Self-attenuation
Self-attenuationMarie-Christine LépyLaboratoire National Henri Becquerel - LNE / CEA-DRT-LISTCEA Saclay – F-91191 GIF-SUR-YVETTE Cedex - FRANCEE-mail : marie-christine.lepy@cea.fr
Self-attenuation Introduction Attenuation coefficients Self-attenuation– Simple analytical formula– Generalisation– Practical tools Examples
Introduction Emission of photons attenuated through thesample If sample different from the calibration (size,shape, density, chemical composition)– Reduction of the photon beam– « False » peak areas– Correction factor required to get the true activity Homogeneity ?
Calibration sources
Attenuation coefficients Definition – Beer-Lambert law Tables Experimental measurement
Attenuation coefficientsBeer-Lamber law : attenuation of a narrow parallell photon beamµ ρxI(x) I0 e µx I0 e ρAbsorbingmaterialMonochromaticphoton sourceI0Ixρ density (g.cm-3)µ total linear attenuation coefficient of material i for enegy E (cm-1)ρ x mass thickness (g.cm-2)µ / ρ mass attenuation coefficient (cm2.g-1)µ depends on E and ZDetector
Attenuation coefficients (2)Practical parameter : attenuation coefficientPartial interaction coefficients:Photoelectric absorption:Compton scattering:Pair production effect:τi(E)σi(E)κi(E)τ const. Z4.5 E 3(major at low energies)σ const Z E 1κ const Z2(only if E 1022 keV)Linear attenuationcoefficient (cm-1)Mass attenuationcoefficient (cm2.g-1)Photoelectricττ/ρComptonσσ/ρPair productionκκ/ρµ τ σ κµ/ρ τ/ρ σ/ρ κ/ρInteractionTotalDepend on the energy, E, and the material (Z)For practical use : tables function of Z and ETables : cross sections (1 barn 10-24 cm2) or mass attenuation (cm2.g-1)
Attenuation coefficients (3)Photoelectric absorption coefficient sum of photoelectric effect ineach electronic shell (subshells):τ τΚ (τ L1 τ L2 τ L3 ) (τ M1 τ M2 τ M3 τ M4 τ M5 ) .If E binding energy of shell i, τ i 0For E Ei : absorption discontinuity: maximum ionisation probability in shell iτ variation versus the energy shows discontinuities corresponding to binding energies ofelectrons shells and subshells K, L, M.Ln(τ)Since µ τ σ κµ has the same discontinuities, function ofthe material atomic structure (Z)Ln(E)
Germanium mass attenuation coefficientAttenuation coefficients (4)Ge bindingenergies :L1: 1.4143L2: 1.2478L3: 1.2167K: 11.1031
Lead mass attenuation coefficientAttenuation coefficients (5)Pb bindingenergies :M1: 3.8507M2: 3.5542M3: 3.0664M4: 2.5856M5: 2.4840L1: 15.8608L2: 15.2000L3: 13.0352K: 88.0045
Mass attenuation coefficients Composition known - calculation Composition unknown - measurement Calculation: Attenuation coefficient table– XCOM (NIST Database)– Example for HCl 1N
XCOM : mixture Defining the mass fraction of each compound for HCl 1N: Matrix : HCl 1N 1 mole of HCl in 1 liter of solution HCl 1N density 1.016 (1L 1016 g) Mass of one HCl mole 1 35.45 36.45 g Resulting input parameters for XCOM Compound 1: HCl Mass fraction: 36.45 Compound 2: H2O Mass fraction 1016 – 36.45 979.55
xcom1.html
XCOM input-output
XCOM Results
Experimental measurementPrinciple : Use the unknown matrix and a collimated photon beamPhotonbeamPb ntainerN1(E)N2(E)Two successive measurements- Empty container- Container filled with unknown matrix with thickness x
Experimental measurementPhotonbeamPb collimatorsFor each energy:N2(E) N1(E) . exp (-µ(E) . nerN1(E)1 N 2 (E ) µ ( E ) ln x N1 ( E ) N2(E)Associated relative uncertainty:u 2 (µ) u2 ( x ) 22µx u 2 ( N 0 (E) ) u 2 ( N ( E ) ) 22 N(E)NE ()N(E)020 ln N (E) 1
Experimental arrangement
New experimental arrangementSourceSampleCollimatorDetector
Experimental measurementProblems:- Single line gamma emitters should be used to avoidcoincidence summing effects- At low energy – small angle Compton scatteringcontribution the collimated source and the sample far fromdetector High intensity sources required – storage problem ?- Time consuming
Measured linearattenuation coefficientx 2.5 cm-1Energy/keVFEP counting rate(spectrum 1) N1/t1FEP counting rateµm (cm ) (spectrum 2) N2/t2 (1/x) 1063837.255.630.10166260.0648.780.083
