An electromagnetic physics constructor for low energy polarised X-/gamma ray transport in Geant4
AAn electromagnetic physics constructor for low energy polarised X- / gamma raytransport in Geant4 Jeremy M. C. Brown a , b , and Matthew R. Dimmock c a Department of Radiation Science and Technology, Delft University of Technology, The Netherlands b Centre for Medical Radiation Physics, University of Wollongong, Wollongong, Australia c Department of Medical Imaging and Radiation Sciences, Monash University, Melbourne, Australia
Abstract
The production, application, and / or measurement of polarised X- / gamma rays are key to the fields of synchrotronscience and X- / gamma-ray astronomy. The design, development and optimisation of experimental equipment utilisedin these fields typically relies on the use of Monte Carlo radiation transport modelling toolkits such as Geant4. Inthis work the Geant4 “G4LowEPPhysics” electromagnetic physics constructor has been reconfigured to o ff er a “bestset” of electromagnetic physics models for studies exploring the transport of low energy polarised X- / gamma rays.An overview of the physics models implemented in “G4LowEPPhysics”, and it’s experimental validation againstCompton X-ray polarimetry measurements of the BL38B1 beamline at the SPring-8 synchrotron (Sayo, Japan) isreported. “G4LowEPPhysics” is shown to be able to reproduce the experimental results obtained at the BL38B1beamline (SPring-8) to within a level of accuracy on the same order as Geant4’s X- / gamma ray interaction cross-sectional data uncertainty (approximately ± Keywords:
Geant4, Polarized gamma ray, Compton scattering, X-ray astronomy, Gamma-ray astronomy,Synchrotron radiation facility
1. Introduction
The production, application, and / or measurement of polarised X- / gamma rays are of significant interest to the fieldsof synchrotron science [1–4] and X- / gamma-ray astronomy [5–9]. In synchrotron science specialised equipment andend-stations are required to exploit the properties of polarised X- / gamma ray interactions to modify the state and / orprobe the structure of a target object [10–12]. In the case of X- / gamma-ray astronomy, coded aperture, Compton andpair production telescopes are utilised to determine specific structural properties of astronomical bodies through themeasurement of the relative polarisation strength of the their emitted X- / gamma ray radiation [13–19]. In both ofthese fields the design, development and optimsation processes of their respective equipment typically relies on theuse of Monte Carlo radiation transport modelling toolkits [20–27]. Of the available Monte Carlo radiation transportmodelling toolkits Geant4 [28–30] is the most commonly utilised for these tasks due to its flexible nature and widearray of polarised radiation physics transport models [31].The Geant4 toolkit for the simulation of the passage of particles through matter is the result of a world widecollaboration of over 100 scientists and software engineers that has spanned the last 26 years [32]. To date a total often versions have been released, with each release incrementally improving and optimising the core tracking, geometryand hits collection architecture. At the same time new particle types and physics models, including electromagnetic,hadronic and optical processes, spanning energies of a few eV to hundreds of TeV have been added to increase thefunctionality of Geant4 [28–31]. In the release of Geant4 version 8.2 an extensive set of polarised particle transportmodels were added to complement the existing models for polarised X- / gamma ray photoelectric absorption, Comptonscattering, and Rayleigh scattering [33]. Since then new polarised X- / gamma rays transport models have been addedfor gamma conversion / pair production in 2009 [34] and 2018 [35, 36], Compton scattering in 2016 [31], and elasticscattering (Rayleigh, Delbr¨uck and Nuclear Thomson scattering) in 2019 [37].The present work outlines the reconfiguration of the “G4LowEPPhysics” electromagnetic physics constructorfor polarised X- / gamma ray transport in Geant4. This electromagnetic physics constructor from Geant4 version Preprint submitted to XXXX February 9, 2021 a r X i v : . [ phy s i c s . c o m p - ph ] F e b ff er users an easy way to implement the “best set” of electromagnetic physics models for studiesexploring the transport of low energy polarised X- / gamma rays. Section 2 contains an overview of the physics modelsimplemented in “G4LowEPPhysics” and outlines it’s experimental validation against Compton X-ray polarimetrymeasurements from the BL38B1 beamline at the SPring-8 synchrotron (Sayo, Japan). The results and discussionfrom this experimental validation, and an overall conclusion then follow in Sections 3 and 4 respectively.
