Enabling three-dimensional densitometric measurements using laboratory source X-ray micro-computed tomography

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We present new software allowing significantly improved quantitative mapping of the three-dimensional density distribution of objects using laboratory source polychromatic X-rays via a beam characterisation approach (c.f. filtering or comparison to
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  SoftwareX 7 (2018) 115–121 Contents lists available at ScienceDirect SoftwareX  journal homepage: www.elsevier.com/locate/softx Original software publication Enabling three-dimensional densitometric measurements usinglaboratory source X-ray micro-computed tomography M.J. Pankhurst a,b,c,d,e , R. Fowler f  , L. Courtois a,b , S. Nonni a,b , F. Zuddas g , R.C. Atwood a ,G.R. Davis h , P.D. Lee a,b, * a Research Complex at Harwell, Harwell Campus, OX11 0QX, UK  b School of Materials, The University of Manchester, Manchester, M13 9PL, UK  c School of Earth and Environment, University of Leeds, Leeds, LS29 9ET, UK  d Instituto Technológico y de Energías Renovables (ITER), 38900 Granadilla de Abona, Tenerife, Canary Islands, Spain e Instituto Volcanológico de Canaries (INVOLCAN), 38400 Puerto de la Cruz, Tenerife, Canary Islands, Spain f  Scientific Computing Department, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Campus, OX11 0QX, UK  g Instrument Design Division, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Campus, OX11 0QX, UK  h Institute of Dentistry, Queen Mary University of London, London, E1 4NS, UK  a r t i c l e i n f o  Article history: Received 11 July 2017Received in revised form 15 February 2018Accepted 14 March 2018 Keywords: Laboratory X-ray micro-computedtomographyBeam characterisationPythonBeam hardeningThree-dimensional densitometry a b s t r a c t Wepresentnewsoftwareallowingsignificantlyimprovedquantitativemappingofthethree-dimensionaldensity distribution of objects using laboratory source polychromatic X-rays via a beam characterisationapproach (c.f. filtering or comparison to phantoms). One key advantage is that a precise representationof the specimen material is not required. The method exploits well-established, widely available, non-destructive and increasingly accessible laboratory-source X-ray tomography. Beam characterisation isperformed in two stages: (1) projection data are collected through a range of known materials utilisinga novel hardware design integrated into the rotation stage; and (2) a Python code optimises a spectralresponse model of the system. We provide hardware designs for use with a rotation stage able to betilted, yet the concept is easily adaptable to virtually any laboratory system and sample, and implicitlycorrects the image artefact known as beam hardening. © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/). Code metadata Current code version  1.0 Permanent link to code/repository used of this code version https://github.com/ElsevierSoftwareX/SOFTX-D-17-00053Legal Code License  Apache 2.0 Code versioning system used  SVN  Software code languages, tools, and services used  Python 2.7 Compilation requirements, operating environments & dependencies  The main Python modules that users may need to install are numpy, matplotlib, scipy, tifffile If available Link to developer documentation/manual https://ccpforge.cse.rl.ac.uk/svn/tomo_bhc/trunk/doc/Support email for questions ronald.fowler@stfc.ac.uk Software metadata Current software version  1.0 Permanent link to executables of this version  NA Legal Software License  Apache 2.0 Computing platforms/Operating Systems  Linux, Windows, MacOS Installation requirements & dependencies  Python 2.7 If available, link to user manual — if formally published include areference to the publication in the reference list NA Support email for questions ronald.fowler@stfc.ac.uk *  Corresponding author at: School of Materials, The University of Manchester, Manchester, M13 9PL, UK. E-mail address:  pdlee123@gmail.com (P.D. Lee).https://doi.org/10.1016/j.softx.2018.03.0042352-7110/ © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).  