/TV (the ratio of bone volume to totalvolume). In certain applications, the mean cell size andthe distribution of cell sizes of a foam must be specifiedin order for macroscopic properties to be predicted. Alsoimportant is the 3D distribution of solid material, thecomponents of which can be in the form of plates andstruts (rods); these are characterised by quantities suchas the surface area per unit volume SV and meanthickness ,Th. of the structural elements. Accuratevalues of SV and ,Th. cannot be derived from isolatedslices unless one can assume the individual structuralelements are all plates or all rods: this is onecircumstance where a dataset of contiguous slices isessential. As discussed in detail elsewhere,239 one cannotsimply make measurements of apparent thickness in theindividual slices of a volume without risk of introducingsignificant, unpredictable bias into the data.

An approach called the distance transformmethod240,241 is a powerful method for determining anaccurate mean ‘trabecular’ thickness or distribution ofthicknesses. Analysis proceeds by calculating the metricdistance of each solid voxel to the nearest solid(empty)space surface, i.e. this distance is the radius ofa sphere centred on this voxel and fitting inside thestructure. Redundant (smaller) spheres are eliminatedproducing a set of centres of maximal spheres filling thestructure completely (Fig. 7).242 Thicknesses Th for eachportion of the structure are twice the radii, and thisallows maps of local thickness value to be produced in3D renderings as well as ,Th. or distribution ofthicknesses. Mean spacing ,Sp. between structuralelements is calculated with the same method by simplyswitching the background and object voxels. Iterativeopening and closing in 3D (n erosions followed by ndilations with increasing n until no volume remains inthe image: note that n erosions remove all structuressmaller than 2n voxels) is the basis of another method(granulometry) of rapidly computing the distributionof wall thicknesses in a cellular material;243 thederivative of the remaining volume with respect tostructuring element size n gives the (size) distribution ofthicknesses.244

Additional quantities of importance include theconnectivity density Conn.D, the structural anisotropyand the structure model index (SMI). Connectivityreports the number of redundant trabeculae in thestructure, that is, trabeculae that can be cut withoutincreasing the number of separate parts of the structure,and Conn.D is calculated by dividing the connectivity bythe examination volume. A more complete discussion ofEuler numbers, connectivity and edge effects is beyondthe scope of this review238 as these topics are not

emphasised in the examples below. Anisotropy, follow-ing Odgard,238 can be defined by main directions(perpendiculars to symmetry planes in the structure)and by numbers quantifying the concentration ofdirections around the main direction. The fabric tensorcompactly describes orthotropic architectural aniso-tropy via a 363 matrix of eigenvectors giving maindirections and eigenvalues the degree of concentrationaround main directions.245 Alternatively, the degree ofanisotropy (DA) can be computed using the meanintercept length (MIL) method.238,239 The structuremodel index (SMI)246 relates the convexity of the struc-ture to a model type and allows one to determine, forexample, whether a given structure is more rod like ormore plate like. An array of ideal (flat) plates hasSMI50, a set of ideal cylindrical rods has SMI53 and aset of spheres has SMI54. If sufficient ‘air bubbles’ arepresent within the structure, SMI,0.

Generally, the quantification techniques describedabove depend on, or at least, are implemented with,

7 Two-dimensional illustration of distance transformation

determination of plate or strut thickness, process actu-

ally applied in 3D. a Dashed circles show that local

thicknesses are t9 at A and t0 at B. At C, the largest

sphere defines local thickness. b Effect of threshold

level and voxel size on thickness determined. Grey

areas represent same section of ‘bone’ and large

square represents region of interest (ROI) for analysis.

Left column shows ROI sampled by 464 voxels whileright column shows ROI sampled with (smaller)

767 voxels. Diagonal slashes show voxels consideredto be ‘bone’: in upper row, voxels must be totally

occupied while in lower row, voxels more than one-

half occupied are considered solid. Above/below each

column of voxels is number of ‘bone’ voxels in that

column. Reprinted from Ref. 242 with permission



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binary segmentation and selection of a reasonablethreshold separating the phase of interest from all otherphases. Specimens containing high contrast phases (e.g.bone where the bone/marrow contrast is y10 : 1 for alab microCT system operating with an effective X-rayenergy of y25 keV7) have histograms with peaksseparated by a valley; these materials can be segmentedby choosing a threshold within the valley. Confoundingeffects that necessitate less routine segmentation includelarge populations of partial voxels resulting, forexample, from structures with minimum dimensions onthe order of the voxel size (Fig. 7).

One frequent segmentation approach is assignment byinspection: the operator examines a typical slice or slicesand selects the threshold which best (to his or her eye)preserves the important fine scale features of both thesolid and the surrounding empty space. Given that thisis a highly subjective process, considerable effort hasbeen devoted to assessing the robustness of conclusionsderived from small shifts in threshold; the generalconsensus is that absolute numbers (VV, ,Th., etc.)will change somewhat with changing threshold, but solong as the features being quantified have minimumdimensions greater than perhaps 4 voxels, comparisonsbetween specimens will be valid (see the subsection onmicroCT accuracy toward the end of this paper forspecifics). The author uses this trial and error methodbut with the following precaution: the threshold ischosen based on evaluation of a preliminary subset ofspecimens, a subset explicitly excluded from the actualstatistical comparison of different treatment groups.247

Before other thresholding approaches are described, itis useful to examine an example of determination ofquantities such as ,Th., ,Sp. and SMI for a cellularsolid, the mineralised tissue of the sea urchin. Theskeletal elements of sea urchins are termed ossicles andconsist of calcite, i.e. calcium carbonate. In all but a fewspecialised cases, all of the ossicles are single crystals,despite having complex external and internal geometriesreflecting their different, highly specialised functions.The design motif of sea urchin calcite (except in teeth) isa highly porous structure (y50 vol.-% occupied by softtissue and fluid) that is termed stereom. Stereom hasmany different fabrics (dimensions and arrangements ofstruts and plates),248 and synchrotron microCT has highenough resolving power to study many types of stereom.Figure 8 shows a slice of one of the many platescomprising the test (protective globe enclosing the seaurchins internal organs) and of a demipyramid (part ofthe jaw structure).242 Within the region indicated inFig. 8b, BV/TV50?487, ,Th.519?5 mm, ,Sp.520?7 mmand SMI50?22, i.e. the structure consisted primarily ofplates. Determination of specific stereom fabric type(e.g. galleried, labyrinthic and perforate)248 from thesegmented volumes will require further development.The 3D views shown in Fig. 8c and d compare tworepresentations: three orthogonal grey scale views (onthe sides of a cube) versus a 3D rendering of thesegmented volume. For situations where the solid andempty space fractions are anywhere near equal, theformer representation will generally be more informativethan the latter.

One alternative thresholding method is use of thegradient in greyscale value to define the boundarybetween phases.249 Adaptive or dynamic thresholding,

which explicitly accounts for varying background, isanother approach.244,250,251 In structures where the solidphase is particularly thin and diff

recent advances in x-ray microtomography applied to...

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