2. Method
The electromagnetic physics constructor “G4LowEPPhysics” aims to o ff er the “best set” of electromagneticphysics models available in Geant4 for low energy polarised X- / gamma ray transport. It was developed from thelibrary of available electromagnetic physics “Model Classes” of Geant4 version 11.0 and will be reviewed with eachnew Geant4 release. A list of the X- / gamma ray, electron and positron physics “Model Classes” implemented in“G4LowEPPhysics” for each physical process with their respective energy activation range in Geant4 version 11.0is displayed in Table 1. Whilst it can be seen that the applicable energy range of “G4LowEPPhysics” spans theev to TeV scale, these “Model Classes” were selected as they are known to be based on theoretical models thatpossess high physical accuracy below 10 MeV [30, 31]. In addition these models are also applicable to the simu-lation of non-polarised X- / gamma rays as during their first interaction a random axis of polarisation is sampled ifnot defined at creation / emission, and then tracked for remainder of the X- / gamma ray’s propagation. Finally, with“G4LowEPPhysics” both X-ray fluorescence and Auger electron emission from atomic deexcitation are enabled bydefault. More information on these “Model Classes” can be found in the references outlined in Table 1 and the Geant4Physics Reference Manual [31].Physical Model Energy ReferencesProcess Class Range X- / Gamma ray
Photoelectric Absorption G4LivermorePolarizedPhotoElectricModel eV - TeV [38, 39]Rayleigh Scattering G4LivermorePolarizedRayleighModel 250 eV - TeV [40]Compton Scattering G4LowEPPolarizedComptonModel eV - TeV [41]Gamma Conversion G4BetheHeitler5DModel 1.022 MeV - TeV [35, 36]
Electron
Ionisation G4LivermoreIonisationModel eV - 100 keV [42]G4UniversalFluctuation 100 keV - TeV [43]Bremsstrahlung G4SeltzerBergerModel eV - GeV [44]G4eBremsstrahlungRelModel GeV - TeV [44]Multiple Scattering G4GoudsmitSaundersonMscModel eV - 100 MeV [45]G4WentzelVIModel 100 MeV - TeV [46]
Positron
Annihilation G4eplusAnnihilation 1.022 MeV - TeV [47, 48]Ionisation G4PenelopeIonisationModel eV - 100 keV [49]G4UniversalFluctuation 100 keV - TeV [43]Bremsstrahlung G4SeltzerBergerModel eV - GeV [44]G4eBremsstrahlungRelModel GeV - TeV [44]Multiple Scattering G4GoudsmitSaundersonMscModel eV - 100 MeV [45]G4WentzelVIModel 100 MeV - TeV [46]
Table 1: The X- / gamma ray, electron and positron physics models classes and their respective energy activation range implemented for eachphysical process in “G4LowEPPhysics”. Detail descriptions of these “Model Classes” can be found in their respective references above and theGeant4 Physics Reference Manual [31]. .2. Experimental Validation of “G4LowEPPhysics” Experimental validation of the “G4LowEPPhysics” electromagnetic physics constructor was undertaken using theCompton X-ray polarimetry measurement data collected at the SPring-8 synchrotron BL38B1 beamline reported inTokanai et al. [50]. The following provides an overview of the experimental setup and measurements undertakenby Tokanai et al. [50], outlines the development of a Geant4 application based on the geometry of the SPring-8synchrotron BL38B1 beamline, and describes the simulation parameters that were implemented to experimentallyvalidate “G4LowEPPhysics”.
