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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