116  M.J. Pankhurst et al. / SoftwareX 7 (2018) 115–121 1. Introduction Three-dimensional (3D) densitometry can be conducted usingmonochromatic X-ray imaging (synchrotron) and tomographic re-construction [1,2]. The relationship between attenuation and a homogeneous object’s thickness is linear for a single X-ray energy(e.g. [3]). Single energy calculated attenuation is also linear sincethedetectorresponse,intheory,isconstant(see[4]foradiscussion of detectors and sources).Measuringdensityquantitativelyandaccuratelyusingatypicallaboratory X-ray imaging setup, however, is non-trivial. This is be-cause conventional impact X-ray sources produce polychromaticbeams (which can change from scan to scan), and attenuation isstronglydependentonX-rayenergy(Fig.1).Furthermore,conven-tional detectors do not differentiate energy (only flux) and do nothave uniform response over the whole energy range. Finally, theremay be no practical way of placing precisely known thicknesses of theexactmaterialofinterestintothebeam,whichwouldallowaninternalcalibrationbetweenattenuationandthicknesstobemade(for that material only).The detected signal is an outcome of the combination of threevariables: the incoming spectrum, the sample-specific interactionwith that beam, and the response of the detector. Our aim here isto make quantitative densitometry practical, and adaptable to anylaboratory setting, by demonstrating a method of characterisingthe beam spectra that can be easily integrated into day-to-daylaboratory procedure. Once the beam is characterised using ourcode, correction factors for any given material can be calculatedwith respect to that material’s attenuation of a monochromaticbeam. With the correction applied to the projection data, the re-constructed tomograms are a quantitative and reproducible mea-sureofthatobjects’density,andwithbeam-hardeningminimised. 2. Background In theory, if the proportions of different energies and the com-positionofthespecimenareknown,agoodestimateofdensitycanbederivedfromthereconstructedX-rayimage.Allthatisrequiredin order to calculate the attenuation and thus density of the objectthe beam passes through is knowledge of the X-ray spectra used,and the response function of the detector. The non-linearity in theresponse due to polychromatic X-rays can then be corrected to alinear relationship between response and sample thickness.X-rayspectracanbecalculated,whichgivesagoodapproxima-tion for the energies emitted from polychromatic X-ray sources.Yet these values are not precisely known for real X-ray tubes andthere are a number of other uncertainties, such as the efficiencyof the detectors, which influence the signal recorded. Today’s in-dustrial X-ray radiography and tomography equipment does notattempt to apply corrections based on calculations from measure-ments made from the beam itself. Instead, the density phantomssuitableforsomepurposesareprovidedandareusedascalibrationstandards to apply to images ([5]; see also method notes in [6]). Qualitativecorrectionroutinesthatimprovethevisualappearanceoftheresult–butdonotprovideanestimateofthetrueabsorptionproperties – are also provided by scanner manufacturers. Whilethe artefacts appearing in such images may be neglected for somepurposes, these can at best complicate the analysis and at worstlead to spurious results.During a tomography acquisition, the average X-ray pathlengths common to a single voxel are shorter when that voxel isnear the edge of the object (Fig. 2a). This causes ‘beam harden-ing’ to manifest as image cupping in tomographic reconstructionsbased upon linear absorption. The artefact manifests as relativebrighteningattheedgesofreconstructedobjectsanddarkeninginthe middle (Fig. 2b). Without correction of the srcinal projection data (i.e. the response per pixel) this artefact precludes accuratedensitometry. For objects that actually have a radial distributionof density such as a tooth or a bone, or chemically zoned crystals,the beam hardening effect becomes confounded with the veryproperty the experiment is intended to measure (see Fig. 3).Understanding and overcoming image artefacts inherent to thepolychromatic nature of laboratory-source X-ray spectra is thus avital task (e.g. [7]). This is because the greyscale value assigned to a reconstructed voxel is routinely used to digitally map an object’sfeatures, in order to extract textural [8] and chemical information[9]. Applications that rely on high confidence when using the greyscale value as a key image parameter range from geologicaland environmental [10–13] to biomedical [14], to transport and energy [15] and material engineering applications [16]. Due to thisnumerical‘smearing’,however,beamhardeningartefactshavelong posed a major limitation to quantitative 3D image analysis. 