Tokanai et al. constructed an X-ray polarimeter from two cadmium telluride (CdTe) detectors (Amptek XR-100T-CdTe) and a custom built vertically orientated acrylic rotational stage [50]. These two CdTe detectors were mountedonto the rotational stage perpendicular to one another, and focused towards a scattering sample stage that is located atthe centre of rotation. Each detector was placed on an independent linear travel stage that enabled the radial distancebetween their detection window and the scattering target to be controlled in order to optimise the scattered radiationdetection sensitivity. The whole unit was placed onto the BL38B1 beamline with the central beam path orientatedperpendicular to the plane defined by these three elements, and focused at the centre of the scattering sample stage[50].The orientation of the three key elements of the X-ray polarimeter, the scattering target and both CdTe detectors,with respect to other detector and filtering elements utilised on the BL38B1 beamline can be seen in Figure 1. Inthis experimental configuration a near 100% horizontally polarised 100 µ m by 100 µ m collimated mono-energeticX-ray beam (represented via the dashed line) propagated left to right along the z-axis from the beam defining slitsto the surface of the scattering target through a He gas flight tube. Relative to the incident beam, the two CdTedetectors were orientated at a 90 degree radial scattering angle ( θ = ◦ ) 150 mm away from the centre of the samplescattering stage [50]. Through the vertically orientated acrylic rotational stage these two CdTe detectors were able tomeasure the azimuthal angular scattering ( φ ) modulation of the BL38B1 beamline’s mono-energetic X-ray beam dueto its horizontal plane polarisation. In addition to the X-ray polarimeter, Figure 1 illustrates that a 170 mm long Hegas-flow type ionisation chamber, set of metal filters, and custom YAP(Ce) scintillator based energy discriminatingphoton counting detector were present downstream 700 mm, 920 mm, and 1170 mm from the centre of the scatteringsample stage respectively (Tokanai F. Personal Communication , March 2020). Whilst the He gas-flow type ionisationchamber was present in the experimental configuration, none of its measured data was utilised or reported in Tokanaiet al. [50].A total of three di ff erent sets of experimental measurements were undertaken and reported in Tokanai et al. [50]to observe the azimithal scattering modulation of the linearly polarised X-ray BL38B1 beamline. Two of these ex-perimental measurement sets were collected for a 20 keV mono-energetic X-ray beam using two di ff erent cylindricalpolypropylene scattering targets placed with their circular face perpendicular to the incident beam. The first cylindri-cal polypropylene scattering target (S1) had a 10 mm diameter and 10 mm length, whereas the second (S2) had a 5mm diameter and 7 mm length [50]. In both 20 keV mono-energetic X-ray beam experimental measurements a 300 µ m thick copper filter was used to attenuate the X-ray beam before striking the YAP(Ce) scintillator photon count-ing detector to avoid detector saturation and limit dead-time. The energy window of the YAP(Ce) scintillator photoncounting detector was optimised to target the 20 keV X-ray photopeak signal, and the two CdTe detectors obtained theazimithal angle ( φ ) modulated X-ray scattering spectra at 15 degree intervals over a 360 degree range [50]. The third,and final, set experimental measurements was undertaken for a 40 keV mono-energetic X-ray beam using the secondcylindrical polypropylene scattering target S2. In this set of experimental measurements a 600 µ m thick lead filterwas used to attenuate the X-ray beam before striking the YAP(Ce) scintillator photon counting detector (Tokanai F. Personal Communication , March 2020). As with the two previous experimental measurements, the YAP(Ce) scin-tillator photon counting detector energy window was optimsed to target the 40 keV X-ray photopeak signal and twoCdTe detectors obtained the azimithal angle ( φ ) modulated