Nityanand gopalika spectrum validation - nde 2003
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The document evaluates mathematical models for x-ray spectrum generation, particularly focusing on models suitable for industrial radiography applications. It highlights the Ellery Storm model as the most effective, achieving over 95% accuracy in photon fluence per roentgen and exhibiting low error rates in average energy and half-value layer metrics. The study includes comparisons of simulated and experimental data, confirming the models' reliability and validity for practical use.
Nityanand gopalika spectrum validation - nde 2003
- 1. Evaluation of Mathematical Models for X-ray Spectrum Generation suitable for Industrial Radiography Applications Nityanand Gopalika, A. V. K Satish, V. Manoharan Industrial Imaging and Modeling Lab Imaging Technologies John F. Welch Technology Centre Bangalore
- 2. Presentation Outline Different X-Ray generation models Validation approach: Variation of Photon Fluence / mR with Average Energy Relationship between Average Energy and kVp for different filters Half Value Layer (HVL) for different cases Dose validation with experiment Summary
- 3. Birch and Marshall model Intensity produced in a solid target Governing Relationships dT Nρ T −1 v Iv = A ∫ dx T0 Q dT Physics • Theoretical model Effect of target absorption • Target absorption taken care T = (T02 − Cxρ ) 0.5 (improvement over Kramer's theory) Substituting the above gives −1 Nρ Tv T0 dT µv Iv = ∫ 1 + m0C 2 Q dx exp( (T 2 − T02 ) cot θ ) dT A T0 Cρ Characteristic Intensity I ch = K (U 0 − 1)1.63 Drawbacks Applicable only from 30-150 kV. Small target angles greater error. Back Scatter not considered. Suited for medical applications
- 4. Ellery Storm Model Thick target energy loss as an integral of thin target energy loss: E0 dE dE = Energy loss in thin strip of target I E0 ,K = ∫ I E0 ,k ,E E >k −dE /dx E = Initial electron energy at photon emission Correction for electron backscatter losses, photon attenuation and target angle E0 dE I E0 ,k = ∫k E> I E0 ,k ,E (1−ηε E 0 ,k )*exp( −µ k x/ tanα ) −dE /dx Emission per unit solid angle in the photon energy −3 k 11 ( E0 −k )(1−e ) Ek 1.0 I E0 ,k ≅( Z ) f E0 ,k ,α 4π 1 E0 ( k / E0 ) 3 (1−e Ek ) 40 kV 60 kV Photon Attenuation Correction Factor C E0 , k f E0 ,k ,α ≅ exp(−0.2C E0 ,k ℜ E0 µ k / tan α ) 100 kV 0.5 200kV E0 Initial Electron Energy Ek K Edge Energy 300 kV K Photon Energy 0.0 10 20 40 Z Atomic Weight Photon Energy (keV) Best suited for industrial applications
- 5. Photon Fluence /mR & Average Energy Photon Fluence per Roentgen Photon Fluence 4.E+10 3.E+10 / mR 2.E+10 1.E+10 Photon Fluence /mR = ∫Θ( E )*E*dE 0.E+00 ∫Θ( E )*(µ ( E )/ ρ )*E*dE 0 50 100 150 200 250 300 350 Average Energy Average energy 70 60 Average energy kev no filter Average Energy = ∫Θ( E )*dE 50 40 1 mm aluminium 2 mm aluminium ∫dE 30 20 3 mm aluminium 4 mm aluminium 10 5 mm aluminum 0 0 50 100 150 kVP Literature data available below 150 kVp