3. Our approach In this contribution, we report an advance in the developmentof a method of three-dimensional densitometric measurement bycharacterising the polychromatic beam and the detector response[17–21]. First, the scan settings are decided upon, and then that beam is characterised. The beam is used to take projection datathrough different thicknesses of materials of known attenuation(that bracket that of the object). The images provide raw intensitydata that can be then compared to a modelled system [17]. Since themodelisnotexact,itisnecessarytoadjustsomeoftheparam-eters to obtain an optimal fit to the measured data.Measurements are conducted using a nonlinear optimisationprocess to obtain a function that represents the X-ray energyresponseofthesystem[17].Wherethespecimenmaterialcompo-sition is known, the function can be used to generate a calibrationcurve for that material using published X-ray attenuation values,for instance see [22]. This approach produces a curve approximat-ing the real, non-linear relationship between total polychromaticbeam attenuation and the expected attenuation with monochro-matic radiation [20] which may be easily and simply applied inexisting tomography equipment.A current limitation of this algorithm is that the resulting cor-rection curve is specific to a single phase. If, for example, thematerial of interest is encapsulated or held in place by resin,or surrounded by soft tissue etc., the presence of this secondphase will decrease the accuracy of our approach. In cases whereone phase contributes little to the attenuation, the method stillgives an accurate estimate of the dominant phase. Similarly, formulti-phase specimens where there is a macroscopically uniformdistribution of the phases, the method gives good overall beam-hardening correction that can improve the segmentation of theindividual phases. An enhanced version of this method for moreaccurate densitometric measurement in dual phase systems isunder development [23]. Ourapproachisdistinctfromfiltration,whichworkstoremovelow energy X-rays from the beam, thereby narrowing the windowof beam energy used toward an ideal case (see first paragraph).Sincetheidealcaseisnotpossibleinthelaboratory(evenifasingleenergy was achieved the flux would be too low for imaging in anypractical scenario), filtration serves to reduce the effects of beamhardening, but does not provide quantitative densitometry. 4. Method developments 4.1. Hardware It has long been common practice to use a step wedge of aluminium as an attenuation standard (e.g. [24]). Aluminium is  M.J. Pankhurst et al. / SoftwareX 7 (2018) 115–121  117(a) X-ray path in a typical laboratory scanner.(b) Effect of 2D thickness. Fig.1.  Schematicdescribingthephysicalcauseofbeam-hardeningintomographicimagereconstructionsfromapolychromaticX-raysource.(a)X-raysofdifferentenergiesare generated by excitation of a source (usually W metal) using a focussed electron beam. Lower energy X-rays attenuate more easily and as such fewer reach the detectorrelative to higher energies, for a given thickness of material. (b) The attenuation at all energies is proportional to object thickness, and thus the combined effect describedin (a) and (b) is that the response at the detector (I) is disproportionately lower from ray paths that interact over long distances through an object, compared to those thatinteract over a short distance. easy to work with and available in high purity. The step wedge ispractical;projectiondatathroughknownthicknessesareobtainedeither simultaneously, or by simply moving different thicknessesof the step wedge into the field of view.Usingasinglematerialissimpleandself-consistent,yettheuseof a number of different materials provides a more complete, andthus better constrained, characterisation of the beam [18,21]. The use of multiple elements is also practical; if the attenuator wasall aluminium, some parts would need to be several cm at highenergies. If they were all copper, some parts would need to be afew  µ m thick at low energies. A simple design that incorporatednumerous materials was built by Evershed [25], allowing the insertion of a variety of materials between the source and thedetector.In Fig. 4 we show a new development; a ‘crown’ of materialsset into individual pegs arranged around the outside of a singlecircularbaseplate.Thisgeometryallowsustoloadthecrownwithmany materials, in this case 18. Full design drawings can be foundinthesupplementarymaterial.Itshouldbenotedthatthisspecificdesignisourpreferredoptionhere,becauseourstagecanbetilted.For systems that do not have a tilt option on the rotation stage,the carousel solution of Davis et al. [20] can be used instead. If  permanentmountingisnotpossible(i.e.integratedwiththestage)it can be scanned separately as if it were a specimen.  