X-ray scattering spectra in 15 degree intervals over a 360degrees range [50]. Geant4 version 10.6 was used to construct an application of the experimental SPring-8 synchrotron BL38B1beamline setup illustrated in Figure 1. In this Geant4 application a 100% horizontally polarised 100 by 100 µ m3ollimated mono-energetic X-ray source was implemented originating 10 cm from the centre of the scattering samplestage in a “experimental hall” filled with air. Six di ff erent objects were simulated in the “experimental hall” to mimicthe geometry seen in Figure 1 that can be classified as one of two general object types: “structural objects” and“active radiation detectors”. “Structural objects” are objects that were present along the collimated mono-energeticX-ray beam path (represented via the dashed line in Figure 1) and that did not yield any experimental data that wasutilised / reported in Tokanai et al. [50]. This includes the scattering target, He gas-flow type ionisation chamber,and the set of metal filters. For the scattering target a cylindrical volume composed of solid polypropylene wasimplemented with the ability to modify its diameter and length to match that of S1 and S2. In the case of the Hegas-flow type ionisation chamber a 5 mm thick stainless steel box of dimensions 110 × ×
170 mm, with 50 µ mthick Kapton film 80 mm ×
10 mm entrance / exit windows, filled with He gas at standard laboratory condition wasimplement to mimic the unit available at the BL38B1 beamline (Tokanai F. Personal Communication , March 2020).Whereas for the set of metal filter a single slab of solid variable material composition, i.e. copper or lead, and thicknesswith a cross-sectional surface area of 50 mm ×
50 mm was implemented orientated perpendicular to the X-ray beam.Three “active radiation detectors” were implemented: two Amptek XR-100T-CdTe detectors, and a customYAP(Ce) scintillator based energy discriminating photon counting detector. For the Amptek XR-100T-CdTe detectorsthe geometry and material composition of the CdTe detection element, peltier cooler, mounting stud, Beryllium win-dow, and Ni metal housing were implemented based on the 3 mm × × // ffi ciency of each energy deposition location for a given incident X-ray within the CdTe chip wasmodelled relative to its electrode structure with the Hecht relation: η ( x ) = (cid:20) λ e T (cid:16) − e − x λ e (cid:17) + λ h T (cid:18) − e − T − x λ h (cid:19)(cid:21) (1)where T = λ e =
132 mm is the electron trapping length, λ h = x is the relative interaction depth of the incident X-ray within the CdTe chip active volume [51]. For the secondstep, the total energy deposited within the CdTe chip’s active region was then calculated for each simulated primaryX-ray through the weighted summation of the charge collection e ffi ciency of each energy deposition location: E n = n (cid:88) i = η i ( x ) E i (2)where E i is the energy deposited at each interaction location within the CdTe chip’s active region. The total energydeposited within the CdTe chip’s active region was then blurred using a Gaussian function of 0.45 keV full width athalf maximum (FWHM).In the case of the custom YAP(Ce) scintillator based energy discriminating photon counting detector, it was con-structed through taping a solid puck of YAP(Ce) onto the surface of a 3 inch diameter Photomultiplier Tube (PMT)with 3M Scotch Super 88 Premium Vinyl Electrical Tape and read out using a single channel analyser (SCA) withan approximate low energy window threshold of 10 keV (Tokanai F. Personal Communication , March 2020). Toapproximate it’s geometry and material composition, a butted 50 mm diameter-1 mm thick puck of solid YAP(Ce)and 76 mm diameter-1 mm thick glass puck was implemented inside of a 76.88 mm diameter-2.88 mm thick solidPolyvinylchloride (PVC) cylinder. The SCA based electronics readout was modelled through the use of a simple logiccounter with a 10 keV low energy window threshold. Again, it was assumed that there was no pulse pile up due tomultiple primary X-ray detection or electronics dead-time.