Mass attenuation coefficients/ cm2.g-110Standard solution HClStandard solution HClPhosphogypsum10,10,01101001000Energy/keV10000
Interpolated attenuation coefficientExample: attenuation in a 10 cm thick matrix for 300 keV energyMesurement of µ for some energies:Energy/keV100200500N1 (s-1)1000600200N2 (s-1)18016073N1 / N20.1800.2670.365µ (cm-1)0.1710.1320,101Interpolation for E 300 keV:0.1800.170Measured valuesInterpolated value0.160Linear interpolation: µ 0.122 cm-1Logarithmic interpolation: µ 0.117 cm-1µ 200300Energy (keV)400500600
Software for visualization of the dependence ofinteraction coefficients on element and energyEPICSHOW (NEA databank)EPICSHOW is part of the EPIC (Electron Photon Interaction Code) system.The program allows interactive viewing and comparison of data in the EPICdata bases.Plots and listings can be obtained.The EPIC electron, photon, and charged particle data bases are availablewith this package.The data bases include data for elements hydrogen (Z 1) to fermium(Z 100) over the energy range 10 eV to 1 GeV.
Self attenuation Simple formula Generalisation
Self-attenuation in a volume sampleIntrinsic photon flux: I0 (What you wish to know to derive the activity)Emitted photon flux: I (What is recorded by the detector)For a thin layer, with thickness de:I0dI 0 dexThis partial photon flux is attenuated through thickness e:I0dI exp( µ e ) dexOnly true if thesample ishomogeneous !xSampledeµ linear attenuation cofficient (cm-1)For the whole volume with thickness x :xe0de1 exp( µ x )I I 0 exp( µ e ) I0 xµ x0
Self-attenuation in a volume sampleI I0 1 exp( µ x )µ xIntrinsic photon flux: I0 (What you wish to know to derive the activity)Emitted photon flux: I (What is recorded by the detector)Self-attenuation:Catt1 exp( µx ) µx Approximation for a thin source (µx 1) : µ x I I0 1 2 Catt 1 µ x2
Interpolated attenuation coefficientExample: self-attenuation in a 10 cm thick matrix for 300 keV energy0.180Interpolation for E 300 keV :0.170Measured valuesInterpolated value0.160Linear interpolation: µ 0.122 cm-1Logarithmic interpolation: µ 0.117 cm-1µ 200300400500600Energy (keV)Self-attenuation at 300 keV :1 exp( µ300 x) 1 exp( 0.117 10)Catt 0.589µ300 x0.117 10
Self-attenuation in a volume sampleSelf-attenuation: Catt If the measured sample is subject to attenuation and the calibrationsource is not, a correction factor must be applied to the peak area that is:1/CSattCself Catt 1 exp( µx )µx 1µx 1 exp( µx )If both are subject to self-attenuation, the corrective factor is the ratio ofthe self attenuation for each materialCself 1Catt mes 1Catt cal[[]] µx 1 exp( µx ) mes µx 1 exp( µx ) calMes measuredsampleCal : calibrationsource
Self-attenuation in a volume sample Can also be computed as a transfer factor from anefficiency calibration established reference material tomeasure a different mateial (in the same geometry)ε mes ε cal fSelf Thus the efficiency transfer factor is:fSelf [Catt ]mes[Catt ]cal 1 exp( µx ) µx mes 1 exp( µx ) µx calMes measuredsampleCal : calibrationsource
Transfer from an efficiency calibration established with a liquid source(filled with 10 cm HCl) for matrixes silica and sand:ε mes ε cal fSelf ε cal[C ] [C ]att mesatt calDensities:water/HCl 1.016silica 0.25sand/resin 1.54Energy (keV)µ HCl (cm2.g-1)µ HCl (cm-1)[Catt ]calµ silica 0874µ silica (cm-1)0.0420.0310.0270.022[Catt]fSelf (silica)µ sand (cm2.g-1)µ sand .510.1130.1740.8981.410.09190.142[Catt]fSelf (sand)0.3540.750.4290.790.4740.820.5340.84
General formula Realistic if the source is far from the detector (parallel beam - normalincidence) - small source Not true for environment measurements (d’, d" » d)dSampled’dGecrystald’’d’SampleGecrystal
General formula Must consider all possible trajectories for each point of the volumesample - integration over solid angle and sample volumeP (r , t )Samplee dV exp( µ(E ) e(r , t ))dΩCatt VΩ dV dΩVΩΩPoint P with position r, and emissiondirection te: path in the sample matrixAdd the container absorption and probabilityof full-absorption of the photon in thedetector active volume