118  M.J. Pankhurst et al. / SoftwareX 7 (2018) 115–121 Fig. 2.  Schematic explanation of beam hardening. (a) With increasing thickness,proportionately fewer X-rays are transmitted through an object. The relationshipis linear for monochromatic beams. When using polychromatic beams, the lowenergy X-rays are attenuated more strongly than the higher energy X-rays, andare disproportionately removed by comparatively thin interaction lengths. Thusat position A, more signal is detected than if a monochromatic beam was used;position B results in less signal. (b) Since reconstructions assume a linear response,the observed signal is calculated as higher than real density (recorded as imagebrightness) at position A, and lower at position B.  Table 1 Materials used to acquire projection data. Note: thicknesses were measured withelectronic callipers.Position Material Thickness (mm) 2 σ   ( n  =  4)1 Copper 1.992 0.0152 Aluminium 0.051 0.0023 Aluminium 0.097 0.0014 Aluminium 0.255 0.0035 Aluminium 0.509 0.0066 Aluminium 0.999 0.0027 Aluminium 2.0 0.0078 Aluminium 3.0 0.007 4.2. Software The Python code significantly expands upon, and simplifies, anInteractiveDataLanguage(IDL)scriptthatwasfirstwrittenduringthe formulation of the srcinal concept [17]. The code can be ob- tained via the web at https://ccpforge.cse.rl.ac.uk/svn/tomo_bhc/trunk/, along with a user guide. We have taken this opportunityto produce a correction factor as a 4 th order polynomial, whichis more suitable for a wide range of instruments to employ (i.e. acustom 4 th order polynomial can be used in standard  Nikon X-Tek software). A high-level workflow of the method is illustrated inFig. 5. See also supplementary data for detailed code description,includingvalidationagainsttheIDLscript.Thecode’sfunctionsarecomputationallybasic;curvefittingandsimplemodellingofX-rayattenuation. 4.3. Application to a number of materials We have conducted a number of scans and corrections thatdemonstrate the software’s applicability across fields of researchranging from aerospace components (e.g. [26]), to geological (e.g. [27]) and biomedical applications (e.g. [28]), and for different imaging purposes. The first cases selected were light alloy compo-nents,astomographyisroutinelyusedfordefectdetection[29,30]) and for designing new compositions [31,32]. Furthermore, typify- ing such alloys using laboratory source X-rays for use as randomabsorptionmasksinphasescatteringimagingisanemergingappli-cation [33]. A block of high purity aluminium and a block of Al–Cualloy(15%Cu;see[34,35]fordetails)werescannedusingthesame equipment described above, set at a nominal maximum energy of 70 kV, taking 3154 projections around 360 ◦ and using a 1.0 mmAl filter. We used the calibrated modelling approach to correctthese projections to those expected of a 40 kV monochromaticbeam using a calibration curve generated for Al, and Al–15%Cu,respectively. A chicken wing bone (dry) was scanned at a nominalmaximum of 35 kV with no pre-filtration of the polychromaticbeam, as a key application is biomedical [36] and determining the efficacy of biomaterials in implants [14,37]. 5. Results Fig. 6 shows typical results from these materials ranging fromphysical to life sciences applications, and illustrates potential ap-plications and some limitations. The method accurately deter-mines the linear attenuation coefficient of high purity aluminiumin three-dimensions with little to no discernible beam hardeningartefacts (Fig. 6ai), within approximately 1% precision (Fig. 6aii). Noise would be further lessened using additional frames per pro- jection.Theresultsareasignificantimprovementoveruncorrectedor automated proprietary beam-hardening corrections.When applied to a heterogeneous material comprised of twophases with different densities, such as an Al–Cu alloy (Fig. 6b), themethodcancorrectforbeamhardeningusingthebulkcompo-sition. However, retrieving accurate densitometric measurementson a per-voxel basis is non-trivial. This is due to the correctionbeing applied assuming a perfectly mixed material, whereas thealloy is composed of dendritic crystals of Al and Cu at a fine scale(Fig. 6bi, ii). Although the method removes the bulk beam hard-ening (Fig. 6biii) and provides a reproducible image intensity for each of the phases, there is an additional uncertainty as comparedto a single phase material when calculating density on the basis of measured linear attenuation co-efficient per voxel. The use of   insitu  calibration samples would overcome this