Table 2 presents a summary of the parameters for the three di ff erent sets of simulations that were undertaken withthe developed Geant4 BL38B1 beamline model and “G4LowEPPhysics” electromagnetic physics constructor. In eachsimulation set the incident mono-energetic X-ray energy, scattering target, and metal filters were modified to matchthe experimental configurations of one of the three di ff erent experimental measurements reported in Tokanai et al. [50](see Section 2.2.1). For each of these di ff erent incident mono-energetic X-ray energy, scattering target, and metal filter4imulation Incident X-ray Polypropylene Metal Filter Metal Filter Detector AzimithalSet Energy Scattering Target Material Thicknesses Angle Positions1 20 keV 10 mm diameter, Copper (Cu) 300 µ m 0 ◦ , ◦ , ◦ , ..., ◦
10 mm length (S1) ±
25, 50 µ m2 20 keV 5 mm diameter, Copper (Cu) 300 µ m 0 ◦ , ◦ , ◦ , ..., ◦ ±
25, 50 µ m3 40 keV 5 mm diameter, Lead (Pb) 600 µ m 0 ◦ , ◦ , ◦ , ..., ◦ ±
25, 50 µ m Table 2: Simulation parameters for the three di ff erent sets of simulations that were undertaken with the developed Geant4 BL38B1 beamlinemodel and “G4LowEPPhysics” electromagnetic physics constructor. Here the set of detector azimithal angle positions was limited to range of0 ◦ ≤ φ ≤ ◦ in steps of 15 ◦ to exploit the scattering symmetry around the plane of X-ray source polarisation (i.e. the horizontal plane) andreduce the extent of required computational resources. configurations two geometrical parameters were varied: 1) the relative Amptek XR-100T-CdTe detector’s azimithalangular ( φ ) orientations over a range of 0 ◦ ≤ φ ≤ ◦ in steps of 15 ◦ (see Figure 1); and 2) the metal filter thicknessesover a range of ± µ m in steps of 25 µ m around their stated thicknesses in Section 2.2.1. These two parametersweeps were undertaken to: 1) emulate the procedure employed to measure the reported experimental azimithal angle( φ ) modulated X-ray scattering spectra and normalised CdTe to YAP(Ce) detector signal ratios in Tokanai et al. [50] ;and 2) illustrate the accuracy of “G4LowEPPhysics” validation with respect to one of the more significant sources ofexperimental uncertainty (e ff ective metal filter thickness due to alignment accuracy and manufacturing tolerances).Finally, for each CdTe detector azimithal angle ( φ ) and metal foil thickness configuration 10 primary X-rays weresimulated using a maximum particle step length of 10 µ m and a low-energy particle cut o ff of 250 eV.
3. Results and Discussion
The results from the experimental and developed Geant4 application simulation output with the “G4LowEPPhysics”electromagnetic physics constructor for Simulation Set 1 in Table 2 (20 keV incident X-ray energy, scattering targetS1, and a Cu metal filter) is presented in Figure 2. Three di ff erent data-sets are displayed in Fig. 2: the AmptekXR-100T-CdTe detector scattered X-ray energy spectra at φ = ◦ (top), the Amptek XR-100T-CdTe detector scat-tered X-ray energy spectra at φ = ◦ (middle), and the azimithal angle ( φ ) normalised CdTe to YAP(Ce) detectorsignal ratios for 0 ◦ ≤ φ ≤ ◦ in steps of 15 ◦ (bottom). Here, both the experimental and simulated energy spectrasets are normalised with respect to their maximum intensity of the θ ≈ ◦ Compton scattered X-ray peak seen inFig. 2 (middle). Comparison of the experimental and simulation energy spectra for φ = ◦ (Fig. 2 (top)) illustratea high level of correlation between the combined θ ≈ ◦ Rayleigh scattering and Compton scattered X-ray peaks.In these energy spectra the level of correlation is such that even the statistical variance within the energy spectra isnear identical. When a similar comparison is undertaken for Fig. 2 (middle) ( φ = ◦ ), a similarly high level ofcorrelation between the two energy spectra can be observed with the exception that the Compton scattered X-ray peaktail is reduced in the simulated spectra. This observed reduction in Compton scattered X-ray peak tail in the simulatedspectra can be attributed to the first order approach that was employed in modelling the charge collection process inthe CdTe chip [51]. However even with the use of the first order approach, the normalised intensity of all features ofthe energy spectra obtained with the “G4LowEPPhysics” electromagnetic physics constructor are a near exact matchto the experimental energy spectra presented in Fig. 2 (top) and (middle).Figure 2 (bottom) contains the experimental and simulated azimithal angle ( φ ) normalised CdTe to YAP(Ce)detector signal ratios for 0 ◦ ≤ φ ≤ ◦ in steps of 15 ◦ . In the case of the simulated data, five di ff erent thickness of themetal