General formulaP (r , t )Sample dV exp( µ(E ) e(r , t )) T (E, r , t ) P (E, r , t ) dΩCatt VeΩ dV T (E, r , t ) P (E, r , t ) dΩVΩΩDenominator « self attenuation » for a transparent sampleNµ(E) : attenuation coefficient of the sample material for theenergy Ee : trajectory through the sampleT : Transmission through absorbers (container, detectorwindow, )P : Probability of full-energy absorption in the detectorThis correction can be numerically computed (Gauss-Legendre integration)
Efficiency transfer factor Transfer factor from an efficiency calibrationestablished reference material to measure a differentmaterial (in the same geometry)[Catt ]mesfSelf [Catt ]calε mes ε cal fSelf ε cal[C ] [C ]att mesatt calThis transfer factor can be numerically computed (Gauss-Legendreintegration)
Self-attenuation in Marinelli geometrySample dV exp( µ(E ) e(r , t )) T (E, r , t ) P (E, r , t ) dΩCatt VΩ dV T (E, r , t ) P (E, r , t ) dΩVGecrystalΩThe general expression must be extended todifferent parts of the sample, according to thepath of the photonsNumerical integration using different volumesThis correction can be numerically computed (Gauss-Legendre integration)
Monte Carlo simulation Self attenuation can be computed usingMonte Carlo methods– General codes (GEANT, MCNP,PENELOPE, etc)– Dedicated software (DETEFF, GESPECOR,etc.) Any geometry (including non-cylindricalsymmetry) can be considered Time-consuming ? Dedicated sofwareare optimizedSampleGecrystal
Practical toolsMethods for self-attenuation correction Empirical methods – simplified computing Analytic approach– ANGLE– ETNA , etc. Monte Carlo methods– DETEFF– GESPECOR– General codes (GEANT, PENELOPE, MCNP)
Examples Importance of the material density Influence of the filling height Change of matrix
Self –attenuation in silica Silica low density (0.25 g.cm-3) Sand (mainly silica) (2.5 g.cm-3) Thickness 1 cmRadionuclideEnergy/keVMass 7730.9900.90940K1460.80.05260.9930.937
Self –attenuation in steel Fe (7.5 g.cm-3)RadionuclideEnergy/keVMass attcoefficient(cm2.g-1)Selfattenuation1 cmSelfattenuation1 mmSelfattenuation0.1 90.9730.99740K1460.80.04950.8350.9820.998For the low energies, only the very first thickness contributes
Influence of the filling height?
Influence of the filling heightPlastic vial filled with HCl 1N - Reference height 46,5 mm – diameter 39 mmAt 10 cm1,20At contact1,21,1540 mm filling height1,1542 mm filling heightFilling height 35 mm1,10Filling height 40 mmFilling height 43 mm1,05Filling height 45 mmFilling height 48 mm1,001,144 mm filling height45 mm filling height1,0547 mm filling height150 mm filling heightFilling height 50 000About 5 % variation for 10% change in filling heightMore important when the height is reducedMore sensitive for low-energiesMore sensitive at short source-to-detector distance2500
Influence of the filling heightPlastic vial at contact - Reference height 46,5 mm – diameter 39 mmSilica (d 0.24)Sand-resin (d 1.54)Efficiency transfer for sandEfficiency transfer for silica1,21,21,1540 mm42 mm1,142 mm44 mm1,0544 mm145 mm145 mm0,9547 mm0,9547 mm0,948 mm0,948 mm1,1540 mm1,11,050500100015002000250050 mm0500Energy/keV10001500Energy/keV40 mm – 500 keV: HCl 1.11; silica 1.10; sand 1.1250 mm – 500 keV: HCl 0.946; silica 0.951; sand 0.9442000250050 mm
Influence of the filling heightPlastic vial at contact - Reference height 20 mm – diameter 39 mmHCl (d 1.016)Sand-resin (d 2.54)20 mm /- 2 mm - Sand at contact1,061,041,02Filled 22 mm1Filled 18 mm0,980,960,940500100015002000Efficie nc y trans fer fac torE fficiency tyransfer factor20 mm /- 2 mm HCl at contact1,11,05Filled 18 mm1Filled 22 mm0,950,905002500Energy/keV18 mm – 500 keV: HCl 1.049; sand 1.05922 mm – 500 keV: HCl 0.955; sand 0.94710001500Energy/keV20002500
Efficiency calibration for different geometries0,10Source ponctuelle à 2 cmSource volumique (silice d 0,25) au contactSource volumique liquide (d 1,016) au contactSource volumique (sable/résine d 1,54) au contactSource ponctuelle à 5 cmSource ponctuelle à 10 cm (référence)Source ponctuelle à 20 cm0,08Experimental calibrationwith volume sourcesSilica low density (d 0.24)Rendement0,06HCl 1N (d 1.016)Sand-resin (d 1.54)0,040,020,00100Energie (keV)1000