limitation, allowingnormalisation of the now regularised image. Since the imaging ismadereproduciblewhenbeamcalibrationsareperformed,calibra-tion would only need to be performed once, and the calibrationscould be used throughout large-scale tomography campaigns.Finally, we chose the bone as a life sciences example in whichthe hardening artefact is confounded with the real density vari-ation (Fig. 6c). Bone is a material that is also comprised of two phases, and exhibits a radially distributed density distribution.Beamhardeningaccentuatesthebiastowardhigherintensityvox-els at the edges of the chicken bone (Fig. 6ci) as well-illustratedbytheuncorrectedprofile(Fig.6cii).Inthesecircumstancesitmaybe tempting to use beam hardening corrections within proprietysoftware to arrive at an image wherein the peaks are of equalheight, yet this would risk overcorrecting and blurring the image.Sincethesofttissuehaslowattenuation(andthusisinfluencedby beam hardening less so than hard tissue), we corrected usinga calibration curve generated for bone alone. In the correctedimage and profile, the density distribution still exhibits significantincrease with distance from the centre, but this is a genuine char-acteristic of bone. Our method has not spuriously removed thisvariation as would happen with the methods described above.  M.J. Pankhurst et al. / SoftwareX 7 (2018) 115–121  119 Fig.3.  Example of beam hardening artefacts in (a) a homogeneous object; aluminium and (b) heterogeneous object; natural lava exhibiting a number of crystal phases withdifferent densities. Cupping is illustrated by an  X   direction profile across the aluminium block (aii), whereas the influence is cryptic in the lava (bi), yet can be observed toimparts errors when relating chemical zonation to differences in image brightness (bii). Fig. 4.  Crown mounted within a typical laboratory XMT scanner. For collection of projectionsthematerialiswithin1cmoftheX-raytarget;greaterdistanceisshownfor illustrative purposes. For description of the materials see Table 1. 6. Discussion Many commercially available software packages that are cou-pled with X-ray tomography systems offer a suite of options toapply pre-reconstruction beam hardening corrections. These areeitherpolynomialequationsfittoanassumedbackgroundwhichisthen removed via applying a correction factor, or are determinedby automated proprietary methods, but these techniques are notmaterial specific. In practice, several of these are usually appliedduring the reconstruction of a small selection of slices.The eventual choice of technique to be used for the entire vol-ume is determined by the user or by basic image analysis (e.g. seeFig. 6), by seeking a flat profile across a slice where density isassumed to be constant. Any such approach introduces the poten-tial to ‘correct-out’ real signal, or over- or under-estimate beamhardening, potentially leading to spurious results and interpreta-tion. Where density is assumed to be homogeneous (on a givenscale, i.e. Fig. 6b), and especially where density is likely to not behomogeneous (Fig. 6c) this potential for error is amplified.If we are to use laboratory XMT as a quantitative and re-producible 3D densitometric tool a more rigorous and repro-ducible approach is required. Our spectrum and response mod-elling method characterises the beam at the time of acquisitionfrom a specific sample, which imlicitly allows for variations in thehardware through time. The corrections may be calculated andappliedline-by-line,thus,accountingfortherelationshipbetweenX-ray take-off angle and energy spectrum.Our methodology addresses issues that are impossible to mon-itor when traditional non-specific, qualitative, beam hardeningcorrections are used. For example, anode pitting increases self-absorption in the target material [18], producing changes in the spectrum emitted. In turn, these changes are reflected in the cal-culated attenuation of a specimen, leading to deviations in appar-ent density. These changes are immediately incorporated via thecarousel/crowncalibration.Further,thecalibrationchangescanbemonitored to diagnose such problems and trigger maintenance.Calibration curves and correction factors specific to the sam-ple of interest may be generated using publicly available data(i.e. XCOM). Thus our approach has value for a wide range of research questions. The calibration data can be archived so thatanyfuturedevelopmentsincalibrationmethods,orreconstructionalgorithms, can be applied retrospectively to improve the quality
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