filter were explored with the value matching that stated for the experimental measurement of Tokanai et al. [50](Cu: 300 µ m) represented via the solid circle markers. The other four explored metal filter thickness are separatedinto two groups, 300 ± µ m (275 µ m and 325 µ m) and 300 ± µ m (250 µ m and 350 µ m), to emulate the potential Note that the simulated normalised CdTe to YAP(Ce) detector signal ratios were calculated in the same manner as the experimental dataoutlined in Tokanai et al. [50]: i.e. the sum of the CdTe spectra channels above 10 keV divided by the logic counter output of the YAP(Ce) detector. ff ective metal filter thickness due to experimental alignment accuracy and manufacturing tolerances.In Fig. 2 (bottom) the ± µ m and ± µ m simulation results are indicated by the dark-shaded and light-shadedregion bounds respectively. Inspection of Fig. 2 (bottom) illustrates that a high level of correlation exists betweenthe experimental (solid diamonds) and the 300 µ m thick Cu metal filter thickness simulation (solid circle) normalisedCdTe to YAP(Ce) detector signal ratios. It can be seen that across the entire azimithal angle ( φ ) range the experimentaldiamond markers overlap with their respective 300 µ m simulation circle markers, and, in turn, fall well within the ± µ m shaded region that represents a less than ±
10 % di ff erence from the true simulated metal filter thickness.The experimental and simulated azimithal angle ( φ ) normalised CdTe to YAP(Ce) detector signal ratios for Simu-lation Set 2 and 3 outlined in Table 2 is presented in Fig. 3. Figure 3 (top) contains the experimental and simulationdata for Simulation Set 2 (20 keV incident X-ray energy, scattering target S2, and a Cu metal filter), and Fig. 3 (bot-tom) contains the experimental and simulation data for Simulation Set 3 (40 keV incident X-ray energy, scatteringtarget S2, and a Pb metal filter). In both sets of simulated result the metal thickness values stated in Tokanai et al. [50](Cu: 300 µ m and Pb: 600 µ m) are represented via the solid circle markers, and the ± µ m and ± µ m simula-tion results through the dark-shaded and light-shaded region bounds respectively. Inspection of the Simulation Set 2results in Fig. 3 (top) illustrates that a high level of correlation exists between the experimental (solid diamonds) andsimulation (solid circle) normalised CdTe to YAP(Ce) detector signal ratios. As with the Simulation Set 1 presentedin Fig. 2 (bottom), it can be seen that across the entire φ range the experimental diamond markers overlap with theirrespective 300 µ m simulation circle markers, and, in turn, fall well within the ± µ m shaded region that representsa less than ±
10 % di ff erence from the true simulated metal filter thickness. Whereas for the the Simulation Set 3presented in Fig. 3 (bottom), the level of the correlation between the experimental (solid diamonds) and 600 µ m thickPb filter simulation (solid circle) is weaker with the experimental results aligning strongly with the upper bound ofthe ± µ m shaded region. However, it should be noted that in the case of the Simulation Set 3 results the ± µ mshaded region represents a less than ± ff erence from the true simulated metal filter thickness.The results presented above illustrate a high level of correlation between the experimental results of Tokanai etal. [50] and developed Geant4 application simulation output with the “G4LowEPPhysics” electromagnetic physicsconstructor. Of the di ff erent incident X-ray energy, scattering target, and metal filter combinations, the 40 keV incidentX-ray energy, scattering target S2, and a Pb metal filter results (Simulation Set 3 in Fig. 3 (bottom)) showed the largestdi ff erence between the normalised CdTe to YAP(Ce) detector signal ratios. In Fig. 3 (bottom) the experimental resultsof Tokanai et al. [50] normalised CdTe to YAP(Ce) detector signal ratios appear to have a high level of correlationwith the simulated 625 µ m Pb metal filter results across the entire azimithal angle ( φ ) range. The fact that experimentalresults of Tokanai et al. [50] more closely aligns to the simulation results for a Pb metal filter that is 25 µ m thickercan be attributed that Pb metal sheets of less than 1 mm are very delicate, to the point that they can be easily tornor distorted through standard handling, and typically have manufacturing tolerance on the order of 50 to 100 µ m.Furthermore, this data represents a less than ± ff erence from the true simulated metal filter thickness which ison the order of the uncertainty of Geant4’s X- / gamma ray interaction cross-sectional data [52, 53].