Efficiency transferTransfer from an efficiency calibration established with a liquid source(filled with 4.65 cm HCl) for matrixes silica and sand:EnergyHClDensities:water/HCl 1.016silica 0.25sand/resin 1.54ε mes ε cal fSelf ε cal[C ] [C ]att mesSimple expression :[Catt ]mesfSelf [Catt 0,975f self20508010020050010002000µ (cm -1)0,5740,0670,0430,0380,0300,0210,0150,011µ 0,0860,4650,5650,6580,6530,7330,7940,849f self20508010020050010002000Silicaatt cal 1 exp( µx ) µx mes 1 exp( µx ) µx ,3910,7500,8360,9500,8830,9130,9340,952
Application exampleTransfer from an efficiency calibration established with a liquid source(filled with 4.65 cm HCl) for matrixes silica and sand:[Catt ]mesfSelf [Catt ]calComparisonof the generalised formula(ETNA code) with thesimple 0107Sand1,54 ,9480,963
Summary Self attenuation is of main importance for low energiesand high densities In case of high attenuation only a thin layer of thesample located close to the detector is important In case of homogeneous matrix, it can be computed ifthe attenuation cœfficient is knownMethods for self-attenuation correction Empirical methods – simplified computing Analytic approach Monte Carlo methods
Partial interaction coefficients: Photoelectric absorption: τi(E) (major at low energies) Compton scattering: σi(E) Pair production effect: κi(E) (only if E 1022 keV) Depend on the energy, E, and the material (Z) For practical use : tables function of Z and E Tables : cross sections (1 barn 10-24 cm 2) or mass attenuation(cm 2.g-1)
VXT - B 5 Open Cooling Towers. because temperature matters Sound Attenuation XB Sound Attenuation for VX-Line Cooling Towers (1) VXT-55 attenuation is shipped in 4 pieces (1) VXT-75 and VXT 85 attenuation is shipped in 4 pieces (2) VXT-95 attenuation is shipped in 3 pieces (3) Intake Attenuator: Access opening is 775 mm
values for the attenuation coefficient. Therefore, a new method was proposed, tested and validated to measure the attenuation coefficient of these special materials and any others. A new methodology having been derived, it was then applied to glass/epoxy particulate composites where longitudinal wave speeds and attenuation coefficients
tive attenuation measurements. In some cases, anestimate of attenuation can be made from a B-scan image which shows shadowing beneath an object, such as a gallstone [11]. These effects depend, to a certain extent, on the time-varying gain selected bythe clinician to boost signals returning fromdeeper tissues. For small attenuation differences .
three attenuation estimation techniques are then compared as a function of ROI size in all the simulation cases. The spectral difference method and the spectral log difference method make no prior assumption about the frequency de-pendence of the attenuation. The hybrid method, however, assumes that the attenuation increases linearly with fre .
All 3 (couch, CT and PET) must be in accurate alignment Imaging FDG uptake (PET) with anatomical localization (CT) and CT-based attenuation correction Function Function Anatomy and CT-based attenuation correction Anatomy CT images are also used for calibration (attenuation correction) of the PET data Data flow for data processing X-ray .
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Column 3 in Table 1 provides the theoretical estimates of mass attenuation coefficients derived from the total photon attenuation cross-section obtained by combining the photo electric cross-sections of Scofield coh[2]e-rent and incoherent scattering cross-sections of Hubbel [3] and Hubbell & Overbo [4] respectively. Table 1.
The total attenuation cross-section and effective atomic number are basic quantities required in determining the penetration of X-ray and gamma rays in matter [1]. The knowledge of mass attenuation coefficients, atomic and electronic cross sections and effective atomic number is useful for understanding * Corresponding author. Tel.: 6-683-287 .