- 6. Model Performance Verification Average Energy Vs. kvp (Simulation) Photon Fluence per roentgen Vs. Average Energy (Simulation) 140 120 3.00E+05 Average Energy Thick = 1mm Photon Fluence / mR 100 Thick = 2mm 2.50E+05 Thick = 1mm 80 Thick = 3mm 2.00E+05 Thick = 2mm 60 Thick = 4mm 1.50E+05 Thick = 3mm 40 Thick = 5mm 1.00E+05 Thick = 4mm 20 Thick = 5mm 5.00E+04 0 0.00E+00 0 100 200 300 400 500 0 20 40 60 80 100 120 140 kvp Average Energy Average Energy Vs. kvp Photon Fluence / mR Vs. Average Energy (Simulation & Liturature) (Simulation & Literature) 140 3.E+05 Photon Fluence / mR 120 3.E+05 Average Energy 100 2.E+05 80 Thick = 5mm, Simulation 2.E+05 60 Thick = 5mm, Literature 1.E+05 Thick = 5mm, Simulation 40 Thick = 5mm, Experimental 5.E+04 20 0 0.E+00 0 20 40 60 80 100 120 140 0 50 100 150 200 250 300 350 400 450 kvp Average Energy High accuracy in the range of 30 – 150 kVp
- 7. HVL Study: Comparison with NIST Data Tube HVL Dose Dose Potential Inherent (mm) - Before After Cases (KvP) Filter Added Filter Object NIST Object Object % Error 1 100 1 mm Be % Difference in HVL 1.98 mm Al Al 2.77 12.668 6.744 -6.475 2 100 3 mm Be 5 mm Al Al 5.02 6.080 3.043 -0.106 3 100 8 3 mm Be 4 mm Al + 5.2 mm Cu Al 13.5 0.025 0.012 2.393 4 100 6 3 mm Be 4 mm Al + 5.2 mm Cu Cu 1.14 0.025 0.012 3.496 5 120 3 mm Be 6.87 mm Al Al 6.79 6.887 3.440 0.100 6 150 4 3 mm Be 5 mm Al + 0.25 mm Cu Al 10.2 8.405 4.177 0.610 % Difference 7 150 3 mm Be 5 mm Al + 0.25 mm Cu Cu 0.67 8.405 4.125 1.851 8 150 2 3 mm Be 4 mm Al + 4 mm Cu + 1.51 mm Sn Al 17 0.187 0.092 2.147 9 150 3 mm Be 4 mm Al + 4 mm Cu + 1.51 mm Sn Cu 2.5 0.187 0.087 7.005 10 200 0 3 mm Be 4.1 mm Al + 1.12 mm Cu Al 14.9 9.782 4.831 1.217 11 200 3 mm Be 4.1 mm Al + 1.12 mm Cu Cu 1.69 9.782 4.785 2.169 12 200 -2 3 mm Be 4 mm Al + 0.6 mm Cu + 4.16 mm Sn + 0.77 mm Pb Al 19.8 0.141 0.070 1.665 13 200 -4 3 mm Be 4 mm Al + 0.6 mm Cu + 4.16 mm Sn + 0.77 mm Pb Cu 4.1 0.141 0.068 4.188 14 250 3 mm Be 5 mm Al + 3.2 mm Cu Al 18.5 9.624 4.740 1.504 15 250 -6 3 mm Be 5 mm Al + 3.2 mm Cu Cu 3.2 9.624 4.695 2.425 16 250 3 mm Be 4 mm Al + 0.6 mm Cu + 1.04 mm Sn + 2.72 mm Pb Al 22 0.206 0.101 2.119 17 250 -8 3 mm Be 4 mm Al + 0.6 mm Cu + 1.04 mm Sn + 2.72 mm Pb Cu 5.2 0.206 0.102 0.613 18 300 3 mm Be 75 125 4 mm Al + 6.5 mm Sn 175 225 Al 27522 4.395 2.169 325 1.280 19 300 3 mm Be 4 mm Al + 6.5 mm Sn Cu 5.3 4.395 2.201 -0.149 20 300 3 mm Be kVp 4.1 mm Al + 3 mm Sn + 5 mm Pb Al 23 0.164 0.083 -0.839 21 300 3 mm Be 4.1 mm Al + 3 mm Sn + 5 mm Pb Cu 6.2 0.164 0.086 -4.415 % Difference in HVL between NIST and simulation is within +/- 8%
- 8. Experimental Dose Measurement Experimental Conditions: Simulation Conditions: X-Ray Tube: Target Voltage : 20 < kV < 420 kVp Current : 1 mA 1. KM16010E-A MicroFocus Target Material – W 2. Seifert ISOVOLT 420/10 Dose = 1.828*10-11∑φ(E).(µ(E)/ρ) air.E.dE Dosimeter: Keithley 35050A Dosimeter % Difference in Dose : Kevex, SDD = 1m % Difference in Dose: Seifert, SDD = 1m (Experimental and Simulated) (Experimental and Simulated) 6 8 0.4 mm Cu Filter 4 6 9 mm Al Filter 4 % Difference 2 % Difference 2 0 0 -2 -2 -4 0.4 mm Cu Filter -4 -6 9 mm Al Filter -6 -8 -8 30 50 70 90 110 130 150 170 30 130 230 330 430 Tube Potential (kvp) Tube Potential (kvp) KM16010E-A MicroFocus Seifert ISOVOLT 420/10 Less than 7% difference is observed between simulation and experiments
- 9. Summary Ellery Storm Model best suited for X-ray Spectrum Generation Model performance metrics: Accuracy for Photon Fluence / mR > 95% Error in Average Energy < 5% Deviation in HVL < 8% Simulated Dose is in good agreement with Experiments