4. Conclusion
The Geant4 “G4LowEPPhysics” electromagnetic physics constructor has been reconfigured to o ff er a “best set”of electromagnetic physics models for studies exploring the transport of low energy polarised X- / gamma rays. Anoverview of the physics models implemented in “G4LowEPPhysics”, and it’s experimental validation against Comp-ton X-ray polarimetry measurements of the BL38B1 beamline at the SPring-8 synchrotron (Sayo, Japan) was reportedthrough the use of a custom Geant4 application. It was found that “G4LowEPPhysics” is able to reproduce the ex-perimental results obtained at the BL38B1 beamline (SPring-8) to within a level of accuracy on the same order asGeant4’s X- / gamma ray interaction cross-sectional data uncertainty (approximately ± / gammaray studies, and will be reviewed with each new Geant4 release from version 11.0. Acknowledgements
J. M. C. Brown would like to acknowledge Professor Fuyuki Tokanai of Yamagata University (Japan) for theirhelpful clarification of the experimental setup and methodology implemented in Tokanai et al. [50].6 eferences [1] Paganin D. M.
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Report on G4-Med: a Geant4 benchmarking system for medical physics applications developed by the Geant4 Medical Simula-tion Benchmarking Group , Medical Physics: In Press (2020). igure 1: Orientation of the three key elements of the X-ray polarimeter, the scattering target (S.T.) and both CdTe detectors (D1 and D2), withrespect to the 170 mm long He gas-flow type ionisation chamber (I.C.), set of metal filters (F), and YAP(Ce) scintillator based energy discriminatingphoton counting detector (D3) locations at the BL38B1 beamline (SPring-8) in the y-z (top) and x-y (bottom left) planes [50]. The dashed linerepresents the propagation of the near 100% linear horizontally polarised 100 µ m by 100 µ m collimated mono-energetic X-ray beam along thez-axis, and the scattering coordinate system of the experiment setup is displayed in the bottom right panel. Tokanai et al. measured the azimuthalangular modulation of the scattered polarised X-ray beam with D1 and D2 150 mm away from the centre of the S.T. for θ = ◦ and over a rangeof 0 ◦ ≤ φ ≤ ◦ in steps of 15 ◦ . igure 2: Comparison of the experimental and simulation output for Simulation Set 1 (20 keV incident X-ray energy, scattering target S1, and a Cumetal filter) in Table 2. Three di ff erent data-sets are displayed: the Amptek XR-100T-CdTe detector scattered X-ray energy spectra at φ = ◦ (top),the Amptek XR-100T-CdTe detector scattered X-ray energy spectra at φ = ◦ (middle), and the azimithal angle ( φ ) normalised CdTe to YAP(Ce)detector signal ratios (bottom). In (bottom) the markers and solid black line represent the ideal filter thickness simulated data, with the two greyinner and outer bands corresponding to the ± µ m and ± µ m filter simulation outputs respectively. igure 3: Comparison of the experimental and simulation azimithal angle ( φ ) normalised CdTe to YAP(Ce) detector signal ratios for SimulationSet 2 and 3 in Table 2. Here the (top) panel contains the experimental and simulation data for Simulation Set 2 (20 keV incident X-ray energy,scattering target S2, and a Cu metal filter), and the (bottom) panel contains the experimental and simulation data for Simulation Set 3 (40 keVincident X-ray energy, scattering target S2, and a Pb metal filter). The markers and solid black line represent the ideal filter thickness simulateddata, with the two grey inner and outer bands corresponding to the ± µ m and ± µ m filter simulation outputs respectively.m filter simulation outputs respectively.